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- Committer: Bazaar Package Importer
- Author(s): Johannes Ring
- Date: 2010-07-01 19:54:32 UTC
- mfrom: (1.1.5 upstream)
- Revision ID: james.westby@ubuntu.com-20100701195432-xz3gw5nprdj79jcb
Tags: 0.9.3-1
* New upstream release.
* debian/control:
- Minor fix in Vcs fields.
- Bump Standards-Version to 3.9.0 (no changes needed).
- Update version for python-ufc, python-fiat, and python-ufl in
Depends field.
* Switch to dpkg-source 3.0 (quilt) format.
* Update debian/copyright and debian/copyright_hints.
* debian/control:
- Minor fix in Vcs fields.
- Bump Standards-Version to 3.9.0 (no changes needed).
- Update version for python-ufc, python-fiat, and python-ufl in
Depends field.
* Switch to dpkg-source 3.0 (quilt) format.
* Update debian/copyright and debian/copyright_hints.
- files added:
- bench/MassH1_2D_1.ufl
- bench/results
- debian/source
- files removed:
- bench/NavierStokes.form
- files modified:
- ChangeLog
added
removed
test/regression/references/VectorLaplaceGradCurl.h
1
// This code conforms with the UFC specification version 1.4
2
// and was automatically generated by FFC version 0.9.2.
1
// This code conforms with the UFC specification version 1.4.1
2
// and was automatically generated by FFC version 0.9.3.
3
3
//
4
4
// This code was generated with the following parameters:
5
5
//
124
124
125
125
// Reset values.
126
126
*values = 0.00000000;
127
128
// Map degree of freedom to element degree of freedom
129
const unsigned int dof = i;
130
131
// Array of basisvalues.
132
double basisvalues[10] = {0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000};
133
134
// Declare helper variables.
135
unsigned int rr = 0;
136
unsigned int ss = 0;
137
unsigned int tt = 0;
138
double tmp5 = 0.00000000;
139
double tmp6 = 0.00000000;
140
double tmp7 = 0.00000000;
141
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
142
double tmp1 = 0.25000000*(Y + Z)*(Y + Z);
143
double tmp2 = 0.50000000*(1.00000000 + Z + 2.00000000*Y);
144
double tmp3 = 0.50000000*(1.00000000 - Z);
145
double tmp4 = tmp3*tmp3;
146
147
// Compute basisvalues.
148
basisvalues[0] = 1.00000000;
149
basisvalues[1] = tmp0;
150
for (unsigned int r = 1; r < 2; r++)
151
{
152
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
153
ss = r*(r + 1)*(r + 2)/6;
154
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
155
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.00000000 + 2.00000000*r)/(1.00000000 + r) - basisvalues[tt]*tmp1*r/(1.00000000 + r));
156
}// end loop over 'r'
157
for (unsigned int r = 0; r < 2; r++)
158
{
159
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
160
ss = r*(r + 1)*(r + 2)/6;
161
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
162
}// end loop over 'r'
163
for (unsigned int r = 0; r < 1; r++)
164
{
165
for (unsigned int s = 1; s < 2 - r; s++)
166
{
167
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
168
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
169
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
170
tmp5 = (2.00000000 + 2.00000000*r + 2.00000000*s)*(3.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
171
tmp6 = (1.00000000 + 4.00000000*r*r + 4.00000000*r)*(2.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
172
tmp7 = (1.00000000 + s + 2.00000000*r)*(3.00000000 + 2.00000000*r + 2.00000000*s)*s/((1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
173
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
174
}// end loop over 's'
175
}// end loop over 'r'
176
for (unsigned int r = 0; r < 2; r++)
177
{
178
for (unsigned int s = 0; s < 2 - r; s++)
179
{
180
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
181
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
182
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
183
}// end loop over 's'
184
}// end loop over 'r'
185
for (unsigned int r = 0; r < 1; r++)
186
{
187
for (unsigned int s = 0; s < 1 - r; s++)
188
{
189
for (unsigned int t = 1; t < 2 - r - s; t++)
190
{
191
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
192
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
193
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
194
tmp5 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)/(2.00000000*(1.00000000 + t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
195
tmp6 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 4.00000000*r*r + 4.00000000*s*s + 8.00000000*r*s + 8.00000000*r + 8.00000000*s)/(2.00000000*(1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
196
tmp7 = (2.00000000 + t + 2.00000000*r + 2.00000000*s)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*t/((1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
197
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
198
}// end loop over 't'
199
}// end loop over 's'
200
}// end loop over 'r'
201
for (unsigned int r = 0; r < 3; r++)
202
{
203
for (unsigned int s = 0; s < 3 - r; s++)
204
{
205
for (unsigned int t = 0; t < 3 - r - s; t++)
206
{
207
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
208
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
209
}// end loop over 't'
210
}// end loop over 's'
211
}// end loop over 'r'
212
213
// Table(s) of coefficients.
214
static const double coefficients0[10][10] = \
215
{{-0.05773503, -0.06085806, -0.03513642, -0.02484520, 0.06506000, 0.05039526, 0.04114756, 0.02909572, 0.02375655, 0.01679842},
216
{-0.05773503, 0.06085806, -0.03513642, -0.02484520, 0.06506000, -0.05039526, -0.04114756, 0.02909572, 0.02375655, 0.01679842},
217
{-0.05773503, 0.00000000, 0.07027284, -0.02484520, 0.00000000, 0.00000000, 0.00000000, 0.08728716, -0.04751311, 0.01679842},
218
{-0.05773503, 0.00000000, 0.00000000, 0.07453560, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.10079053},
219
{0.23094011, 0.00000000, 0.14054567, 0.09938080, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.11878277, -0.06719368},
220
{0.23094011, 0.12171612, -0.07027284, 0.09938080, 0.00000000, 0.00000000, 0.10286890, 0.00000000, -0.05939139, -0.06719368},
221
{0.23094011, 0.12171612, 0.07027284, -0.09938080, 0.00000000, 0.10079053, -0.02057378, -0.08728716, -0.01187828, 0.01679842},
222
{0.23094011, -0.12171612, -0.07027284, 0.09938080, 0.00000000, 0.00000000, -0.10286890, 0.00000000, -0.05939139, -0.06719368},
223
{0.23094011, -0.12171612, 0.07027284, -0.09938080, 0.00000000, -0.10079053, 0.02057378, -0.08728716, -0.01187828, 0.01679842},
224
{0.23094011, 0.00000000, -0.14054567, -0.09938080, -0.13012001, 0.00000000, 0.00000000, 0.02909572, 0.02375655, 0.01679842}};
225
226
// Compute value(s).
227
for (unsigned int r = 0; r < 10; r++)
228
{
229
*values += coefficients0[dof][r]*basisvalues[r];
230
}// end loop over 'r'
127
switch (i)
128
{
129
case 0:
130
{
131
132
// Array of basisvalues.
133
double basisvalues[10] = {0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000};
134
135
// Declare helper variables.
136
unsigned int rr = 0;
137
unsigned int ss = 0;
138
unsigned int tt = 0;
139
double tmp5 = 0.00000000;
140
double tmp6 = 0.00000000;
141
double tmp7 = 0.00000000;
142
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
143
double tmp1 = 0.25000000*(Y + Z)*(Y + Z);
144
double tmp2 = 0.50000000*(1.00000000 + Z + 2.00000000*Y);
145
double tmp3 = 0.50000000*(1.00000000 - Z);
146
double tmp4 = tmp3*tmp3;
147
148
// Compute basisvalues.
149
basisvalues[0] = 1.00000000;
150
basisvalues[1] = tmp0;
151
for (unsigned int r = 1; r < 2; r++)
152
{
153
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
154
ss = r*(r + 1)*(r + 2)/6;
155
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
156
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.00000000 + 2.00000000*r)/(1.00000000 + r) - basisvalues[tt]*tmp1*r/(1.00000000 + r));
157
}// end loop over 'r'
158
for (unsigned int r = 0; r < 2; r++)
159
{
160
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
161
ss = r*(r + 1)*(r + 2)/6;
162
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
163
}// end loop over 'r'
164
for (unsigned int r = 0; r < 1; r++)
165
{
166
for (unsigned int s = 1; s < 2 - r; s++)
167
{
168
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
169
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
170
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
171
tmp5 = (2.00000000 + 2.00000000*r + 2.00000000*s)*(3.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
172
tmp6 = (1.00000000 + 4.00000000*r*r + 4.00000000*r)*(2.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
173
tmp7 = (1.00000000 + s + 2.00000000*r)*(3.00000000 + 2.00000000*r + 2.00000000*s)*s/((1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
174
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
175
}// end loop over 's'
176
}// end loop over 'r'
177
for (unsigned int r = 0; r < 2; r++)
178
{
179
for (unsigned int s = 0; s < 2 - r; s++)
180
{
181
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
182
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
183
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
184
}// end loop over 's'
185
}// end loop over 'r'
186
for (unsigned int r = 0; r < 1; r++)
187
{
188
for (unsigned int s = 0; s < 1 - r; s++)
189
{
190
for (unsigned int t = 1; t < 2 - r - s; t++)
191
{
192
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
193
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
194
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
195
tmp5 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)/(2.00000000*(1.00000000 + t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
196
tmp6 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 4.00000000*r*r + 4.00000000*s*s + 8.00000000*r*s + 8.00000000*r + 8.00000000*s)/(2.00000000*(1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
197
tmp7 = (2.00000000 + t + 2.00000000*r + 2.00000000*s)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*t/((1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
198
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
199
}// end loop over 't'
200
}// end loop over 's'
201
}// end loop over 'r'
202
for (unsigned int r = 0; r < 3; r++)
203
{
204
for (unsigned int s = 0; s < 3 - r; s++)
205
{
206
for (unsigned int t = 0; t < 3 - r - s; t++)
207
{
208
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
209
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
210
}// end loop over 't'
211
}// end loop over 's'
212
}// end loop over 'r'
213
214
// Table(s) of coefficients.
215
static const double coefficients0[10] = \
216
{-0.05773503, -0.06085806, -0.03513642, -0.02484520, 0.06506000, 0.05039526, 0.04114756, 0.02909572, 0.02375655, 0.01679842};
217
218
// Compute value(s).
219
for (unsigned int r = 0; r < 10; r++)
220
{
221
*values += coefficients0[r]*basisvalues[r];
222
}// end loop over 'r'
223
break;
224
}
225
case 1:
226
{
227
228
// Array of basisvalues.
229
double basisvalues[10] = {0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000};
230
231
// Declare helper variables.
232
unsigned int rr = 0;
233
unsigned int ss = 0;
234
unsigned int tt = 0;
235
double tmp5 = 0.00000000;
236
double tmp6 = 0.00000000;
237
double tmp7 = 0.00000000;
238
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
239
double tmp1 = 0.25000000*(Y + Z)*(Y + Z);
240
double tmp2 = 0.50000000*(1.00000000 + Z + 2.00000000*Y);
241
double tmp3 = 0.50000000*(1.00000000 - Z);
242
double tmp4 = tmp3*tmp3;
243
244
// Compute basisvalues.
245
basisvalues[0] = 1.00000000;
246
basisvalues[1] = tmp0;
247
for (unsigned int r = 1; r < 2; r++)
248
{
249
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
250
ss = r*(r + 1)*(r + 2)/6;
251
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
252
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.00000000 + 2.00000000*r)/(1.00000000 + r) - basisvalues[tt]*tmp1*r/(1.00000000 + r));
253
}// end loop over 'r'
254
for (unsigned int r = 0; r < 2; r++)
255
{
256
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
257
ss = r*(r + 1)*(r + 2)/6;
258
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
259
}// end loop over 'r'
260
for (unsigned int r = 0; r < 1; r++)
261
{
262
for (unsigned int s = 1; s < 2 - r; s++)
263
{
264
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
265
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
266
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
267
tmp5 = (2.00000000 + 2.00000000*r + 2.00000000*s)*(3.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
268
tmp6 = (1.00000000 + 4.00000000*r*r + 4.00000000*r)*(2.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
269
tmp7 = (1.00000000 + s + 2.00000000*r)*(3.00000000 + 2.00000000*r + 2.00000000*s)*s/((1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
270
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
271
}// end loop over 's'
272
}// end loop over 'r'
273
for (unsigned int r = 0; r < 2; r++)
274
{
275
for (unsigned int s = 0; s < 2 - r; s++)
276
{
277
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
278
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
279
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
280
}// end loop over 's'
281
}// end loop over 'r'
282
for (unsigned int r = 0; r < 1; r++)
283
{
284
for (unsigned int s = 0; s < 1 - r; s++)
285
{
286
for (unsigned int t = 1; t < 2 - r - s; t++)
287
{
288
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
289
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
290
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
291
tmp5 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)/(2.00000000*(1.00000000 + t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
292
tmp6 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 4.00000000*r*r + 4.00000000*s*s + 8.00000000*r*s + 8.00000000*r + 8.00000000*s)/(2.00000000*(1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
293
tmp7 = (2.00000000 + t + 2.00000000*r + 2.00000000*s)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*t/((1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
294
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
295
}// end loop over 't'
296
}// end loop over 's'
297
}// end loop over 'r'
298
for (unsigned int r = 0; r < 3; r++)
299
{
300
for (unsigned int s = 0; s < 3 - r; s++)
301
{
302
for (unsigned int t = 0; t < 3 - r - s; t++)
303
{
304
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
305
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
306
}// end loop over 't'
307
}// end loop over 's'
308
}// end loop over 'r'
309
310
// Table(s) of coefficients.
311
static const double coefficients0[10] = \
312
{-0.05773503, 0.06085806, -0.03513642, -0.02484520, 0.06506000, -0.05039526, -0.04114756, 0.02909572, 0.02375655, 0.01679842};
313
314
// Compute value(s).
315
for (unsigned int r = 0; r < 10; r++)
316
{
317
*values += coefficients0[r]*basisvalues[r];
318
}// end loop over 'r'
319
break;
320
}
321
case 2:
322
{
323
324
// Array of basisvalues.
325
double basisvalues[10] = {0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000};
326
327
// Declare helper variables.
328
unsigned int rr = 0;
329
unsigned int ss = 0;
330
unsigned int tt = 0;
331
double tmp5 = 0.00000000;
332
double tmp6 = 0.00000000;
333
double tmp7 = 0.00000000;
334
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
335
double tmp1 = 0.25000000*(Y + Z)*(Y + Z);
336
double tmp2 = 0.50000000*(1.00000000 + Z + 2.00000000*Y);
337
double tmp3 = 0.50000000*(1.00000000 - Z);
338
double tmp4 = tmp3*tmp3;
339
340
// Compute basisvalues.
341
basisvalues[0] = 1.00000000;
342
basisvalues[1] = tmp0;
343
for (unsigned int r = 1; r < 2; r++)
344
{
345
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
346
ss = r*(r + 1)*(r + 2)/6;
347
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
348
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.00000000 + 2.00000000*r)/(1.00000000 + r) - basisvalues[tt]*tmp1*r/(1.00000000 + r));
349
}// end loop over 'r'
350
for (unsigned int r = 0; r < 2; r++)
351
{
352
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
353
ss = r*(r + 1)*(r + 2)/6;
354
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
355
}// end loop over 'r'
356
for (unsigned int r = 0; r < 1; r++)
357
{
358
for (unsigned int s = 1; s < 2 - r; s++)
359
{
360
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
361
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
362
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
363
tmp5 = (2.00000000 + 2.00000000*r + 2.00000000*s)*(3.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
364
tmp6 = (1.00000000 + 4.00000000*r*r + 4.00000000*r)*(2.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
365
tmp7 = (1.00000000 + s + 2.00000000*r)*(3.00000000 + 2.00000000*r + 2.00000000*s)*s/((1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
366
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
367
}// end loop over 's'
368
}// end loop over 'r'
369
for (unsigned int r = 0; r < 2; r++)
370
{
371
for (unsigned int s = 0; s < 2 - r; s++)
372
{
373
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
374
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
375
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
376
}// end loop over 's'
377
}// end loop over 'r'
378
for (unsigned int r = 0; r < 1; r++)
379
{
380
for (unsigned int s = 0; s < 1 - r; s++)
381
{
382
for (unsigned int t = 1; t < 2 - r - s; t++)
383
{
384
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
385
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
386
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
387
tmp5 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)/(2.00000000*(1.00000000 + t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
388
tmp6 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 4.00000000*r*r + 4.00000000*s*s + 8.00000000*r*s + 8.00000000*r + 8.00000000*s)/(2.00000000*(1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
389
tmp7 = (2.00000000 + t + 2.00000000*r + 2.00000000*s)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*t/((1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
390
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
391
}// end loop over 't'
392
}// end loop over 's'
393
}// end loop over 'r'
394
for (unsigned int r = 0; r < 3; r++)
395
{
396
for (unsigned int s = 0; s < 3 - r; s++)
397
{
398
for (unsigned int t = 0; t < 3 - r - s; t++)
399
{
400
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
401
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
402
}// end loop over 't'
403
}// end loop over 's'
404
}// end loop over 'r'
405
406
// Table(s) of coefficients.
407
static const double coefficients0[10] = \
408
{-0.05773503, 0.00000000, 0.07027284, -0.02484520, 0.00000000, 0.00000000, 0.00000000, 0.08728716, -0.04751311, 0.01679842};
409
410
// Compute value(s).
411
for (unsigned int r = 0; r < 10; r++)
412
{
413
*values += coefficients0[r]*basisvalues[r];
414
}// end loop over 'r'
415
break;
416
}
417
case 3:
418
{
419
420
// Array of basisvalues.
421
double basisvalues[10] = {0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000};
422
423
// Declare helper variables.
424
unsigned int rr = 0;
425
unsigned int ss = 0;
426
unsigned int tt = 0;
427
double tmp5 = 0.00000000;
428
double tmp6 = 0.00000000;
429
double tmp7 = 0.00000000;
430
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
431
double tmp1 = 0.25000000*(Y + Z)*(Y + Z);
432
double tmp2 = 0.50000000*(1.00000000 + Z + 2.00000000*Y);
433
double tmp3 = 0.50000000*(1.00000000 - Z);
434
double tmp4 = tmp3*tmp3;
435
436
// Compute basisvalues.
437
basisvalues[0] = 1.00000000;
438
basisvalues[1] = tmp0;
439
for (unsigned int r = 1; r < 2; r++)
440
{
441
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
442
ss = r*(r + 1)*(r + 2)/6;
443
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
444
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.00000000 + 2.00000000*r)/(1.00000000 + r) - basisvalues[tt]*tmp1*r/(1.00000000 + r));
445
}// end loop over 'r'
446
for (unsigned int r = 0; r < 2; r++)
447
{
448
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
449
ss = r*(r + 1)*(r + 2)/6;
450
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
451
}// end loop over 'r'
452
for (unsigned int r = 0; r < 1; r++)
453
{
454
for (unsigned int s = 1; s < 2 - r; s++)
455
{
456
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
457
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
458
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
459
tmp5 = (2.00000000 + 2.00000000*r + 2.00000000*s)*(3.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
460
tmp6 = (1.00000000 + 4.00000000*r*r + 4.00000000*r)*(2.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
461
tmp7 = (1.00000000 + s + 2.00000000*r)*(3.00000000 + 2.00000000*r + 2.00000000*s)*s/((1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
462
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
463
}// end loop over 's'
464
}// end loop over 'r'
465
for (unsigned int r = 0; r < 2; r++)
466
{
467
for (unsigned int s = 0; s < 2 - r; s++)
468
{
469
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
470
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
471
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
472
}// end loop over 's'
473
}// end loop over 'r'
474
for (unsigned int r = 0; r < 1; r++)
475
{
476
for (unsigned int s = 0; s < 1 - r; s++)
477
{
478
for (unsigned int t = 1; t < 2 - r - s; t++)
479
{
480
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
481
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
482
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
483
tmp5 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)/(2.00000000*(1.00000000 + t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
484
tmp6 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 4.00000000*r*r + 4.00000000*s*s + 8.00000000*r*s + 8.00000000*r + 8.00000000*s)/(2.00000000*(1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
485
tmp7 = (2.00000000 + t + 2.00000000*r + 2.00000000*s)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*t/((1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
486
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
487
}// end loop over 't'
488
}// end loop over 's'
489
}// end loop over 'r'
490
for (unsigned int r = 0; r < 3; r++)
491
{
492
for (unsigned int s = 0; s < 3 - r; s++)
493
{
494
for (unsigned int t = 0; t < 3 - r - s; t++)
495
{
496
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
497
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
498
}// end loop over 't'
499
}// end loop over 's'
500
}// end loop over 'r'
501
502
// Table(s) of coefficients.
503
static const double coefficients0[10] = \
504
{-0.05773503, 0.00000000, 0.00000000, 0.07453560, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.10079053};
505
506
// Compute value(s).
507
for (unsigned int r = 0; r < 10; r++)
508
{
509
*values += coefficients0[r]*basisvalues[r];
510
}// end loop over 'r'
511
break;
512
}
513
case 4:
514
{
515
516
// Array of basisvalues.
517
double basisvalues[10] = {0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000};
518
519
// Declare helper variables.
520
unsigned int rr = 0;
521
unsigned int ss = 0;
522
unsigned int tt = 0;
523
double tmp5 = 0.00000000;
524
double tmp6 = 0.00000000;
525
double tmp7 = 0.00000000;
526
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
527
double tmp1 = 0.25000000*(Y + Z)*(Y + Z);
528
double tmp2 = 0.50000000*(1.00000000 + Z + 2.00000000*Y);
529
double tmp3 = 0.50000000*(1.00000000 - Z);
530
double tmp4 = tmp3*tmp3;
531
532
// Compute basisvalues.
533
basisvalues[0] = 1.00000000;
534
basisvalues[1] = tmp0;
535
for (unsigned int r = 1; r < 2; r++)
536
{
537
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
538
ss = r*(r + 1)*(r + 2)/6;
539
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
540
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.00000000 + 2.00000000*r)/(1.00000000 + r) - basisvalues[tt]*tmp1*r/(1.00000000 + r));
541
}// end loop over 'r'
542
for (unsigned int r = 0; r < 2; r++)
543
{
544
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
545
ss = r*(r + 1)*(r + 2)/6;
546
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
547
}// end loop over 'r'
548
for (unsigned int r = 0; r < 1; r++)
549
{
550
for (unsigned int s = 1; s < 2 - r; s++)
551
{
552
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
553
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
554
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
555
tmp5 = (2.00000000 + 2.00000000*r + 2.00000000*s)*(3.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
556
tmp6 = (1.00000000 + 4.00000000*r*r + 4.00000000*r)*(2.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
557
tmp7 = (1.00000000 + s + 2.00000000*r)*(3.00000000 + 2.00000000*r + 2.00000000*s)*s/((1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
558
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
559
}// end loop over 's'
560
}// end loop over 'r'
561
for (unsigned int r = 0; r < 2; r++)
562
{
563
for (unsigned int s = 0; s < 2 - r; s++)
564
{
565
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
566
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
567
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
568
}// end loop over 's'
569
}// end loop over 'r'
570
for (unsigned int r = 0; r < 1; r++)
571
{
572
for (unsigned int s = 0; s < 1 - r; s++)
573
{
574
for (unsigned int t = 1; t < 2 - r - s; t++)
575
{
576
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
577
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
578
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
579
tmp5 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)/(2.00000000*(1.00000000 + t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
580
tmp6 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 4.00000000*r*r + 4.00000000*s*s + 8.00000000*r*s + 8.00000000*r + 8.00000000*s)/(2.00000000*(1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
581
tmp7 = (2.00000000 + t + 2.00000000*r + 2.00000000*s)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*t/((1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
582
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
583
}// end loop over 't'
584
}// end loop over 's'
585
}// end loop over 'r'
586
for (unsigned int r = 0; r < 3; r++)
587
{
588
for (unsigned int s = 0; s < 3 - r; s++)
589
{
590
for (unsigned int t = 0; t < 3 - r - s; t++)
591
{
592
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
593
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
594
}// end loop over 't'
595
}// end loop over 's'
596
}// end loop over 'r'
597
598
// Table(s) of coefficients.
599
static const double coefficients0[10] = \
600
{0.23094011, 0.00000000, 0.14054567, 0.09938080, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.11878277, -0.06719368};
601
602
// Compute value(s).
603
for (unsigned int r = 0; r < 10; r++)
604
{
605
*values += coefficients0[r]*basisvalues[r];
606
}// end loop over 'r'
607
break;
608
}
609
case 5:
610
{
611
612
// Array of basisvalues.
613
double basisvalues[10] = {0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000};
614
615
// Declare helper variables.
616
unsigned int rr = 0;
617
unsigned int ss = 0;
618
unsigned int tt = 0;
619
double tmp5 = 0.00000000;
620
double tmp6 = 0.00000000;
621
double tmp7 = 0.00000000;
622
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
623
double tmp1 = 0.25000000*(Y + Z)*(Y + Z);
624
double tmp2 = 0.50000000*(1.00000000 + Z + 2.00000000*Y);
625
double tmp3 = 0.50000000*(1.00000000 - Z);
626
double tmp4 = tmp3*tmp3;
627
628
// Compute basisvalues.
629
basisvalues[0] = 1.00000000;
630
basisvalues[1] = tmp0;
631
for (unsigned int r = 1; r < 2; r++)
632
{
633
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
634
ss = r*(r + 1)*(r + 2)/6;
635
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
636
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.00000000 + 2.00000000*r)/(1.00000000 + r) - basisvalues[tt]*tmp1*r/(1.00000000 + r));
637
}// end loop over 'r'
638
for (unsigned int r = 0; r < 2; r++)
639
{
640
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
641
ss = r*(r + 1)*(r + 2)/6;
642
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
643
}// end loop over 'r'
644
for (unsigned int r = 0; r < 1; r++)
645
{
646
for (unsigned int s = 1; s < 2 - r; s++)
647
{
648
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
649
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
650
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
651
tmp5 = (2.00000000 + 2.00000000*r + 2.00000000*s)*(3.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
652
tmp6 = (1.00000000 + 4.00000000*r*r + 4.00000000*r)*(2.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
653
tmp7 = (1.00000000 + s + 2.00000000*r)*(3.00000000 + 2.00000000*r + 2.00000000*s)*s/((1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
654
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
655
}// end loop over 's'
656
}// end loop over 'r'
657
for (unsigned int r = 0; r < 2; r++)
658
{
659
for (unsigned int s = 0; s < 2 - r; s++)
660
{
661
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
662
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
663
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
664
}// end loop over 's'
665
}// end loop over 'r'
666
for (unsigned int r = 0; r < 1; r++)
667
{
668
for (unsigned int s = 0; s < 1 - r; s++)
669
{
670
for (unsigned int t = 1; t < 2 - r - s; t++)
671
{
672
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
673
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
674
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
675
tmp5 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)/(2.00000000*(1.00000000 + t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
676
tmp6 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 4.00000000*r*r + 4.00000000*s*s + 8.00000000*r*s + 8.00000000*r + 8.00000000*s)/(2.00000000*(1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
677
tmp7 = (2.00000000 + t + 2.00000000*r + 2.00000000*s)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*t/((1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
678
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
679
}// end loop over 't'
680
}// end loop over 's'
681
}// end loop over 'r'
682
for (unsigned int r = 0; r < 3; r++)
683
{
684
for (unsigned int s = 0; s < 3 - r; s++)
685
{
686
for (unsigned int t = 0; t < 3 - r - s; t++)
687
{
688
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
689
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
690
}// end loop over 't'
691
}// end loop over 's'
692
}// end loop over 'r'
693
694
// Table(s) of coefficients.
695
static const double coefficients0[10] = \
696
{0.23094011, 0.12171612, -0.07027284, 0.09938080, 0.00000000, 0.00000000, 0.10286890, 0.00000000, -0.05939139, -0.06719368};
697
698
// Compute value(s).
699
for (unsigned int r = 0; r < 10; r++)
700
{
701
*values += coefficients0[r]*basisvalues[r];
702
}// end loop over 'r'
703
break;
704
}
705
case 6:
706
{
707
708
// Array of basisvalues.
709
double basisvalues[10] = {0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000};
710
711
// Declare helper variables.
712
unsigned int rr = 0;
713
unsigned int ss = 0;
714
unsigned int tt = 0;
715
double tmp5 = 0.00000000;
716
double tmp6 = 0.00000000;
717
double tmp7 = 0.00000000;
718
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
719
double tmp1 = 0.25000000*(Y + Z)*(Y + Z);
720
double tmp2 = 0.50000000*(1.00000000 + Z + 2.00000000*Y);
721
double tmp3 = 0.50000000*(1.00000000 - Z);
722
double tmp4 = tmp3*tmp3;
723
724
// Compute basisvalues.
725
basisvalues[0] = 1.00000000;
726
basisvalues[1] = tmp0;
727
for (unsigned int r = 1; r < 2; r++)
728
{
729
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
730
ss = r*(r + 1)*(r + 2)/6;
731
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
732
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.00000000 + 2.00000000*r)/(1.00000000 + r) - basisvalues[tt]*tmp1*r/(1.00000000 + r));
733
}// end loop over 'r'
734
for (unsigned int r = 0; r < 2; r++)
735
{
736
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
737
ss = r*(r + 1)*(r + 2)/6;
738
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
739
}// end loop over 'r'
740
for (unsigned int r = 0; r < 1; r++)
741
{
742
for (unsigned int s = 1; s < 2 - r; s++)
743
{
744
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
745
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
746
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
747
tmp5 = (2.00000000 + 2.00000000*r + 2.00000000*s)*(3.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
748
tmp6 = (1.00000000 + 4.00000000*r*r + 4.00000000*r)*(2.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
749
tmp7 = (1.00000000 + s + 2.00000000*r)*(3.00000000 + 2.00000000*r + 2.00000000*s)*s/((1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
750
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
751
}// end loop over 's'
752
}// end loop over 'r'
753
for (unsigned int r = 0; r < 2; r++)
754
{
755
for (unsigned int s = 0; s < 2 - r; s++)
756
{
757
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
758
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
759
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
760
}// end loop over 's'
761
}// end loop over 'r'
762
for (unsigned int r = 0; r < 1; r++)
763
{
764
for (unsigned int s = 0; s < 1 - r; s++)
765
{
766
for (unsigned int t = 1; t < 2 - r - s; t++)
767
{
768
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
769
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
770
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
771
tmp5 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)/(2.00000000*(1.00000000 + t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
772
tmp6 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 4.00000000*r*r + 4.00000000*s*s + 8.00000000*r*s + 8.00000000*r + 8.00000000*s)/(2.00000000*(1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
773
tmp7 = (2.00000000 + t + 2.00000000*r + 2.00000000*s)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*t/((1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
774
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
775
}// end loop over 't'
776
}// end loop over 's'
777
}// end loop over 'r'
778
for (unsigned int r = 0; r < 3; r++)
779
{
780
for (unsigned int s = 0; s < 3 - r; s++)
781
{
782
for (unsigned int t = 0; t < 3 - r - s; t++)
783
{
784
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
785
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
786
}// end loop over 't'
787
}// end loop over 's'
788
}// end loop over 'r'
789
790
// Table(s) of coefficients.
791
static const double coefficients0[10] = \
792
{0.23094011, 0.12171612, 0.07027284, -0.09938080, 0.00000000, 0.10079053, -0.02057378, -0.08728716, -0.01187828, 0.01679842};
793
794
// Compute value(s).
795
for (unsigned int r = 0; r < 10; r++)
796
{
797
*values += coefficients0[r]*basisvalues[r];
798
}// end loop over 'r'
799
break;
800
}
801
case 7:
802
{
803
804
// Array of basisvalues.
805
double basisvalues[10] = {0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000};
806
807
// Declare helper variables.
808
unsigned int rr = 0;
809
unsigned int ss = 0;
810
unsigned int tt = 0;
811
double tmp5 = 0.00000000;
812
double tmp6 = 0.00000000;
813
double tmp7 = 0.00000000;
814
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
815
double tmp1 = 0.25000000*(Y + Z)*(Y + Z);
816
double tmp2 = 0.50000000*(1.00000000 + Z + 2.00000000*Y);
817
double tmp3 = 0.50000000*(1.00000000 - Z);
818
double tmp4 = tmp3*tmp3;
819
820
// Compute basisvalues.
821
basisvalues[0] = 1.00000000;
822
basisvalues[1] = tmp0;
823
for (unsigned int r = 1; r < 2; r++)
824
{
825
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
826
ss = r*(r + 1)*(r + 2)/6;
827
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
828
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.00000000 + 2.00000000*r)/(1.00000000 + r) - basisvalues[tt]*tmp1*r/(1.00000000 + r));
829
}// end loop over 'r'
830
for (unsigned int r = 0; r < 2; r++)
831
{
832
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
833
ss = r*(r + 1)*(r + 2)/6;
834
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
835
}// end loop over 'r'
836
for (unsigned int r = 0; r < 1; r++)
837
{
838
for (unsigned int s = 1; s < 2 - r; s++)
839
{
840
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
841
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
842
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
843
tmp5 = (2.00000000 + 2.00000000*r + 2.00000000*s)*(3.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
844
tmp6 = (1.00000000 + 4.00000000*r*r + 4.00000000*r)*(2.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
845
tmp7 = (1.00000000 + s + 2.00000000*r)*(3.00000000 + 2.00000000*r + 2.00000000*s)*s/((1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
846
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
847
}// end loop over 's'
848
}// end loop over 'r'
849
for (unsigned int r = 0; r < 2; r++)
850
{
851
for (unsigned int s = 0; s < 2 - r; s++)
852
{
853
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
854
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
855
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
856
}// end loop over 's'
857
}// end loop over 'r'
858
for (unsigned int r = 0; r < 1; r++)
859
{
860
for (unsigned int s = 0; s < 1 - r; s++)
861
{
862
for (unsigned int t = 1; t < 2 - r - s; t++)
863
{
864
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
865
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
866
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
867
tmp5 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)/(2.00000000*(1.00000000 + t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
868
tmp6 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 4.00000000*r*r + 4.00000000*s*s + 8.00000000*r*s + 8.00000000*r + 8.00000000*s)/(2.00000000*(1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
869
tmp7 = (2.00000000 + t + 2.00000000*r + 2.00000000*s)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*t/((1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
870
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
871
}// end loop over 't'
872
}// end loop over 's'
873
}// end loop over 'r'
874
for (unsigned int r = 0; r < 3; r++)
875
{
876
for (unsigned int s = 0; s < 3 - r; s++)
877
{
878
for (unsigned int t = 0; t < 3 - r - s; t++)
879
{
880
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
881
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
882
}// end loop over 't'
883
}// end loop over 's'
884
}// end loop over 'r'
885
886
// Table(s) of coefficients.
887
static const double coefficients0[10] = \
888
{0.23094011, -0.12171612, -0.07027284, 0.09938080, 0.00000000, 0.00000000, -0.10286890, 0.00000000, -0.05939139, -0.06719368};
889
890
// Compute value(s).
891
for (unsigned int r = 0; r < 10; r++)
892
{
893
*values += coefficients0[r]*basisvalues[r];
894
}// end loop over 'r'
895
break;
896
}
897
case 8:
898
{
899
900
// Array of basisvalues.
901
double basisvalues[10] = {0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000};
902
903
// Declare helper variables.
904
unsigned int rr = 0;
905
unsigned int ss = 0;
906
unsigned int tt = 0;
907
double tmp5 = 0.00000000;
908
double tmp6 = 0.00000000;
909
double tmp7 = 0.00000000;
910
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
911
double tmp1 = 0.25000000*(Y + Z)*(Y + Z);
912
double tmp2 = 0.50000000*(1.00000000 + Z + 2.00000000*Y);
913
double tmp3 = 0.50000000*(1.00000000 - Z);
914
double tmp4 = tmp3*tmp3;
915
916
// Compute basisvalues.
917
basisvalues[0] = 1.00000000;
918
basisvalues[1] = tmp0;
919
for (unsigned int r = 1; r < 2; r++)
920
{
921
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
922
ss = r*(r + 1)*(r + 2)/6;
923
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
924
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.00000000 + 2.00000000*r)/(1.00000000 + r) - basisvalues[tt]*tmp1*r/(1.00000000 + r));
925
}// end loop over 'r'
926
for (unsigned int r = 0; r < 2; r++)
927
{
928
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
929
ss = r*(r + 1)*(r + 2)/6;
930
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
931
}// end loop over 'r'
932
for (unsigned int r = 0; r < 1; r++)
933
{
934
for (unsigned int s = 1; s < 2 - r; s++)
935
{
936
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
937
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
938
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
939
tmp5 = (2.00000000 + 2.00000000*r + 2.00000000*s)*(3.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
940
tmp6 = (1.00000000 + 4.00000000*r*r + 4.00000000*r)*(2.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
941
tmp7 = (1.00000000 + s + 2.00000000*r)*(3.00000000 + 2.00000000*r + 2.00000000*s)*s/((1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
942
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
943
}// end loop over 's'
944
}// end loop over 'r'
945
for (unsigned int r = 0; r < 2; r++)
946
{
947
for (unsigned int s = 0; s < 2 - r; s++)
948
{
949
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
950
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
951
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
952
}// end loop over 's'
953
}// end loop over 'r'
954
for (unsigned int r = 0; r < 1; r++)
955
{
956
for (unsigned int s = 0; s < 1 - r; s++)
957
{
958
for (unsigned int t = 1; t < 2 - r - s; t++)
959
{
960
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
961
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
962
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
963
tmp5 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)/(2.00000000*(1.00000000 + t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
964
tmp6 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 4.00000000*r*r + 4.00000000*s*s + 8.00000000*r*s + 8.00000000*r + 8.00000000*s)/(2.00000000*(1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
965
tmp7 = (2.00000000 + t + 2.00000000*r + 2.00000000*s)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*t/((1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
966
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
967
}// end loop over 't'
968
}// end loop over 's'
969
}// end loop over 'r'
970
for (unsigned int r = 0; r < 3; r++)
971
{
972
for (unsigned int s = 0; s < 3 - r; s++)
973
{
974
for (unsigned int t = 0; t < 3 - r - s; t++)
975
{
976
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
977
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
978
}// end loop over 't'
979
}// end loop over 's'
980
}// end loop over 'r'
981
982
// Table(s) of coefficients.
983
static const double coefficients0[10] = \
984
{0.23094011, -0.12171612, 0.07027284, -0.09938080, 0.00000000, -0.10079053, 0.02057378, -0.08728716, -0.01187828, 0.01679842};
985
986
// Compute value(s).
987
for (unsigned int r = 0; r < 10; r++)
988
{
989
*values += coefficients0[r]*basisvalues[r];
990
}// end loop over 'r'
991
break;
992
}
993
case 9:
994
{
995
996
// Array of basisvalues.
997
double basisvalues[10] = {0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000};
998
999
// Declare helper variables.
1000
unsigned int rr = 0;
1001
unsigned int ss = 0;
1002
unsigned int tt = 0;
1003
double tmp5 = 0.00000000;
1004
double tmp6 = 0.00000000;
1005
double tmp7 = 0.00000000;
1006
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
1007
double tmp1 = 0.25000000*(Y + Z)*(Y + Z);
1008
double tmp2 = 0.50000000*(1.00000000 + Z + 2.00000000*Y);
1009
double tmp3 = 0.50000000*(1.00000000 - Z);
1010
double tmp4 = tmp3*tmp3;
1011
1012
// Compute basisvalues.
1013
basisvalues[0] = 1.00000000;
1014
basisvalues[1] = tmp0;
1015
for (unsigned int r = 1; r < 2; r++)
1016
{
1017
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
1018
ss = r*(r + 1)*(r + 2)/6;
1019
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
1020
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.00000000 + 2.00000000*r)/(1.00000000 + r) - basisvalues[tt]*tmp1*r/(1.00000000 + r));
1021
}// end loop over 'r'
1022
for (unsigned int r = 0; r < 2; r++)
1023
{
1024
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
1025
ss = r*(r + 1)*(r + 2)/6;
1026
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
1027
}// end loop over 'r'
1028
for (unsigned int r = 0; r < 1; r++)
1029
{
1030
for (unsigned int s = 1; s < 2 - r; s++)
1031
{
1032
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
1033
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
1034
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
1035
tmp5 = (2.00000000 + 2.00000000*r + 2.00000000*s)*(3.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
1036
tmp6 = (1.00000000 + 4.00000000*r*r + 4.00000000*r)*(2.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
1037
tmp7 = (1.00000000 + s + 2.00000000*r)*(3.00000000 + 2.00000000*r + 2.00000000*s)*s/((1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
1038
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
1039
}// end loop over 's'
1040
}// end loop over 'r'
1041
for (unsigned int r = 0; r < 2; r++)
1042
{
1043
for (unsigned int s = 0; s < 2 - r; s++)
1044
{
1045
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
1046
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
1047
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
1048
}// end loop over 's'
1049
}// end loop over 'r'
1050
for (unsigned int r = 0; r < 1; r++)
1051
{
1052
for (unsigned int s = 0; s < 1 - r; s++)
1053
{
1054
for (unsigned int t = 1; t < 2 - r - s; t++)
1055
{
1056
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
1057
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
1058
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
1059
tmp5 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)/(2.00000000*(1.00000000 + t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
1060
tmp6 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 4.00000000*r*r + 4.00000000*s*s + 8.00000000*r*s + 8.00000000*r + 8.00000000*s)/(2.00000000*(1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
1061
tmp7 = (2.00000000 + t + 2.00000000*r + 2.00000000*s)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*t/((1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
1062
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
1063
}// end loop over 't'
1064
}// end loop over 's'
1065
}// end loop over 'r'
1066
for (unsigned int r = 0; r < 3; r++)
1067
{
1068
for (unsigned int s = 0; s < 3 - r; s++)
1069
{
1070
for (unsigned int t = 0; t < 3 - r - s; t++)
1071
{
1072
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
1073
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
1074
}// end loop over 't'
1075
}// end loop over 's'
1076
}// end loop over 'r'
1077
1078
// Table(s) of coefficients.
1079
static const double coefficients0[10] = \
1080
{0.23094011, 0.00000000, -0.14054567, -0.09938080, -0.13012001, 0.00000000, 0.00000000, 0.02909572, 0.02375655, 0.01679842};
1081
1082
// Compute value(s).
1083
for (unsigned int r = 0; r < 10; r++)
1084
{
1085
*values += coefficients0[r]*basisvalues[r];
1086
}// end loop over 'r'
1087
break;
1088
}
1089
}
1090
231
1091
}
232
1092
233
1093
/// Evaluate all basis functions at given point in cell
367
1227
values[r] = 0.00000000;
368
1228
}// end loop over 'r'
369
1229
370
// Map degree of freedom to element degree of freedom
371
const unsigned int dof = i;
372
373
// Array of basisvalues.
374
double basisvalues[10] = {0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000};
375
376
// Declare helper variables.
377
unsigned int rr = 0;
378
unsigned int ss = 0;
379
unsigned int tt = 0;
380
double tmp5 = 0.00000000;
381
double tmp6 = 0.00000000;
382
double tmp7 = 0.00000000;
383
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
384
double tmp1 = 0.25000000*(Y + Z)*(Y + Z);
385
double tmp2 = 0.50000000*(1.00000000 + Z + 2.00000000*Y);
386
double tmp3 = 0.50000000*(1.00000000 - Z);
387
double tmp4 = tmp3*tmp3;
388
389
// Compute basisvalues.
390
basisvalues[0] = 1.00000000;
391
basisvalues[1] = tmp0;
392
for (unsigned int r = 1; r < 2; r++)
393
{
394
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
395
ss = r*(r + 1)*(r + 2)/6;
396
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
397
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.00000000 + 2.00000000*r)/(1.00000000 + r) - basisvalues[tt]*tmp1*r/(1.00000000 + r));
398
}// end loop over 'r'
399
for (unsigned int r = 0; r < 2; r++)
400
{
401
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
402
ss = r*(r + 1)*(r + 2)/6;
403
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
404
}// end loop over 'r'
405
for (unsigned int r = 0; r < 1; r++)
406
{
407
for (unsigned int s = 1; s < 2 - r; s++)
408
{
409
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
410
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
411
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
412
tmp5 = (2.00000000 + 2.00000000*r + 2.00000000*s)*(3.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
413
tmp6 = (1.00000000 + 4.00000000*r*r + 4.00000000*r)*(2.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
414
tmp7 = (1.00000000 + s + 2.00000000*r)*(3.00000000 + 2.00000000*r + 2.00000000*s)*s/((1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
415
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
416
}// end loop over 's'
417
}// end loop over 'r'
418
for (unsigned int r = 0; r < 2; r++)
419
{
420
for (unsigned int s = 0; s < 2 - r; s++)
421
{
422
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
423
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
424
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
425
}// end loop over 's'
426
}// end loop over 'r'
427
for (unsigned int r = 0; r < 1; r++)
428
{
429
for (unsigned int s = 0; s < 1 - r; s++)
430
{
431
for (unsigned int t = 1; t < 2 - r - s; t++)
432
{
433
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
434
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
435
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
436
tmp5 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)/(2.00000000*(1.00000000 + t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
437
tmp6 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 4.00000000*r*r + 4.00000000*s*s + 8.00000000*r*s + 8.00000000*r + 8.00000000*s)/(2.00000000*(1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
438
tmp7 = (2.00000000 + t + 2.00000000*r + 2.00000000*s)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*t/((1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
439
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
440
}// end loop over 't'
441
}// end loop over 's'
442
}// end loop over 'r'
443
for (unsigned int r = 0; r < 3; r++)
444
{
445
for (unsigned int s = 0; s < 3 - r; s++)
446
{
447
for (unsigned int t = 0; t < 3 - r - s; t++)
448
{
449
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
450
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
451
}// end loop over 't'
452
}// end loop over 's'
453
}// end loop over 'r'
454
455
// Table(s) of coefficients.
456
static const double coefficients0[10][10] = \
457
{{-0.05773503, -0.06085806, -0.03513642, -0.02484520, 0.06506000, 0.05039526, 0.04114756, 0.02909572, 0.02375655, 0.01679842},
458
{-0.05773503, 0.06085806, -0.03513642, -0.02484520, 0.06506000, -0.05039526, -0.04114756, 0.02909572, 0.02375655, 0.01679842},
459
{-0.05773503, 0.00000000, 0.07027284, -0.02484520, 0.00000000, 0.00000000, 0.00000000, 0.08728716, -0.04751311, 0.01679842},
460
{-0.05773503, 0.00000000, 0.00000000, 0.07453560, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.10079053},
461
{0.23094011, 0.00000000, 0.14054567, 0.09938080, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.11878277, -0.06719368},
462
{0.23094011, 0.12171612, -0.07027284, 0.09938080, 0.00000000, 0.00000000, 0.10286890, 0.00000000, -0.05939139, -0.06719368},
463
{0.23094011, 0.12171612, 0.07027284, -0.09938080, 0.00000000, 0.10079053, -0.02057378, -0.08728716, -0.01187828, 0.01679842},
464
{0.23094011, -0.12171612, -0.07027284, 0.09938080, 0.00000000, 0.00000000, -0.10286890, 0.00000000, -0.05939139, -0.06719368},
465
{0.23094011, -0.12171612, 0.07027284, -0.09938080, 0.00000000, -0.10079053, 0.02057378, -0.08728716, -0.01187828, 0.01679842},
466
{0.23094011, 0.00000000, -0.14054567, -0.09938080, -0.13012001, 0.00000000, 0.00000000, 0.02909572, 0.02375655, 0.01679842}};
467
468
// Tables of derivatives of the polynomial base (transpose).
469
static const double dmats0[10][10] = \
470
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
471
{6.32455532, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
472
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
473
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
474
{0.00000000, 11.22497216, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
475
{4.58257569, 0.00000000, 8.36660027, -1.18321596, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
476
{3.74165739, 0.00000000, 0.00000000, 8.69482605, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
477
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
478
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
479
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
480
481
static const double dmats1[10][10] = \
482
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
483
{3.16227766, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
484
{5.47722558, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
485
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
486
{2.95803989, 5.61248608, -1.08012345, -0.76376262, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
487
{2.29128785, 7.24568837, 4.18330013, -0.59160798, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
488
{1.87082869, 0.00000000, 0.00000000, 4.34741302, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
489
{-2.64575131, 0.00000000, 9.66091783, 0.68313005, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
490
{3.24037035, 0.00000000, 0.00000000, 7.52994024, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
491
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
492
493
static const double dmats2[10][10] = \
494
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
495
{3.16227766, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
496
{1.82574186, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
497
{5.16397779, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
498
{2.95803989, 5.61248608, -1.08012345, -0.76376262, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
499
{2.29128785, 1.44913767, 4.18330013, -0.59160798, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
500
{1.87082869, 7.09929574, 0.00000000, 4.34741302, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
501
{1.32287566, 0.00000000, 3.86436713, -0.34156503, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
502
{1.08012345, 0.00000000, 7.09929574, 2.50998008, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
503
{-3.81881308, 0.00000000, 0.00000000, 8.87411967, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
504
505
// Compute reference derivatives.
506
// Declare pointer to array of derivatives on FIAT element.
507
double *derivatives = new double[num_derivatives];
508
for (unsigned int r = 0; r < num_derivatives; r++)
509
{
510
derivatives[r] = 0.00000000;
511
}// end loop over 'r'
512
513
// Declare derivative matrix (of polynomial basis).
514
double dmats[10][10] = \
515
{{1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
516
{0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
517
{0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
518
{0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
519
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
520
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
521
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000},
522
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000},
523
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000},
524
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000}};
525
526
// Declare (auxiliary) derivative matrix (of polynomial basis).
527
double dmats_old[10][10] = \
528
{{1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
529
{0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
530
{0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
531
{0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
532
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
533
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
534
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000},
535
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000},
536
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000},
537
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000}};
538
539
// Loop possible derivatives.
540
for (unsigned int r = 0; r < num_derivatives; r++)
541
{
542
// Resetting dmats values to compute next derivative.
543
for (unsigned int t = 0; t < 10; t++)
544
{
545
for (unsigned int u = 0; u < 10; u++)
546
{
547
dmats[t][u] = 0.00000000;
548
if (t == u)
549
{
550
dmats[t][u] = 1.00000000;
551
}
552
553
}// end loop over 'u'
554
}// end loop over 't'
555
556
// Looping derivative order to generate dmats.
557
for (unsigned int s = 0; s < n; s++)
558
{
559
// Updating dmats_old with new values and resetting dmats.
560
for (unsigned int t = 0; t < 10; t++)
561
{
562
for (unsigned int u = 0; u < 10; u++)
563
{
564
dmats_old[t][u] = dmats[t][u];
565
dmats[t][u] = 0.00000000;
566
}// end loop over 'u'
567
}// end loop over 't'
568
569
// Update dmats using an inner product.
570
if (combinations[r][s] == 0)
571
{
572
for (unsigned int t = 0; t < 10; t++)
573
{
574
for (unsigned int u = 0; u < 10; u++)
575
{
576
for (unsigned int tu = 0; tu < 10; tu++)
577
{
578
dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
579
}// end loop over 'tu'
580
}// end loop over 'u'
581
}// end loop over 't'
582
}
583
584
if (combinations[r][s] == 1)
585
{
586
for (unsigned int t = 0; t < 10; t++)
587
{
588
for (unsigned int u = 0; u < 10; u++)
589
{
590
for (unsigned int tu = 0; tu < 10; tu++)
591
{
592
dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
593
}// end loop over 'tu'
594
}// end loop over 'u'
595
}// end loop over 't'
596
}
597
598
if (combinations[r][s] == 2)
599
{
600
for (unsigned int t = 0; t < 10; t++)
601
{
602
for (unsigned int u = 0; u < 10; u++)
603
{
604
for (unsigned int tu = 0; tu < 10; tu++)
605
{
606
dmats[t][u] += dmats2[t][tu]*dmats_old[tu][u];
607
}// end loop over 'tu'
608
}// end loop over 'u'
609
}// end loop over 't'
610
}
611
612
}// end loop over 's'
613
for (unsigned int s = 0; s < 10; s++)
614
{
615
for (unsigned int t = 0; t < 10; t++)
616
{
617
derivatives[r] += coefficients0[dof][s]*dmats[s][t]*basisvalues[t];
618
}// end loop over 't'
619
}// end loop over 's'
620
}// end loop over 'r'
621
622
// Transform derivatives back to physical element
623
for (unsigned int r = 0; r < num_derivatives; r++)
624
{
625
for (unsigned int s = 0; s < num_derivatives; s++)
626
{
627
values[r] += transform[r][s]*derivatives[s];
628
}// end loop over 's'
629
}// end loop over 'r'
630
631
// Delete pointer to array of derivatives on FIAT element
632
delete [] derivatives;
633
634
// Delete pointer to array of combinations of derivatives and transform
635
for (unsigned int r = 0; r < num_derivatives; r++)
636
{
637
delete [] combinations[r];
638
}// end loop over 'r'
639
delete [] combinations;
640
for (unsigned int r = 0; r < num_derivatives; r++)
641
{
642
delete [] transform[r];
643
}// end loop over 'r'
644
delete [] transform;
1230
switch (i)
1231
{
1232
case 0:
1233
{
1234
1235
// Array of basisvalues.
1236
double basisvalues[10] = {0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000};
1237
1238
// Declare helper variables.
1239
unsigned int rr = 0;
1240
unsigned int ss = 0;
1241
unsigned int tt = 0;
1242
double tmp5 = 0.00000000;
1243
double tmp6 = 0.00000000;
1244
double tmp7 = 0.00000000;
1245
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
1246
double tmp1 = 0.25000000*(Y + Z)*(Y + Z);
1247
double tmp2 = 0.50000000*(1.00000000 + Z + 2.00000000*Y);
1248
double tmp3 = 0.50000000*(1.00000000 - Z);
1249
double tmp4 = tmp3*tmp3;
1250
1251
// Compute basisvalues.
1252
basisvalues[0] = 1.00000000;
1253
basisvalues[1] = tmp0;
1254
for (unsigned int r = 1; r < 2; r++)
1255
{
1256
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
1257
ss = r*(r + 1)*(r + 2)/6;
1258
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
1259
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.00000000 + 2.00000000*r)/(1.00000000 + r) - basisvalues[tt]*tmp1*r/(1.00000000 + r));
1260
}// end loop over 'r'
1261
for (unsigned int r = 0; r < 2; r++)
1262
{
1263
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
1264
ss = r*(r + 1)*(r + 2)/6;
1265
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
1266
}// end loop over 'r'
1267
for (unsigned int r = 0; r < 1; r++)
1268
{
1269
for (unsigned int s = 1; s < 2 - r; s++)
1270
{
1271
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
1272
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
1273
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
1274
tmp5 = (2.00000000 + 2.00000000*r + 2.00000000*s)*(3.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
1275
tmp6 = (1.00000000 + 4.00000000*r*r + 4.00000000*r)*(2.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
1276
tmp7 = (1.00000000 + s + 2.00000000*r)*(3.00000000 + 2.00000000*r + 2.00000000*s)*s/((1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
1277
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
1278
}// end loop over 's'
1279
}// end loop over 'r'
1280
for (unsigned int r = 0; r < 2; r++)
1281
{
1282
for (unsigned int s = 0; s < 2 - r; s++)
1283
{
1284
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
1285
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
1286
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
1287
}// end loop over 's'
1288
}// end loop over 'r'
1289
for (unsigned int r = 0; r < 1; r++)
1290
{
1291
for (unsigned int s = 0; s < 1 - r; s++)
1292
{
1293
for (unsigned int t = 1; t < 2 - r - s; t++)
1294
{
1295
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
1296
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
1297
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
1298
tmp5 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)/(2.00000000*(1.00000000 + t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
1299
tmp6 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 4.00000000*r*r + 4.00000000*s*s + 8.00000000*r*s + 8.00000000*r + 8.00000000*s)/(2.00000000*(1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
1300
tmp7 = (2.00000000 + t + 2.00000000*r + 2.00000000*s)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*t/((1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
1301
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
1302
}// end loop over 't'
1303
}// end loop over 's'
1304
}// end loop over 'r'
1305
for (unsigned int r = 0; r < 3; r++)
1306
{
1307
for (unsigned int s = 0; s < 3 - r; s++)
1308
{
1309
for (unsigned int t = 0; t < 3 - r - s; t++)
1310
{
1311
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
1312
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
1313
}// end loop over 't'
1314
}// end loop over 's'
1315
}// end loop over 'r'
1316
1317
// Table(s) of coefficients.
1318
static const double coefficients0[10] = \
1319
{-0.05773503, -0.06085806, -0.03513642, -0.02484520, 0.06506000, 0.05039526, 0.04114756, 0.02909572, 0.02375655, 0.01679842};
1320
1321
// Tables of derivatives of the polynomial base (transpose).
1322
static const double dmats0[10][10] = \
1323
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1324
{6.32455532, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1325
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1326
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1327
{0.00000000, 11.22497216, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1328
{4.58257569, 0.00000000, 8.36660027, -1.18321596, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1329
{3.74165739, 0.00000000, 0.00000000, 8.69482605, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1330
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1331
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1332
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
1333
1334
static const double dmats1[10][10] = \
1335
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1336
{3.16227766, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1337
{5.47722558, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1338
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1339
{2.95803989, 5.61248608, -1.08012345, -0.76376262, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1340
{2.29128785, 7.24568837, 4.18330013, -0.59160798, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1341
{1.87082869, 0.00000000, 0.00000000, 4.34741302, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1342
{-2.64575131, 0.00000000, 9.66091783, 0.68313005, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1343
{3.24037035, 0.00000000, 0.00000000, 7.52994024, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1344
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
1345
1346
static const double dmats2[10][10] = \
1347
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1348
{3.16227766, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1349
{1.82574186, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1350
{5.16397779, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1351
{2.95803989, 5.61248608, -1.08012345, -0.76376262, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1352
{2.29128785, 1.44913767, 4.18330013, -0.59160798, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1353
{1.87082869, 7.09929574, 0.00000000, 4.34741302, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1354
{1.32287566, 0.00000000, 3.86436713, -0.34156503, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1355
{1.08012345, 0.00000000, 7.09929574, 2.50998008, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1356
{-3.81881308, 0.00000000, 0.00000000, 8.87411967, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
1357
1358
// Compute reference derivatives.
1359
// Declare pointer to array of derivatives on FIAT element.
1360
double *derivatives = new double[num_derivatives];
1361
for (unsigned int r = 0; r < num_derivatives; r++)
1362
{
1363
derivatives[r] = 0.00000000;
1364
}// end loop over 'r'
1365
1366
// Declare derivative matrix (of polynomial basis).
1367
double dmats[10][10] = \
1368
{{1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1369
{0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1370
{0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1371
{0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1372
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1373
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1374
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000},
1375
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000},
1376
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000},
1377
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000}};
1378
1379
// Declare (auxiliary) derivative matrix (of polynomial basis).
1380
double dmats_old[10][10] = \
1381
{{1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1382
{0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1383
{0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1384
{0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1385
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1386
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1387
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000},
1388
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000},
1389
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000},
1390
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000}};
1391
1392
// Loop possible derivatives.
1393
for (unsigned int r = 0; r < num_derivatives; r++)
1394
{
1395
// Resetting dmats values to compute next derivative.
1396
for (unsigned int t = 0; t < 10; t++)
1397
{
1398
for (unsigned int u = 0; u < 10; u++)
1399
{
1400
dmats[t][u] = 0.00000000;
1401
if (t == u)
1402
{
1403
dmats[t][u] = 1.00000000;
1404
}
1405
1406
}// end loop over 'u'
1407
}// end loop over 't'
1408
1409
// Looping derivative order to generate dmats.
1410
for (unsigned int s = 0; s < n; s++)
1411
{
1412
// Updating dmats_old with new values and resetting dmats.
1413
for (unsigned int t = 0; t < 10; t++)
1414
{
1415
for (unsigned int u = 0; u < 10; u++)
1416
{
1417
dmats_old[t][u] = dmats[t][u];
1418
dmats[t][u] = 0.00000000;
1419
}// end loop over 'u'
1420
}// end loop over 't'
1421
1422
// Update dmats using an inner product.
1423
if (combinations[r][s] == 0)
1424
{
1425
for (unsigned int t = 0; t < 10; t++)
1426
{
1427
for (unsigned int u = 0; u < 10; u++)
1428
{
1429
for (unsigned int tu = 0; tu < 10; tu++)
1430
{
1431
dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
1432
}// end loop over 'tu'
1433
}// end loop over 'u'
1434
}// end loop over 't'
1435
}
1436
1437
if (combinations[r][s] == 1)
1438
{
1439
for (unsigned int t = 0; t < 10; t++)
1440
{
1441
for (unsigned int u = 0; u < 10; u++)
1442
{
1443
for (unsigned int tu = 0; tu < 10; tu++)
1444
{
1445
dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
1446
}// end loop over 'tu'
1447
}// end loop over 'u'
1448
}// end loop over 't'
1449
}
1450
1451
if (combinations[r][s] == 2)
1452
{
1453
for (unsigned int t = 0; t < 10; t++)
1454
{
1455
for (unsigned int u = 0; u < 10; u++)
1456
{
1457
for (unsigned int tu = 0; tu < 10; tu++)
1458
{
1459
dmats[t][u] += dmats2[t][tu]*dmats_old[tu][u];
1460
}// end loop over 'tu'
1461
}// end loop over 'u'
1462
}// end loop over 't'
1463
}
1464
1465
}// end loop over 's'
1466
for (unsigned int s = 0; s < 10; s++)
1467
{
1468
for (unsigned int t = 0; t < 10; t++)
1469
{
1470
derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
1471
}// end loop over 't'
1472
}// end loop over 's'
1473
}// end loop over 'r'
1474
1475
// Transform derivatives back to physical element
1476
for (unsigned int r = 0; r < num_derivatives; r++)
1477
{
1478
for (unsigned int s = 0; s < num_derivatives; s++)
1479
{
1480
values[r] += transform[r][s]*derivatives[s];
1481
}// end loop over 's'
1482
}// end loop over 'r'
1483
1484
// Delete pointer to array of derivatives on FIAT element
1485
delete [] derivatives;
1486
1487
// Delete pointer to array of combinations of derivatives and transform
1488
for (unsigned int r = 0; r < num_derivatives; r++)
1489
{
1490
delete [] combinations[r];
1491
}// end loop over 'r'
1492
delete [] combinations;
1493
for (unsigned int r = 0; r < num_derivatives; r++)
1494
{
1495
delete [] transform[r];
1496
}// end loop over 'r'
1497
delete [] transform;
1498
break;
1499
}
1500
case 1:
1501
{
1502
1503
// Array of basisvalues.
1504
double basisvalues[10] = {0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000};
1505
1506
// Declare helper variables.
1507
unsigned int rr = 0;
1508
unsigned int ss = 0;
1509
unsigned int tt = 0;
1510
double tmp5 = 0.00000000;
1511
double tmp6 = 0.00000000;
1512
double tmp7 = 0.00000000;
1513
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
1514
double tmp1 = 0.25000000*(Y + Z)*(Y + Z);
1515
double tmp2 = 0.50000000*(1.00000000 + Z + 2.00000000*Y);
1516
double tmp3 = 0.50000000*(1.00000000 - Z);
1517
double tmp4 = tmp3*tmp3;
1518
1519
// Compute basisvalues.
1520
basisvalues[0] = 1.00000000;
1521
basisvalues[1] = tmp0;
1522
for (unsigned int r = 1; r < 2; r++)
1523
{
1524
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
1525
ss = r*(r + 1)*(r + 2)/6;
1526
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
1527
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.00000000 + 2.00000000*r)/(1.00000000 + r) - basisvalues[tt]*tmp1*r/(1.00000000 + r));
1528
}// end loop over 'r'
1529
for (unsigned int r = 0; r < 2; r++)
1530
{
1531
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
1532
ss = r*(r + 1)*(r + 2)/6;
1533
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
1534
}// end loop over 'r'
1535
for (unsigned int r = 0; r < 1; r++)
1536
{
1537
for (unsigned int s = 1; s < 2 - r; s++)
1538
{
1539
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
1540
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
1541
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
1542
tmp5 = (2.00000000 + 2.00000000*r + 2.00000000*s)*(3.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
1543
tmp6 = (1.00000000 + 4.00000000*r*r + 4.00000000*r)*(2.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
1544
tmp7 = (1.00000000 + s + 2.00000000*r)*(3.00000000 + 2.00000000*r + 2.00000000*s)*s/((1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
1545
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
1546
}// end loop over 's'
1547
}// end loop over 'r'
1548
for (unsigned int r = 0; r < 2; r++)
1549
{
1550
for (unsigned int s = 0; s < 2 - r; s++)
1551
{
1552
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
1553
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
1554
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
1555
}// end loop over 's'
1556
}// end loop over 'r'
1557
for (unsigned int r = 0; r < 1; r++)
1558
{
1559
for (unsigned int s = 0; s < 1 - r; s++)
1560
{
1561
for (unsigned int t = 1; t < 2 - r - s; t++)
1562
{
1563
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
1564
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
1565
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
1566
tmp5 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)/(2.00000000*(1.00000000 + t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
1567
tmp6 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 4.00000000*r*r + 4.00000000*s*s + 8.00000000*r*s + 8.00000000*r + 8.00000000*s)/(2.00000000*(1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
1568
tmp7 = (2.00000000 + t + 2.00000000*r + 2.00000000*s)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*t/((1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
1569
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
1570
}// end loop over 't'
1571
}// end loop over 's'
1572
}// end loop over 'r'
1573
for (unsigned int r = 0; r < 3; r++)
1574
{
1575
for (unsigned int s = 0; s < 3 - r; s++)
1576
{
1577
for (unsigned int t = 0; t < 3 - r - s; t++)
1578
{
1579
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
1580
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
1581
}// end loop over 't'
1582
}// end loop over 's'
1583
}// end loop over 'r'
1584
1585
// Table(s) of coefficients.
1586
static const double coefficients0[10] = \
1587
{-0.05773503, 0.06085806, -0.03513642, -0.02484520, 0.06506000, -0.05039526, -0.04114756, 0.02909572, 0.02375655, 0.01679842};
1588
1589
// Tables of derivatives of the polynomial base (transpose).
1590
static const double dmats0[10][10] = \
1591
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1592
{6.32455532, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1593
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1594
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1595
{0.00000000, 11.22497216, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1596
{4.58257569, 0.00000000, 8.36660027, -1.18321596, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1597
{3.74165739, 0.00000000, 0.00000000, 8.69482605, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1598
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1599
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1600
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
1601
1602
static const double dmats1[10][10] = \
1603
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1604
{3.16227766, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1605
{5.47722558, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1606
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1607
{2.95803989, 5.61248608, -1.08012345, -0.76376262, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1608
{2.29128785, 7.24568837, 4.18330013, -0.59160798, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1609
{1.87082869, 0.00000000, 0.00000000, 4.34741302, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1610
{-2.64575131, 0.00000000, 9.66091783, 0.68313005, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1611
{3.24037035, 0.00000000, 0.00000000, 7.52994024, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1612
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
1613
1614
static const double dmats2[10][10] = \
1615
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1616
{3.16227766, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1617
{1.82574186, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1618
{5.16397779, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1619
{2.95803989, 5.61248608, -1.08012345, -0.76376262, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1620
{2.29128785, 1.44913767, 4.18330013, -0.59160798, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1621
{1.87082869, 7.09929574, 0.00000000, 4.34741302, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1622
{1.32287566, 0.00000000, 3.86436713, -0.34156503, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1623
{1.08012345, 0.00000000, 7.09929574, 2.50998008, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1624
{-3.81881308, 0.00000000, 0.00000000, 8.87411967, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
1625
1626
// Compute reference derivatives.
1627
// Declare pointer to array of derivatives on FIAT element.
1628
double *derivatives = new double[num_derivatives];
1629
for (unsigned int r = 0; r < num_derivatives; r++)
1630
{
1631
derivatives[r] = 0.00000000;
1632
}// end loop over 'r'
1633
1634
// Declare derivative matrix (of polynomial basis).
1635
double dmats[10][10] = \
1636
{{1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1637
{0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1638
{0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1639
{0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1640
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1641
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1642
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000},
1643
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000},
1644
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000},
1645
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000}};
1646
1647
// Declare (auxiliary) derivative matrix (of polynomial basis).
1648
double dmats_old[10][10] = \
1649
{{1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1650
{0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1651
{0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1652
{0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1653
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1654
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1655
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000},
1656
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000},
1657
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000},
1658
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000}};
1659
1660
// Loop possible derivatives.
1661
for (unsigned int r = 0; r < num_derivatives; r++)
1662
{
1663
// Resetting dmats values to compute next derivative.
1664
for (unsigned int t = 0; t < 10; t++)
1665
{
1666
for (unsigned int u = 0; u < 10; u++)
1667
{
1668
dmats[t][u] = 0.00000000;
1669
if (t == u)
1670
{
1671
dmats[t][u] = 1.00000000;
1672
}
1673
1674
}// end loop over 'u'
1675
}// end loop over 't'
1676
1677
// Looping derivative order to generate dmats.
1678
for (unsigned int s = 0; s < n; s++)
1679
{
1680
// Updating dmats_old with new values and resetting dmats.
1681
for (unsigned int t = 0; t < 10; t++)
1682
{
1683
for (unsigned int u = 0; u < 10; u++)
1684
{
1685
dmats_old[t][u] = dmats[t][u];
1686
dmats[t][u] = 0.00000000;
1687
}// end loop over 'u'
1688
}// end loop over 't'
1689
1690
// Update dmats using an inner product.
1691
if (combinations[r][s] == 0)
1692
{
1693
for (unsigned int t = 0; t < 10; t++)
1694
{
1695
for (unsigned int u = 0; u < 10; u++)
1696
{
1697
for (unsigned int tu = 0; tu < 10; tu++)
1698
{
1699
dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
1700
}// end loop over 'tu'
1701
}// end loop over 'u'
1702
}// end loop over 't'
1703
}
1704
1705
if (combinations[r][s] == 1)
1706
{
1707
for (unsigned int t = 0; t < 10; t++)
1708
{
1709
for (unsigned int u = 0; u < 10; u++)
1710
{
1711
for (unsigned int tu = 0; tu < 10; tu++)
1712
{
1713
dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
1714
}// end loop over 'tu'
1715
}// end loop over 'u'
1716
}// end loop over 't'
1717
}
1718
1719
if (combinations[r][s] == 2)
1720
{
1721
for (unsigned int t = 0; t < 10; t++)
1722
{
1723
for (unsigned int u = 0; u < 10; u++)
1724
{
1725
for (unsigned int tu = 0; tu < 10; tu++)
1726
{
1727
dmats[t][u] += dmats2[t][tu]*dmats_old[tu][u];
1728
}// end loop over 'tu'
1729
}// end loop over 'u'
1730
}// end loop over 't'
1731
}
1732
1733
}// end loop over 's'
1734
for (unsigned int s = 0; s < 10; s++)
1735
{
1736
for (unsigned int t = 0; t < 10; t++)
1737
{
1738
derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
1739
}// end loop over 't'
1740
}// end loop over 's'
1741
}// end loop over 'r'
1742
1743
// Transform derivatives back to physical element
1744
for (unsigned int r = 0; r < num_derivatives; r++)
1745
{
1746
for (unsigned int s = 0; s < num_derivatives; s++)
1747
{
1748
values[r] += transform[r][s]*derivatives[s];
1749
}// end loop over 's'
1750
}// end loop over 'r'
1751
1752
// Delete pointer to array of derivatives on FIAT element
1753
delete [] derivatives;
1754
1755
// Delete pointer to array of combinations of derivatives and transform
1756
for (unsigned int r = 0; r < num_derivatives; r++)
1757
{
1758
delete [] combinations[r];
1759
}// end loop over 'r'
1760
delete [] combinations;
1761
for (unsigned int r = 0; r < num_derivatives; r++)
1762
{
1763
delete [] transform[r];
1764
}// end loop over 'r'
1765
delete [] transform;
1766
break;
1767
}
1768
case 2:
1769
{
1770
1771
// Array of basisvalues.
1772
double basisvalues[10] = {0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000};
1773
1774
// Declare helper variables.
1775
unsigned int rr = 0;
1776
unsigned int ss = 0;
1777
unsigned int tt = 0;
1778
double tmp5 = 0.00000000;
1779
double tmp6 = 0.00000000;
1780
double tmp7 = 0.00000000;
1781
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
1782
double tmp1 = 0.25000000*(Y + Z)*(Y + Z);
1783
double tmp2 = 0.50000000*(1.00000000 + Z + 2.00000000*Y);
1784
double tmp3 = 0.50000000*(1.00000000 - Z);
1785
double tmp4 = tmp3*tmp3;
1786
1787
// Compute basisvalues.
1788
basisvalues[0] = 1.00000000;
1789
basisvalues[1] = tmp0;
1790
for (unsigned int r = 1; r < 2; r++)
1791
{
1792
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
1793
ss = r*(r + 1)*(r + 2)/6;
1794
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
1795
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.00000000 + 2.00000000*r)/(1.00000000 + r) - basisvalues[tt]*tmp1*r/(1.00000000 + r));
1796
}// end loop over 'r'
1797
for (unsigned int r = 0; r < 2; r++)
1798
{
1799
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
1800
ss = r*(r + 1)*(r + 2)/6;
1801
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
1802
}// end loop over 'r'
1803
for (unsigned int r = 0; r < 1; r++)
1804
{
1805
for (unsigned int s = 1; s < 2 - r; s++)
1806
{
1807
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
1808
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
1809
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
1810
tmp5 = (2.00000000 + 2.00000000*r + 2.00000000*s)*(3.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
1811
tmp6 = (1.00000000 + 4.00000000*r*r + 4.00000000*r)*(2.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
1812
tmp7 = (1.00000000 + s + 2.00000000*r)*(3.00000000 + 2.00000000*r + 2.00000000*s)*s/((1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
1813
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
1814
}// end loop over 's'
1815
}// end loop over 'r'
1816
for (unsigned int r = 0; r < 2; r++)
1817
{
1818
for (unsigned int s = 0; s < 2 - r; s++)
1819
{
1820
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
1821
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
1822
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
1823
}// end loop over 's'
1824
}// end loop over 'r'
1825
for (unsigned int r = 0; r < 1; r++)
1826
{
1827
for (unsigned int s = 0; s < 1 - r; s++)
1828
{
1829
for (unsigned int t = 1; t < 2 - r - s; t++)
1830
{
1831
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
1832
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
1833
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
1834
tmp5 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)/(2.00000000*(1.00000000 + t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
1835
tmp6 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 4.00000000*r*r + 4.00000000*s*s + 8.00000000*r*s + 8.00000000*r + 8.00000000*s)/(2.00000000*(1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
1836
tmp7 = (2.00000000 + t + 2.00000000*r + 2.00000000*s)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*t/((1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
1837
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
1838
}// end loop over 't'
1839
}// end loop over 's'
1840
}// end loop over 'r'
1841
for (unsigned int r = 0; r < 3; r++)
1842
{
1843
for (unsigned int s = 0; s < 3 - r; s++)
1844
{
1845
for (unsigned int t = 0; t < 3 - r - s; t++)
1846
{
1847
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
1848
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
1849
}// end loop over 't'
1850
}// end loop over 's'
1851
}// end loop over 'r'
1852
1853
// Table(s) of coefficients.
1854
static const double coefficients0[10] = \
1855
{-0.05773503, 0.00000000, 0.07027284, -0.02484520, 0.00000000, 0.00000000, 0.00000000, 0.08728716, -0.04751311, 0.01679842};
1856
1857
// Tables of derivatives of the polynomial base (transpose).
1858
static const double dmats0[10][10] = \
1859
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1860
{6.32455532, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1861
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1862
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1863
{0.00000000, 11.22497216, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1864
{4.58257569, 0.00000000, 8.36660027, -1.18321596, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1865
{3.74165739, 0.00000000, 0.00000000, 8.69482605, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1866
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1867
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1868
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
1869
1870
static const double dmats1[10][10] = \
1871
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1872
{3.16227766, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1873
{5.47722558, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1874
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1875
{2.95803989, 5.61248608, -1.08012345, -0.76376262, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1876
{2.29128785, 7.24568837, 4.18330013, -0.59160798, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1877
{1.87082869, 0.00000000, 0.00000000, 4.34741302, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1878
{-2.64575131, 0.00000000, 9.66091783, 0.68313005, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1879
{3.24037035, 0.00000000, 0.00000000, 7.52994024, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1880
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
1881
1882
static const double dmats2[10][10] = \
1883
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1884
{3.16227766, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1885
{1.82574186, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1886
{5.16397779, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1887
{2.95803989, 5.61248608, -1.08012345, -0.76376262, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1888
{2.29128785, 1.44913767, 4.18330013, -0.59160798, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1889
{1.87082869, 7.09929574, 0.00000000, 4.34741302, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1890
{1.32287566, 0.00000000, 3.86436713, -0.34156503, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1891
{1.08012345, 0.00000000, 7.09929574, 2.50998008, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1892
{-3.81881308, 0.00000000, 0.00000000, 8.87411967, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
1893
1894
// Compute reference derivatives.
1895
// Declare pointer to array of derivatives on FIAT element.
1896
double *derivatives = new double[num_derivatives];
1897
for (unsigned int r = 0; r < num_derivatives; r++)
1898
{
1899
derivatives[r] = 0.00000000;
1900
}// end loop over 'r'
1901
1902
// Declare derivative matrix (of polynomial basis).
1903
double dmats[10][10] = \
1904
{{1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1905
{0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1906
{0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1907
{0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1908
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1909
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1910
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000},
1911
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000},
1912
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000},
1913
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000}};
1914
1915
// Declare (auxiliary) derivative matrix (of polynomial basis).
1916
double dmats_old[10][10] = \
1917
{{1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1918
{0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1919
{0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1920
{0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1921
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1922
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1923
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000},
1924
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000},
1925
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000},
1926
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000}};
1927
1928
// Loop possible derivatives.
1929
for (unsigned int r = 0; r < num_derivatives; r++)
1930
{
1931
// Resetting dmats values to compute next derivative.
1932
for (unsigned int t = 0; t < 10; t++)
1933
{
1934
for (unsigned int u = 0; u < 10; u++)
1935
{
1936
dmats[t][u] = 0.00000000;
1937
if (t == u)
1938
{
1939
dmats[t][u] = 1.00000000;
1940
}
1941
1942
}// end loop over 'u'
1943
}// end loop over 't'
1944
1945
// Looping derivative order to generate dmats.
1946
for (unsigned int s = 0; s < n; s++)
1947
{
1948
// Updating dmats_old with new values and resetting dmats.
1949
for (unsigned int t = 0; t < 10; t++)
1950
{
1951
for (unsigned int u = 0; u < 10; u++)
1952
{
1953
dmats_old[t][u] = dmats[t][u];
1954
dmats[t][u] = 0.00000000;
1955
}// end loop over 'u'
1956
}// end loop over 't'
1957
1958
// Update dmats using an inner product.
1959
if (combinations[r][s] == 0)
1960
{
1961
for (unsigned int t = 0; t < 10; t++)
1962
{
1963
for (unsigned int u = 0; u < 10; u++)
1964
{
1965
for (unsigned int tu = 0; tu < 10; tu++)
1966
{
1967
dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
1968
}// end loop over 'tu'
1969
}// end loop over 'u'
1970
}// end loop over 't'
1971
}
1972
1973
if (combinations[r][s] == 1)
1974
{
1975
for (unsigned int t = 0; t < 10; t++)
1976
{
1977
for (unsigned int u = 0; u < 10; u++)
1978
{
1979
for (unsigned int tu = 0; tu < 10; tu++)
1980
{
1981
dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
1982
}// end loop over 'tu'
1983
}// end loop over 'u'
1984
}// end loop over 't'
1985
}
1986
1987
if (combinations[r][s] == 2)
1988
{
1989
for (unsigned int t = 0; t < 10; t++)
1990
{
1991
for (unsigned int u = 0; u < 10; u++)
1992
{
1993
for (unsigned int tu = 0; tu < 10; tu++)
1994
{
1995
dmats[t][u] += dmats2[t][tu]*dmats_old[tu][u];
1996
}// end loop over 'tu'
1997
}// end loop over 'u'
1998
}// end loop over 't'
1999
}
2000
2001
}// end loop over 's'
2002
for (unsigned int s = 0; s < 10; s++)
2003
{
2004
for (unsigned int t = 0; t < 10; t++)
2005
{
2006
derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
2007
}// end loop over 't'
2008
}// end loop over 's'
2009
}// end loop over 'r'
2010
2011
// Transform derivatives back to physical element
2012
for (unsigned int r = 0; r < num_derivatives; r++)
2013
{
2014
for (unsigned int s = 0; s < num_derivatives; s++)
2015
{
2016
values[r] += transform[r][s]*derivatives[s];
2017
}// end loop over 's'
2018
}// end loop over 'r'
2019
2020
// Delete pointer to array of derivatives on FIAT element
2021
delete [] derivatives;
2022
2023
// Delete pointer to array of combinations of derivatives and transform
2024
for (unsigned int r = 0; r < num_derivatives; r++)
2025
{
2026
delete [] combinations[r];
2027
}// end loop over 'r'
2028
delete [] combinations;
2029
for (unsigned int r = 0; r < num_derivatives; r++)
2030
{
2031
delete [] transform[r];
2032
}// end loop over 'r'
2033
delete [] transform;
2034
break;
2035
}
2036
case 3:
2037
{
2038
2039
// Array of basisvalues.
2040
double basisvalues[10] = {0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000};
2041
2042
// Declare helper variables.
2043
unsigned int rr = 0;
2044
unsigned int ss = 0;
2045
unsigned int tt = 0;
2046
double tmp5 = 0.00000000;
2047
double tmp6 = 0.00000000;
2048
double tmp7 = 0.00000000;
2049
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
2050
double tmp1 = 0.25000000*(Y + Z)*(Y + Z);
2051
double tmp2 = 0.50000000*(1.00000000 + Z + 2.00000000*Y);
2052
double tmp3 = 0.50000000*(1.00000000 - Z);
2053
double tmp4 = tmp3*tmp3;
2054
2055
// Compute basisvalues.
2056
basisvalues[0] = 1.00000000;
2057
basisvalues[1] = tmp0;
2058
for (unsigned int r = 1; r < 2; r++)
2059
{
2060
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
2061
ss = r*(r + 1)*(r + 2)/6;
2062
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
2063
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.00000000 + 2.00000000*r)/(1.00000000 + r) - basisvalues[tt]*tmp1*r/(1.00000000 + r));
2064
}// end loop over 'r'
2065
for (unsigned int r = 0; r < 2; r++)
2066
{
2067
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
2068
ss = r*(r + 1)*(r + 2)/6;
2069
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
2070
}// end loop over 'r'
2071
for (unsigned int r = 0; r < 1; r++)
2072
{
2073
for (unsigned int s = 1; s < 2 - r; s++)
2074
{
2075
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
2076
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
2077
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
2078
tmp5 = (2.00000000 + 2.00000000*r + 2.00000000*s)*(3.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
2079
tmp6 = (1.00000000 + 4.00000000*r*r + 4.00000000*r)*(2.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
2080
tmp7 = (1.00000000 + s + 2.00000000*r)*(3.00000000 + 2.00000000*r + 2.00000000*s)*s/((1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
2081
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
2082
}// end loop over 's'
2083
}// end loop over 'r'
2084
for (unsigned int r = 0; r < 2; r++)
2085
{
2086
for (unsigned int s = 0; s < 2 - r; s++)
2087
{
2088
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
2089
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
2090
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
2091
}// end loop over 's'
2092
}// end loop over 'r'
2093
for (unsigned int r = 0; r < 1; r++)
2094
{
2095
for (unsigned int s = 0; s < 1 - r; s++)
2096
{
2097
for (unsigned int t = 1; t < 2 - r - s; t++)
2098
{
2099
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
2100
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
2101
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
2102
tmp5 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)/(2.00000000*(1.00000000 + t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
2103
tmp6 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 4.00000000*r*r + 4.00000000*s*s + 8.00000000*r*s + 8.00000000*r + 8.00000000*s)/(2.00000000*(1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
2104
tmp7 = (2.00000000 + t + 2.00000000*r + 2.00000000*s)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*t/((1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
2105
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
2106
}// end loop over 't'
2107
}// end loop over 's'
2108
}// end loop over 'r'
2109
for (unsigned int r = 0; r < 3; r++)
2110
{
2111
for (unsigned int s = 0; s < 3 - r; s++)
2112
{
2113
for (unsigned int t = 0; t < 3 - r - s; t++)
2114
{
2115
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
2116
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
2117
}// end loop over 't'
2118
}// end loop over 's'
2119
}// end loop over 'r'
2120
2121
// Table(s) of coefficients.
2122
static const double coefficients0[10] = \
2123
{-0.05773503, 0.00000000, 0.00000000, 0.07453560, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.10079053};
2124
2125
// Tables of derivatives of the polynomial base (transpose).
2126
static const double dmats0[10][10] = \
2127
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2128
{6.32455532, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2129
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2130
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2131
{0.00000000, 11.22497216, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2132
{4.58257569, 0.00000000, 8.36660027, -1.18321596, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2133
{3.74165739, 0.00000000, 0.00000000, 8.69482605, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2134
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2135
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2136
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
2137
2138
static const double dmats1[10][10] = \
2139
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2140
{3.16227766, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2141
{5.47722558, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2142
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2143
{2.95803989, 5.61248608, -1.08012345, -0.76376262, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2144
{2.29128785, 7.24568837, 4.18330013, -0.59160798, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2145
{1.87082869, 0.00000000, 0.00000000, 4.34741302, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2146
{-2.64575131, 0.00000000, 9.66091783, 0.68313005, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2147
{3.24037035, 0.00000000, 0.00000000, 7.52994024, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2148
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
2149
2150
static const double dmats2[10][10] = \
2151
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2152
{3.16227766, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2153
{1.82574186, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2154
{5.16397779, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2155
{2.95803989, 5.61248608, -1.08012345, -0.76376262, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2156
{2.29128785, 1.44913767, 4.18330013, -0.59160798, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2157
{1.87082869, 7.09929574, 0.00000000, 4.34741302, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2158
{1.32287566, 0.00000000, 3.86436713, -0.34156503, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2159
{1.08012345, 0.00000000, 7.09929574, 2.50998008, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2160
{-3.81881308, 0.00000000, 0.00000000, 8.87411967, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
2161
2162
// Compute reference derivatives.
2163
// Declare pointer to array of derivatives on FIAT element.
2164
double *derivatives = new double[num_derivatives];
2165
for (unsigned int r = 0; r < num_derivatives; r++)
2166
{
2167
derivatives[r] = 0.00000000;
2168
}// end loop over 'r'
2169
2170
// Declare derivative matrix (of polynomial basis).
2171
double dmats[10][10] = \
2172
{{1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2173
{0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2174
{0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2175
{0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2176
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2177
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2178
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000},
2179
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000},
2180
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000},
2181
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000}};
2182
2183
// Declare (auxiliary) derivative matrix (of polynomial basis).
2184
double dmats_old[10][10] = \
2185
{{1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2186
{0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2187
{0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2188
{0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2189
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2190
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2191
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000},
2192
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000},
2193
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000},
2194
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000}};
2195
2196
// Loop possible derivatives.
2197
for (unsigned int r = 0; r < num_derivatives; r++)
2198
{
2199
// Resetting dmats values to compute next derivative.
2200
for (unsigned int t = 0; t < 10; t++)
2201
{
2202
for (unsigned int u = 0; u < 10; u++)
2203
{
2204
dmats[t][u] = 0.00000000;
2205
if (t == u)
2206
{
2207
dmats[t][u] = 1.00000000;
2208
}
2209
2210
}// end loop over 'u'
2211
}// end loop over 't'
2212
2213
// Looping derivative order to generate dmats.
2214
for (unsigned int s = 0; s < n; s++)
2215
{
2216
// Updating dmats_old with new values and resetting dmats.
2217
for (unsigned int t = 0; t < 10; t++)
2218
{
2219
for (unsigned int u = 0; u < 10; u++)
2220
{
2221
dmats_old[t][u] = dmats[t][u];
2222
dmats[t][u] = 0.00000000;
2223
}// end loop over 'u'
2224
}// end loop over 't'
2225
2226
// Update dmats using an inner product.
2227
if (combinations[r][s] == 0)
2228
{
2229
for (unsigned int t = 0; t < 10; t++)
2230
{
2231
for (unsigned int u = 0; u < 10; u++)
2232
{
2233
for (unsigned int tu = 0; tu < 10; tu++)
2234
{
2235
dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
2236
}// end loop over 'tu'
2237
}// end loop over 'u'
2238
}// end loop over 't'
2239
}
2240
2241
if (combinations[r][s] == 1)
2242
{
2243
for (unsigned int t = 0; t < 10; t++)
2244
{
2245
for (unsigned int u = 0; u < 10; u++)
2246
{
2247
for (unsigned int tu = 0; tu < 10; tu++)
2248
{
2249
dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
2250
}// end loop over 'tu'
2251
}// end loop over 'u'
2252
}// end loop over 't'
2253
}
2254
2255
if (combinations[r][s] == 2)
2256
{
2257
for (unsigned int t = 0; t < 10; t++)
2258
{
2259
for (unsigned int u = 0; u < 10; u++)
2260
{
2261
for (unsigned int tu = 0; tu < 10; tu++)
2262
{
2263
dmats[t][u] += dmats2[t][tu]*dmats_old[tu][u];
2264
}// end loop over 'tu'
2265
}// end loop over 'u'
2266
}// end loop over 't'
2267
}
2268
2269
}// end loop over 's'
2270
for (unsigned int s = 0; s < 10; s++)
2271
{
2272
for (unsigned int t = 0; t < 10; t++)
2273
{
2274
derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
2275
}// end loop over 't'
2276
}// end loop over 's'
2277
}// end loop over 'r'
2278
2279
// Transform derivatives back to physical element
2280
for (unsigned int r = 0; r < num_derivatives; r++)
2281
{
2282
for (unsigned int s = 0; s < num_derivatives; s++)
2283
{
2284
values[r] += transform[r][s]*derivatives[s];
2285
}// end loop over 's'
2286
}// end loop over 'r'
2287
2288
// Delete pointer to array of derivatives on FIAT element
2289
delete [] derivatives;
2290
2291
// Delete pointer to array of combinations of derivatives and transform
2292
for (unsigned int r = 0; r < num_derivatives; r++)
2293
{
2294
delete [] combinations[r];
2295
}// end loop over 'r'
2296
delete [] combinations;
2297
for (unsigned int r = 0; r < num_derivatives; r++)
2298
{
2299
delete [] transform[r];
2300
}// end loop over 'r'
2301
delete [] transform;
2302
break;
2303
}
2304
case 4:
2305
{
2306
2307
// Array of basisvalues.
2308
double basisvalues[10] = {0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000};
2309
2310
// Declare helper variables.
2311
unsigned int rr = 0;
2312
unsigned int ss = 0;
2313
unsigned int tt = 0;
2314
double tmp5 = 0.00000000;
2315
double tmp6 = 0.00000000;
2316
double tmp7 = 0.00000000;
2317
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
2318
double tmp1 = 0.25000000*(Y + Z)*(Y + Z);
2319
double tmp2 = 0.50000000*(1.00000000 + Z + 2.00000000*Y);
2320
double tmp3 = 0.50000000*(1.00000000 - Z);
2321
double tmp4 = tmp3*tmp3;
2322
2323
// Compute basisvalues.
2324
basisvalues[0] = 1.00000000;
2325
basisvalues[1] = tmp0;
2326
for (unsigned int r = 1; r < 2; r++)
2327
{
2328
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
2329
ss = r*(r + 1)*(r + 2)/6;
2330
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
2331
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.00000000 + 2.00000000*r)/(1.00000000 + r) - basisvalues[tt]*tmp1*r/(1.00000000 + r));
2332
}// end loop over 'r'
2333
for (unsigned int r = 0; r < 2; r++)
2334
{
2335
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
2336
ss = r*(r + 1)*(r + 2)/6;
2337
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
2338
}// end loop over 'r'
2339
for (unsigned int r = 0; r < 1; r++)
2340
{
2341
for (unsigned int s = 1; s < 2 - r; s++)
2342
{
2343
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
2344
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
2345
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
2346
tmp5 = (2.00000000 + 2.00000000*r + 2.00000000*s)*(3.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
2347
tmp6 = (1.00000000 + 4.00000000*r*r + 4.00000000*r)*(2.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
2348
tmp7 = (1.00000000 + s + 2.00000000*r)*(3.00000000 + 2.00000000*r + 2.00000000*s)*s/((1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
2349
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
2350
}// end loop over 's'
2351
}// end loop over 'r'
2352
for (unsigned int r = 0; r < 2; r++)
2353
{
2354
for (unsigned int s = 0; s < 2 - r; s++)
2355
{
2356
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
2357
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
2358
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
2359
}// end loop over 's'
2360
}// end loop over 'r'
2361
for (unsigned int r = 0; r < 1; r++)
2362
{
2363
for (unsigned int s = 0; s < 1 - r; s++)
2364
{
2365
for (unsigned int t = 1; t < 2 - r - s; t++)
2366
{
2367
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
2368
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
2369
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
2370
tmp5 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)/(2.00000000*(1.00000000 + t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
2371
tmp6 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 4.00000000*r*r + 4.00000000*s*s + 8.00000000*r*s + 8.00000000*r + 8.00000000*s)/(2.00000000*(1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
2372
tmp7 = (2.00000000 + t + 2.00000000*r + 2.00000000*s)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*t/((1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
2373
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
2374
}// end loop over 't'
2375
}// end loop over 's'
2376
}// end loop over 'r'
2377
for (unsigned int r = 0; r < 3; r++)
2378
{
2379
for (unsigned int s = 0; s < 3 - r; s++)
2380
{
2381
for (unsigned int t = 0; t < 3 - r - s; t++)
2382
{
2383
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
2384
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
2385
}// end loop over 't'
2386
}// end loop over 's'
2387
}// end loop over 'r'
2388
2389
// Table(s) of coefficients.
2390
static const double coefficients0[10] = \
2391
{0.23094011, 0.00000000, 0.14054567, 0.09938080, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.11878277, -0.06719368};
2392
2393
// Tables of derivatives of the polynomial base (transpose).
2394
static const double dmats0[10][10] = \
2395
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2396
{6.32455532, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2397
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2398
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2399
{0.00000000, 11.22497216, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2400
{4.58257569, 0.00000000, 8.36660027, -1.18321596, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2401
{3.74165739, 0.00000000, 0.00000000, 8.69482605, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2402
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2403
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2404
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
2405
2406
static const double dmats1[10][10] = \
2407
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2408
{3.16227766, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2409
{5.47722558, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2410
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2411
{2.95803989, 5.61248608, -1.08012345, -0.76376262, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2412
{2.29128785, 7.24568837, 4.18330013, -0.59160798, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2413
{1.87082869, 0.00000000, 0.00000000, 4.34741302, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2414
{-2.64575131, 0.00000000, 9.66091783, 0.68313005, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2415
{3.24037035, 0.00000000, 0.00000000, 7.52994024, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2416
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
2417
2418
static const double dmats2[10][10] = \
2419
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2420
{3.16227766, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2421
{1.82574186, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2422
{5.16397779, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2423
{2.95803989, 5.61248608, -1.08012345, -0.76376262, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2424
{2.29128785, 1.44913767, 4.18330013, -0.59160798, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2425
{1.87082869, 7.09929574, 0.00000000, 4.34741302, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2426
{1.32287566, 0.00000000, 3.86436713, -0.34156503, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2427
{1.08012345, 0.00000000, 7.09929574, 2.50998008, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2428
{-3.81881308, 0.00000000, 0.00000000, 8.87411967, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
2429
2430
// Compute reference derivatives.
2431
// Declare pointer to array of derivatives on FIAT element.
2432
double *derivatives = new double[num_derivatives];
2433
for (unsigned int r = 0; r < num_derivatives; r++)
2434
{
2435
derivatives[r] = 0.00000000;
2436
}// end loop over 'r'
2437
2438
// Declare derivative matrix (of polynomial basis).
2439
double dmats[10][10] = \
2440
{{1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2441
{0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2442
{0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2443
{0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2444
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2445
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2446
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000},
2447
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000},
2448
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000},
2449
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000}};
2450
2451
// Declare (auxiliary) derivative matrix (of polynomial basis).
2452
double dmats_old[10][10] = \
2453
{{1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2454
{0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2455
{0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2456
{0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2457
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2458
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2459
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000},
2460
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000},
2461
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000},
2462
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000}};
2463
2464
// Loop possible derivatives.
2465
for (unsigned int r = 0; r < num_derivatives; r++)
2466
{
2467
// Resetting dmats values to compute next derivative.
2468
for (unsigned int t = 0; t < 10; t++)
2469
{
2470
for (unsigned int u = 0; u < 10; u++)
2471
{
2472
dmats[t][u] = 0.00000000;
2473
if (t == u)
2474
{
2475
dmats[t][u] = 1.00000000;
2476
}
2477
2478
}// end loop over 'u'
2479
}// end loop over 't'
2480
2481
// Looping derivative order to generate dmats.
2482
for (unsigned int s = 0; s < n; s++)
2483
{
2484
// Updating dmats_old with new values and resetting dmats.
2485
for (unsigned int t = 0; t < 10; t++)
2486
{
2487
for (unsigned int u = 0; u < 10; u++)
2488
{
2489
dmats_old[t][u] = dmats[t][u];
2490
dmats[t][u] = 0.00000000;
2491
}// end loop over 'u'
2492
}// end loop over 't'
2493
2494
// Update dmats using an inner product.
2495
if (combinations[r][s] == 0)
2496
{
2497
for (unsigned int t = 0; t < 10; t++)
2498
{
2499
for (unsigned int u = 0; u < 10; u++)
2500
{
2501
for (unsigned int tu = 0; tu < 10; tu++)
2502
{
2503
dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
2504
}// end loop over 'tu'
2505
}// end loop over 'u'
2506
}// end loop over 't'
2507
}
2508
2509
if (combinations[r][s] == 1)
2510
{
2511
for (unsigned int t = 0; t < 10; t++)
2512
{
2513
for (unsigned int u = 0; u < 10; u++)
2514
{
2515
for (unsigned int tu = 0; tu < 10; tu++)
2516
{
2517
dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
2518
}// end loop over 'tu'
2519
}// end loop over 'u'
2520
}// end loop over 't'
2521
}
2522
2523
if (combinations[r][s] == 2)
2524
{
2525
for (unsigned int t = 0; t < 10; t++)
2526
{
2527
for (unsigned int u = 0; u < 10; u++)
2528
{
2529
for (unsigned int tu = 0; tu < 10; tu++)
2530
{
2531
dmats[t][u] += dmats2[t][tu]*dmats_old[tu][u];
2532
}// end loop over 'tu'
2533
}// end loop over 'u'
2534
}// end loop over 't'
2535
}
2536
2537
}// end loop over 's'
2538
for (unsigned int s = 0; s < 10; s++)
2539
{
2540
for (unsigned int t = 0; t < 10; t++)
2541
{
2542
derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
2543
}// end loop over 't'
2544
}// end loop over 's'
2545
}// end loop over 'r'
2546
2547
// Transform derivatives back to physical element
2548
for (unsigned int r = 0; r < num_derivatives; r++)
2549
{
2550
for (unsigned int s = 0; s < num_derivatives; s++)
2551
{
2552
values[r] += transform[r][s]*derivatives[s];
2553
}// end loop over 's'
2554
}// end loop over 'r'
2555
2556
// Delete pointer to array of derivatives on FIAT element
2557
delete [] derivatives;
2558
2559
// Delete pointer to array of combinations of derivatives and transform
2560
for (unsigned int r = 0; r < num_derivatives; r++)
2561
{
2562
delete [] combinations[r];
2563
}// end loop over 'r'
2564
delete [] combinations;
2565
for (unsigned int r = 0; r < num_derivatives; r++)
2566
{
2567
delete [] transform[r];
2568
}// end loop over 'r'
2569
delete [] transform;
2570
break;
2571
}
2572
case 5:
2573
{
2574
2575
// Array of basisvalues.
2576
double basisvalues[10] = {0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000};
2577
2578
// Declare helper variables.
2579
unsigned int rr = 0;
2580
unsigned int ss = 0;
2581
unsigned int tt = 0;
2582
double tmp5 = 0.00000000;
2583
double tmp6 = 0.00000000;
2584
double tmp7 = 0.00000000;
2585
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
2586
double tmp1 = 0.25000000*(Y + Z)*(Y + Z);
2587
double tmp2 = 0.50000000*(1.00000000 + Z + 2.00000000*Y);
2588
double tmp3 = 0.50000000*(1.00000000 - Z);
2589
double tmp4 = tmp3*tmp3;
2590
2591
// Compute basisvalues.
2592
basisvalues[0] = 1.00000000;
2593
basisvalues[1] = tmp0;
2594
for (unsigned int r = 1; r < 2; r++)
2595
{
2596
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
2597
ss = r*(r + 1)*(r + 2)/6;
2598
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
2599
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.00000000 + 2.00000000*r)/(1.00000000 + r) - basisvalues[tt]*tmp1*r/(1.00000000 + r));
2600
}// end loop over 'r'
2601
for (unsigned int r = 0; r < 2; r++)
2602
{
2603
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
2604
ss = r*(r + 1)*(r + 2)/6;
2605
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
2606
}// end loop over 'r'
2607
for (unsigned int r = 0; r < 1; r++)
2608
{
2609
for (unsigned int s = 1; s < 2 - r; s++)
2610
{
2611
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
2612
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
2613
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
2614
tmp5 = (2.00000000 + 2.00000000*r + 2.00000000*s)*(3.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
2615
tmp6 = (1.00000000 + 4.00000000*r*r + 4.00000000*r)*(2.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
2616
tmp7 = (1.00000000 + s + 2.00000000*r)*(3.00000000 + 2.00000000*r + 2.00000000*s)*s/((1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
2617
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
2618
}// end loop over 's'
2619
}// end loop over 'r'
2620
for (unsigned int r = 0; r < 2; r++)
2621
{
2622
for (unsigned int s = 0; s < 2 - r; s++)
2623
{
2624
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
2625
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
2626
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
2627
}// end loop over 's'
2628
}// end loop over 'r'
2629
for (unsigned int r = 0; r < 1; r++)
2630
{
2631
for (unsigned int s = 0; s < 1 - r; s++)
2632
{
2633
for (unsigned int t = 1; t < 2 - r - s; t++)
2634
{
2635
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
2636
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
2637
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
2638
tmp5 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)/(2.00000000*(1.00000000 + t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
2639
tmp6 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 4.00000000*r*r + 4.00000000*s*s + 8.00000000*r*s + 8.00000000*r + 8.00000000*s)/(2.00000000*(1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
2640
tmp7 = (2.00000000 + t + 2.00000000*r + 2.00000000*s)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*t/((1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
2641
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
2642
}// end loop over 't'
2643
}// end loop over 's'
2644
}// end loop over 'r'
2645
for (unsigned int r = 0; r < 3; r++)
2646
{
2647
for (unsigned int s = 0; s < 3 - r; s++)
2648
{
2649
for (unsigned int t = 0; t < 3 - r - s; t++)
2650
{
2651
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
2652
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
2653
}// end loop over 't'
2654
}// end loop over 's'
2655
}// end loop over 'r'
2656
2657
// Table(s) of coefficients.
2658
static const double coefficients0[10] = \
2659
{0.23094011, 0.12171612, -0.07027284, 0.09938080, 0.00000000, 0.00000000, 0.10286890, 0.00000000, -0.05939139, -0.06719368};
2660
2661
// Tables of derivatives of the polynomial base (transpose).
2662
static const double dmats0[10][10] = \
2663
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2664
{6.32455532, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2665
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2666
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2667
{0.00000000, 11.22497216, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2668
{4.58257569, 0.00000000, 8.36660027, -1.18321596, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2669
{3.74165739, 0.00000000, 0.00000000, 8.69482605, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2670
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2671
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2672
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
2673
2674
static const double dmats1[10][10] = \
2675
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2676
{3.16227766, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2677
{5.47722558, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2678
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2679
{2.95803989, 5.61248608, -1.08012345, -0.76376262, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2680
{2.29128785, 7.24568837, 4.18330013, -0.59160798, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2681
{1.87082869, 0.00000000, 0.00000000, 4.34741302, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2682
{-2.64575131, 0.00000000, 9.66091783, 0.68313005, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2683
{3.24037035, 0.00000000, 0.00000000, 7.52994024, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2684
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
2685
2686
static const double dmats2[10][10] = \
2687
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2688
{3.16227766, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2689
{1.82574186, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2690
{5.16397779, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2691
{2.95803989, 5.61248608, -1.08012345, -0.76376262, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2692
{2.29128785, 1.44913767, 4.18330013, -0.59160798, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2693
{1.87082869, 7.09929574, 0.00000000, 4.34741302, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2694
{1.32287566, 0.00000000, 3.86436713, -0.34156503, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2695
{1.08012345, 0.00000000, 7.09929574, 2.50998008, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2696
{-3.81881308, 0.00000000, 0.00000000, 8.87411967, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
2697
2698
// Compute reference derivatives.
2699
// Declare pointer to array of derivatives on FIAT element.
2700
double *derivatives = new double[num_derivatives];
2701
for (unsigned int r = 0; r < num_derivatives; r++)
2702
{
2703
derivatives[r] = 0.00000000;
2704
}// end loop over 'r'
2705
2706
// Declare derivative matrix (of polynomial basis).
2707
double dmats[10][10] = \
2708
{{1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2709
{0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2710
{0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2711
{0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2712
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2713
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2714
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000},
2715
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000},
2716
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000},
2717
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000}};
2718
2719
// Declare (auxiliary) derivative matrix (of polynomial basis).
2720
double dmats_old[10][10] = \
2721
{{1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2722
{0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2723
{0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2724
{0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2725
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2726
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2727
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000},
2728
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000},
2729
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000},
2730
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000}};
2731
2732
// Loop possible derivatives.
2733
for (unsigned int r = 0; r < num_derivatives; r++)
2734
{
2735
// Resetting dmats values to compute next derivative.
2736
for (unsigned int t = 0; t < 10; t++)
2737
{
2738
for (unsigned int u = 0; u < 10; u++)
2739
{
2740
dmats[t][u] = 0.00000000;
2741
if (t == u)
2742
{
2743
dmats[t][u] = 1.00000000;
2744
}
2745
2746
}// end loop over 'u'
2747
}// end loop over 't'
2748
2749
// Looping derivative order to generate dmats.
2750
for (unsigned int s = 0; s < n; s++)
2751
{
2752
// Updating dmats_old with new values and resetting dmats.
2753
for (unsigned int t = 0; t < 10; t++)
2754
{
2755
for (unsigned int u = 0; u < 10; u++)
2756
{
2757
dmats_old[t][u] = dmats[t][u];
2758
dmats[t][u] = 0.00000000;
2759
}// end loop over 'u'
2760
}// end loop over 't'
2761
2762
// Update dmats using an inner product.
2763
if (combinations[r][s] == 0)
2764
{
2765
for (unsigned int t = 0; t < 10; t++)
2766
{
2767
for (unsigned int u = 0; u < 10; u++)
2768
{
2769
for (unsigned int tu = 0; tu < 10; tu++)
2770
{
2771
dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
2772
}// end loop over 'tu'
2773
}// end loop over 'u'
2774
}// end loop over 't'
2775
}
2776
2777
if (combinations[r][s] == 1)
2778
{
2779
for (unsigned int t = 0; t < 10; t++)
2780
{
2781
for (unsigned int u = 0; u < 10; u++)
2782
{
2783
for (unsigned int tu = 0; tu < 10; tu++)
2784
{
2785
dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
2786
}// end loop over 'tu'
2787
}// end loop over 'u'
2788
}// end loop over 't'
2789
}
2790
2791
if (combinations[r][s] == 2)
2792
{
2793
for (unsigned int t = 0; t < 10; t++)
2794
{
2795
for (unsigned int u = 0; u < 10; u++)
2796
{
2797
for (unsigned int tu = 0; tu < 10; tu++)
2798
{
2799
dmats[t][u] += dmats2[t][tu]*dmats_old[tu][u];
2800
}// end loop over 'tu'
2801
}// end loop over 'u'
2802
}// end loop over 't'
2803
}
2804
2805
}// end loop over 's'
2806
for (unsigned int s = 0; s < 10; s++)
2807
{
2808
for (unsigned int t = 0; t < 10; t++)
2809
{
2810
derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
2811
}// end loop over 't'
2812
}// end loop over 's'
2813
}// end loop over 'r'
2814
2815
// Transform derivatives back to physical element
2816
for (unsigned int r = 0; r < num_derivatives; r++)
2817
{
2818
for (unsigned int s = 0; s < num_derivatives; s++)
2819
{
2820
values[r] += transform[r][s]*derivatives[s];
2821
}// end loop over 's'
2822
}// end loop over 'r'
2823
2824
// Delete pointer to array of derivatives on FIAT element
2825
delete [] derivatives;
2826
2827
// Delete pointer to array of combinations of derivatives and transform
2828
for (unsigned int r = 0; r < num_derivatives; r++)
2829
{
2830
delete [] combinations[r];
2831
}// end loop over 'r'
2832
delete [] combinations;
2833
for (unsigned int r = 0; r < num_derivatives; r++)
2834
{
2835
delete [] transform[r];
2836
}// end loop over 'r'
2837
delete [] transform;
2838
break;
2839
}
2840
case 6:
2841
{
2842
2843
// Array of basisvalues.
2844
double basisvalues[10] = {0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000};
2845
2846
// Declare helper variables.
2847
unsigned int rr = 0;
2848
unsigned int ss = 0;
2849
unsigned int tt = 0;
2850
double tmp5 = 0.00000000;
2851
double tmp6 = 0.00000000;
2852
double tmp7 = 0.00000000;
2853
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
2854
double tmp1 = 0.25000000*(Y + Z)*(Y + Z);
2855
double tmp2 = 0.50000000*(1.00000000 + Z + 2.00000000*Y);
2856
double tmp3 = 0.50000000*(1.00000000 - Z);
2857
double tmp4 = tmp3*tmp3;
2858
2859
// Compute basisvalues.
2860
basisvalues[0] = 1.00000000;
2861
basisvalues[1] = tmp0;
2862
for (unsigned int r = 1; r < 2; r++)
2863
{
2864
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
2865
ss = r*(r + 1)*(r + 2)/6;
2866
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
2867
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.00000000 + 2.00000000*r)/(1.00000000 + r) - basisvalues[tt]*tmp1*r/(1.00000000 + r));
2868
}// end loop over 'r'
2869
for (unsigned int r = 0; r < 2; r++)
2870
{
2871
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
2872
ss = r*(r + 1)*(r + 2)/6;
2873
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
2874
}// end loop over 'r'
2875
for (unsigned int r = 0; r < 1; r++)
2876
{
2877
for (unsigned int s = 1; s < 2 - r; s++)
2878
{
2879
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
2880
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
2881
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
2882
tmp5 = (2.00000000 + 2.00000000*r + 2.00000000*s)*(3.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
2883
tmp6 = (1.00000000 + 4.00000000*r*r + 4.00000000*r)*(2.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
2884
tmp7 = (1.00000000 + s + 2.00000000*r)*(3.00000000 + 2.00000000*r + 2.00000000*s)*s/((1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
2885
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
2886
}// end loop over 's'
2887
}// end loop over 'r'
2888
for (unsigned int r = 0; r < 2; r++)
2889
{
2890
for (unsigned int s = 0; s < 2 - r; s++)
2891
{
2892
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
2893
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
2894
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
2895
}// end loop over 's'
2896
}// end loop over 'r'
2897
for (unsigned int r = 0; r < 1; r++)
2898
{
2899
for (unsigned int s = 0; s < 1 - r; s++)
2900
{
2901
for (unsigned int t = 1; t < 2 - r - s; t++)
2902
{
2903
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
2904
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
2905
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
2906
tmp5 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)/(2.00000000*(1.00000000 + t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
2907
tmp6 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 4.00000000*r*r + 4.00000000*s*s + 8.00000000*r*s + 8.00000000*r + 8.00000000*s)/(2.00000000*(1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
2908
tmp7 = (2.00000000 + t + 2.00000000*r + 2.00000000*s)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*t/((1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
2909
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
2910
}// end loop over 't'
2911
}// end loop over 's'
2912
}// end loop over 'r'
2913
for (unsigned int r = 0; r < 3; r++)
2914
{
2915
for (unsigned int s = 0; s < 3 - r; s++)
2916
{
2917
for (unsigned int t = 0; t < 3 - r - s; t++)
2918
{
2919
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
2920
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
2921
}// end loop over 't'
2922
}// end loop over 's'
2923
}// end loop over 'r'
2924
2925
// Table(s) of coefficients.
2926
static const double coefficients0[10] = \
2927
{0.23094011, 0.12171612, 0.07027284, -0.09938080, 0.00000000, 0.10079053, -0.02057378, -0.08728716, -0.01187828, 0.01679842};
2928
2929
// Tables of derivatives of the polynomial base (transpose).
2930
static const double dmats0[10][10] = \
2931
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2932
{6.32455532, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2933
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2934
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2935
{0.00000000, 11.22497216, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2936
{4.58257569, 0.00000000, 8.36660027, -1.18321596, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2937
{3.74165739, 0.00000000, 0.00000000, 8.69482605, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2938
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2939
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2940
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
2941
2942
static const double dmats1[10][10] = \
2943
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2944
{3.16227766, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2945
{5.47722558, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2946
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2947
{2.95803989, 5.61248608, -1.08012345, -0.76376262, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2948
{2.29128785, 7.24568837, 4.18330013, -0.59160798, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2949
{1.87082869, 0.00000000, 0.00000000, 4.34741302, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2950
{-2.64575131, 0.00000000, 9.66091783, 0.68313005, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2951
{3.24037035, 0.00000000, 0.00000000, 7.52994024, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2952
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
2953
2954
static const double dmats2[10][10] = \
2955
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2956
{3.16227766, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2957
{1.82574186, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2958
{5.16397779, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2959
{2.95803989, 5.61248608, -1.08012345, -0.76376262, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2960
{2.29128785, 1.44913767, 4.18330013, -0.59160798, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2961
{1.87082869, 7.09929574, 0.00000000, 4.34741302, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2962
{1.32287566, 0.00000000, 3.86436713, -0.34156503, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2963
{1.08012345, 0.00000000, 7.09929574, 2.50998008, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2964
{-3.81881308, 0.00000000, 0.00000000, 8.87411967, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
2965
2966
// Compute reference derivatives.
2967
// Declare pointer to array of derivatives on FIAT element.
2968
double *derivatives = new double[num_derivatives];
2969
for (unsigned int r = 0; r < num_derivatives; r++)
2970
{
2971
derivatives[r] = 0.00000000;
2972
}// end loop over 'r'
2973
2974
// Declare derivative matrix (of polynomial basis).
2975
double dmats[10][10] = \
2976
{{1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2977
{0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2978
{0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2979
{0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2980
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2981
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2982
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000},
2983
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000},
2984
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000},
2985
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000}};
2986
2987
// Declare (auxiliary) derivative matrix (of polynomial basis).
2988
double dmats_old[10][10] = \
2989
{{1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2990
{0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2991
{0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2992
{0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2993
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2994
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2995
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000},
2996
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000},
2997
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000},
2998
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000}};
2999
3000
// Loop possible derivatives.
3001
for (unsigned int r = 0; r < num_derivatives; r++)
3002
{
3003
// Resetting dmats values to compute next derivative.
3004
for (unsigned int t = 0; t < 10; t++)
3005
{
3006
for (unsigned int u = 0; u < 10; u++)
3007
{
3008
dmats[t][u] = 0.00000000;
3009
if (t == u)
3010
{
3011
dmats[t][u] = 1.00000000;
3012
}
3013
3014
}// end loop over 'u'
3015
}// end loop over 't'
3016
3017
// Looping derivative order to generate dmats.
3018
for (unsigned int s = 0; s < n; s++)
3019
{
3020
// Updating dmats_old with new values and resetting dmats.
3021
for (unsigned int t = 0; t < 10; t++)
3022
{
3023
for (unsigned int u = 0; u < 10; u++)
3024
{
3025
dmats_old[t][u] = dmats[t][u];
3026
dmats[t][u] = 0.00000000;
3027
}// end loop over 'u'
3028
}// end loop over 't'
3029
3030
// Update dmats using an inner product.
3031
if (combinations[r][s] == 0)
3032
{
3033
for (unsigned int t = 0; t < 10; t++)
3034
{
3035
for (unsigned int u = 0; u < 10; u++)
3036
{
3037
for (unsigned int tu = 0; tu < 10; tu++)
3038
{
3039
dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
3040
}// end loop over 'tu'
3041
}// end loop over 'u'
3042
}// end loop over 't'
3043
}
3044
3045
if (combinations[r][s] == 1)
3046
{
3047
for (unsigned int t = 0; t < 10; t++)
3048
{
3049
for (unsigned int u = 0; u < 10; u++)
3050
{
3051
for (unsigned int tu = 0; tu < 10; tu++)
3052
{
3053
dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
3054
}// end loop over 'tu'
3055
}// end loop over 'u'
3056
}// end loop over 't'
3057
}
3058
3059
if (combinations[r][s] == 2)
3060
{
3061
for (unsigned int t = 0; t < 10; t++)
3062
{
3063
for (unsigned int u = 0; u < 10; u++)
3064
{
3065
for (unsigned int tu = 0; tu < 10; tu++)
3066
{
3067
dmats[t][u] += dmats2[t][tu]*dmats_old[tu][u];
3068
}// end loop over 'tu'
3069
}// end loop over 'u'
3070
}// end loop over 't'
3071
}
3072
3073
}// end loop over 's'
3074
for (unsigned int s = 0; s < 10; s++)
3075
{
3076
for (unsigned int t = 0; t < 10; t++)
3077
{
3078
derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
3079
}// end loop over 't'
3080
}// end loop over 's'
3081
}// end loop over 'r'
3082
3083
// Transform derivatives back to physical element
3084
for (unsigned int r = 0; r < num_derivatives; r++)
3085
{
3086
for (unsigned int s = 0; s < num_derivatives; s++)
3087
{
3088
values[r] += transform[r][s]*derivatives[s];
3089
}// end loop over 's'
3090
}// end loop over 'r'
3091
3092
// Delete pointer to array of derivatives on FIAT element
3093
delete [] derivatives;
3094
3095
// Delete pointer to array of combinations of derivatives and transform
3096
for (unsigned int r = 0; r < num_derivatives; r++)
3097
{
3098
delete [] combinations[r];
3099
}// end loop over 'r'
3100
delete [] combinations;
3101
for (unsigned int r = 0; r < num_derivatives; r++)
3102
{
3103
delete [] transform[r];
3104
}// end loop over 'r'
3105
delete [] transform;
3106
break;
3107
}
3108
case 7:
3109
{
3110
3111
// Array of basisvalues.
3112
double basisvalues[10] = {0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000};
3113
3114
// Declare helper variables.
3115
unsigned int rr = 0;
3116
unsigned int ss = 0;
3117
unsigned int tt = 0;
3118
double tmp5 = 0.00000000;
3119
double tmp6 = 0.00000000;
3120
double tmp7 = 0.00000000;
3121
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
3122
double tmp1 = 0.25000000*(Y + Z)*(Y + Z);
3123
double tmp2 = 0.50000000*(1.00000000 + Z + 2.00000000*Y);
3124
double tmp3 = 0.50000000*(1.00000000 - Z);
3125
double tmp4 = tmp3*tmp3;
3126
3127
// Compute basisvalues.
3128
basisvalues[0] = 1.00000000;
3129
basisvalues[1] = tmp0;
3130
for (unsigned int r = 1; r < 2; r++)
3131
{
3132
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
3133
ss = r*(r + 1)*(r + 2)/6;
3134
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
3135
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.00000000 + 2.00000000*r)/(1.00000000 + r) - basisvalues[tt]*tmp1*r/(1.00000000 + r));
3136
}// end loop over 'r'
3137
for (unsigned int r = 0; r < 2; r++)
3138
{
3139
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
3140
ss = r*(r + 1)*(r + 2)/6;
3141
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
3142
}// end loop over 'r'
3143
for (unsigned int r = 0; r < 1; r++)
3144
{
3145
for (unsigned int s = 1; s < 2 - r; s++)
3146
{
3147
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
3148
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
3149
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
3150
tmp5 = (2.00000000 + 2.00000000*r + 2.00000000*s)*(3.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
3151
tmp6 = (1.00000000 + 4.00000000*r*r + 4.00000000*r)*(2.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
3152
tmp7 = (1.00000000 + s + 2.00000000*r)*(3.00000000 + 2.00000000*r + 2.00000000*s)*s/((1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
3153
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
3154
}// end loop over 's'
3155
}// end loop over 'r'
3156
for (unsigned int r = 0; r < 2; r++)
3157
{
3158
for (unsigned int s = 0; s < 2 - r; s++)
3159
{
3160
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
3161
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
3162
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
3163
}// end loop over 's'
3164
}// end loop over 'r'
3165
for (unsigned int r = 0; r < 1; r++)
3166
{
3167
for (unsigned int s = 0; s < 1 - r; s++)
3168
{
3169
for (unsigned int t = 1; t < 2 - r - s; t++)
3170
{
3171
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
3172
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
3173
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
3174
tmp5 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)/(2.00000000*(1.00000000 + t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
3175
tmp6 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 4.00000000*r*r + 4.00000000*s*s + 8.00000000*r*s + 8.00000000*r + 8.00000000*s)/(2.00000000*(1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
3176
tmp7 = (2.00000000 + t + 2.00000000*r + 2.00000000*s)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*t/((1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
3177
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
3178
}// end loop over 't'
3179
}// end loop over 's'
3180
}// end loop over 'r'
3181
for (unsigned int r = 0; r < 3; r++)
3182
{
3183
for (unsigned int s = 0; s < 3 - r; s++)
3184
{
3185
for (unsigned int t = 0; t < 3 - r - s; t++)
3186
{
3187
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
3188
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
3189
}// end loop over 't'
3190
}// end loop over 's'
3191
}// end loop over 'r'
3192
3193
// Table(s) of coefficients.
3194
static const double coefficients0[10] = \
3195
{0.23094011, -0.12171612, -0.07027284, 0.09938080, 0.00000000, 0.00000000, -0.10286890, 0.00000000, -0.05939139, -0.06719368};
3196
3197
// Tables of derivatives of the polynomial base (transpose).
3198
static const double dmats0[10][10] = \
3199
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
3200
{6.32455532, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
3201
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
3202
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
3203
{0.00000000, 11.22497216, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
3204
{4.58257569, 0.00000000, 8.36660027, -1.18321596, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
3205
{3.74165739, 0.00000000, 0.00000000, 8.69482605, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
3206
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
3207
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
3208
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
3209
3210
static const double dmats1[10][10] = \
3211
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
3212
{3.16227766, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
3213
{5.47722558, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
3214
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
3215
{2.95803989, 5.61248608, -1.08012345, -0.76376262, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
3216
{2.29128785, 7.24568837, 4.18330013, -0.59160798, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
3217
{1.87082869, 0.00000000, 0.00000000, 4.34741302, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
3218
{-2.64575131, 0.00000000, 9.66091783, 0.68313005, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
3219
{3.24037035, 0.00000000, 0.00000000, 7.52994024, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
3220
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
3221
3222
static const double dmats2[10][10] = \
3223
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
3224
{3.16227766, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
3225
{1.82574186, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
3226
{5.16397779, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
3227
{2.95803989, 5.61248608, -1.08012345, -0.76376262, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
3228
{2.29128785, 1.44913767, 4.18330013, -0.59160798, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
3229
{1.87082869, 7.09929574, 0.00000000, 4.34741302, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
3230
{1.32287566, 0.00000000, 3.86436713, -0.34156503, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
3231
{1.08012345, 0.00000000, 7.09929574, 2.50998008, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
3232
{-3.81881308, 0.00000000, 0.00000000, 8.87411967, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
3233
3234
// Compute reference derivatives.
3235
// Declare pointer to array of derivatives on FIAT element.
3236
double *derivatives = new double[num_derivatives];
3237
for (unsigned int r = 0; r < num_derivatives; r++)
3238
{
3239
derivatives[r] = 0.00000000;
3240
}// end loop over 'r'
3241
3242
// Declare derivative matrix (of polynomial basis).
3243
double dmats[10][10] = \
3244
{{1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
3245
{0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
3246
{0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
3247
{0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
3248
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
3249
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
3250
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000},
3251
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000},
3252
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000},
3253
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000}};
3254
3255
// Declare (auxiliary) derivative matrix (of polynomial basis).
3256
double dmats_old[10][10] = \
3257
{{1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
3258
{0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
3259
{0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
3260
{0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
3261
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
3262
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
3263
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000},
3264
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000},
3265
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000},
3266
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000}};
3267
3268
// Loop possible derivatives.
3269
for (unsigned int r = 0; r < num_derivatives; r++)
3270
{
3271
// Resetting dmats values to compute next derivative.
3272
for (unsigned int t = 0; t < 10; t++)
3273
{
3274
for (unsigned int u = 0; u < 10; u++)
3275
{
3276
dmats[t][u] = 0.00000000;
3277
if (t == u)
3278
{
3279
dmats[t][u] = 1.00000000;
3280
}
3281
3282
}// end loop over 'u'
3283
}// end loop over 't'
3284
3285
// Looping derivative order to generate dmats.
3286
for (unsigned int s = 0; s < n; s++)
3287
{
3288
// Updating dmats_old with new values and resetting dmats.
3289
for (unsigned int t = 0; t < 10; t++)
3290
{
3291
for (unsigned int u = 0; u < 10; u++)
3292
{
3293
dmats_old[t][u] = dmats[t][u];
3294
dmats[t][u] = 0.00000000;
3295
}// end loop over 'u'
3296
}// end loop over 't'
3297
3298
// Update dmats using an inner product.
3299
if (combinations[r][s] == 0)
3300
{
3301
for (unsigned int t = 0; t < 10; t++)
3302
{
3303
for (unsigned int u = 0; u < 10; u++)
3304
{
3305
for (unsigned int tu = 0; tu < 10; tu++)
3306
{
3307
dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
3308
}// end loop over 'tu'
3309
}// end loop over 'u'
3310
}// end loop over 't'
3311
}
3312
3313
if (combinations[r][s] == 1)
3314
{
3315
for (unsigned int t = 0; t < 10; t++)
3316
{
3317
for (unsigned int u = 0; u < 10; u++)
3318
{
3319
for (unsigned int tu = 0; tu < 10; tu++)
3320
{
3321
dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
3322
}// end loop over 'tu'
3323
}// end loop over 'u'
3324
}// end loop over 't'
3325
}
3326
3327
if (combinations[r][s] == 2)
3328
{
3329
for (unsigned int t = 0; t < 10; t++)
3330
{
3331
for (unsigned int u = 0; u < 10; u++)
3332
{
3333
for (unsigned int tu = 0; tu < 10; tu++)
3334
{
3335
dmats[t][u] += dmats2[t][tu]*dmats_old[tu][u];
3336
}// end loop over 'tu'
3337
}// end loop over 'u'
3338
}// end loop over 't'
3339
}
3340
3341
}// end loop over 's'
3342
for (unsigned int s = 0; s < 10; s++)
3343
{
3344
for (unsigned int t = 0; t < 10; t++)
3345
{
3346
derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
3347
}// end loop over 't'
3348
}// end loop over 's'
3349
}// end loop over 'r'
3350
3351
// Transform derivatives back to physical element
3352
for (unsigned int r = 0; r < num_derivatives; r++)
3353
{
3354
for (unsigned int s = 0; s < num_derivatives; s++)
3355
{
3356
values[r] += transform[r][s]*derivatives[s];
3357
}// end loop over 's'
3358
}// end loop over 'r'
3359
3360
// Delete pointer to array of derivatives on FIAT element
3361
delete [] derivatives;
3362
3363
// Delete pointer to array of combinations of derivatives and transform
3364
for (unsigned int r = 0; r < num_derivatives; r++)
3365
{
3366
delete [] combinations[r];
3367
}// end loop over 'r'
3368
delete [] combinations;
3369
for (unsigned int r = 0; r < num_derivatives; r++)
3370
{
3371
delete [] transform[r];
3372
}// end loop over 'r'
3373
delete [] transform;
3374
break;
3375
}
3376
case 8:
3377
{
3378
3379
// Array of basisvalues.
3380
double basisvalues[10] = {0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000};
3381
3382
// Declare helper variables.
3383
unsigned int rr = 0;
3384
unsigned int ss = 0;
3385
unsigned int tt = 0;
3386
double tmp5 = 0.00000000;
3387
double tmp6 = 0.00000000;
3388
double tmp7 = 0.00000000;
3389
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
3390
double tmp1 = 0.25000000*(Y + Z)*(Y + Z);
3391
double tmp2 = 0.50000000*(1.00000000 + Z + 2.00000000*Y);
3392
double tmp3 = 0.50000000*(1.00000000 - Z);
3393
double tmp4 = tmp3*tmp3;
3394
3395
// Compute basisvalues.
3396
basisvalues[0] = 1.00000000;
3397
basisvalues[1] = tmp0;
3398
for (unsigned int r = 1; r < 2; r++)
3399
{
3400
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
3401
ss = r*(r + 1)*(r + 2)/6;
3402
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
3403
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.00000000 + 2.00000000*r)/(1.00000000 + r) - basisvalues[tt]*tmp1*r/(1.00000000 + r));
3404
}// end loop over 'r'
3405
for (unsigned int r = 0; r < 2; r++)
3406
{
3407
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
3408
ss = r*(r + 1)*(r + 2)/6;
3409
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
3410
}// end loop over 'r'
3411
for (unsigned int r = 0; r < 1; r++)
3412
{
3413
for (unsigned int s = 1; s < 2 - r; s++)
3414
{
3415
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
3416
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
3417
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
3418
tmp5 = (2.00000000 + 2.00000000*r + 2.00000000*s)*(3.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
3419
tmp6 = (1.00000000 + 4.00000000*r*r + 4.00000000*r)*(2.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
3420
tmp7 = (1.00000000 + s + 2.00000000*r)*(3.00000000 + 2.00000000*r + 2.00000000*s)*s/((1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
3421
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
3422
}// end loop over 's'
3423
}// end loop over 'r'
3424
for (unsigned int r = 0; r < 2; r++)
3425
{
3426
for (unsigned int s = 0; s < 2 - r; s++)
3427
{
3428
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
3429
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
3430
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
3431
}// end loop over 's'
3432
}// end loop over 'r'
3433
for (unsigned int r = 0; r < 1; r++)
3434
{
3435
for (unsigned int s = 0; s < 1 - r; s++)
3436
{
3437
for (unsigned int t = 1; t < 2 - r - s; t++)
3438
{
3439
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
3440
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
3441
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
3442
tmp5 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)/(2.00000000*(1.00000000 + t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
3443
tmp6 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 4.00000000*r*r + 4.00000000*s*s + 8.00000000*r*s + 8.00000000*r + 8.00000000*s)/(2.00000000*(1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
3444
tmp7 = (2.00000000 + t + 2.00000000*r + 2.00000000*s)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*t/((1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
3445
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
3446
}// end loop over 't'
3447
}// end loop over 's'
3448
}// end loop over 'r'
3449
for (unsigned int r = 0; r < 3; r++)
3450
{
3451
for (unsigned int s = 0; s < 3 - r; s++)
3452
{
3453
for (unsigned int t = 0; t < 3 - r - s; t++)
3454
{
3455
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
3456
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
3457
}// end loop over 't'
3458
}// end loop over 's'
3459
}// end loop over 'r'
3460
3461
// Table(s) of coefficients.
3462
static const double coefficients0[10] = \
3463
{0.23094011, -0.12171612, 0.07027284, -0.09938080, 0.00000000, -0.10079053, 0.02057378, -0.08728716, -0.01187828, 0.01679842};
3464
3465
// Tables of derivatives of the polynomial base (transpose).
3466
static const double dmats0[10][10] = \
3467
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
3468
{6.32455532, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
3469
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
3470
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
3471
{0.00000000, 11.22497216, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
3472
{4.58257569, 0.00000000, 8.36660027, -1.18321596, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
3473
{3.74165739, 0.00000000, 0.00000000, 8.69482605, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
3474
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
3475
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
3476
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
3477
3478
static const double dmats1[10][10] = \
3479
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
3480
{3.16227766, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
3481
{5.47722558, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
3482
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
3483
{2.95803989, 5.61248608, -1.08012345, -0.76376262, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
3484
{2.29128785, 7.24568837, 4.18330013, -0.59160798, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
3485
{1.87082869, 0.00000000, 0.00000000, 4.34741302, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
3486
{-2.64575131, 0.00000000, 9.66091783, 0.68313005, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
3487
{3.24037035, 0.00000000, 0.00000000, 7.52994024, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
3488
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
3489
3490
static const double dmats2[10][10] = \
3491
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
3492
{3.16227766, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
3493
{1.82574186, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
3494
{5.16397779, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
3495
{2.95803989, 5.61248608, -1.08012345, -0.76376262, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
3496
{2.29128785, 1.44913767, 4.18330013, -0.59160798, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
3497
{1.87082869, 7.09929574, 0.00000000, 4.34741302, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
3498
{1.32287566, 0.00000000, 3.86436713, -0.34156503, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
3499
{1.08012345, 0.00000000, 7.09929574, 2.50998008, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
3500
{-3.81881308, 0.00000000, 0.00000000, 8.87411967, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
3501
3502
// Compute reference derivatives.
3503
// Declare pointer to array of derivatives on FIAT element.
3504
double *derivatives = new double[num_derivatives];
3505
for (unsigned int r = 0; r < num_derivatives; r++)
3506
{
3507
derivatives[r] = 0.00000000;
3508
}// end loop over 'r'
3509
3510
// Declare derivative matrix (of polynomial basis).
3511
double dmats[10][10] = \
3512
{{1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
3513
{0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
3514
{0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
3515
{0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
3516
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
3517
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
3518
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000},
3519
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000},
3520
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000},
3521
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000}};
3522
3523
// Declare (auxiliary) derivative matrix (of polynomial basis).
3524
double dmats_old[10][10] = \
3525
{{1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
3526
{0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
3527
{0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
3528
{0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
3529
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
3530
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
3531
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000},
3532
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000},
3533
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000},
3534
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000}};
3535
3536
// Loop possible derivatives.
3537
for (unsigned int r = 0; r < num_derivatives; r++)
3538
{
3539
// Resetting dmats values to compute next derivative.
3540
for (unsigned int t = 0; t < 10; t++)
3541
{
3542
for (unsigned int u = 0; u < 10; u++)
3543
{
3544
dmats[t][u] = 0.00000000;
3545
if (t == u)
3546
{
3547
dmats[t][u] = 1.00000000;
3548
}
3549
3550
}// end loop over 'u'
3551
}// end loop over 't'
3552
3553
// Looping derivative order to generate dmats.
3554
for (unsigned int s = 0; s < n; s++)
3555
{
3556
// Updating dmats_old with new values and resetting dmats.
3557
for (unsigned int t = 0; t < 10; t++)
3558
{
3559
for (unsigned int u = 0; u < 10; u++)
3560
{
3561
dmats_old[t][u] = dmats[t][u];
3562
dmats[t][u] = 0.00000000;
3563
}// end loop over 'u'
3564
}// end loop over 't'
3565
3566
// Update dmats using an inner product.
3567
if (combinations[r][s] == 0)
3568
{
3569
for (unsigned int t = 0; t < 10; t++)
3570
{
3571
for (unsigned int u = 0; u < 10; u++)
3572
{
3573
for (unsigned int tu = 0; tu < 10; tu++)
3574
{
3575
dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
3576
}// end loop over 'tu'
3577
}// end loop over 'u'
3578
}// end loop over 't'
3579
}
3580
3581
if (combinations[r][s] == 1)
3582
{
3583
for (unsigned int t = 0; t < 10; t++)
3584
{
3585
for (unsigned int u = 0; u < 10; u++)
3586
{
3587
for (unsigned int tu = 0; tu < 10; tu++)
3588
{
3589
dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
3590
}// end loop over 'tu'
3591
}// end loop over 'u'
3592
}// end loop over 't'
3593
}
3594
3595
if (combinations[r][s] == 2)
3596
{
3597
for (unsigned int t = 0; t < 10; t++)
3598
{
3599
for (unsigned int u = 0; u < 10; u++)
3600
{
3601
for (unsigned int tu = 0; tu < 10; tu++)
3602
{
3603
dmats[t][u] += dmats2[t][tu]*dmats_old[tu][u];
3604
}// end loop over 'tu'
3605
}// end loop over 'u'
3606
}// end loop over 't'
3607
}
3608
3609
}// end loop over 's'
3610
for (unsigned int s = 0; s < 10; s++)
3611
{
3612
for (unsigned int t = 0; t < 10; t++)
3613
{
3614
derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
3615
}// end loop over 't'
3616
}// end loop over 's'
3617
}// end loop over 'r'
3618
3619
// Transform derivatives back to physical element
3620
for (unsigned int r = 0; r < num_derivatives; r++)
3621
{
3622
for (unsigned int s = 0; s < num_derivatives; s++)
3623
{
3624
values[r] += transform[r][s]*derivatives[s];
3625
}// end loop over 's'
3626
}// end loop over 'r'
3627
3628
// Delete pointer to array of derivatives on FIAT element
3629
delete [] derivatives;
3630
3631
// Delete pointer to array of combinations of derivatives and transform
3632
for (unsigned int r = 0; r < num_derivatives; r++)
3633
{
3634
delete [] combinations[r];
3635
}// end loop over 'r'
3636
delete [] combinations;
3637
for (unsigned int r = 0; r < num_derivatives; r++)
3638
{
3639
delete [] transform[r];
3640
}// end loop over 'r'
3641
delete [] transform;
3642
break;
3643
}
3644
case 9:
3645
{
3646
3647
// Array of basisvalues.
3648
double basisvalues[10] = {0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000};
3649
3650
// Declare helper variables.
3651
unsigned int rr = 0;
3652
unsigned int ss = 0;
3653
unsigned int tt = 0;
3654
double tmp5 = 0.00000000;
3655
double tmp6 = 0.00000000;
3656
double tmp7 = 0.00000000;
3657
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
3658
double tmp1 = 0.25000000*(Y + Z)*(Y + Z);
3659
double tmp2 = 0.50000000*(1.00000000 + Z + 2.00000000*Y);
3660
double tmp3 = 0.50000000*(1.00000000 - Z);
3661
double tmp4 = tmp3*tmp3;
3662
3663
// Compute basisvalues.
3664
basisvalues[0] = 1.00000000;
3665
basisvalues[1] = tmp0;
3666
for (unsigned int r = 1; r < 2; r++)
3667
{
3668
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
3669
ss = r*(r + 1)*(r + 2)/6;
3670
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
3671
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.00000000 + 2.00000000*r)/(1.00000000 + r) - basisvalues[tt]*tmp1*r/(1.00000000 + r));
3672
}// end loop over 'r'
3673
for (unsigned int r = 0; r < 2; r++)
3674
{
3675
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
3676
ss = r*(r + 1)*(r + 2)/6;
3677
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
3678
}// end loop over 'r'
3679
for (unsigned int r = 0; r < 1; r++)
3680
{
3681
for (unsigned int s = 1; s < 2 - r; s++)
3682
{
3683
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
3684
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
3685
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
3686
tmp5 = (2.00000000 + 2.00000000*r + 2.00000000*s)*(3.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
3687
tmp6 = (1.00000000 + 4.00000000*r*r + 4.00000000*r)*(2.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
3688
tmp7 = (1.00000000 + s + 2.00000000*r)*(3.00000000 + 2.00000000*r + 2.00000000*s)*s/((1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
3689
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
3690
}// end loop over 's'
3691
}// end loop over 'r'
3692
for (unsigned int r = 0; r < 2; r++)
3693
{
3694
for (unsigned int s = 0; s < 2 - r; s++)
3695
{
3696
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
3697
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
3698
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
3699
}// end loop over 's'
3700
}// end loop over 'r'
3701
for (unsigned int r = 0; r < 1; r++)
3702
{
3703
for (unsigned int s = 0; s < 1 - r; s++)
3704
{
3705
for (unsigned int t = 1; t < 2 - r - s; t++)
3706
{
3707
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
3708
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
3709
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
3710
tmp5 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)/(2.00000000*(1.00000000 + t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
3711
tmp6 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 4.00000000*r*r + 4.00000000*s*s + 8.00000000*r*s + 8.00000000*r + 8.00000000*s)/(2.00000000*(1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
3712
tmp7 = (2.00000000 + t + 2.00000000*r + 2.00000000*s)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*t/((1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
3713
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
3714
}// end loop over 't'
3715
}// end loop over 's'
3716
}// end loop over 'r'
3717
for (unsigned int r = 0; r < 3; r++)
3718
{
3719
for (unsigned int s = 0; s < 3 - r; s++)
3720
{
3721
for (unsigned int t = 0; t < 3 - r - s; t++)
3722
{
3723
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
3724
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
3725
}// end loop over 't'
3726
}// end loop over 's'
3727
}// end loop over 'r'
3728
3729
// Table(s) of coefficients.
3730
static const double coefficients0[10] = \
3731
{0.23094011, 0.00000000, -0.14054567, -0.09938080, -0.13012001, 0.00000000, 0.00000000, 0.02909572, 0.02375655, 0.01679842};
3732
3733
// Tables of derivatives of the polynomial base (transpose).
3734
static const double dmats0[10][10] = \
3735
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
3736
{6.32455532, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
3737
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
3738
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
3739
{0.00000000, 11.22497216, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
3740
{4.58257569, 0.00000000, 8.36660027, -1.18321596, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
3741
{3.74165739, 0.00000000, 0.00000000, 8.69482605, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
3742
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
3743
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
3744
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
3745
3746
static const double dmats1[10][10] = \
3747
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
3748
{3.16227766, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
3749
{5.47722558, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
3750
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
3751
{2.95803989, 5.61248608, -1.08012345, -0.76376262, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
3752
{2.29128785, 7.24568837, 4.18330013, -0.59160798, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
3753
{1.87082869, 0.00000000, 0.00000000, 4.34741302, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
3754
{-2.64575131, 0.00000000, 9.66091783, 0.68313005, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
3755
{3.24037035, 0.00000000, 0.00000000, 7.52994024, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
3756
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
3757
3758
static const double dmats2[10][10] = \
3759
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
3760
{3.16227766, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
3761
{1.82574186, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
3762
{5.16397779, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
3763
{2.95803989, 5.61248608, -1.08012345, -0.76376262, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
3764
{2.29128785, 1.44913767, 4.18330013, -0.59160798, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
3765
{1.87082869, 7.09929574, 0.00000000, 4.34741302, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
3766
{1.32287566, 0.00000000, 3.86436713, -0.34156503, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
3767
{1.08012345, 0.00000000, 7.09929574, 2.50998008, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
3768
{-3.81881308, 0.00000000, 0.00000000, 8.87411967, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
3769
3770
// Compute reference derivatives.
3771
// Declare pointer to array of derivatives on FIAT element.
3772
double *derivatives = new double[num_derivatives];
3773
for (unsigned int r = 0; r < num_derivatives; r++)
3774
{
3775
derivatives[r] = 0.00000000;
3776
}// end loop over 'r'
3777
3778
// Declare derivative matrix (of polynomial basis).
3779
double dmats[10][10] = \
3780
{{1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
3781
{0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
3782
{0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
3783
{0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
3784
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
3785
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
3786
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000},
3787
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000},
3788
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000},
3789
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000}};
3790
3791
// Declare (auxiliary) derivative matrix (of polynomial basis).
3792
double dmats_old[10][10] = \
3793
{{1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
3794
{0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
3795
{0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
3796
{0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
3797
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
3798
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
3799
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000},
3800
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000},
3801
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000},
3802
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000}};
3803
3804
// Loop possible derivatives.
3805
for (unsigned int r = 0; r < num_derivatives; r++)
3806
{
3807
// Resetting dmats values to compute next derivative.
3808
for (unsigned int t = 0; t < 10; t++)
3809
{
3810
for (unsigned int u = 0; u < 10; u++)
3811
{
3812
dmats[t][u] = 0.00000000;
3813
if (t == u)
3814
{
3815
dmats[t][u] = 1.00000000;
3816
}
3817
3818
}// end loop over 'u'
3819
}// end loop over 't'
3820
3821
// Looping derivative order to generate dmats.
3822
for (unsigned int s = 0; s < n; s++)
3823
{
3824
// Updating dmats_old with new values and resetting dmats.
3825
for (unsigned int t = 0; t < 10; t++)
3826
{
3827
for (unsigned int u = 0; u < 10; u++)
3828
{
3829
dmats_old[t][u] = dmats[t][u];
3830
dmats[t][u] = 0.00000000;
3831
}// end loop over 'u'
3832
}// end loop over 't'
3833
3834
// Update dmats using an inner product.
3835
if (combinations[r][s] == 0)
3836
{
3837
for (unsigned int t = 0; t < 10; t++)
3838
{
3839
for (unsigned int u = 0; u < 10; u++)
3840
{
3841
for (unsigned int tu = 0; tu < 10; tu++)
3842
{
3843
dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
3844
}// end loop over 'tu'
3845
}// end loop over 'u'
3846
}// end loop over 't'
3847
}
3848
3849
if (combinations[r][s] == 1)
3850
{
3851
for (unsigned int t = 0; t < 10; t++)
3852
{
3853
for (unsigned int u = 0; u < 10; u++)
3854
{
3855
for (unsigned int tu = 0; tu < 10; tu++)
3856
{
3857
dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
3858
}// end loop over 'tu'
3859
}// end loop over 'u'
3860
}// end loop over 't'
3861
}
3862
3863
if (combinations[r][s] == 2)
3864
{
3865
for (unsigned int t = 0; t < 10; t++)
3866
{
3867
for (unsigned int u = 0; u < 10; u++)
3868
{
3869
for (unsigned int tu = 0; tu < 10; tu++)
3870
{
3871
dmats[t][u] += dmats2[t][tu]*dmats_old[tu][u];
3872
}// end loop over 'tu'
3873
}// end loop over 'u'
3874
}// end loop over 't'
3875
}
3876
3877
}// end loop over 's'
3878
for (unsigned int s = 0; s < 10; s++)
3879
{
3880
for (unsigned int t = 0; t < 10; t++)
3881
{
3882
derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
3883
}// end loop over 't'
3884
}// end loop over 's'
3885
}// end loop over 'r'
3886
3887
// Transform derivatives back to physical element
3888
for (unsigned int r = 0; r < num_derivatives; r++)
3889
{
3890
for (unsigned int s = 0; s < num_derivatives; s++)
3891
{
3892
values[r] += transform[r][s]*derivatives[s];
3893
}// end loop over 's'
3894
}// end loop over 'r'
3895
3896
// Delete pointer to array of derivatives on FIAT element
3897
delete [] derivatives;
3898
3899
// Delete pointer to array of combinations of derivatives and transform
3900
for (unsigned int r = 0; r < num_derivatives; r++)
3901
{
3902
delete [] combinations[r];
3903
}// end loop over 'r'
3904
delete [] combinations;
3905
for (unsigned int r = 0; r < num_derivatives; r++)
3906
{
3907
delete [] transform[r];
3908
}// end loop over 'r'
3909
delete [] transform;
3910
break;
3911
}
3912
}
3913
645
3914
}
646
3915
647
3916
/// Evaluate order n derivatives of all basis functions at given point in cell
983
4252
values[0] = 0.00000000;
984
4253
values[1] = 0.00000000;
985
4254
values[2] = 0.00000000;
986
if (0 <= i && i <= 9)
987
{
988
// Map degree of freedom to element degree of freedom
989
const unsigned int dof = i;
990
991
// Array of basisvalues.
992
double basisvalues[10] = {0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000};
993
994
// Declare helper variables.
995
unsigned int rr = 0;
996
unsigned int ss = 0;
997
unsigned int tt = 0;
998
double tmp5 = 0.00000000;
999
double tmp6 = 0.00000000;
1000
double tmp7 = 0.00000000;
1001
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
1002
double tmp1 = 0.25000000*(Y + Z)*(Y + Z);
1003
double tmp2 = 0.50000000*(1.00000000 + Z + 2.00000000*Y);
1004
double tmp3 = 0.50000000*(1.00000000 - Z);
1005
double tmp4 = tmp3*tmp3;
1006
1007
// Compute basisvalues.
1008
basisvalues[0] = 1.00000000;
1009
basisvalues[1] = tmp0;
1010
for (unsigned int r = 1; r < 2; r++)
1011
{
1012
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
1013
ss = r*(r + 1)*(r + 2)/6;
1014
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
1015
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.00000000 + 2.00000000*r)/(1.00000000 + r) - basisvalues[tt]*tmp1*r/(1.00000000 + r));
1016
}// end loop over 'r'
1017
for (unsigned int r = 0; r < 2; r++)
1018
{
1019
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
1020
ss = r*(r + 1)*(r + 2)/6;
1021
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
1022
}// end loop over 'r'
1023
for (unsigned int r = 0; r < 1; r++)
1024
{
1025
for (unsigned int s = 1; s < 2 - r; s++)
1026
{
1027
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
1028
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
1029
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
1030
tmp5 = (2.00000000 + 2.00000000*r + 2.00000000*s)*(3.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
1031
tmp6 = (1.00000000 + 4.00000000*r*r + 4.00000000*r)*(2.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
1032
tmp7 = (1.00000000 + s + 2.00000000*r)*(3.00000000 + 2.00000000*r + 2.00000000*s)*s/((1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
1033
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
1034
}// end loop over 's'
1035
}// end loop over 'r'
1036
for (unsigned int r = 0; r < 2; r++)
1037
{
1038
for (unsigned int s = 0; s < 2 - r; s++)
1039
{
1040
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
1041
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
1042
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
1043
}// end loop over 's'
1044
}// end loop over 'r'
1045
for (unsigned int r = 0; r < 1; r++)
1046
{
1047
for (unsigned int s = 0; s < 1 - r; s++)
1048
{
1049
for (unsigned int t = 1; t < 2 - r - s; t++)
1050
{
1051
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
1052
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
1053
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
1054
tmp5 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)/(2.00000000*(1.00000000 + t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
1055
tmp6 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 4.00000000*r*r + 4.00000000*s*s + 8.00000000*r*s + 8.00000000*r + 8.00000000*s)/(2.00000000*(1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
1056
tmp7 = (2.00000000 + t + 2.00000000*r + 2.00000000*s)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*t/((1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
1057
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
1058
}// end loop over 't'
1059
}// end loop over 's'
1060
}// end loop over 'r'
1061
for (unsigned int r = 0; r < 3; r++)
1062
{
1063
for (unsigned int s = 0; s < 3 - r; s++)
1064
{
1065
for (unsigned int t = 0; t < 3 - r - s; t++)
1066
{
1067
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
1068
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
1069
}// end loop over 't'
1070
}// end loop over 's'
1071
}// end loop over 'r'
1072
1073
// Table(s) of coefficients.
1074
static const double coefficients0[10][10] = \
1075
{{-0.05773503, -0.06085806, -0.03513642, -0.02484520, 0.06506000, 0.05039526, 0.04114756, 0.02909572, 0.02375655, 0.01679842},
1076
{-0.05773503, 0.06085806, -0.03513642, -0.02484520, 0.06506000, -0.05039526, -0.04114756, 0.02909572, 0.02375655, 0.01679842},
1077
{-0.05773503, 0.00000000, 0.07027284, -0.02484520, 0.00000000, 0.00000000, 0.00000000, 0.08728716, -0.04751311, 0.01679842},
1078
{-0.05773503, 0.00000000, 0.00000000, 0.07453560, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.10079053},
1079
{0.23094011, 0.00000000, 0.14054567, 0.09938080, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.11878277, -0.06719368},
1080
{0.23094011, 0.12171612, -0.07027284, 0.09938080, 0.00000000, 0.00000000, 0.10286890, 0.00000000, -0.05939139, -0.06719368},
1081
{0.23094011, 0.12171612, 0.07027284, -0.09938080, 0.00000000, 0.10079053, -0.02057378, -0.08728716, -0.01187828, 0.01679842},
1082
{0.23094011, -0.12171612, -0.07027284, 0.09938080, 0.00000000, 0.00000000, -0.10286890, 0.00000000, -0.05939139, -0.06719368},
1083
{0.23094011, -0.12171612, 0.07027284, -0.09938080, 0.00000000, -0.10079053, 0.02057378, -0.08728716, -0.01187828, 0.01679842},
1084
{0.23094011, 0.00000000, -0.14054567, -0.09938080, -0.13012001, 0.00000000, 0.00000000, 0.02909572, 0.02375655, 0.01679842}};
1085
1086
// Compute value(s).
1087
for (unsigned int r = 0; r < 10; r++)
1088
{
1089
values[0] += coefficients0[dof][r]*basisvalues[r];
1090
}// end loop over 'r'
1091
}
1092
1093
if (10 <= i && i <= 19)
1094
{
1095
// Map degree of freedom to element degree of freedom
1096
const unsigned int dof = i - 10;
1097
1098
// Array of basisvalues.
1099
double basisvalues[10] = {0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000};
1100
1101
// Declare helper variables.
1102
unsigned int rr = 0;
1103
unsigned int ss = 0;
1104
unsigned int tt = 0;
1105
double tmp5 = 0.00000000;
1106
double tmp6 = 0.00000000;
1107
double tmp7 = 0.00000000;
1108
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
1109
double tmp1 = 0.25000000*(Y + Z)*(Y + Z);
1110
double tmp2 = 0.50000000*(1.00000000 + Z + 2.00000000*Y);
1111
double tmp3 = 0.50000000*(1.00000000 - Z);
1112
double tmp4 = tmp3*tmp3;
1113
1114
// Compute basisvalues.
1115
basisvalues[0] = 1.00000000;
1116
basisvalues[1] = tmp0;
1117
for (unsigned int r = 1; r < 2; r++)
1118
{
1119
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
1120
ss = r*(r + 1)*(r + 2)/6;
1121
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
1122
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.00000000 + 2.00000000*r)/(1.00000000 + r) - basisvalues[tt]*tmp1*r/(1.00000000 + r));
1123
}// end loop over 'r'
1124
for (unsigned int r = 0; r < 2; r++)
1125
{
1126
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
1127
ss = r*(r + 1)*(r + 2)/6;
1128
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
1129
}// end loop over 'r'
1130
for (unsigned int r = 0; r < 1; r++)
1131
{
1132
for (unsigned int s = 1; s < 2 - r; s++)
1133
{
1134
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
1135
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
1136
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
1137
tmp5 = (2.00000000 + 2.00000000*r + 2.00000000*s)*(3.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
1138
tmp6 = (1.00000000 + 4.00000000*r*r + 4.00000000*r)*(2.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
1139
tmp7 = (1.00000000 + s + 2.00000000*r)*(3.00000000 + 2.00000000*r + 2.00000000*s)*s/((1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
1140
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
1141
}// end loop over 's'
1142
}// end loop over 'r'
1143
for (unsigned int r = 0; r < 2; r++)
1144
{
1145
for (unsigned int s = 0; s < 2 - r; s++)
1146
{
1147
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
1148
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
1149
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
1150
}// end loop over 's'
1151
}// end loop over 'r'
1152
for (unsigned int r = 0; r < 1; r++)
1153
{
1154
for (unsigned int s = 0; s < 1 - r; s++)
1155
{
1156
for (unsigned int t = 1; t < 2 - r - s; t++)
1157
{
1158
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
1159
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
1160
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
1161
tmp5 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)/(2.00000000*(1.00000000 + t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
1162
tmp6 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 4.00000000*r*r + 4.00000000*s*s + 8.00000000*r*s + 8.00000000*r + 8.00000000*s)/(2.00000000*(1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
1163
tmp7 = (2.00000000 + t + 2.00000000*r + 2.00000000*s)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*t/((1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
1164
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
1165
}// end loop over 't'
1166
}// end loop over 's'
1167
}// end loop over 'r'
1168
for (unsigned int r = 0; r < 3; r++)
1169
{
1170
for (unsigned int s = 0; s < 3 - r; s++)
1171
{
1172
for (unsigned int t = 0; t < 3 - r - s; t++)
1173
{
1174
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
1175
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
1176
}// end loop over 't'
1177
}// end loop over 's'
1178
}// end loop over 'r'
1179
1180
// Table(s) of coefficients.
1181
static const double coefficients0[10][10] = \
1182
{{-0.05773503, -0.06085806, -0.03513642, -0.02484520, 0.06506000, 0.05039526, 0.04114756, 0.02909572, 0.02375655, 0.01679842},
1183
{-0.05773503, 0.06085806, -0.03513642, -0.02484520, 0.06506000, -0.05039526, -0.04114756, 0.02909572, 0.02375655, 0.01679842},
1184
{-0.05773503, 0.00000000, 0.07027284, -0.02484520, 0.00000000, 0.00000000, 0.00000000, 0.08728716, -0.04751311, 0.01679842},
1185
{-0.05773503, 0.00000000, 0.00000000, 0.07453560, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.10079053},
1186
{0.23094011, 0.00000000, 0.14054567, 0.09938080, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.11878277, -0.06719368},
1187
{0.23094011, 0.12171612, -0.07027284, 0.09938080, 0.00000000, 0.00000000, 0.10286890, 0.00000000, -0.05939139, -0.06719368},
1188
{0.23094011, 0.12171612, 0.07027284, -0.09938080, 0.00000000, 0.10079053, -0.02057378, -0.08728716, -0.01187828, 0.01679842},
1189
{0.23094011, -0.12171612, -0.07027284, 0.09938080, 0.00000000, 0.00000000, -0.10286890, 0.00000000, -0.05939139, -0.06719368},
1190
{0.23094011, -0.12171612, 0.07027284, -0.09938080, 0.00000000, -0.10079053, 0.02057378, -0.08728716, -0.01187828, 0.01679842},
1191
{0.23094011, 0.00000000, -0.14054567, -0.09938080, -0.13012001, 0.00000000, 0.00000000, 0.02909572, 0.02375655, 0.01679842}};
1192
1193
// Compute value(s).
1194
for (unsigned int r = 0; r < 10; r++)
1195
{
1196
values[1] += coefficients0[dof][r]*basisvalues[r];
1197
}// end loop over 'r'
1198
}
1199
1200
if (20 <= i && i <= 29)
1201
{
1202
// Map degree of freedom to element degree of freedom
1203
const unsigned int dof = i - 20;
1204
1205
// Array of basisvalues.
1206
double basisvalues[10] = {0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000};
1207
1208
// Declare helper variables.
1209
unsigned int rr = 0;
1210
unsigned int ss = 0;
1211
unsigned int tt = 0;
1212
double tmp5 = 0.00000000;
1213
double tmp6 = 0.00000000;
1214
double tmp7 = 0.00000000;
1215
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
1216
double tmp1 = 0.25000000*(Y + Z)*(Y + Z);
1217
double tmp2 = 0.50000000*(1.00000000 + Z + 2.00000000*Y);
1218
double tmp3 = 0.50000000*(1.00000000 - Z);
1219
double tmp4 = tmp3*tmp3;
1220
1221
// Compute basisvalues.
1222
basisvalues[0] = 1.00000000;
1223
basisvalues[1] = tmp0;
1224
for (unsigned int r = 1; r < 2; r++)
1225
{
1226
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
1227
ss = r*(r + 1)*(r + 2)/6;
1228
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
1229
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.00000000 + 2.00000000*r)/(1.00000000 + r) - basisvalues[tt]*tmp1*r/(1.00000000 + r));
1230
}// end loop over 'r'
1231
for (unsigned int r = 0; r < 2; r++)
1232
{
1233
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
1234
ss = r*(r + 1)*(r + 2)/6;
1235
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
1236
}// end loop over 'r'
1237
for (unsigned int r = 0; r < 1; r++)
1238
{
1239
for (unsigned int s = 1; s < 2 - r; s++)
1240
{
1241
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
1242
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
1243
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
1244
tmp5 = (2.00000000 + 2.00000000*r + 2.00000000*s)*(3.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
1245
tmp6 = (1.00000000 + 4.00000000*r*r + 4.00000000*r)*(2.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
1246
tmp7 = (1.00000000 + s + 2.00000000*r)*(3.00000000 + 2.00000000*r + 2.00000000*s)*s/((1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
1247
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
1248
}// end loop over 's'
1249
}// end loop over 'r'
1250
for (unsigned int r = 0; r < 2; r++)
1251
{
1252
for (unsigned int s = 0; s < 2 - r; s++)
1253
{
1254
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
1255
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
1256
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
1257
}// end loop over 's'
1258
}// end loop over 'r'
1259
for (unsigned int r = 0; r < 1; r++)
1260
{
1261
for (unsigned int s = 0; s < 1 - r; s++)
1262
{
1263
for (unsigned int t = 1; t < 2 - r - s; t++)
1264
{
1265
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
1266
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
1267
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
1268
tmp5 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)/(2.00000000*(1.00000000 + t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
1269
tmp6 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 4.00000000*r*r + 4.00000000*s*s + 8.00000000*r*s + 8.00000000*r + 8.00000000*s)/(2.00000000*(1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
1270
tmp7 = (2.00000000 + t + 2.00000000*r + 2.00000000*s)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*t/((1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
1271
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
1272
}// end loop over 't'
1273
}// end loop over 's'
1274
}// end loop over 'r'
1275
for (unsigned int r = 0; r < 3; r++)
1276
{
1277
for (unsigned int s = 0; s < 3 - r; s++)
1278
{
1279
for (unsigned int t = 0; t < 3 - r - s; t++)
1280
{
1281
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
1282
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
1283
}// end loop over 't'
1284
}// end loop over 's'
1285
}// end loop over 'r'
1286
1287
// Table(s) of coefficients.
1288
static const double coefficients0[10][10] = \
1289
{{-0.05773503, -0.06085806, -0.03513642, -0.02484520, 0.06506000, 0.05039526, 0.04114756, 0.02909572, 0.02375655, 0.01679842},
1290
{-0.05773503, 0.06085806, -0.03513642, -0.02484520, 0.06506000, -0.05039526, -0.04114756, 0.02909572, 0.02375655, 0.01679842},
1291
{-0.05773503, 0.00000000, 0.07027284, -0.02484520, 0.00000000, 0.00000000, 0.00000000, 0.08728716, -0.04751311, 0.01679842},
1292
{-0.05773503, 0.00000000, 0.00000000, 0.07453560, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.10079053},
1293
{0.23094011, 0.00000000, 0.14054567, 0.09938080, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.11878277, -0.06719368},
1294
{0.23094011, 0.12171612, -0.07027284, 0.09938080, 0.00000000, 0.00000000, 0.10286890, 0.00000000, -0.05939139, -0.06719368},
1295
{0.23094011, 0.12171612, 0.07027284, -0.09938080, 0.00000000, 0.10079053, -0.02057378, -0.08728716, -0.01187828, 0.01679842},
1296
{0.23094011, -0.12171612, -0.07027284, 0.09938080, 0.00000000, 0.00000000, -0.10286890, 0.00000000, -0.05939139, -0.06719368},
1297
{0.23094011, -0.12171612, 0.07027284, -0.09938080, 0.00000000, -0.10079053, 0.02057378, -0.08728716, -0.01187828, 0.01679842},
1298
{0.23094011, 0.00000000, -0.14054567, -0.09938080, -0.13012001, 0.00000000, 0.00000000, 0.02909572, 0.02375655, 0.01679842}};
1299
1300
// Compute value(s).
1301
for (unsigned int r = 0; r < 10; r++)
1302
{
1303
values[2] += coefficients0[dof][r]*basisvalues[r];
1304
}// end loop over 'r'
4255
switch (i)
4256
{
4257
case 0:
4258
{
4259
4260
// Array of basisvalues.
4261
double basisvalues[10] = {0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000};
4262
4263
// Declare helper variables.
4264
unsigned int rr = 0;
4265
unsigned int ss = 0;
4266
unsigned int tt = 0;
4267
double tmp5 = 0.00000000;
4268
double tmp6 = 0.00000000;
4269
double tmp7 = 0.00000000;
4270
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
4271
double tmp1 = 0.25000000*(Y + Z)*(Y + Z);
4272
double tmp2 = 0.50000000*(1.00000000 + Z + 2.00000000*Y);
4273
double tmp3 = 0.50000000*(1.00000000 - Z);
4274
double tmp4 = tmp3*tmp3;
4275
4276
// Compute basisvalues.
4277
basisvalues[0] = 1.00000000;
4278
basisvalues[1] = tmp0;
4279
for (unsigned int r = 1; r < 2; r++)
4280
{
4281
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
4282
ss = r*(r + 1)*(r + 2)/6;
4283
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
4284
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.00000000 + 2.00000000*r)/(1.00000000 + r) - basisvalues[tt]*tmp1*r/(1.00000000 + r));
4285
}// end loop over 'r'
4286
for (unsigned int r = 0; r < 2; r++)
4287
{
4288
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
4289
ss = r*(r + 1)*(r + 2)/6;
4290
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
4291
}// end loop over 'r'
4292
for (unsigned int r = 0; r < 1; r++)
4293
{
4294
for (unsigned int s = 1; s < 2 - r; s++)
4295
{
4296
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
4297
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
4298
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
4299
tmp5 = (2.00000000 + 2.00000000*r + 2.00000000*s)*(3.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
4300
tmp6 = (1.00000000 + 4.00000000*r*r + 4.00000000*r)*(2.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
4301
tmp7 = (1.00000000 + s + 2.00000000*r)*(3.00000000 + 2.00000000*r + 2.00000000*s)*s/((1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
4302
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
4303
}// end loop over 's'
4304
}// end loop over 'r'
4305
for (unsigned int r = 0; r < 2; r++)
4306
{
4307
for (unsigned int s = 0; s < 2 - r; s++)
4308
{
4309
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
4310
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
4311
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
4312
}// end loop over 's'
4313
}// end loop over 'r'
4314
for (unsigned int r = 0; r < 1; r++)
4315
{
4316
for (unsigned int s = 0; s < 1 - r; s++)
4317
{
4318
for (unsigned int t = 1; t < 2 - r - s; t++)
4319
{
4320
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
4321
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
4322
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
4323
tmp5 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)/(2.00000000*(1.00000000 + t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
4324
tmp6 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 4.00000000*r*r + 4.00000000*s*s + 8.00000000*r*s + 8.00000000*r + 8.00000000*s)/(2.00000000*(1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
4325
tmp7 = (2.00000000 + t + 2.00000000*r + 2.00000000*s)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*t/((1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
4326
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
4327
}// end loop over 't'
4328
}// end loop over 's'
4329
}// end loop over 'r'
4330
for (unsigned int r = 0; r < 3; r++)
4331
{
4332
for (unsigned int s = 0; s < 3 - r; s++)
4333
{
4334
for (unsigned int t = 0; t < 3 - r - s; t++)
4335
{
4336
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
4337
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
4338
}// end loop over 't'
4339
}// end loop over 's'
4340
}// end loop over 'r'
4341
4342
// Table(s) of coefficients.
4343
static const double coefficients0[10] = \
4344
{-0.05773503, -0.06085806, -0.03513642, -0.02484520, 0.06506000, 0.05039526, 0.04114756, 0.02909572, 0.02375655, 0.01679842};
4345
4346
// Compute value(s).
4347
for (unsigned int r = 0; r < 10; r++)
4348
{
4349
values[0] += coefficients0[r]*basisvalues[r];
4350
}// end loop over 'r'
4351
break;
4352
}
4353
case 1:
4354
{
4355
4356
// Array of basisvalues.
4357
double basisvalues[10] = {0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000};
4358
4359
// Declare helper variables.
4360
unsigned int rr = 0;
4361
unsigned int ss = 0;
4362
unsigned int tt = 0;
4363
double tmp5 = 0.00000000;
4364
double tmp6 = 0.00000000;
4365
double tmp7 = 0.00000000;
4366
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
4367
double tmp1 = 0.25000000*(Y + Z)*(Y + Z);
4368
double tmp2 = 0.50000000*(1.00000000 + Z + 2.00000000*Y);
4369
double tmp3 = 0.50000000*(1.00000000 - Z);
4370
double tmp4 = tmp3*tmp3;
4371
4372
// Compute basisvalues.
4373
basisvalues[0] = 1.00000000;
4374
basisvalues[1] = tmp0;
4375
for (unsigned int r = 1; r < 2; r++)
4376
{
4377
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
4378
ss = r*(r + 1)*(r + 2)/6;
4379
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
4380
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.00000000 + 2.00000000*r)/(1.00000000 + r) - basisvalues[tt]*tmp1*r/(1.00000000 + r));
4381
}// end loop over 'r'
4382
for (unsigned int r = 0; r < 2; r++)
4383
{
4384
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
4385
ss = r*(r + 1)*(r + 2)/6;
4386
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
4387
}// end loop over 'r'
4388
for (unsigned int r = 0; r < 1; r++)
4389
{
4390
for (unsigned int s = 1; s < 2 - r; s++)
4391
{
4392
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
4393
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
4394
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
4395
tmp5 = (2.00000000 + 2.00000000*r + 2.00000000*s)*(3.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
4396
tmp6 = (1.00000000 + 4.00000000*r*r + 4.00000000*r)*(2.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
4397
tmp7 = (1.00000000 + s + 2.00000000*r)*(3.00000000 + 2.00000000*r + 2.00000000*s)*s/((1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
4398
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
4399
}// end loop over 's'
4400
}// end loop over 'r'
4401
for (unsigned int r = 0; r < 2; r++)
4402
{
4403
for (unsigned int s = 0; s < 2 - r; s++)
4404
{
4405
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
4406
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
4407
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
4408
}// end loop over 's'
4409
}// end loop over 'r'
4410
for (unsigned int r = 0; r < 1; r++)
4411
{
4412
for (unsigned int s = 0; s < 1 - r; s++)
4413
{
4414
for (unsigned int t = 1; t < 2 - r - s; t++)
4415
{
4416
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
4417
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
4418
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
4419
tmp5 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)/(2.00000000*(1.00000000 + t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
4420
tmp6 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 4.00000000*r*r + 4.00000000*s*s + 8.00000000*r*s + 8.00000000*r + 8.00000000*s)/(2.00000000*(1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
4421
tmp7 = (2.00000000 + t + 2.00000000*r + 2.00000000*s)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*t/((1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
4422
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
4423
}// end loop over 't'
4424
}// end loop over 's'
4425
}// end loop over 'r'
4426
for (unsigned int r = 0; r < 3; r++)
4427
{
4428
for (unsigned int s = 0; s < 3 - r; s++)
4429
{
4430
for (unsigned int t = 0; t < 3 - r - s; t++)
4431
{
4432
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
4433
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
4434
}// end loop over 't'
4435
}// end loop over 's'
4436
}// end loop over 'r'
4437
4438
// Table(s) of coefficients.
4439
static const double coefficients0[10] = \
4440
{-0.05773503, 0.06085806, -0.03513642, -0.02484520, 0.06506000, -0.05039526, -0.04114756, 0.02909572, 0.02375655, 0.01679842};
4441
4442
// Compute value(s).
4443
for (unsigned int r = 0; r < 10; r++)
4444
{
4445
values[0] += coefficients0[r]*basisvalues[r];
4446
}// end loop over 'r'
4447
break;
4448
}
4449
case 2:
4450
{
4451
4452
// Array of basisvalues.
4453
double basisvalues[10] = {0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000};
4454
4455
// Declare helper variables.
4456
unsigned int rr = 0;
4457
unsigned int ss = 0;
4458
unsigned int tt = 0;
4459
double tmp5 = 0.00000000;
4460
double tmp6 = 0.00000000;
4461
double tmp7 = 0.00000000;
4462
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
4463
double tmp1 = 0.25000000*(Y + Z)*(Y + Z);
4464
double tmp2 = 0.50000000*(1.00000000 + Z + 2.00000000*Y);
4465
double tmp3 = 0.50000000*(1.00000000 - Z);
4466
double tmp4 = tmp3*tmp3;
4467
4468
// Compute basisvalues.
4469
basisvalues[0] = 1.00000000;
4470
basisvalues[1] = tmp0;
4471
for (unsigned int r = 1; r < 2; r++)
4472
{
4473
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
4474
ss = r*(r + 1)*(r + 2)/6;
4475
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
4476
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.00000000 + 2.00000000*r)/(1.00000000 + r) - basisvalues[tt]*tmp1*r/(1.00000000 + r));
4477
}// end loop over 'r'
4478
for (unsigned int r = 0; r < 2; r++)
4479
{
4480
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
4481
ss = r*(r + 1)*(r + 2)/6;
4482
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
4483
}// end loop over 'r'
4484
for (unsigned int r = 0; r < 1; r++)
4485
{
4486
for (unsigned int s = 1; s < 2 - r; s++)
4487
{
4488
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
4489
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
4490
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
4491
tmp5 = (2.00000000 + 2.00000000*r + 2.00000000*s)*(3.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
4492
tmp6 = (1.00000000 + 4.00000000*r*r + 4.00000000*r)*(2.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
4493
tmp7 = (1.00000000 + s + 2.00000000*r)*(3.00000000 + 2.00000000*r + 2.00000000*s)*s/((1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
4494
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
4495
}// end loop over 's'
4496
}// end loop over 'r'
4497
for (unsigned int r = 0; r < 2; r++)
4498
{
4499
for (unsigned int s = 0; s < 2 - r; s++)
4500
{
4501
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
4502
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
4503
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
4504
}// end loop over 's'
4505
}// end loop over 'r'
4506
for (unsigned int r = 0; r < 1; r++)
4507
{
4508
for (unsigned int s = 0; s < 1 - r; s++)
4509
{
4510
for (unsigned int t = 1; t < 2 - r - s; t++)
4511
{
4512
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
4513
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
4514
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
4515
tmp5 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)/(2.00000000*(1.00000000 + t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
4516
tmp6 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 4.00000000*r*r + 4.00000000*s*s + 8.00000000*r*s + 8.00000000*r + 8.00000000*s)/(2.00000000*(1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
4517
tmp7 = (2.00000000 + t + 2.00000000*r + 2.00000000*s)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*t/((1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
4518
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
4519
}// end loop over 't'
4520
}// end loop over 's'
4521
}// end loop over 'r'
4522
for (unsigned int r = 0; r < 3; r++)
4523
{
4524
for (unsigned int s = 0; s < 3 - r; s++)
4525
{
4526
for (unsigned int t = 0; t < 3 - r - s; t++)
4527
{
4528
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
4529
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
4530
}// end loop over 't'
4531
}// end loop over 's'
4532
}// end loop over 'r'
4533
4534
// Table(s) of coefficients.
4535
static const double coefficients0[10] = \
4536
{-0.05773503, 0.00000000, 0.07027284, -0.02484520, 0.00000000, 0.00000000, 0.00000000, 0.08728716, -0.04751311, 0.01679842};
4537
4538
// Compute value(s).
4539
for (unsigned int r = 0; r < 10; r++)
4540
{
4541
values[0] += coefficients0[r]*basisvalues[r];
4542
}// end loop over 'r'
4543
break;
4544
}
4545
case 3:
4546
{
4547
4548
// Array of basisvalues.
4549
double basisvalues[10] = {0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000};
4550
4551
// Declare helper variables.
4552
unsigned int rr = 0;
4553
unsigned int ss = 0;
4554
unsigned int tt = 0;
4555
double tmp5 = 0.00000000;
4556
double tmp6 = 0.00000000;
4557
double tmp7 = 0.00000000;
4558
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
4559
double tmp1 = 0.25000000*(Y + Z)*(Y + Z);
4560
double tmp2 = 0.50000000*(1.00000000 + Z + 2.00000000*Y);
4561
double tmp3 = 0.50000000*(1.00000000 - Z);
4562
double tmp4 = tmp3*tmp3;
4563
4564
// Compute basisvalues.
4565
basisvalues[0] = 1.00000000;
4566
basisvalues[1] = tmp0;
4567
for (unsigned int r = 1; r < 2; r++)
4568
{
4569
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
4570
ss = r*(r + 1)*(r + 2)/6;
4571
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
4572
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.00000000 + 2.00000000*r)/(1.00000000 + r) - basisvalues[tt]*tmp1*r/(1.00000000 + r));
4573
}// end loop over 'r'
4574
for (unsigned int r = 0; r < 2; r++)
4575
{
4576
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
4577
ss = r*(r + 1)*(r + 2)/6;
4578
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
4579
}// end loop over 'r'
4580
for (unsigned int r = 0; r < 1; r++)
4581
{
4582
for (unsigned int s = 1; s < 2 - r; s++)
4583
{
4584
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
4585
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
4586
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
4587
tmp5 = (2.00000000 + 2.00000000*r + 2.00000000*s)*(3.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
4588
tmp6 = (1.00000000 + 4.00000000*r*r + 4.00000000*r)*(2.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
4589
tmp7 = (1.00000000 + s + 2.00000000*r)*(3.00000000 + 2.00000000*r + 2.00000000*s)*s/((1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
4590
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
4591
}// end loop over 's'
4592
}// end loop over 'r'
4593
for (unsigned int r = 0; r < 2; r++)
4594
{
4595
for (unsigned int s = 0; s < 2 - r; s++)
4596
{
4597
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
4598
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
4599
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
4600
}// end loop over 's'
4601
}// end loop over 'r'
4602
for (unsigned int r = 0; r < 1; r++)
4603
{
4604
for (unsigned int s = 0; s < 1 - r; s++)
4605
{
4606
for (unsigned int t = 1; t < 2 - r - s; t++)
4607
{
4608
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
4609
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
4610
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
4611
tmp5 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)/(2.00000000*(1.00000000 + t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
4612
tmp6 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 4.00000000*r*r + 4.00000000*s*s + 8.00000000*r*s + 8.00000000*r + 8.00000000*s)/(2.00000000*(1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
4613
tmp7 = (2.00000000 + t + 2.00000000*r + 2.00000000*s)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*t/((1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
4614
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
4615
}// end loop over 't'
4616
}// end loop over 's'
4617
}// end loop over 'r'
4618
for (unsigned int r = 0; r < 3; r++)
4619
{
4620
for (unsigned int s = 0; s < 3 - r; s++)
4621
{
4622
for (unsigned int t = 0; t < 3 - r - s; t++)
4623
{
4624
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
4625
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
4626
}// end loop over 't'
4627
}// end loop over 's'
4628
}// end loop over 'r'
4629
4630
// Table(s) of coefficients.
4631
static const double coefficients0[10] = \
4632
{-0.05773503, 0.00000000, 0.00000000, 0.07453560, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.10079053};
4633
4634
// Compute value(s).
4635
for (unsigned int r = 0; r < 10; r++)
4636
{
4637
values[0] += coefficients0[r]*basisvalues[r];
4638
}// end loop over 'r'
4639
break;
4640
}
4641
case 4:
4642
{
4643
4644
// Array of basisvalues.
4645
double basisvalues[10] = {0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000};
4646
4647
// Declare helper variables.
4648
unsigned int rr = 0;
4649
unsigned int ss = 0;
4650
unsigned int tt = 0;
4651
double tmp5 = 0.00000000;
4652
double tmp6 = 0.00000000;
4653
double tmp7 = 0.00000000;
4654
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
4655
double tmp1 = 0.25000000*(Y + Z)*(Y + Z);
4656
double tmp2 = 0.50000000*(1.00000000 + Z + 2.00000000*Y);
4657
double tmp3 = 0.50000000*(1.00000000 - Z);
4658
double tmp4 = tmp3*tmp3;
4659
4660
// Compute basisvalues.
4661
basisvalues[0] = 1.00000000;
4662
basisvalues[1] = tmp0;
4663
for (unsigned int r = 1; r < 2; r++)
4664
{
4665
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
4666
ss = r*(r + 1)*(r + 2)/6;
4667
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
4668
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.00000000 + 2.00000000*r)/(1.00000000 + r) - basisvalues[tt]*tmp1*r/(1.00000000 + r));
4669
}// end loop over 'r'
4670
for (unsigned int r = 0; r < 2; r++)
4671
{
4672
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
4673
ss = r*(r + 1)*(r + 2)/6;
4674
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
4675
}// end loop over 'r'
4676
for (unsigned int r = 0; r < 1; r++)
4677
{
4678
for (unsigned int s = 1; s < 2 - r; s++)
4679
{
4680
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
4681
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
4682
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
4683
tmp5 = (2.00000000 + 2.00000000*r + 2.00000000*s)*(3.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
4684
tmp6 = (1.00000000 + 4.00000000*r*r + 4.00000000*r)*(2.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
4685
tmp7 = (1.00000000 + s + 2.00000000*r)*(3.00000000 + 2.00000000*r + 2.00000000*s)*s/((1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
4686
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
4687
}// end loop over 's'
4688
}// end loop over 'r'
4689
for (unsigned int r = 0; r < 2; r++)
4690
{
4691
for (unsigned int s = 0; s < 2 - r; s++)
4692
{
4693
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
4694
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
4695
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
4696
}// end loop over 's'
4697
}// end loop over 'r'
4698
for (unsigned int r = 0; r < 1; r++)
4699
{
4700
for (unsigned int s = 0; s < 1 - r; s++)
4701
{
4702
for (unsigned int t = 1; t < 2 - r - s; t++)
4703
{
4704
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
4705
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
4706
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
4707
tmp5 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)/(2.00000000*(1.00000000 + t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
4708
tmp6 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 4.00000000*r*r + 4.00000000*s*s + 8.00000000*r*s + 8.00000000*r + 8.00000000*s)/(2.00000000*(1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
4709
tmp7 = (2.00000000 + t + 2.00000000*r + 2.00000000*s)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*t/((1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
4710
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
4711
}// end loop over 't'
4712
}// end loop over 's'
4713
}// end loop over 'r'
4714
for (unsigned int r = 0; r < 3; r++)
4715
{
4716
for (unsigned int s = 0; s < 3 - r; s++)
4717
{
4718
for (unsigned int t = 0; t < 3 - r - s; t++)
4719
{
4720
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
4721
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
4722
}// end loop over 't'
4723
}// end loop over 's'
4724
}// end loop over 'r'
4725
4726
// Table(s) of coefficients.
4727
static const double coefficients0[10] = \
4728
{0.23094011, 0.00000000, 0.14054567, 0.09938080, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.11878277, -0.06719368};
4729
4730
// Compute value(s).
4731
for (unsigned int r = 0; r < 10; r++)
4732
{
4733
values[0] += coefficients0[r]*basisvalues[r];
4734
}// end loop over 'r'
4735
break;
4736
}
4737
case 5:
4738
{
4739
4740
// Array of basisvalues.
4741
double basisvalues[10] = {0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000};
4742
4743
// Declare helper variables.
4744
unsigned int rr = 0;
4745
unsigned int ss = 0;
4746
unsigned int tt = 0;
4747
double tmp5 = 0.00000000;
4748
double tmp6 = 0.00000000;
4749
double tmp7 = 0.00000000;
4750
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
4751
double tmp1 = 0.25000000*(Y + Z)*(Y + Z);
4752
double tmp2 = 0.50000000*(1.00000000 + Z + 2.00000000*Y);
4753
double tmp3 = 0.50000000*(1.00000000 - Z);
4754
double tmp4 = tmp3*tmp3;
4755
4756
// Compute basisvalues.
4757
basisvalues[0] = 1.00000000;
4758
basisvalues[1] = tmp0;
4759
for (unsigned int r = 1; r < 2; r++)
4760
{
4761
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
4762
ss = r*(r + 1)*(r + 2)/6;
4763
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
4764
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.00000000 + 2.00000000*r)/(1.00000000 + r) - basisvalues[tt]*tmp1*r/(1.00000000 + r));
4765
}// end loop over 'r'
4766
for (unsigned int r = 0; r < 2; r++)
4767
{
4768
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
4769
ss = r*(r + 1)*(r + 2)/6;
4770
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
4771
}// end loop over 'r'
4772
for (unsigned int r = 0; r < 1; r++)
4773
{
4774
for (unsigned int s = 1; s < 2 - r; s++)
4775
{
4776
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
4777
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
4778
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
4779
tmp5 = (2.00000000 + 2.00000000*r + 2.00000000*s)*(3.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
4780
tmp6 = (1.00000000 + 4.00000000*r*r + 4.00000000*r)*(2.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
4781
tmp7 = (1.00000000 + s + 2.00000000*r)*(3.00000000 + 2.00000000*r + 2.00000000*s)*s/((1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
4782
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
4783
}// end loop over 's'
4784
}// end loop over 'r'
4785
for (unsigned int r = 0; r < 2; r++)
4786
{
4787
for (unsigned int s = 0; s < 2 - r; s++)
4788
{
4789
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
4790
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
4791
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
4792
}// end loop over 's'
4793
}// end loop over 'r'
4794
for (unsigned int r = 0; r < 1; r++)
4795
{
4796
for (unsigned int s = 0; s < 1 - r; s++)
4797
{
4798
for (unsigned int t = 1; t < 2 - r - s; t++)
4799
{
4800
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
4801
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
4802
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
4803
tmp5 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)/(2.00000000*(1.00000000 + t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
4804
tmp6 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 4.00000000*r*r + 4.00000000*s*s + 8.00000000*r*s + 8.00000000*r + 8.00000000*s)/(2.00000000*(1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
4805
tmp7 = (2.00000000 + t + 2.00000000*r + 2.00000000*s)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*t/((1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
4806
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
4807
}// end loop over 't'
4808
}// end loop over 's'
4809
}// end loop over 'r'
4810
for (unsigned int r = 0; r < 3; r++)
4811
{
4812
for (unsigned int s = 0; s < 3 - r; s++)
4813
{
4814
for (unsigned int t = 0; t < 3 - r - s; t++)
4815
{
4816
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
4817
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
4818
}// end loop over 't'
4819
}// end loop over 's'
4820
}// end loop over 'r'
4821
4822
// Table(s) of coefficients.
4823
static const double coefficients0[10] = \
4824
{0.23094011, 0.12171612, -0.07027284, 0.09938080, 0.00000000, 0.00000000, 0.10286890, 0.00000000, -0.05939139, -0.06719368};
4825
4826
// Compute value(s).
4827
for (unsigned int r = 0; r < 10; r++)
4828
{
4829
values[0] += coefficients0[r]*basisvalues[r];
4830
}// end loop over 'r'
4831
break;
4832
}
4833
case 6:
4834
{
4835
4836
// Array of basisvalues.
4837
double basisvalues[10] = {0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000};
4838
4839
// Declare helper variables.
4840
unsigned int rr = 0;
4841
unsigned int ss = 0;
4842
unsigned int tt = 0;
4843
double tmp5 = 0.00000000;
4844
double tmp6 = 0.00000000;
4845
double tmp7 = 0.00000000;
4846
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
4847
double tmp1 = 0.25000000*(Y + Z)*(Y + Z);
4848
double tmp2 = 0.50000000*(1.00000000 + Z + 2.00000000*Y);
4849
double tmp3 = 0.50000000*(1.00000000 - Z);
4850
double tmp4 = tmp3*tmp3;
4851
4852
// Compute basisvalues.
4853
basisvalues[0] = 1.00000000;
4854
basisvalues[1] = tmp0;
4855
for (unsigned int r = 1; r < 2; r++)
4856
{
4857
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
4858
ss = r*(r + 1)*(r + 2)/6;
4859
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
4860
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.00000000 + 2.00000000*r)/(1.00000000 + r) - basisvalues[tt]*tmp1*r/(1.00000000 + r));
4861
}// end loop over 'r'
4862
for (unsigned int r = 0; r < 2; r++)
4863
{
4864
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
4865
ss = r*(r + 1)*(r + 2)/6;
4866
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
4867
}// end loop over 'r'
4868
for (unsigned int r = 0; r < 1; r++)
4869
{
4870
for (unsigned int s = 1; s < 2 - r; s++)
4871
{
4872
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
4873
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
4874
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
4875
tmp5 = (2.00000000 + 2.00000000*r + 2.00000000*s)*(3.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
4876
tmp6 = (1.00000000 + 4.00000000*r*r + 4.00000000*r)*(2.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
4877
tmp7 = (1.00000000 + s + 2.00000000*r)*(3.00000000 + 2.00000000*r + 2.00000000*s)*s/((1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
4878
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
4879
}// end loop over 's'
4880
}// end loop over 'r'
4881
for (unsigned int r = 0; r < 2; r++)
4882
{
4883
for (unsigned int s = 0; s < 2 - r; s++)
4884
{
4885
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
4886
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
4887
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
4888
}// end loop over 's'
4889
}// end loop over 'r'
4890
for (unsigned int r = 0; r < 1; r++)
4891
{
4892
for (unsigned int s = 0; s < 1 - r; s++)
4893
{
4894
for (unsigned int t = 1; t < 2 - r - s; t++)
4895
{
4896
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
4897
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
4898
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
4899
tmp5 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)/(2.00000000*(1.00000000 + t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
4900
tmp6 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 4.00000000*r*r + 4.00000000*s*s + 8.00000000*r*s + 8.00000000*r + 8.00000000*s)/(2.00000000*(1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
4901
tmp7 = (2.00000000 + t + 2.00000000*r + 2.00000000*s)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*t/((1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
4902
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
4903
}// end loop over 't'
4904
}// end loop over 's'
4905
}// end loop over 'r'
4906
for (unsigned int r = 0; r < 3; r++)
4907
{
4908
for (unsigned int s = 0; s < 3 - r; s++)
4909
{
4910
for (unsigned int t = 0; t < 3 - r - s; t++)
4911
{
4912
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
4913
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
4914
}// end loop over 't'
4915
}// end loop over 's'
4916
}// end loop over 'r'
4917
4918
// Table(s) of coefficients.
4919
static const double coefficients0[10] = \
4920
{0.23094011, 0.12171612, 0.07027284, -0.09938080, 0.00000000, 0.10079053, -0.02057378, -0.08728716, -0.01187828, 0.01679842};
4921
4922
// Compute value(s).
4923
for (unsigned int r = 0; r < 10; r++)
4924
{
4925
values[0] += coefficients0[r]*basisvalues[r];
4926
}// end loop over 'r'
4927
break;
4928
}
4929
case 7:
4930
{
4931
4932
// Array of basisvalues.
4933
double basisvalues[10] = {0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000};
4934
4935
// Declare helper variables.
4936
unsigned int rr = 0;
4937
unsigned int ss = 0;
4938
unsigned int tt = 0;
4939
double tmp5 = 0.00000000;
4940
double tmp6 = 0.00000000;
4941
double tmp7 = 0.00000000;
4942
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
4943
double tmp1 = 0.25000000*(Y + Z)*(Y + Z);
4944
double tmp2 = 0.50000000*(1.00000000 + Z + 2.00000000*Y);
4945
double tmp3 = 0.50000000*(1.00000000 - Z);
4946
double tmp4 = tmp3*tmp3;
4947
4948
// Compute basisvalues.
4949
basisvalues[0] = 1.00000000;
4950
basisvalues[1] = tmp0;
4951
for (unsigned int r = 1; r < 2; r++)
4952
{
4953
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
4954
ss = r*(r + 1)*(r + 2)/6;
4955
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
4956
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.00000000 + 2.00000000*r)/(1.00000000 + r) - basisvalues[tt]*tmp1*r/(1.00000000 + r));
4957
}// end loop over 'r'
4958
for (unsigned int r = 0; r < 2; r++)
4959
{
4960
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
4961
ss = r*(r + 1)*(r + 2)/6;
4962
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
4963
}// end loop over 'r'
4964
for (unsigned int r = 0; r < 1; r++)
4965
{
4966
for (unsigned int s = 1; s < 2 - r; s++)
4967
{
4968
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
4969
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
4970
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
4971
tmp5 = (2.00000000 + 2.00000000*r + 2.00000000*s)*(3.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
4972
tmp6 = (1.00000000 + 4.00000000*r*r + 4.00000000*r)*(2.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
4973
tmp7 = (1.00000000 + s + 2.00000000*r)*(3.00000000 + 2.00000000*r + 2.00000000*s)*s/((1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
4974
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
4975
}// end loop over 's'
4976
}// end loop over 'r'
4977
for (unsigned int r = 0; r < 2; r++)
4978
{
4979
for (unsigned int s = 0; s < 2 - r; s++)
4980
{
4981
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
4982
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
4983
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
4984
}// end loop over 's'
4985
}// end loop over 'r'
4986
for (unsigned int r = 0; r < 1; r++)
4987
{
4988
for (unsigned int s = 0; s < 1 - r; s++)
4989
{
4990
for (unsigned int t = 1; t < 2 - r - s; t++)
4991
{
4992
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
4993
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
4994
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
4995
tmp5 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)/(2.00000000*(1.00000000 + t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
4996
tmp6 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 4.00000000*r*r + 4.00000000*s*s + 8.00000000*r*s + 8.00000000*r + 8.00000000*s)/(2.00000000*(1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
4997
tmp7 = (2.00000000 + t + 2.00000000*r + 2.00000000*s)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*t/((1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
4998
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
4999
}// end loop over 't'
5000
}// end loop over 's'
5001
}// end loop over 'r'
5002
for (unsigned int r = 0; r < 3; r++)
5003
{
5004
for (unsigned int s = 0; s < 3 - r; s++)
5005
{
5006
for (unsigned int t = 0; t < 3 - r - s; t++)
5007
{
5008
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
5009
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
5010
}// end loop over 't'
5011
}// end loop over 's'
5012
}// end loop over 'r'
5013
5014
// Table(s) of coefficients.
5015
static const double coefficients0[10] = \
5016
{0.23094011, -0.12171612, -0.07027284, 0.09938080, 0.00000000, 0.00000000, -0.10286890, 0.00000000, -0.05939139, -0.06719368};
5017
5018
// Compute value(s).
5019
for (unsigned int r = 0; r < 10; r++)
5020
{
5021
values[0] += coefficients0[r]*basisvalues[r];
5022
}// end loop over 'r'
5023
break;
5024
}
5025
case 8:
5026
{
5027
5028
// Array of basisvalues.
5029
double basisvalues[10] = {0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000};
5030
5031
// Declare helper variables.
5032
unsigned int rr = 0;
5033
unsigned int ss = 0;
5034
unsigned int tt = 0;
5035
double tmp5 = 0.00000000;
5036
double tmp6 = 0.00000000;
5037
double tmp7 = 0.00000000;
5038
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
5039
double tmp1 = 0.25000000*(Y + Z)*(Y + Z);
5040
double tmp2 = 0.50000000*(1.00000000 + Z + 2.00000000*Y);
5041
double tmp3 = 0.50000000*(1.00000000 - Z);
5042
double tmp4 = tmp3*tmp3;
5043
5044
// Compute basisvalues.
5045
basisvalues[0] = 1.00000000;
5046
basisvalues[1] = tmp0;
5047
for (unsigned int r = 1; r < 2; r++)
5048
{
5049
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
5050
ss = r*(r + 1)*(r + 2)/6;
5051
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
5052
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.00000000 + 2.00000000*r)/(1.00000000 + r) - basisvalues[tt]*tmp1*r/(1.00000000 + r));
5053
}// end loop over 'r'
5054
for (unsigned int r = 0; r < 2; r++)
5055
{
5056
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
5057
ss = r*(r + 1)*(r + 2)/6;
5058
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
5059
}// end loop over 'r'
5060
for (unsigned int r = 0; r < 1; r++)
5061
{
5062
for (unsigned int s = 1; s < 2 - r; s++)
5063
{
5064
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
5065
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
5066
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
5067
tmp5 = (2.00000000 + 2.00000000*r + 2.00000000*s)*(3.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
5068
tmp6 = (1.00000000 + 4.00000000*r*r + 4.00000000*r)*(2.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
5069
tmp7 = (1.00000000 + s + 2.00000000*r)*(3.00000000 + 2.00000000*r + 2.00000000*s)*s/((1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
5070
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
5071
}// end loop over 's'
5072
}// end loop over 'r'
5073
for (unsigned int r = 0; r < 2; r++)
5074
{
5075
for (unsigned int s = 0; s < 2 - r; s++)
5076
{
5077
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
5078
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
5079
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
5080
}// end loop over 's'
5081
}// end loop over 'r'
5082
for (unsigned int r = 0; r < 1; r++)
5083
{
5084
for (unsigned int s = 0; s < 1 - r; s++)
5085
{
5086
for (unsigned int t = 1; t < 2 - r - s; t++)
5087
{
5088
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
5089
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
5090
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
5091
tmp5 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)/(2.00000000*(1.00000000 + t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
5092
tmp6 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 4.00000000*r*r + 4.00000000*s*s + 8.00000000*r*s + 8.00000000*r + 8.00000000*s)/(2.00000000*(1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
5093
tmp7 = (2.00000000 + t + 2.00000000*r + 2.00000000*s)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*t/((1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
5094
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
5095
}// end loop over 't'
5096
}// end loop over 's'
5097
}// end loop over 'r'
5098
for (unsigned int r = 0; r < 3; r++)
5099
{
5100
for (unsigned int s = 0; s < 3 - r; s++)
5101
{
5102
for (unsigned int t = 0; t < 3 - r - s; t++)
5103
{
5104
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
5105
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
5106
}// end loop over 't'
5107
}// end loop over 's'
5108
}// end loop over 'r'
5109
5110
// Table(s) of coefficients.
5111
static const double coefficients0[10] = \
5112
{0.23094011, -0.12171612, 0.07027284, -0.09938080, 0.00000000, -0.10079053, 0.02057378, -0.08728716, -0.01187828, 0.01679842};
5113
5114
// Compute value(s).
5115
for (unsigned int r = 0; r < 10; r++)
5116
{
5117
values[0] += coefficients0[r]*basisvalues[r];
5118
}// end loop over 'r'
5119
break;
5120
}
5121
case 9:
5122
{
5123
5124
// Array of basisvalues.
5125
double basisvalues[10] = {0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000};
5126
5127
// Declare helper variables.
5128
unsigned int rr = 0;
5129
unsigned int ss = 0;
5130
unsigned int tt = 0;
5131
double tmp5 = 0.00000000;
5132
double tmp6 = 0.00000000;
5133
double tmp7 = 0.00000000;
5134
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
5135
double tmp1 = 0.25000000*(Y + Z)*(Y + Z);
5136
double tmp2 = 0.50000000*(1.00000000 + Z + 2.00000000*Y);
5137
double tmp3 = 0.50000000*(1.00000000 - Z);
5138
double tmp4 = tmp3*tmp3;
5139
5140
// Compute basisvalues.
5141
basisvalues[0] = 1.00000000;
5142
basisvalues[1] = tmp0;
5143
for (unsigned int r = 1; r < 2; r++)
5144
{
5145
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
5146
ss = r*(r + 1)*(r + 2)/6;
5147
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
5148
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.00000000 + 2.00000000*r)/(1.00000000 + r) - basisvalues[tt]*tmp1*r/(1.00000000 + r));
5149
}// end loop over 'r'
5150
for (unsigned int r = 0; r < 2; r++)
5151
{
5152
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
5153
ss = r*(r + 1)*(r + 2)/6;
5154
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
5155
}// end loop over 'r'
5156
for (unsigned int r = 0; r < 1; r++)
5157
{
5158
for (unsigned int s = 1; s < 2 - r; s++)
5159
{
5160
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
5161
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
5162
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
5163
tmp5 = (2.00000000 + 2.00000000*r + 2.00000000*s)*(3.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
5164
tmp6 = (1.00000000 + 4.00000000*r*r + 4.00000000*r)*(2.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
5165
tmp7 = (1.00000000 + s + 2.00000000*r)*(3.00000000 + 2.00000000*r + 2.00000000*s)*s/((1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
5166
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
5167
}// end loop over 's'
5168
}// end loop over 'r'
5169
for (unsigned int r = 0; r < 2; r++)
5170
{
5171
for (unsigned int s = 0; s < 2 - r; s++)
5172
{
5173
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
5174
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
5175
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
5176
}// end loop over 's'
5177
}// end loop over 'r'
5178
for (unsigned int r = 0; r < 1; r++)
5179
{
5180
for (unsigned int s = 0; s < 1 - r; s++)
5181
{
5182
for (unsigned int t = 1; t < 2 - r - s; t++)
5183
{
5184
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
5185
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
5186
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
5187
tmp5 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)/(2.00000000*(1.00000000 + t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
5188
tmp6 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 4.00000000*r*r + 4.00000000*s*s + 8.00000000*r*s + 8.00000000*r + 8.00000000*s)/(2.00000000*(1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
5189
tmp7 = (2.00000000 + t + 2.00000000*r + 2.00000000*s)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*t/((1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
5190
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
5191
}// end loop over 't'
5192
}// end loop over 's'
5193
}// end loop over 'r'
5194
for (unsigned int r = 0; r < 3; r++)
5195
{
5196
for (unsigned int s = 0; s < 3 - r; s++)
5197
{
5198
for (unsigned int t = 0; t < 3 - r - s; t++)
5199
{
5200
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
5201
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
5202
}// end loop over 't'
5203
}// end loop over 's'
5204
}// end loop over 'r'
5205
5206
// Table(s) of coefficients.
5207
static const double coefficients0[10] = \
5208
{0.23094011, 0.00000000, -0.14054567, -0.09938080, -0.13012001, 0.00000000, 0.00000000, 0.02909572, 0.02375655, 0.01679842};
5209
5210
// Compute value(s).
5211
for (unsigned int r = 0; r < 10; r++)
5212
{
5213
values[0] += coefficients0[r]*basisvalues[r];
5214
}// end loop over 'r'
5215
break;
5216
}
5217
case 10:
5218
{
5219
5220
// Array of basisvalues.
5221
double basisvalues[10] = {0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000};
5222
5223
// Declare helper variables.
5224
unsigned int rr = 0;
5225
unsigned int ss = 0;
5226
unsigned int tt = 0;
5227
double tmp5 = 0.00000000;
5228
double tmp6 = 0.00000000;
5229
double tmp7 = 0.00000000;
5230
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
5231
double tmp1 = 0.25000000*(Y + Z)*(Y + Z);
5232
double tmp2 = 0.50000000*(1.00000000 + Z + 2.00000000*Y);
5233
double tmp3 = 0.50000000*(1.00000000 - Z);
5234
double tmp4 = tmp3*tmp3;
5235
5236
// Compute basisvalues.
5237
basisvalues[0] = 1.00000000;
5238
basisvalues[1] = tmp0;
5239
for (unsigned int r = 1; r < 2; r++)
5240
{
5241
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
5242
ss = r*(r + 1)*(r + 2)/6;
5243
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
5244
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.00000000 + 2.00000000*r)/(1.00000000 + r) - basisvalues[tt]*tmp1*r/(1.00000000 + r));
5245
}// end loop over 'r'
5246
for (unsigned int r = 0; r < 2; r++)
5247
{
5248
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
5249
ss = r*(r + 1)*(r + 2)/6;
5250
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
5251
}// end loop over 'r'
5252
for (unsigned int r = 0; r < 1; r++)
5253
{
5254
for (unsigned int s = 1; s < 2 - r; s++)
5255
{
5256
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
5257
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
5258
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
5259
tmp5 = (2.00000000 + 2.00000000*r + 2.00000000*s)*(3.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
5260
tmp6 = (1.00000000 + 4.00000000*r*r + 4.00000000*r)*(2.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
5261
tmp7 = (1.00000000 + s + 2.00000000*r)*(3.00000000 + 2.00000000*r + 2.00000000*s)*s/((1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
5262
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
5263
}// end loop over 's'
5264
}// end loop over 'r'
5265
for (unsigned int r = 0; r < 2; r++)
5266
{
5267
for (unsigned int s = 0; s < 2 - r; s++)
5268
{
5269
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
5270
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
5271
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
5272
}// end loop over 's'
5273
}// end loop over 'r'
5274
for (unsigned int r = 0; r < 1; r++)
5275
{
5276
for (unsigned int s = 0; s < 1 - r; s++)
5277
{
5278
for (unsigned int t = 1; t < 2 - r - s; t++)
5279
{
5280
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
5281
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
5282
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
5283
tmp5 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)/(2.00000000*(1.00000000 + t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
5284
tmp6 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 4.00000000*r*r + 4.00000000*s*s + 8.00000000*r*s + 8.00000000*r + 8.00000000*s)/(2.00000000*(1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
5285
tmp7 = (2.00000000 + t + 2.00000000*r + 2.00000000*s)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*t/((1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
5286
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
5287
}// end loop over 't'
5288
}// end loop over 's'
5289
}// end loop over 'r'
5290
for (unsigned int r = 0; r < 3; r++)
5291
{
5292
for (unsigned int s = 0; s < 3 - r; s++)
5293
{
5294
for (unsigned int t = 0; t < 3 - r - s; t++)
5295
{
5296
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
5297
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
5298
}// end loop over 't'
5299
}// end loop over 's'
5300
}// end loop over 'r'
5301
5302
// Table(s) of coefficients.
5303
static const double coefficients0[10] = \
5304
{-0.05773503, -0.06085806, -0.03513642, -0.02484520, 0.06506000, 0.05039526, 0.04114756, 0.02909572, 0.02375655, 0.01679842};
5305
5306
// Compute value(s).
5307
for (unsigned int r = 0; r < 10; r++)
5308
{
5309
values[1] += coefficients0[r]*basisvalues[r];
5310
}// end loop over 'r'
5311
break;
5312
}
5313
case 11:
5314
{
5315
5316
// Array of basisvalues.
5317
double basisvalues[10] = {0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000};
5318
5319
// Declare helper variables.
5320
unsigned int rr = 0;
5321
unsigned int ss = 0;
5322
unsigned int tt = 0;
5323
double tmp5 = 0.00000000;
5324
double tmp6 = 0.00000000;
5325
double tmp7 = 0.00000000;
5326
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
5327
double tmp1 = 0.25000000*(Y + Z)*(Y + Z);
5328
double tmp2 = 0.50000000*(1.00000000 + Z + 2.00000000*Y);
5329
double tmp3 = 0.50000000*(1.00000000 - Z);
5330
double tmp4 = tmp3*tmp3;
5331
5332
// Compute basisvalues.
5333
basisvalues[0] = 1.00000000;
5334
basisvalues[1] = tmp0;
5335
for (unsigned int r = 1; r < 2; r++)
5336
{
5337
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
5338
ss = r*(r + 1)*(r + 2)/6;
5339
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
5340
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.00000000 + 2.00000000*r)/(1.00000000 + r) - basisvalues[tt]*tmp1*r/(1.00000000 + r));
5341
}// end loop over 'r'
5342
for (unsigned int r = 0; r < 2; r++)
5343
{
5344
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
5345
ss = r*(r + 1)*(r + 2)/6;
5346
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
5347
}// end loop over 'r'
5348
for (unsigned int r = 0; r < 1; r++)
5349
{
5350
for (unsigned int s = 1; s < 2 - r; s++)
5351
{
5352
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
5353
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
5354
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
5355
tmp5 = (2.00000000 + 2.00000000*r + 2.00000000*s)*(3.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
5356
tmp6 = (1.00000000 + 4.00000000*r*r + 4.00000000*r)*(2.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
5357
tmp7 = (1.00000000 + s + 2.00000000*r)*(3.00000000 + 2.00000000*r + 2.00000000*s)*s/((1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
5358
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
5359
}// end loop over 's'
5360
}// end loop over 'r'
5361
for (unsigned int r = 0; r < 2; r++)
5362
{
5363
for (unsigned int s = 0; s < 2 - r; s++)
5364
{
5365
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
5366
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
5367
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
5368
}// end loop over 's'
5369
}// end loop over 'r'
5370
for (unsigned int r = 0; r < 1; r++)
5371
{
5372
for (unsigned int s = 0; s < 1 - r; s++)
5373
{
5374
for (unsigned int t = 1; t < 2 - r - s; t++)
5375
{
5376
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
5377
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
5378
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
5379
tmp5 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)/(2.00000000*(1.00000000 + t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
5380
tmp6 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 4.00000000*r*r + 4.00000000*s*s + 8.00000000*r*s + 8.00000000*r + 8.00000000*s)/(2.00000000*(1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
5381
tmp7 = (2.00000000 + t + 2.00000000*r + 2.00000000*s)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*t/((1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
5382
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
5383
}// end loop over 't'
5384
}// end loop over 's'
5385
}// end loop over 'r'
5386
for (unsigned int r = 0; r < 3; r++)
5387
{
5388
for (unsigned int s = 0; s < 3 - r; s++)
5389
{
5390
for (unsigned int t = 0; t < 3 - r - s; t++)
5391
{
5392
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
5393
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
5394
}// end loop over 't'
5395
}// end loop over 's'
5396
}// end loop over 'r'
5397
5398
// Table(s) of coefficients.
5399
static const double coefficients0[10] = \
5400
{-0.05773503, 0.06085806, -0.03513642, -0.02484520, 0.06506000, -0.05039526, -0.04114756, 0.02909572, 0.02375655, 0.01679842};
5401
5402
// Compute value(s).
5403
for (unsigned int r = 0; r < 10; r++)
5404
{
5405
values[1] += coefficients0[r]*basisvalues[r];
5406
}// end loop over 'r'
5407
break;
5408
}
5409
case 12:
5410
{
5411
5412
// Array of basisvalues.
5413
double basisvalues[10] = {0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000};
5414
5415
// Declare helper variables.
5416
unsigned int rr = 0;
5417
unsigned int ss = 0;
5418
unsigned int tt = 0;
5419
double tmp5 = 0.00000000;
5420
double tmp6 = 0.00000000;
5421
double tmp7 = 0.00000000;
5422
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
5423
double tmp1 = 0.25000000*(Y + Z)*(Y + Z);
5424
double tmp2 = 0.50000000*(1.00000000 + Z + 2.00000000*Y);
5425
double tmp3 = 0.50000000*(1.00000000 - Z);
5426
double tmp4 = tmp3*tmp3;
5427
5428
// Compute basisvalues.
5429
basisvalues[0] = 1.00000000;
5430
basisvalues[1] = tmp0;
5431
for (unsigned int r = 1; r < 2; r++)
5432
{
5433
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
5434
ss = r*(r + 1)*(r + 2)/6;
5435
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
5436
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.00000000 + 2.00000000*r)/(1.00000000 + r) - basisvalues[tt]*tmp1*r/(1.00000000 + r));
5437
}// end loop over 'r'
5438
for (unsigned int r = 0; r < 2; r++)
5439
{
5440
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
5441
ss = r*(r + 1)*(r + 2)/6;
5442
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
5443
}// end loop over 'r'
5444
for (unsigned int r = 0; r < 1; r++)
5445
{
5446
for (unsigned int s = 1; s < 2 - r; s++)
5447
{
5448
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
5449
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
5450
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
5451
tmp5 = (2.00000000 + 2.00000000*r + 2.00000000*s)*(3.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
5452
tmp6 = (1.00000000 + 4.00000000*r*r + 4.00000000*r)*(2.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
5453
tmp7 = (1.00000000 + s + 2.00000000*r)*(3.00000000 + 2.00000000*r + 2.00000000*s)*s/((1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
5454
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
5455
}// end loop over 's'
5456
}// end loop over 'r'
5457
for (unsigned int r = 0; r < 2; r++)
5458
{
5459
for (unsigned int s = 0; s < 2 - r; s++)
5460
{
5461
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
5462
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
5463
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
5464
}// end loop over 's'
5465
}// end loop over 'r'
5466
for (unsigned int r = 0; r < 1; r++)
5467
{
5468
for (unsigned int s = 0; s < 1 - r; s++)
5469
{
5470
for (unsigned int t = 1; t < 2 - r - s; t++)
5471
{
5472
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
5473
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
5474
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
5475
tmp5 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)/(2.00000000*(1.00000000 + t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
5476
tmp6 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 4.00000000*r*r + 4.00000000*s*s + 8.00000000*r*s + 8.00000000*r + 8.00000000*s)/(2.00000000*(1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
5477
tmp7 = (2.00000000 + t + 2.00000000*r + 2.00000000*s)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*t/((1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
5478
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
5479
}// end loop over 't'
5480
}// end loop over 's'
5481
}// end loop over 'r'
5482
for (unsigned int r = 0; r < 3; r++)
5483
{
5484
for (unsigned int s = 0; s < 3 - r; s++)
5485
{
5486
for (unsigned int t = 0; t < 3 - r - s; t++)
5487
{
5488
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
5489
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
5490
}// end loop over 't'
5491
}// end loop over 's'
5492
}// end loop over 'r'
5493
5494
// Table(s) of coefficients.
5495
static const double coefficients0[10] = \
5496
{-0.05773503, 0.00000000, 0.07027284, -0.02484520, 0.00000000, 0.00000000, 0.00000000, 0.08728716, -0.04751311, 0.01679842};
5497
5498
// Compute value(s).
5499
for (unsigned int r = 0; r < 10; r++)
5500
{
5501
values[1] += coefficients0[r]*basisvalues[r];
5502
}// end loop over 'r'
5503
break;
5504
}
5505
case 13:
5506
{
5507
5508
// Array of basisvalues.
5509
double basisvalues[10] = {0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000};
5510
5511
// Declare helper variables.
5512
unsigned int rr = 0;
5513
unsigned int ss = 0;
5514
unsigned int tt = 0;
5515
double tmp5 = 0.00000000;
5516
double tmp6 = 0.00000000;
5517
double tmp7 = 0.00000000;
5518
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
5519
double tmp1 = 0.25000000*(Y + Z)*(Y + Z);
5520
double tmp2 = 0.50000000*(1.00000000 + Z + 2.00000000*Y);
5521
double tmp3 = 0.50000000*(1.00000000 - Z);
5522
double tmp4 = tmp3*tmp3;
5523
5524
// Compute basisvalues.
5525
basisvalues[0] = 1.00000000;
5526
basisvalues[1] = tmp0;
5527
for (unsigned int r = 1; r < 2; r++)
5528
{
5529
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
5530
ss = r*(r + 1)*(r + 2)/6;
5531
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
5532
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.00000000 + 2.00000000*r)/(1.00000000 + r) - basisvalues[tt]*tmp1*r/(1.00000000 + r));
5533
}// end loop over 'r'
5534
for (unsigned int r = 0; r < 2; r++)
5535
{
5536
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
5537
ss = r*(r + 1)*(r + 2)/6;
5538
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
5539
}// end loop over 'r'
5540
for (unsigned int r = 0; r < 1; r++)
5541
{
5542
for (unsigned int s = 1; s < 2 - r; s++)
5543
{
5544
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
5545
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
5546
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
5547
tmp5 = (2.00000000 + 2.00000000*r + 2.00000000*s)*(3.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
5548
tmp6 = (1.00000000 + 4.00000000*r*r + 4.00000000*r)*(2.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
5549
tmp7 = (1.00000000 + s + 2.00000000*r)*(3.00000000 + 2.00000000*r + 2.00000000*s)*s/((1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
5550
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
5551
}// end loop over 's'
5552
}// end loop over 'r'
5553
for (unsigned int r = 0; r < 2; r++)
5554
{
5555
for (unsigned int s = 0; s < 2 - r; s++)
5556
{
5557
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
5558
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
5559
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
5560
}// end loop over 's'
5561
}// end loop over 'r'
5562
for (unsigned int r = 0; r < 1; r++)
5563
{
5564
for (unsigned int s = 0; s < 1 - r; s++)
5565
{
5566
for (unsigned int t = 1; t < 2 - r - s; t++)
5567
{
5568
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
5569
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
5570
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
5571
tmp5 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)/(2.00000000*(1.00000000 + t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
5572
tmp6 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 4.00000000*r*r + 4.00000000*s*s + 8.00000000*r*s + 8.00000000*r + 8.00000000*s)/(2.00000000*(1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
5573
tmp7 = (2.00000000 + t + 2.00000000*r + 2.00000000*s)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*t/((1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
5574
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
5575
}// end loop over 't'
5576
}// end loop over 's'
5577
}// end loop over 'r'
5578
for (unsigned int r = 0; r < 3; r++)
5579
{
5580
for (unsigned int s = 0; s < 3 - r; s++)
5581
{
5582
for (unsigned int t = 0; t < 3 - r - s; t++)
5583
{
5584
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
5585
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
5586
}// end loop over 't'
5587
}// end loop over 's'
5588
}// end loop over 'r'
5589
5590
// Table(s) of coefficients.
5591
static const double coefficients0[10] = \
5592
{-0.05773503, 0.00000000, 0.00000000, 0.07453560, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.10079053};
5593
5594
// Compute value(s).
5595
for (unsigned int r = 0; r < 10; r++)
5596
{
5597
values[1] += coefficients0[r]*basisvalues[r];
5598
}// end loop over 'r'
5599
break;
5600
}
5601
case 14:
5602
{
5603
5604
// Array of basisvalues.
5605
double basisvalues[10] = {0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000};
5606
5607
// Declare helper variables.
5608
unsigned int rr = 0;
5609
unsigned int ss = 0;
5610
unsigned int tt = 0;
5611
double tmp5 = 0.00000000;
5612
double tmp6 = 0.00000000;
5613
double tmp7 = 0.00000000;
5614
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
5615
double tmp1 = 0.25000000*(Y + Z)*(Y + Z);
5616
double tmp2 = 0.50000000*(1.00000000 + Z + 2.00000000*Y);
5617
double tmp3 = 0.50000000*(1.00000000 - Z);
5618
double tmp4 = tmp3*tmp3;
5619
5620
// Compute basisvalues.
5621
basisvalues[0] = 1.00000000;
5622
basisvalues[1] = tmp0;
5623
for (unsigned int r = 1; r < 2; r++)
5624
{
5625
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
5626
ss = r*(r + 1)*(r + 2)/6;
5627
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
5628
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.00000000 + 2.00000000*r)/(1.00000000 + r) - basisvalues[tt]*tmp1*r/(1.00000000 + r));
5629
}// end loop over 'r'
5630
for (unsigned int r = 0; r < 2; r++)
5631
{
5632
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
5633
ss = r*(r + 1)*(r + 2)/6;
5634
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
5635
}// end loop over 'r'
5636
for (unsigned int r = 0; r < 1; r++)
5637
{
5638
for (unsigned int s = 1; s < 2 - r; s++)
5639
{
5640
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
5641
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
5642
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
5643
tmp5 = (2.00000000 + 2.00000000*r + 2.00000000*s)*(3.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
5644
tmp6 = (1.00000000 + 4.00000000*r*r + 4.00000000*r)*(2.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
5645
tmp7 = (1.00000000 + s + 2.00000000*r)*(3.00000000 + 2.00000000*r + 2.00000000*s)*s/((1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
5646
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
5647
}// end loop over 's'
5648
}// end loop over 'r'
5649
for (unsigned int r = 0; r < 2; r++)
5650
{
5651
for (unsigned int s = 0; s < 2 - r; s++)
5652
{
5653
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
5654
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
5655
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
5656
}// end loop over 's'
5657
}// end loop over 'r'
5658
for (unsigned int r = 0; r < 1; r++)
5659
{
5660
for (unsigned int s = 0; s < 1 - r; s++)
5661
{
5662
for (unsigned int t = 1; t < 2 - r - s; t++)
5663
{
5664
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
5665
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
5666
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
5667
tmp5 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)/(2.00000000*(1.00000000 + t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
5668
tmp6 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 4.00000000*r*r + 4.00000000*s*s + 8.00000000*r*s + 8.00000000*r + 8.00000000*s)/(2.00000000*(1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
5669
tmp7 = (2.00000000 + t + 2.00000000*r + 2.00000000*s)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*t/((1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
5670
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
5671
}// end loop over 't'
5672
}// end loop over 's'
5673
}// end loop over 'r'
5674
for (unsigned int r = 0; r < 3; r++)
5675
{
5676
for (unsigned int s = 0; s < 3 - r; s++)
5677
{
5678
for (unsigned int t = 0; t < 3 - r - s; t++)
5679
{
5680
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
5681
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
5682
}// end loop over 't'
5683
}// end loop over 's'
5684
}// end loop over 'r'
5685
5686
// Table(s) of coefficients.
5687
static const double coefficients0[10] = \
5688
{0.23094011, 0.00000000, 0.14054567, 0.09938080, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.11878277, -0.06719368};
5689
5690
// Compute value(s).
5691
for (unsigned int r = 0; r < 10; r++)
5692
{
5693
values[1] += coefficients0[r]*basisvalues[r];
5694
}// end loop over 'r'
5695
break;
5696
}
5697
case 15:
5698
{
5699
5700
// Array of basisvalues.
5701
double basisvalues[10] = {0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000};
5702
5703
// Declare helper variables.
5704
unsigned int rr = 0;
5705
unsigned int ss = 0;
5706
unsigned int tt = 0;
5707
double tmp5 = 0.00000000;
5708
double tmp6 = 0.00000000;
5709
double tmp7 = 0.00000000;
5710
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
5711
double tmp1 = 0.25000000*(Y + Z)*(Y + Z);
5712
double tmp2 = 0.50000000*(1.00000000 + Z + 2.00000000*Y);
5713
double tmp3 = 0.50000000*(1.00000000 - Z);
5714
double tmp4 = tmp3*tmp3;
5715
5716
// Compute basisvalues.
5717
basisvalues[0] = 1.00000000;
5718
basisvalues[1] = tmp0;
5719
for (unsigned int r = 1; r < 2; r++)
5720
{
5721
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
5722
ss = r*(r + 1)*(r + 2)/6;
5723
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
5724
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.00000000 + 2.00000000*r)/(1.00000000 + r) - basisvalues[tt]*tmp1*r/(1.00000000 + r));
5725
}// end loop over 'r'
5726
for (unsigned int r = 0; r < 2; r++)
5727
{
5728
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
5729
ss = r*(r + 1)*(r + 2)/6;
5730
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
5731
}// end loop over 'r'
5732
for (unsigned int r = 0; r < 1; r++)
5733
{
5734
for (unsigned int s = 1; s < 2 - r; s++)
5735
{
5736
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
5737
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
5738
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
5739
tmp5 = (2.00000000 + 2.00000000*r + 2.00000000*s)*(3.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
5740
tmp6 = (1.00000000 + 4.00000000*r*r + 4.00000000*r)*(2.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
5741
tmp7 = (1.00000000 + s + 2.00000000*r)*(3.00000000 + 2.00000000*r + 2.00000000*s)*s/((1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
5742
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
5743
}// end loop over 's'
5744
}// end loop over 'r'
5745
for (unsigned int r = 0; r < 2; r++)
5746
{
5747
for (unsigned int s = 0; s < 2 - r; s++)
5748
{
5749
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
5750
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
5751
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
5752
}// end loop over 's'
5753
}// end loop over 'r'
5754
for (unsigned int r = 0; r < 1; r++)
5755
{
5756
for (unsigned int s = 0; s < 1 - r; s++)
5757
{
5758
for (unsigned int t = 1; t < 2 - r - s; t++)
5759
{
5760
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
5761
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
5762
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
5763
tmp5 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)/(2.00000000*(1.00000000 + t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
5764
tmp6 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 4.00000000*r*r + 4.00000000*s*s + 8.00000000*r*s + 8.00000000*r + 8.00000000*s)/(2.00000000*(1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
5765
tmp7 = (2.00000000 + t + 2.00000000*r + 2.00000000*s)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*t/((1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
5766
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
5767
}// end loop over 't'
5768
}// end loop over 's'
5769
}// end loop over 'r'
5770
for (unsigned int r = 0; r < 3; r++)
5771
{
5772
for (unsigned int s = 0; s < 3 - r; s++)
5773
{
5774
for (unsigned int t = 0; t < 3 - r - s; t++)
5775
{
5776
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
5777
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
5778
}// end loop over 't'
5779
}// end loop over 's'
5780
}// end loop over 'r'
5781
5782
// Table(s) of coefficients.
5783
static const double coefficients0[10] = \
5784
{0.23094011, 0.12171612, -0.07027284, 0.09938080, 0.00000000, 0.00000000, 0.10286890, 0.00000000, -0.05939139, -0.06719368};
5785
5786
// Compute value(s).
5787
for (unsigned int r = 0; r < 10; r++)
5788
{
5789
values[1] += coefficients0[r]*basisvalues[r];
5790
}// end loop over 'r'
5791
break;
5792
}
5793
case 16:
5794
{
5795
5796
// Array of basisvalues.
5797
double basisvalues[10] = {0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000};
5798
5799
// Declare helper variables.
5800
unsigned int rr = 0;
5801
unsigned int ss = 0;
5802
unsigned int tt = 0;
5803
double tmp5 = 0.00000000;
5804
double tmp6 = 0.00000000;
5805
double tmp7 = 0.00000000;
5806
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
5807
double tmp1 = 0.25000000*(Y + Z)*(Y + Z);
5808
double tmp2 = 0.50000000*(1.00000000 + Z + 2.00000000*Y);
5809
double tmp3 = 0.50000000*(1.00000000 - Z);
5810
double tmp4 = tmp3*tmp3;
5811
5812
// Compute basisvalues.
5813
basisvalues[0] = 1.00000000;
5814
basisvalues[1] = tmp0;
5815
for (unsigned int r = 1; r < 2; r++)
5816
{
5817
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
5818
ss = r*(r + 1)*(r + 2)/6;
5819
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
5820
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.00000000 + 2.00000000*r)/(1.00000000 + r) - basisvalues[tt]*tmp1*r/(1.00000000 + r));
5821
}// end loop over 'r'
5822
for (unsigned int r = 0; r < 2; r++)
5823
{
5824
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
5825
ss = r*(r + 1)*(r + 2)/6;
5826
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
5827
}// end loop over 'r'
5828
for (unsigned int r = 0; r < 1; r++)
5829
{
5830
for (unsigned int s = 1; s < 2 - r; s++)
5831
{
5832
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
5833
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
5834
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
5835
tmp5 = (2.00000000 + 2.00000000*r + 2.00000000*s)*(3.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
5836
tmp6 = (1.00000000 + 4.00000000*r*r + 4.00000000*r)*(2.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
5837
tmp7 = (1.00000000 + s + 2.00000000*r)*(3.00000000 + 2.00000000*r + 2.00000000*s)*s/((1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
5838
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
5839
}// end loop over 's'
5840
}// end loop over 'r'
5841
for (unsigned int r = 0; r < 2; r++)
5842
{
5843
for (unsigned int s = 0; s < 2 - r; s++)
5844
{
5845
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
5846
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
5847
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
5848
}// end loop over 's'
5849
}// end loop over 'r'
5850
for (unsigned int r = 0; r < 1; r++)
5851
{
5852
for (unsigned int s = 0; s < 1 - r; s++)
5853
{
5854
for (unsigned int t = 1; t < 2 - r - s; t++)
5855
{
5856
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
5857
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
5858
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
5859
tmp5 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)/(2.00000000*(1.00000000 + t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
5860
tmp6 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 4.00000000*r*r + 4.00000000*s*s + 8.00000000*r*s + 8.00000000*r + 8.00000000*s)/(2.00000000*(1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
5861
tmp7 = (2.00000000 + t + 2.00000000*r + 2.00000000*s)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*t/((1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
5862
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
5863
}// end loop over 't'
5864
}// end loop over 's'
5865
}// end loop over 'r'
5866
for (unsigned int r = 0; r < 3; r++)
5867
{
5868
for (unsigned int s = 0; s < 3 - r; s++)
5869
{
5870
for (unsigned int t = 0; t < 3 - r - s; t++)
5871
{
5872
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
5873
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
5874
}// end loop over 't'
5875
}// end loop over 's'
5876
}// end loop over 'r'
5877
5878
// Table(s) of coefficients.
5879
static const double coefficients0[10] = \
5880
{0.23094011, 0.12171612, 0.07027284, -0.09938080, 0.00000000, 0.10079053, -0.02057378, -0.08728716, -0.01187828, 0.01679842};
5881
5882
// Compute value(s).
5883
for (unsigned int r = 0; r < 10; r++)
5884
{
5885
values[1] += coefficients0[r]*basisvalues[r];
5886
}// end loop over 'r'
5887
break;
5888
}
5889
case 17:
5890
{
5891
5892
// Array of basisvalues.
5893
double basisvalues[10] = {0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000};
5894
5895
// Declare helper variables.
5896
unsigned int rr = 0;
5897
unsigned int ss = 0;
5898
unsigned int tt = 0;
5899
double tmp5 = 0.00000000;
5900
double tmp6 = 0.00000000;
5901
double tmp7 = 0.00000000;
5902
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
5903
double tmp1 = 0.25000000*(Y + Z)*(Y + Z);
5904
double tmp2 = 0.50000000*(1.00000000 + Z + 2.00000000*Y);
5905
double tmp3 = 0.50000000*(1.00000000 - Z);
5906
double tmp4 = tmp3*tmp3;
5907
5908
// Compute basisvalues.
5909
basisvalues[0] = 1.00000000;
5910
basisvalues[1] = tmp0;
5911
for (unsigned int r = 1; r < 2; r++)
5912
{
5913
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
5914
ss = r*(r + 1)*(r + 2)/6;
5915
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
5916
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.00000000 + 2.00000000*r)/(1.00000000 + r) - basisvalues[tt]*tmp1*r/(1.00000000 + r));
5917
}// end loop over 'r'
5918
for (unsigned int r = 0; r < 2; r++)
5919
{
5920
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
5921
ss = r*(r + 1)*(r + 2)/6;
5922
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
5923
}// end loop over 'r'
5924
for (unsigned int r = 0; r < 1; r++)
5925
{
5926
for (unsigned int s = 1; s < 2 - r; s++)
5927
{
5928
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
5929
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
5930
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
5931
tmp5 = (2.00000000 + 2.00000000*r + 2.00000000*s)*(3.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
5932
tmp6 = (1.00000000 + 4.00000000*r*r + 4.00000000*r)*(2.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
5933
tmp7 = (1.00000000 + s + 2.00000000*r)*(3.00000000 + 2.00000000*r + 2.00000000*s)*s/((1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
5934
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
5935
}// end loop over 's'
5936
}// end loop over 'r'
5937
for (unsigned int r = 0; r < 2; r++)
5938
{
5939
for (unsigned int s = 0; s < 2 - r; s++)
5940
{
5941
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
5942
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
5943
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
5944
}// end loop over 's'
5945
}// end loop over 'r'
5946
for (unsigned int r = 0; r < 1; r++)
5947
{
5948
for (unsigned int s = 0; s < 1 - r; s++)
5949
{
5950
for (unsigned int t = 1; t < 2 - r - s; t++)
5951
{
5952
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
5953
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
5954
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
5955
tmp5 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)/(2.00000000*(1.00000000 + t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
5956
tmp6 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 4.00000000*r*r + 4.00000000*s*s + 8.00000000*r*s + 8.00000000*r + 8.00000000*s)/(2.00000000*(1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
5957
tmp7 = (2.00000000 + t + 2.00000000*r + 2.00000000*s)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*t/((1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
5958
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
5959
}// end loop over 't'
5960
}// end loop over 's'
5961
}// end loop over 'r'
5962
for (unsigned int r = 0; r < 3; r++)
5963
{
5964
for (unsigned int s = 0; s < 3 - r; s++)
5965
{
5966
for (unsigned int t = 0; t < 3 - r - s; t++)
5967
{
5968
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
5969
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
5970
}// end loop over 't'
5971
}// end loop over 's'
5972
}// end loop over 'r'
5973
5974
// Table(s) of coefficients.
5975
static const double coefficients0[10] = \
5976
{0.23094011, -0.12171612, -0.07027284, 0.09938080, 0.00000000, 0.00000000, -0.10286890, 0.00000000, -0.05939139, -0.06719368};
5977
5978
// Compute value(s).
5979
for (unsigned int r = 0; r < 10; r++)
5980
{
5981
values[1] += coefficients0[r]*basisvalues[r];
5982
}// end loop over 'r'
5983
break;
5984
}
5985
case 18:
5986
{
5987
5988
// Array of basisvalues.
5989
double basisvalues[10] = {0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000};
5990
5991
// Declare helper variables.
5992
unsigned int rr = 0;
5993
unsigned int ss = 0;
5994
unsigned int tt = 0;
5995
double tmp5 = 0.00000000;
5996
double tmp6 = 0.00000000;
5997
double tmp7 = 0.00000000;
5998
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
5999
double tmp1 = 0.25000000*(Y + Z)*(Y + Z);
6000
double tmp2 = 0.50000000*(1.00000000 + Z + 2.00000000*Y);
6001
double tmp3 = 0.50000000*(1.00000000 - Z);
6002
double tmp4 = tmp3*tmp3;
6003
6004
// Compute basisvalues.
6005
basisvalues[0] = 1.00000000;
6006
basisvalues[1] = tmp0;
6007
for (unsigned int r = 1; r < 2; r++)
6008
{
6009
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
6010
ss = r*(r + 1)*(r + 2)/6;
6011
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
6012
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.00000000 + 2.00000000*r)/(1.00000000 + r) - basisvalues[tt]*tmp1*r/(1.00000000 + r));
6013
}// end loop over 'r'
6014
for (unsigned int r = 0; r < 2; r++)
6015
{
6016
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
6017
ss = r*(r + 1)*(r + 2)/6;
6018
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
6019
}// end loop over 'r'
6020
for (unsigned int r = 0; r < 1; r++)
6021
{
6022
for (unsigned int s = 1; s < 2 - r; s++)
6023
{
6024
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
6025
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
6026
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
6027
tmp5 = (2.00000000 + 2.00000000*r + 2.00000000*s)*(3.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
6028
tmp6 = (1.00000000 + 4.00000000*r*r + 4.00000000*r)*(2.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
6029
tmp7 = (1.00000000 + s + 2.00000000*r)*(3.00000000 + 2.00000000*r + 2.00000000*s)*s/((1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
6030
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
6031
}// end loop over 's'
6032
}// end loop over 'r'
6033
for (unsigned int r = 0; r < 2; r++)
6034
{
6035
for (unsigned int s = 0; s < 2 - r; s++)
6036
{
6037
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
6038
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
6039
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
6040
}// end loop over 's'
6041
}// end loop over 'r'
6042
for (unsigned int r = 0; r < 1; r++)
6043
{
6044
for (unsigned int s = 0; s < 1 - r; s++)
6045
{
6046
for (unsigned int t = 1; t < 2 - r - s; t++)
6047
{
6048
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
6049
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
6050
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
6051
tmp5 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)/(2.00000000*(1.00000000 + t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
6052
tmp6 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 4.00000000*r*r + 4.00000000*s*s + 8.00000000*r*s + 8.00000000*r + 8.00000000*s)/(2.00000000*(1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
6053
tmp7 = (2.00000000 + t + 2.00000000*r + 2.00000000*s)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*t/((1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
6054
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
6055
}// end loop over 't'
6056
}// end loop over 's'
6057
}// end loop over 'r'
6058
for (unsigned int r = 0; r < 3; r++)
6059
{
6060
for (unsigned int s = 0; s < 3 - r; s++)
6061
{
6062
for (unsigned int t = 0; t < 3 - r - s; t++)
6063
{
6064
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
6065
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
6066
}// end loop over 't'
6067
}// end loop over 's'
6068
}// end loop over 'r'
6069
6070
// Table(s) of coefficients.
6071
static const double coefficients0[10] = \
6072
{0.23094011, -0.12171612, 0.07027284, -0.09938080, 0.00000000, -0.10079053, 0.02057378, -0.08728716, -0.01187828, 0.01679842};
6073
6074
// Compute value(s).
6075
for (unsigned int r = 0; r < 10; r++)
6076
{
6077
values[1] += coefficients0[r]*basisvalues[r];
6078
}// end loop over 'r'
6079
break;
6080
}
6081
case 19:
6082
{
6083
6084
// Array of basisvalues.
6085
double basisvalues[10] = {0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000};
6086
6087
// Declare helper variables.
6088
unsigned int rr = 0;
6089
unsigned int ss = 0;
6090
unsigned int tt = 0;
6091
double tmp5 = 0.00000000;
6092
double tmp6 = 0.00000000;
6093
double tmp7 = 0.00000000;
6094
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
6095
double tmp1 = 0.25000000*(Y + Z)*(Y + Z);
6096
double tmp2 = 0.50000000*(1.00000000 + Z + 2.00000000*Y);
6097
double tmp3 = 0.50000000*(1.00000000 - Z);
6098
double tmp4 = tmp3*tmp3;
6099
6100
// Compute basisvalues.
6101
basisvalues[0] = 1.00000000;
6102
basisvalues[1] = tmp0;
6103
for (unsigned int r = 1; r < 2; r++)
6104
{
6105
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
6106
ss = r*(r + 1)*(r + 2)/6;
6107
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
6108
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.00000000 + 2.00000000*r)/(1.00000000 + r) - basisvalues[tt]*tmp1*r/(1.00000000 + r));
6109
}// end loop over 'r'
6110
for (unsigned int r = 0; r < 2; r++)
6111
{
6112
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
6113
ss = r*(r + 1)*(r + 2)/6;
6114
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
6115
}// end loop over 'r'
6116
for (unsigned int r = 0; r < 1; r++)
6117
{
6118
for (unsigned int s = 1; s < 2 - r; s++)
6119
{
6120
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
6121
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
6122
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
6123
tmp5 = (2.00000000 + 2.00000000*r + 2.00000000*s)*(3.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
6124
tmp6 = (1.00000000 + 4.00000000*r*r + 4.00000000*r)*(2.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
6125
tmp7 = (1.00000000 + s + 2.00000000*r)*(3.00000000 + 2.00000000*r + 2.00000000*s)*s/((1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
6126
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
6127
}// end loop over 's'
6128
}// end loop over 'r'
6129
for (unsigned int r = 0; r < 2; r++)
6130
{
6131
for (unsigned int s = 0; s < 2 - r; s++)
6132
{
6133
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
6134
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
6135
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
6136
}// end loop over 's'
6137
}// end loop over 'r'
6138
for (unsigned int r = 0; r < 1; r++)
6139
{
6140
for (unsigned int s = 0; s < 1 - r; s++)
6141
{
6142
for (unsigned int t = 1; t < 2 - r - s; t++)
6143
{
6144
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
6145
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
6146
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
6147
tmp5 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)/(2.00000000*(1.00000000 + t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
6148
tmp6 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 4.00000000*r*r + 4.00000000*s*s + 8.00000000*r*s + 8.00000000*r + 8.00000000*s)/(2.00000000*(1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
6149
tmp7 = (2.00000000 + t + 2.00000000*r + 2.00000000*s)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*t/((1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
6150
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
6151
}// end loop over 't'
6152
}// end loop over 's'
6153
}// end loop over 'r'
6154
for (unsigned int r = 0; r < 3; r++)
6155
{
6156
for (unsigned int s = 0; s < 3 - r; s++)
6157
{
6158
for (unsigned int t = 0; t < 3 - r - s; t++)
6159
{
6160
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
6161
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
6162
}// end loop over 't'
6163
}// end loop over 's'
6164
}// end loop over 'r'
6165
6166
// Table(s) of coefficients.
6167
static const double coefficients0[10] = \
6168
{0.23094011, 0.00000000, -0.14054567, -0.09938080, -0.13012001, 0.00000000, 0.00000000, 0.02909572, 0.02375655, 0.01679842};
6169
6170
// Compute value(s).
6171
for (unsigned int r = 0; r < 10; r++)
6172
{
6173
values[1] += coefficients0[r]*basisvalues[r];
6174
}// end loop over 'r'
6175
break;
6176
}
6177
case 20:
6178
{
6179
6180
// Array of basisvalues.
6181
double basisvalues[10] = {0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000};
6182
6183
// Declare helper variables.
6184
unsigned int rr = 0;
6185
unsigned int ss = 0;
6186
unsigned int tt = 0;
6187
double tmp5 = 0.00000000;
6188
double tmp6 = 0.00000000;
6189
double tmp7 = 0.00000000;
6190
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
6191
double tmp1 = 0.25000000*(Y + Z)*(Y + Z);
6192
double tmp2 = 0.50000000*(1.00000000 + Z + 2.00000000*Y);
6193
double tmp3 = 0.50000000*(1.00000000 - Z);
6194
double tmp4 = tmp3*tmp3;
6195
6196
// Compute basisvalues.
6197
basisvalues[0] = 1.00000000;
6198
basisvalues[1] = tmp0;
6199
for (unsigned int r = 1; r < 2; r++)
6200
{
6201
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
6202
ss = r*(r + 1)*(r + 2)/6;
6203
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
6204
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.00000000 + 2.00000000*r)/(1.00000000 + r) - basisvalues[tt]*tmp1*r/(1.00000000 + r));
6205
}// end loop over 'r'
6206
for (unsigned int r = 0; r < 2; r++)
6207
{
6208
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
6209
ss = r*(r + 1)*(r + 2)/6;
6210
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
6211
}// end loop over 'r'
6212
for (unsigned int r = 0; r < 1; r++)
6213
{
6214
for (unsigned int s = 1; s < 2 - r; s++)
6215
{
6216
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
6217
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
6218
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
6219
tmp5 = (2.00000000 + 2.00000000*r + 2.00000000*s)*(3.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
6220
tmp6 = (1.00000000 + 4.00000000*r*r + 4.00000000*r)*(2.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
6221
tmp7 = (1.00000000 + s + 2.00000000*r)*(3.00000000 + 2.00000000*r + 2.00000000*s)*s/((1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
6222
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
6223
}// end loop over 's'
6224
}// end loop over 'r'
6225
for (unsigned int r = 0; r < 2; r++)
6226
{
6227
for (unsigned int s = 0; s < 2 - r; s++)
6228
{
6229
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
6230
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
6231
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
6232
}// end loop over 's'
6233
}// end loop over 'r'
6234
for (unsigned int r = 0; r < 1; r++)
6235
{
6236
for (unsigned int s = 0; s < 1 - r; s++)
6237
{
6238
for (unsigned int t = 1; t < 2 - r - s; t++)
6239
{
6240
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
6241
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
6242
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
6243
tmp5 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)/(2.00000000*(1.00000000 + t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
6244
tmp6 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 4.00000000*r*r + 4.00000000*s*s + 8.00000000*r*s + 8.00000000*r + 8.00000000*s)/(2.00000000*(1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
6245
tmp7 = (2.00000000 + t + 2.00000000*r + 2.00000000*s)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*t/((1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
6246
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
6247
}// end loop over 't'
6248
}// end loop over 's'
6249
}// end loop over 'r'
6250
for (unsigned int r = 0; r < 3; r++)
6251
{
6252
for (unsigned int s = 0; s < 3 - r; s++)
6253
{
6254
for (unsigned int t = 0; t < 3 - r - s; t++)
6255
{
6256
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
6257
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
6258
}// end loop over 't'
6259
}// end loop over 's'
6260
}// end loop over 'r'
6261
6262
// Table(s) of coefficients.
6263
static const double coefficients0[10] = \
6264
{-0.05773503, -0.06085806, -0.03513642, -0.02484520, 0.06506000, 0.05039526, 0.04114756, 0.02909572, 0.02375655, 0.01679842};
6265
6266
// Compute value(s).
6267
for (unsigned int r = 0; r < 10; r++)
6268
{
6269
values[2] += coefficients0[r]*basisvalues[r];
6270
}// end loop over 'r'
6271
break;
6272
}
6273
case 21:
6274
{
6275
6276
// Array of basisvalues.
6277
double basisvalues[10] = {0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000};
6278
6279
// Declare helper variables.
6280
unsigned int rr = 0;
6281
unsigned int ss = 0;
6282
unsigned int tt = 0;
6283
double tmp5 = 0.00000000;
6284
double tmp6 = 0.00000000;
6285
double tmp7 = 0.00000000;
6286
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
6287
double tmp1 = 0.25000000*(Y + Z)*(Y + Z);
6288
double tmp2 = 0.50000000*(1.00000000 + Z + 2.00000000*Y);
6289
double tmp3 = 0.50000000*(1.00000000 - Z);
6290
double tmp4 = tmp3*tmp3;
6291
6292
// Compute basisvalues.
6293
basisvalues[0] = 1.00000000;
6294
basisvalues[1] = tmp0;
6295
for (unsigned int r = 1; r < 2; r++)
6296
{
6297
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
6298
ss = r*(r + 1)*(r + 2)/6;
6299
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
6300
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.00000000 + 2.00000000*r)/(1.00000000 + r) - basisvalues[tt]*tmp1*r/(1.00000000 + r));
6301
}// end loop over 'r'
6302
for (unsigned int r = 0; r < 2; r++)
6303
{
6304
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
6305
ss = r*(r + 1)*(r + 2)/6;
6306
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
6307
}// end loop over 'r'
6308
for (unsigned int r = 0; r < 1; r++)
6309
{
6310
for (unsigned int s = 1; s < 2 - r; s++)
6311
{
6312
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
6313
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
6314
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
6315
tmp5 = (2.00000000 + 2.00000000*r + 2.00000000*s)*(3.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
6316
tmp6 = (1.00000000 + 4.00000000*r*r + 4.00000000*r)*(2.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
6317
tmp7 = (1.00000000 + s + 2.00000000*r)*(3.00000000 + 2.00000000*r + 2.00000000*s)*s/((1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
6318
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
6319
}// end loop over 's'
6320
}// end loop over 'r'
6321
for (unsigned int r = 0; r < 2; r++)
6322
{
6323
for (unsigned int s = 0; s < 2 - r; s++)
6324
{
6325
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
6326
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
6327
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
6328
}// end loop over 's'
6329
}// end loop over 'r'
6330
for (unsigned int r = 0; r < 1; r++)
6331
{
6332
for (unsigned int s = 0; s < 1 - r; s++)
6333
{
6334
for (unsigned int t = 1; t < 2 - r - s; t++)
6335
{
6336
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
6337
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
6338
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
6339
tmp5 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)/(2.00000000*(1.00000000 + t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
6340
tmp6 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 4.00000000*r*r + 4.00000000*s*s + 8.00000000*r*s + 8.00000000*r + 8.00000000*s)/(2.00000000*(1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
6341
tmp7 = (2.00000000 + t + 2.00000000*r + 2.00000000*s)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*t/((1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
6342
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
6343
}// end loop over 't'
6344
}// end loop over 's'
6345
}// end loop over 'r'
6346
for (unsigned int r = 0; r < 3; r++)
6347
{
6348
for (unsigned int s = 0; s < 3 - r; s++)
6349
{
6350
for (unsigned int t = 0; t < 3 - r - s; t++)
6351
{
6352
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
6353
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
6354
}// end loop over 't'
6355
}// end loop over 's'
6356
}// end loop over 'r'
6357
6358
// Table(s) of coefficients.
6359
static const double coefficients0[10] = \
6360
{-0.05773503, 0.06085806, -0.03513642, -0.02484520, 0.06506000, -0.05039526, -0.04114756, 0.02909572, 0.02375655, 0.01679842};
6361
6362
// Compute value(s).
6363
for (unsigned int r = 0; r < 10; r++)
6364
{
6365
values[2] += coefficients0[r]*basisvalues[r];
6366
}// end loop over 'r'
6367
break;
6368
}
6369
case 22:
6370
{
6371
6372
// Array of basisvalues.
6373
double basisvalues[10] = {0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000};
6374
6375
// Declare helper variables.
6376
unsigned int rr = 0;
6377
unsigned int ss = 0;
6378
unsigned int tt = 0;
6379
double tmp5 = 0.00000000;
6380
double tmp6 = 0.00000000;
6381
double tmp7 = 0.00000000;
6382
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
6383
double tmp1 = 0.25000000*(Y + Z)*(Y + Z);
6384
double tmp2 = 0.50000000*(1.00000000 + Z + 2.00000000*Y);
6385
double tmp3 = 0.50000000*(1.00000000 - Z);
6386
double tmp4 = tmp3*tmp3;
6387
6388
// Compute basisvalues.
6389
basisvalues[0] = 1.00000000;
6390
basisvalues[1] = tmp0;
6391
for (unsigned int r = 1; r < 2; r++)
6392
{
6393
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
6394
ss = r*(r + 1)*(r + 2)/6;
6395
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
6396
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.00000000 + 2.00000000*r)/(1.00000000 + r) - basisvalues[tt]*tmp1*r/(1.00000000 + r));
6397
}// end loop over 'r'
6398
for (unsigned int r = 0; r < 2; r++)
6399
{
6400
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
6401
ss = r*(r + 1)*(r + 2)/6;
6402
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
6403
}// end loop over 'r'
6404
for (unsigned int r = 0; r < 1; r++)
6405
{
6406
for (unsigned int s = 1; s < 2 - r; s++)
6407
{
6408
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
6409
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
6410
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
6411
tmp5 = (2.00000000 + 2.00000000*r + 2.00000000*s)*(3.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
6412
tmp6 = (1.00000000 + 4.00000000*r*r + 4.00000000*r)*(2.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
6413
tmp7 = (1.00000000 + s + 2.00000000*r)*(3.00000000 + 2.00000000*r + 2.00000000*s)*s/((1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
6414
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
6415
}// end loop over 's'
6416
}// end loop over 'r'
6417
for (unsigned int r = 0; r < 2; r++)
6418
{
6419
for (unsigned int s = 0; s < 2 - r; s++)
6420
{
6421
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
6422
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
6423
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
6424
}// end loop over 's'
6425
}// end loop over 'r'
6426
for (unsigned int r = 0; r < 1; r++)
6427
{
6428
for (unsigned int s = 0; s < 1 - r; s++)
6429
{
6430
for (unsigned int t = 1; t < 2 - r - s; t++)
6431
{
6432
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
6433
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
6434
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
6435
tmp5 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)/(2.00000000*(1.00000000 + t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
6436
tmp6 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 4.00000000*r*r + 4.00000000*s*s + 8.00000000*r*s + 8.00000000*r + 8.00000000*s)/(2.00000000*(1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
6437
tmp7 = (2.00000000 + t + 2.00000000*r + 2.00000000*s)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*t/((1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
6438
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
6439
}// end loop over 't'
6440
}// end loop over 's'
6441
}// end loop over 'r'
6442
for (unsigned int r = 0; r < 3; r++)
6443
{
6444
for (unsigned int s = 0; s < 3 - r; s++)
6445
{
6446
for (unsigned int t = 0; t < 3 - r - s; t++)
6447
{
6448
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
6449
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
6450
}// end loop over 't'
6451
}// end loop over 's'
6452
}// end loop over 'r'
6453
6454
// Table(s) of coefficients.
6455
static const double coefficients0[10] = \
6456
{-0.05773503, 0.00000000, 0.07027284, -0.02484520, 0.00000000, 0.00000000, 0.00000000, 0.08728716, -0.04751311, 0.01679842};
6457
6458
// Compute value(s).
6459
for (unsigned int r = 0; r < 10; r++)
6460
{
6461
values[2] += coefficients0[r]*basisvalues[r];
6462
}// end loop over 'r'
6463
break;
6464
}
6465
case 23:
6466
{
6467
6468
// Array of basisvalues.
6469
double basisvalues[10] = {0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000};
6470
6471
// Declare helper variables.
6472
unsigned int rr = 0;
6473
unsigned int ss = 0;
6474
unsigned int tt = 0;
6475
double tmp5 = 0.00000000;
6476
double tmp6 = 0.00000000;
6477
double tmp7 = 0.00000000;
6478
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
6479
double tmp1 = 0.25000000*(Y + Z)*(Y + Z);
6480
double tmp2 = 0.50000000*(1.00000000 + Z + 2.00000000*Y);
6481
double tmp3 = 0.50000000*(1.00000000 - Z);
6482
double tmp4 = tmp3*tmp3;
6483
6484
// Compute basisvalues.
6485
basisvalues[0] = 1.00000000;
6486
basisvalues[1] = tmp0;
6487
for (unsigned int r = 1; r < 2; r++)
6488
{
6489
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
6490
ss = r*(r + 1)*(r + 2)/6;
6491
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
6492
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.00000000 + 2.00000000*r)/(1.00000000 + r) - basisvalues[tt]*tmp1*r/(1.00000000 + r));
6493
}// end loop over 'r'
6494
for (unsigned int r = 0; r < 2; r++)
6495
{
6496
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
6497
ss = r*(r + 1)*(r + 2)/6;
6498
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
6499
}// end loop over 'r'
6500
for (unsigned int r = 0; r < 1; r++)
6501
{
6502
for (unsigned int s = 1; s < 2 - r; s++)
6503
{
6504
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
6505
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
6506
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
6507
tmp5 = (2.00000000 + 2.00000000*r + 2.00000000*s)*(3.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
6508
tmp6 = (1.00000000 + 4.00000000*r*r + 4.00000000*r)*(2.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
6509
tmp7 = (1.00000000 + s + 2.00000000*r)*(3.00000000 + 2.00000000*r + 2.00000000*s)*s/((1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
6510
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
6511
}// end loop over 's'
6512
}// end loop over 'r'
6513
for (unsigned int r = 0; r < 2; r++)
6514
{
6515
for (unsigned int s = 0; s < 2 - r; s++)
6516
{
6517
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
6518
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
6519
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
6520
}// end loop over 's'
6521
}// end loop over 'r'
6522
for (unsigned int r = 0; r < 1; r++)
6523
{
6524
for (unsigned int s = 0; s < 1 - r; s++)
6525
{
6526
for (unsigned int t = 1; t < 2 - r - s; t++)
6527
{
6528
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
6529
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
6530
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
6531
tmp5 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)/(2.00000000*(1.00000000 + t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
6532
tmp6 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 4.00000000*r*r + 4.00000000*s*s + 8.00000000*r*s + 8.00000000*r + 8.00000000*s)/(2.00000000*(1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
6533
tmp7 = (2.00000000 + t + 2.00000000*r + 2.00000000*s)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*t/((1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
6534
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
6535
}// end loop over 't'
6536
}// end loop over 's'
6537
}// end loop over 'r'
6538
for (unsigned int r = 0; r < 3; r++)
6539
{
6540
for (unsigned int s = 0; s < 3 - r; s++)
6541
{
6542
for (unsigned int t = 0; t < 3 - r - s; t++)
6543
{
6544
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
6545
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
6546
}// end loop over 't'
6547
}// end loop over 's'
6548
}// end loop over 'r'
6549
6550
// Table(s) of coefficients.
6551
static const double coefficients0[10] = \
6552
{-0.05773503, 0.00000000, 0.00000000, 0.07453560, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.10079053};
6553
6554
// Compute value(s).
6555
for (unsigned int r = 0; r < 10; r++)
6556
{
6557
values[2] += coefficients0[r]*basisvalues[r];
6558
}// end loop over 'r'
6559
break;
6560
}
6561
case 24:
6562
{
6563
6564
// Array of basisvalues.
6565
double basisvalues[10] = {0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000};
6566
6567
// Declare helper variables.
6568
unsigned int rr = 0;
6569
unsigned int ss = 0;
6570
unsigned int tt = 0;
6571
double tmp5 = 0.00000000;
6572
double tmp6 = 0.00000000;
6573
double tmp7 = 0.00000000;
6574
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
6575
double tmp1 = 0.25000000*(Y + Z)*(Y + Z);
6576
double tmp2 = 0.50000000*(1.00000000 + Z + 2.00000000*Y);
6577
double tmp3 = 0.50000000*(1.00000000 - Z);
6578
double tmp4 = tmp3*tmp3;
6579
6580
// Compute basisvalues.
6581
basisvalues[0] = 1.00000000;
6582
basisvalues[1] = tmp0;
6583
for (unsigned int r = 1; r < 2; r++)
6584
{
6585
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
6586
ss = r*(r + 1)*(r + 2)/6;
6587
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
6588
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.00000000 + 2.00000000*r)/(1.00000000 + r) - basisvalues[tt]*tmp1*r/(1.00000000 + r));
6589
}// end loop over 'r'
6590
for (unsigned int r = 0; r < 2; r++)
6591
{
6592
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
6593
ss = r*(r + 1)*(r + 2)/6;
6594
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
6595
}// end loop over 'r'
6596
for (unsigned int r = 0; r < 1; r++)
6597
{
6598
for (unsigned int s = 1; s < 2 - r; s++)
6599
{
6600
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
6601
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
6602
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
6603
tmp5 = (2.00000000 + 2.00000000*r + 2.00000000*s)*(3.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
6604
tmp6 = (1.00000000 + 4.00000000*r*r + 4.00000000*r)*(2.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
6605
tmp7 = (1.00000000 + s + 2.00000000*r)*(3.00000000 + 2.00000000*r + 2.00000000*s)*s/((1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
6606
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
6607
}// end loop over 's'
6608
}// end loop over 'r'
6609
for (unsigned int r = 0; r < 2; r++)
6610
{
6611
for (unsigned int s = 0; s < 2 - r; s++)
6612
{
6613
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
6614
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
6615
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
6616
}// end loop over 's'
6617
}// end loop over 'r'
6618
for (unsigned int r = 0; r < 1; r++)
6619
{
6620
for (unsigned int s = 0; s < 1 - r; s++)
6621
{
6622
for (unsigned int t = 1; t < 2 - r - s; t++)
6623
{
6624
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
6625
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
6626
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
6627
tmp5 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)/(2.00000000*(1.00000000 + t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
6628
tmp6 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 4.00000000*r*r + 4.00000000*s*s + 8.00000000*r*s + 8.00000000*r + 8.00000000*s)/(2.00000000*(1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
6629
tmp7 = (2.00000000 + t + 2.00000000*r + 2.00000000*s)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*t/((1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
6630
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
6631
}// end loop over 't'
6632
}// end loop over 's'
6633
}// end loop over 'r'
6634
for (unsigned int r = 0; r < 3; r++)
6635
{
6636
for (unsigned int s = 0; s < 3 - r; s++)
6637
{
6638
for (unsigned int t = 0; t < 3 - r - s; t++)
6639
{
6640
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
6641
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
6642
}// end loop over 't'
6643
}// end loop over 's'
6644
}// end loop over 'r'
6645
6646
// Table(s) of coefficients.
6647
static const double coefficients0[10] = \
6648
{0.23094011, 0.00000000, 0.14054567, 0.09938080, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.11878277, -0.06719368};
6649
6650
// Compute value(s).
6651
for (unsigned int r = 0; r < 10; r++)
6652
{
6653
values[2] += coefficients0[r]*basisvalues[r];
6654
}// end loop over 'r'
6655
break;
6656
}
6657
case 25:
6658
{
6659
6660
// Array of basisvalues.
6661
double basisvalues[10] = {0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000};
6662
6663
// Declare helper variables.
6664
unsigned int rr = 0;
6665
unsigned int ss = 0;
6666
unsigned int tt = 0;
6667
double tmp5 = 0.00000000;
6668
double tmp6 = 0.00000000;
6669
double tmp7 = 0.00000000;
6670
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
6671
double tmp1 = 0.25000000*(Y + Z)*(Y + Z);
6672
double tmp2 = 0.50000000*(1.00000000 + Z + 2.00000000*Y);
6673
double tmp3 = 0.50000000*(1.00000000 - Z);
6674
double tmp4 = tmp3*tmp3;
6675
6676
// Compute basisvalues.
6677
basisvalues[0] = 1.00000000;
6678
basisvalues[1] = tmp0;
6679
for (unsigned int r = 1; r < 2; r++)
6680
{
6681
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
6682
ss = r*(r + 1)*(r + 2)/6;
6683
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
6684
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.00000000 + 2.00000000*r)/(1.00000000 + r) - basisvalues[tt]*tmp1*r/(1.00000000 + r));
6685
}// end loop over 'r'
6686
for (unsigned int r = 0; r < 2; r++)
6687
{
6688
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
6689
ss = r*(r + 1)*(r + 2)/6;
6690
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
6691
}// end loop over 'r'
6692
for (unsigned int r = 0; r < 1; r++)
6693
{
6694
for (unsigned int s = 1; s < 2 - r; s++)
6695
{
6696
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
6697
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
6698
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
6699
tmp5 = (2.00000000 + 2.00000000*r + 2.00000000*s)*(3.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
6700
tmp6 = (1.00000000 + 4.00000000*r*r + 4.00000000*r)*(2.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
6701
tmp7 = (1.00000000 + s + 2.00000000*r)*(3.00000000 + 2.00000000*r + 2.00000000*s)*s/((1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
6702
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
6703
}// end loop over 's'
6704
}// end loop over 'r'
6705
for (unsigned int r = 0; r < 2; r++)
6706
{
6707
for (unsigned int s = 0; s < 2 - r; s++)
6708
{
6709
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
6710
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
6711
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
6712
}// end loop over 's'
6713
}// end loop over 'r'
6714
for (unsigned int r = 0; r < 1; r++)
6715
{
6716
for (unsigned int s = 0; s < 1 - r; s++)
6717
{
6718
for (unsigned int t = 1; t < 2 - r - s; t++)
6719
{
6720
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
6721
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
6722
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
6723
tmp5 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)/(2.00000000*(1.00000000 + t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
6724
tmp6 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 4.00000000*r*r + 4.00000000*s*s + 8.00000000*r*s + 8.00000000*r + 8.00000000*s)/(2.00000000*(1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
6725
tmp7 = (2.00000000 + t + 2.00000000*r + 2.00000000*s)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*t/((1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
6726
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
6727
}// end loop over 't'
6728
}// end loop over 's'
6729
}// end loop over 'r'
6730
for (unsigned int r = 0; r < 3; r++)
6731
{
6732
for (unsigned int s = 0; s < 3 - r; s++)
6733
{
6734
for (unsigned int t = 0; t < 3 - r - s; t++)
6735
{
6736
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
6737
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
6738
}// end loop over 't'
6739
}// end loop over 's'
6740
}// end loop over 'r'
6741
6742
// Table(s) of coefficients.
6743
static const double coefficients0[10] = \
6744
{0.23094011, 0.12171612, -0.07027284, 0.09938080, 0.00000000, 0.00000000, 0.10286890, 0.00000000, -0.05939139, -0.06719368};
6745
6746
// Compute value(s).
6747
for (unsigned int r = 0; r < 10; r++)
6748
{
6749
values[2] += coefficients0[r]*basisvalues[r];
6750
}// end loop over 'r'
6751
break;
6752
}
6753
case 26:
6754
{
6755
6756
// Array of basisvalues.
6757
double basisvalues[10] = {0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000};
6758
6759
// Declare helper variables.
6760
unsigned int rr = 0;
6761
unsigned int ss = 0;
6762
unsigned int tt = 0;
6763
double tmp5 = 0.00000000;
6764
double tmp6 = 0.00000000;
6765
double tmp7 = 0.00000000;
6766
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
6767
double tmp1 = 0.25000000*(Y + Z)*(Y + Z);
6768
double tmp2 = 0.50000000*(1.00000000 + Z + 2.00000000*Y);
6769
double tmp3 = 0.50000000*(1.00000000 - Z);
6770
double tmp4 = tmp3*tmp3;
6771
6772
// Compute basisvalues.
6773
basisvalues[0] = 1.00000000;
6774
basisvalues[1] = tmp0;
6775
for (unsigned int r = 1; r < 2; r++)
6776
{
6777
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
6778
ss = r*(r + 1)*(r + 2)/6;
6779
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
6780
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.00000000 + 2.00000000*r)/(1.00000000 + r) - basisvalues[tt]*tmp1*r/(1.00000000 + r));
6781
}// end loop over 'r'
6782
for (unsigned int r = 0; r < 2; r++)
6783
{
6784
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
6785
ss = r*(r + 1)*(r + 2)/6;
6786
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
6787
}// end loop over 'r'
6788
for (unsigned int r = 0; r < 1; r++)
6789
{
6790
for (unsigned int s = 1; s < 2 - r; s++)
6791
{
6792
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
6793
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
6794
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
6795
tmp5 = (2.00000000 + 2.00000000*r + 2.00000000*s)*(3.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
6796
tmp6 = (1.00000000 + 4.00000000*r*r + 4.00000000*r)*(2.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
6797
tmp7 = (1.00000000 + s + 2.00000000*r)*(3.00000000 + 2.00000000*r + 2.00000000*s)*s/((1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
6798
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
6799
}// end loop over 's'
6800
}// end loop over 'r'
6801
for (unsigned int r = 0; r < 2; r++)
6802
{
6803
for (unsigned int s = 0; s < 2 - r; s++)
6804
{
6805
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
6806
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
6807
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
6808
}// end loop over 's'
6809
}// end loop over 'r'
6810
for (unsigned int r = 0; r < 1; r++)
6811
{
6812
for (unsigned int s = 0; s < 1 - r; s++)
6813
{
6814
for (unsigned int t = 1; t < 2 - r - s; t++)
6815
{
6816
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
6817
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
6818
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
6819
tmp5 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)/(2.00000000*(1.00000000 + t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
6820
tmp6 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 4.00000000*r*r + 4.00000000*s*s + 8.00000000*r*s + 8.00000000*r + 8.00000000*s)/(2.00000000*(1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
6821
tmp7 = (2.00000000 + t + 2.00000000*r + 2.00000000*s)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*t/((1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
6822
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
6823
}// end loop over 't'
6824
}// end loop over 's'
6825
}// end loop over 'r'
6826
for (unsigned int r = 0; r < 3; r++)
6827
{
6828
for (unsigned int s = 0; s < 3 - r; s++)
6829
{
6830
for (unsigned int t = 0; t < 3 - r - s; t++)
6831
{
6832
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
6833
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
6834
}// end loop over 't'
6835
}// end loop over 's'
6836
}// end loop over 'r'
6837
6838
// Table(s) of coefficients.
6839
static const double coefficients0[10] = \
6840
{0.23094011, 0.12171612, 0.07027284, -0.09938080, 0.00000000, 0.10079053, -0.02057378, -0.08728716, -0.01187828, 0.01679842};
6841
6842
// Compute value(s).
6843
for (unsigned int r = 0; r < 10; r++)
6844
{
6845
values[2] += coefficients0[r]*basisvalues[r];
6846
}// end loop over 'r'
6847
break;
6848
}
6849
case 27:
6850
{
6851
6852
// Array of basisvalues.
6853
double basisvalues[10] = {0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000};
6854
6855
// Declare helper variables.
6856
unsigned int rr = 0;
6857
unsigned int ss = 0;
6858
unsigned int tt = 0;
6859
double tmp5 = 0.00000000;
6860
double tmp6 = 0.00000000;
6861
double tmp7 = 0.00000000;
6862
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
6863
double tmp1 = 0.25000000*(Y + Z)*(Y + Z);
6864
double tmp2 = 0.50000000*(1.00000000 + Z + 2.00000000*Y);
6865
double tmp3 = 0.50000000*(1.00000000 - Z);
6866
double tmp4 = tmp3*tmp3;
6867
6868
// Compute basisvalues.
6869
basisvalues[0] = 1.00000000;
6870
basisvalues[1] = tmp0;
6871
for (unsigned int r = 1; r < 2; r++)
6872
{
6873
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
6874
ss = r*(r + 1)*(r + 2)/6;
6875
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
6876
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.00000000 + 2.00000000*r)/(1.00000000 + r) - basisvalues[tt]*tmp1*r/(1.00000000 + r));
6877
}// end loop over 'r'
6878
for (unsigned int r = 0; r < 2; r++)
6879
{
6880
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
6881
ss = r*(r + 1)*(r + 2)/6;
6882
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
6883
}// end loop over 'r'
6884
for (unsigned int r = 0; r < 1; r++)
6885
{
6886
for (unsigned int s = 1; s < 2 - r; s++)
6887
{
6888
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
6889
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
6890
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
6891
tmp5 = (2.00000000 + 2.00000000*r + 2.00000000*s)*(3.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
6892
tmp6 = (1.00000000 + 4.00000000*r*r + 4.00000000*r)*(2.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
6893
tmp7 = (1.00000000 + s + 2.00000000*r)*(3.00000000 + 2.00000000*r + 2.00000000*s)*s/((1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
6894
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
6895
}// end loop over 's'
6896
}// end loop over 'r'
6897
for (unsigned int r = 0; r < 2; r++)
6898
{
6899
for (unsigned int s = 0; s < 2 - r; s++)
6900
{
6901
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
6902
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
6903
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
6904
}// end loop over 's'
6905
}// end loop over 'r'
6906
for (unsigned int r = 0; r < 1; r++)
6907
{
6908
for (unsigned int s = 0; s < 1 - r; s++)
6909
{
6910
for (unsigned int t = 1; t < 2 - r - s; t++)
6911
{
6912
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
6913
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
6914
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
6915
tmp5 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)/(2.00000000*(1.00000000 + t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
6916
tmp6 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 4.00000000*r*r + 4.00000000*s*s + 8.00000000*r*s + 8.00000000*r + 8.00000000*s)/(2.00000000*(1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
6917
tmp7 = (2.00000000 + t + 2.00000000*r + 2.00000000*s)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*t/((1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
6918
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
6919
}// end loop over 't'
6920
}// end loop over 's'
6921
}// end loop over 'r'
6922
for (unsigned int r = 0; r < 3; r++)
6923
{
6924
for (unsigned int s = 0; s < 3 - r; s++)
6925
{
6926
for (unsigned int t = 0; t < 3 - r - s; t++)
6927
{
6928
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
6929
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
6930
}// end loop over 't'
6931
}// end loop over 's'
6932
}// end loop over 'r'
6933
6934
// Table(s) of coefficients.
6935
static const double coefficients0[10] = \
6936
{0.23094011, -0.12171612, -0.07027284, 0.09938080, 0.00000000, 0.00000000, -0.10286890, 0.00000000, -0.05939139, -0.06719368};
6937
6938
// Compute value(s).
6939
for (unsigned int r = 0; r < 10; r++)
6940
{
6941
values[2] += coefficients0[r]*basisvalues[r];
6942
}// end loop over 'r'
6943
break;
6944
}
6945
case 28:
6946
{
6947
6948
// Array of basisvalues.
6949
double basisvalues[10] = {0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000};
6950
6951
// Declare helper variables.
6952
unsigned int rr = 0;
6953
unsigned int ss = 0;
6954
unsigned int tt = 0;
6955
double tmp5 = 0.00000000;
6956
double tmp6 = 0.00000000;
6957
double tmp7 = 0.00000000;
6958
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
6959
double tmp1 = 0.25000000*(Y + Z)*(Y + Z);
6960
double tmp2 = 0.50000000*(1.00000000 + Z + 2.00000000*Y);
6961
double tmp3 = 0.50000000*(1.00000000 - Z);
6962
double tmp4 = tmp3*tmp3;
6963
6964
// Compute basisvalues.
6965
basisvalues[0] = 1.00000000;
6966
basisvalues[1] = tmp0;
6967
for (unsigned int r = 1; r < 2; r++)
6968
{
6969
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
6970
ss = r*(r + 1)*(r + 2)/6;
6971
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
6972
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.00000000 + 2.00000000*r)/(1.00000000 + r) - basisvalues[tt]*tmp1*r/(1.00000000 + r));
6973
}// end loop over 'r'
6974
for (unsigned int r = 0; r < 2; r++)
6975
{
6976
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
6977
ss = r*(r + 1)*(r + 2)/6;
6978
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
6979
}// end loop over 'r'
6980
for (unsigned int r = 0; r < 1; r++)
6981
{
6982
for (unsigned int s = 1; s < 2 - r; s++)
6983
{
6984
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
6985
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
6986
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
6987
tmp5 = (2.00000000 + 2.00000000*r + 2.00000000*s)*(3.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
6988
tmp6 = (1.00000000 + 4.00000000*r*r + 4.00000000*r)*(2.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
6989
tmp7 = (1.00000000 + s + 2.00000000*r)*(3.00000000 + 2.00000000*r + 2.00000000*s)*s/((1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
6990
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
6991
}// end loop over 's'
6992
}// end loop over 'r'
6993
for (unsigned int r = 0; r < 2; r++)
6994
{
6995
for (unsigned int s = 0; s < 2 - r; s++)
6996
{
6997
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
6998
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
6999
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
7000
}// end loop over 's'
7001
}// end loop over 'r'
7002
for (unsigned int r = 0; r < 1; r++)
7003
{
7004
for (unsigned int s = 0; s < 1 - r; s++)
7005
{
7006
for (unsigned int t = 1; t < 2 - r - s; t++)
7007
{
7008
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
7009
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
7010
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
7011
tmp5 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)/(2.00000000*(1.00000000 + t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
7012
tmp6 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 4.00000000*r*r + 4.00000000*s*s + 8.00000000*r*s + 8.00000000*r + 8.00000000*s)/(2.00000000*(1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
7013
tmp7 = (2.00000000 + t + 2.00000000*r + 2.00000000*s)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*t/((1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
7014
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
7015
}// end loop over 't'
7016
}// end loop over 's'
7017
}// end loop over 'r'
7018
for (unsigned int r = 0; r < 3; r++)
7019
{
7020
for (unsigned int s = 0; s < 3 - r; s++)
7021
{
7022
for (unsigned int t = 0; t < 3 - r - s; t++)
7023
{
7024
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
7025
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
7026
}// end loop over 't'
7027
}// end loop over 's'
7028
}// end loop over 'r'
7029
7030
// Table(s) of coefficients.
7031
static const double coefficients0[10] = \
7032
{0.23094011, -0.12171612, 0.07027284, -0.09938080, 0.00000000, -0.10079053, 0.02057378, -0.08728716, -0.01187828, 0.01679842};
7033
7034
// Compute value(s).
7035
for (unsigned int r = 0; r < 10; r++)
7036
{
7037
values[2] += coefficients0[r]*basisvalues[r];
7038
}// end loop over 'r'
7039
break;
7040
}
7041
case 29:
7042
{
7043
7044
// Array of basisvalues.
7045
double basisvalues[10] = {0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000};
7046
7047
// Declare helper variables.
7048
unsigned int rr = 0;
7049
unsigned int ss = 0;
7050
unsigned int tt = 0;
7051
double tmp5 = 0.00000000;
7052
double tmp6 = 0.00000000;
7053
double tmp7 = 0.00000000;
7054
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
7055
double tmp1 = 0.25000000*(Y + Z)*(Y + Z);
7056
double tmp2 = 0.50000000*(1.00000000 + Z + 2.00000000*Y);
7057
double tmp3 = 0.50000000*(1.00000000 - Z);
7058
double tmp4 = tmp3*tmp3;
7059
7060
// Compute basisvalues.
7061
basisvalues[0] = 1.00000000;
7062
basisvalues[1] = tmp0;
7063
for (unsigned int r = 1; r < 2; r++)
7064
{
7065
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
7066
ss = r*(r + 1)*(r + 2)/6;
7067
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
7068
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.00000000 + 2.00000000*r)/(1.00000000 + r) - basisvalues[tt]*tmp1*r/(1.00000000 + r));
7069
}// end loop over 'r'
7070
for (unsigned int r = 0; r < 2; r++)
7071
{
7072
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
7073
ss = r*(r + 1)*(r + 2)/6;
7074
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
7075
}// end loop over 'r'
7076
for (unsigned int r = 0; r < 1; r++)
7077
{
7078
for (unsigned int s = 1; s < 2 - r; s++)
7079
{
7080
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
7081
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
7082
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
7083
tmp5 = (2.00000000 + 2.00000000*r + 2.00000000*s)*(3.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
7084
tmp6 = (1.00000000 + 4.00000000*r*r + 4.00000000*r)*(2.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
7085
tmp7 = (1.00000000 + s + 2.00000000*r)*(3.00000000 + 2.00000000*r + 2.00000000*s)*s/((1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
7086
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
7087
}// end loop over 's'
7088
}// end loop over 'r'
7089
for (unsigned int r = 0; r < 2; r++)
7090
{
7091
for (unsigned int s = 0; s < 2 - r; s++)
7092
{
7093
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
7094
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
7095
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
7096
}// end loop over 's'
7097
}// end loop over 'r'
7098
for (unsigned int r = 0; r < 1; r++)
7099
{
7100
for (unsigned int s = 0; s < 1 - r; s++)
7101
{
7102
for (unsigned int t = 1; t < 2 - r - s; t++)
7103
{
7104
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
7105
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
7106
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
7107
tmp5 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)/(2.00000000*(1.00000000 + t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
7108
tmp6 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 4.00000000*r*r + 4.00000000*s*s + 8.00000000*r*s + 8.00000000*r + 8.00000000*s)/(2.00000000*(1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
7109
tmp7 = (2.00000000 + t + 2.00000000*r + 2.00000000*s)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*t/((1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
7110
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
7111
}// end loop over 't'
7112
}// end loop over 's'
7113
}// end loop over 'r'
7114
for (unsigned int r = 0; r < 3; r++)
7115
{
7116
for (unsigned int s = 0; s < 3 - r; s++)
7117
{
7118
for (unsigned int t = 0; t < 3 - r - s; t++)
7119
{
7120
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
7121
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
7122
}// end loop over 't'
7123
}// end loop over 's'
7124
}// end loop over 'r'
7125
7126
// Table(s) of coefficients.
7127
static const double coefficients0[10] = \
7128
{0.23094011, 0.00000000, -0.14054567, -0.09938080, -0.13012001, 0.00000000, 0.00000000, 0.02909572, 0.02375655, 0.01679842};
7129
7130
// Compute value(s).
7131
for (unsigned int r = 0; r < 10; r++)
7132
{
7133
values[2] += coefficients0[r]*basisvalues[r];
7134
}// end loop over 'r'
7135
break;
7136
}
1305
7137
}
1306
7138
1307
7139
}
1446
7278
values[r] = 0.00000000;
1447
7279
}// end loop over 'r'
1448
7280
1449
if (0 <= i && i <= 9)
1450
{
1451
// Map degree of freedom to element degree of freedom
1452
const unsigned int dof = i;
1453
1454
// Array of basisvalues.
1455
double basisvalues[10] = {0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000};
1456
1457
// Declare helper variables.
1458
unsigned int rr = 0;
1459
unsigned int ss = 0;
1460
unsigned int tt = 0;
1461
double tmp5 = 0.00000000;
1462
double tmp6 = 0.00000000;
1463
double tmp7 = 0.00000000;
1464
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
1465
double tmp1 = 0.25000000*(Y + Z)*(Y + Z);
1466
double tmp2 = 0.50000000*(1.00000000 + Z + 2.00000000*Y);
1467
double tmp3 = 0.50000000*(1.00000000 - Z);
1468
double tmp4 = tmp3*tmp3;
1469
1470
// Compute basisvalues.
1471
basisvalues[0] = 1.00000000;
1472
basisvalues[1] = tmp0;
1473
for (unsigned int r = 1; r < 2; r++)
1474
{
1475
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
1476
ss = r*(r + 1)*(r + 2)/6;
1477
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
1478
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.00000000 + 2.00000000*r)/(1.00000000 + r) - basisvalues[tt]*tmp1*r/(1.00000000 + r));
1479
}// end loop over 'r'
1480
for (unsigned int r = 0; r < 2; r++)
1481
{
1482
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
1483
ss = r*(r + 1)*(r + 2)/6;
1484
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
1485
}// end loop over 'r'
1486
for (unsigned int r = 0; r < 1; r++)
1487
{
1488
for (unsigned int s = 1; s < 2 - r; s++)
1489
{
1490
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
1491
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
1492
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
1493
tmp5 = (2.00000000 + 2.00000000*r + 2.00000000*s)*(3.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
1494
tmp6 = (1.00000000 + 4.00000000*r*r + 4.00000000*r)*(2.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
1495
tmp7 = (1.00000000 + s + 2.00000000*r)*(3.00000000 + 2.00000000*r + 2.00000000*s)*s/((1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
1496
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
1497
}// end loop over 's'
1498
}// end loop over 'r'
1499
for (unsigned int r = 0; r < 2; r++)
1500
{
1501
for (unsigned int s = 0; s < 2 - r; s++)
1502
{
1503
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
1504
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
1505
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
1506
}// end loop over 's'
1507
}// end loop over 'r'
1508
for (unsigned int r = 0; r < 1; r++)
1509
{
1510
for (unsigned int s = 0; s < 1 - r; s++)
1511
{
1512
for (unsigned int t = 1; t < 2 - r - s; t++)
1513
{
1514
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
1515
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
1516
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
1517
tmp5 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)/(2.00000000*(1.00000000 + t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
1518
tmp6 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 4.00000000*r*r + 4.00000000*s*s + 8.00000000*r*s + 8.00000000*r + 8.00000000*s)/(2.00000000*(1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
1519
tmp7 = (2.00000000 + t + 2.00000000*r + 2.00000000*s)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*t/((1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
1520
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
1521
}// end loop over 't'
1522
}// end loop over 's'
1523
}// end loop over 'r'
1524
for (unsigned int r = 0; r < 3; r++)
1525
{
1526
for (unsigned int s = 0; s < 3 - r; s++)
1527
{
1528
for (unsigned int t = 0; t < 3 - r - s; t++)
1529
{
1530
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
1531
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
1532
}// end loop over 't'
1533
}// end loop over 's'
1534
}// end loop over 'r'
1535
1536
// Table(s) of coefficients.
1537
static const double coefficients0[10][10] = \
1538
{{-0.05773503, -0.06085806, -0.03513642, -0.02484520, 0.06506000, 0.05039526, 0.04114756, 0.02909572, 0.02375655, 0.01679842},
1539
{-0.05773503, 0.06085806, -0.03513642, -0.02484520, 0.06506000, -0.05039526, -0.04114756, 0.02909572, 0.02375655, 0.01679842},
1540
{-0.05773503, 0.00000000, 0.07027284, -0.02484520, 0.00000000, 0.00000000, 0.00000000, 0.08728716, -0.04751311, 0.01679842},
1541
{-0.05773503, 0.00000000, 0.00000000, 0.07453560, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.10079053},
1542
{0.23094011, 0.00000000, 0.14054567, 0.09938080, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.11878277, -0.06719368},
1543
{0.23094011, 0.12171612, -0.07027284, 0.09938080, 0.00000000, 0.00000000, 0.10286890, 0.00000000, -0.05939139, -0.06719368},
1544
{0.23094011, 0.12171612, 0.07027284, -0.09938080, 0.00000000, 0.10079053, -0.02057378, -0.08728716, -0.01187828, 0.01679842},
1545
{0.23094011, -0.12171612, -0.07027284, 0.09938080, 0.00000000, 0.00000000, -0.10286890, 0.00000000, -0.05939139, -0.06719368},
1546
{0.23094011, -0.12171612, 0.07027284, -0.09938080, 0.00000000, -0.10079053, 0.02057378, -0.08728716, -0.01187828, 0.01679842},
1547
{0.23094011, 0.00000000, -0.14054567, -0.09938080, -0.13012001, 0.00000000, 0.00000000, 0.02909572, 0.02375655, 0.01679842}};
1548
1549
// Tables of derivatives of the polynomial base (transpose).
1550
static const double dmats0[10][10] = \
1551
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1552
{6.32455532, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1553
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1554
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1555
{0.00000000, 11.22497216, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1556
{4.58257569, 0.00000000, 8.36660027, -1.18321596, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1557
{3.74165739, 0.00000000, 0.00000000, 8.69482605, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1558
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1559
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1560
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
1561
1562
static const double dmats1[10][10] = \
1563
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1564
{3.16227766, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1565
{5.47722558, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1566
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1567
{2.95803989, 5.61248608, -1.08012345, -0.76376262, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1568
{2.29128785, 7.24568837, 4.18330013, -0.59160798, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1569
{1.87082869, 0.00000000, 0.00000000, 4.34741302, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1570
{-2.64575131, 0.00000000, 9.66091783, 0.68313005, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1571
{3.24037035, 0.00000000, 0.00000000, 7.52994024, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1572
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
1573
1574
static const double dmats2[10][10] = \
1575
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1576
{3.16227766, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1577
{1.82574186, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1578
{5.16397779, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1579
{2.95803989, 5.61248608, -1.08012345, -0.76376262, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1580
{2.29128785, 1.44913767, 4.18330013, -0.59160798, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1581
{1.87082869, 7.09929574, 0.00000000, 4.34741302, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1582
{1.32287566, 0.00000000, 3.86436713, -0.34156503, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1583
{1.08012345, 0.00000000, 7.09929574, 2.50998008, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1584
{-3.81881308, 0.00000000, 0.00000000, 8.87411967, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
1585
1586
// Compute reference derivatives.
1587
// Declare pointer to array of derivatives on FIAT element.
1588
double *derivatives = new double[num_derivatives];
1589
for (unsigned int r = 0; r < num_derivatives; r++)
1590
{
1591
derivatives[r] = 0.00000000;
1592
}// end loop over 'r'
1593
1594
// Declare derivative matrix (of polynomial basis).
1595
double dmats[10][10] = \
1596
{{1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1597
{0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1598
{0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1599
{0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1600
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1601
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1602
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000},
1603
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000},
1604
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000},
1605
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000}};
1606
1607
// Declare (auxiliary) derivative matrix (of polynomial basis).
1608
double dmats_old[10][10] = \
1609
{{1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1610
{0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1611
{0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1612
{0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1613
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1614
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1615
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000},
1616
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000},
1617
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000},
1618
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000}};
1619
1620
// Loop possible derivatives.
1621
for (unsigned int r = 0; r < num_derivatives; r++)
1622
{
1623
// Resetting dmats values to compute next derivative.
1624
for (unsigned int t = 0; t < 10; t++)
1625
{
1626
for (unsigned int u = 0; u < 10; u++)
1627
{
1628
dmats[t][u] = 0.00000000;
1629
if (t == u)
1630
{
1631
dmats[t][u] = 1.00000000;
1632
}
1633
1634
}// end loop over 'u'
1635
}// end loop over 't'
1636
1637
// Looping derivative order to generate dmats.
1638
for (unsigned int s = 0; s < n; s++)
1639
{
1640
// Updating dmats_old with new values and resetting dmats.
1641
for (unsigned int t = 0; t < 10; t++)
1642
{
1643
for (unsigned int u = 0; u < 10; u++)
1644
{
1645
dmats_old[t][u] = dmats[t][u];
1646
dmats[t][u] = 0.00000000;
1647
}// end loop over 'u'
1648
}// end loop over 't'
1649
1650
// Update dmats using an inner product.
1651
if (combinations[r][s] == 0)
1652
{
1653
for (unsigned int t = 0; t < 10; t++)
1654
{
1655
for (unsigned int u = 0; u < 10; u++)
1656
{
1657
for (unsigned int tu = 0; tu < 10; tu++)
1658
{
1659
dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
1660
}// end loop over 'tu'
1661
}// end loop over 'u'
1662
}// end loop over 't'
1663
}
1664
1665
if (combinations[r][s] == 1)
1666
{
1667
for (unsigned int t = 0; t < 10; t++)
1668
{
1669
for (unsigned int u = 0; u < 10; u++)
1670
{
1671
for (unsigned int tu = 0; tu < 10; tu++)
1672
{
1673
dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
1674
}// end loop over 'tu'
1675
}// end loop over 'u'
1676
}// end loop over 't'
1677
}
1678
1679
if (combinations[r][s] == 2)
1680
{
1681
for (unsigned int t = 0; t < 10; t++)
1682
{
1683
for (unsigned int u = 0; u < 10; u++)
1684
{
1685
for (unsigned int tu = 0; tu < 10; tu++)
1686
{
1687
dmats[t][u] += dmats2[t][tu]*dmats_old[tu][u];
1688
}// end loop over 'tu'
1689
}// end loop over 'u'
1690
}// end loop over 't'
1691
}
1692
1693
}// end loop over 's'
1694
for (unsigned int s = 0; s < 10; s++)
1695
{
1696
for (unsigned int t = 0; t < 10; t++)
1697
{
1698
derivatives[r] += coefficients0[dof][s]*dmats[s][t]*basisvalues[t];
1699
}// end loop over 't'
1700
}// end loop over 's'
1701
}// end loop over 'r'
1702
1703
// Transform derivatives back to physical element
1704
for (unsigned int r = 0; r < num_derivatives; r++)
1705
{
1706
for (unsigned int s = 0; s < num_derivatives; s++)
1707
{
1708
values[r] += transform[r][s]*derivatives[s];
1709
}// end loop over 's'
1710
}// end loop over 'r'
1711
1712
// Delete pointer to array of derivatives on FIAT element
1713
delete [] derivatives;
1714
1715
// Delete pointer to array of combinations of derivatives and transform
1716
for (unsigned int r = 0; r < num_derivatives; r++)
1717
{
1718
delete [] combinations[r];
1719
}// end loop over 'r'
1720
delete [] combinations;
1721
for (unsigned int r = 0; r < num_derivatives; r++)
1722
{
1723
delete [] transform[r];
1724
}// end loop over 'r'
1725
delete [] transform;
1726
}
1727
1728
if (10 <= i && i <= 19)
1729
{
1730
// Map degree of freedom to element degree of freedom
1731
const unsigned int dof = i - 10;
1732
1733
// Array of basisvalues.
1734
double basisvalues[10] = {0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000};
1735
1736
// Declare helper variables.
1737
unsigned int rr = 0;
1738
unsigned int ss = 0;
1739
unsigned int tt = 0;
1740
double tmp5 = 0.00000000;
1741
double tmp6 = 0.00000000;
1742
double tmp7 = 0.00000000;
1743
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
1744
double tmp1 = 0.25000000*(Y + Z)*(Y + Z);
1745
double tmp2 = 0.50000000*(1.00000000 + Z + 2.00000000*Y);
1746
double tmp3 = 0.50000000*(1.00000000 - Z);
1747
double tmp4 = tmp3*tmp3;
1748
1749
// Compute basisvalues.
1750
basisvalues[0] = 1.00000000;
1751
basisvalues[1] = tmp0;
1752
for (unsigned int r = 1; r < 2; r++)
1753
{
1754
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
1755
ss = r*(r + 1)*(r + 2)/6;
1756
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
1757
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.00000000 + 2.00000000*r)/(1.00000000 + r) - basisvalues[tt]*tmp1*r/(1.00000000 + r));
1758
}// end loop over 'r'
1759
for (unsigned int r = 0; r < 2; r++)
1760
{
1761
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
1762
ss = r*(r + 1)*(r + 2)/6;
1763
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
1764
}// end loop over 'r'
1765
for (unsigned int r = 0; r < 1; r++)
1766
{
1767
for (unsigned int s = 1; s < 2 - r; s++)
1768
{
1769
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
1770
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
1771
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
1772
tmp5 = (2.00000000 + 2.00000000*r + 2.00000000*s)*(3.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
1773
tmp6 = (1.00000000 + 4.00000000*r*r + 4.00000000*r)*(2.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
1774
tmp7 = (1.00000000 + s + 2.00000000*r)*(3.00000000 + 2.00000000*r + 2.00000000*s)*s/((1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
1775
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
1776
}// end loop over 's'
1777
}// end loop over 'r'
1778
for (unsigned int r = 0; r < 2; r++)
1779
{
1780
for (unsigned int s = 0; s < 2 - r; s++)
1781
{
1782
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
1783
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
1784
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
1785
}// end loop over 's'
1786
}// end loop over 'r'
1787
for (unsigned int r = 0; r < 1; r++)
1788
{
1789
for (unsigned int s = 0; s < 1 - r; s++)
1790
{
1791
for (unsigned int t = 1; t < 2 - r - s; t++)
1792
{
1793
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
1794
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
1795
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
1796
tmp5 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)/(2.00000000*(1.00000000 + t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
1797
tmp6 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 4.00000000*r*r + 4.00000000*s*s + 8.00000000*r*s + 8.00000000*r + 8.00000000*s)/(2.00000000*(1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
1798
tmp7 = (2.00000000 + t + 2.00000000*r + 2.00000000*s)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*t/((1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
1799
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
1800
}// end loop over 't'
1801
}// end loop over 's'
1802
}// end loop over 'r'
1803
for (unsigned int r = 0; r < 3; r++)
1804
{
1805
for (unsigned int s = 0; s < 3 - r; s++)
1806
{
1807
for (unsigned int t = 0; t < 3 - r - s; t++)
1808
{
1809
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
1810
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
1811
}// end loop over 't'
1812
}// end loop over 's'
1813
}// end loop over 'r'
1814
1815
// Table(s) of coefficients.
1816
static const double coefficients0[10][10] = \
1817
{{-0.05773503, -0.06085806, -0.03513642, -0.02484520, 0.06506000, 0.05039526, 0.04114756, 0.02909572, 0.02375655, 0.01679842},
1818
{-0.05773503, 0.06085806, -0.03513642, -0.02484520, 0.06506000, -0.05039526, -0.04114756, 0.02909572, 0.02375655, 0.01679842},
1819
{-0.05773503, 0.00000000, 0.07027284, -0.02484520, 0.00000000, 0.00000000, 0.00000000, 0.08728716, -0.04751311, 0.01679842},
1820
{-0.05773503, 0.00000000, 0.00000000, 0.07453560, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.10079053},
1821
{0.23094011, 0.00000000, 0.14054567, 0.09938080, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.11878277, -0.06719368},
1822
{0.23094011, 0.12171612, -0.07027284, 0.09938080, 0.00000000, 0.00000000, 0.10286890, 0.00000000, -0.05939139, -0.06719368},
1823
{0.23094011, 0.12171612, 0.07027284, -0.09938080, 0.00000000, 0.10079053, -0.02057378, -0.08728716, -0.01187828, 0.01679842},
1824
{0.23094011, -0.12171612, -0.07027284, 0.09938080, 0.00000000, 0.00000000, -0.10286890, 0.00000000, -0.05939139, -0.06719368},
1825
{0.23094011, -0.12171612, 0.07027284, -0.09938080, 0.00000000, -0.10079053, 0.02057378, -0.08728716, -0.01187828, 0.01679842},
1826
{0.23094011, 0.00000000, -0.14054567, -0.09938080, -0.13012001, 0.00000000, 0.00000000, 0.02909572, 0.02375655, 0.01679842}};
1827
1828
// Tables of derivatives of the polynomial base (transpose).
1829
static const double dmats0[10][10] = \
1830
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1831
{6.32455532, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1832
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1833
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1834
{0.00000000, 11.22497216, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1835
{4.58257569, 0.00000000, 8.36660027, -1.18321596, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1836
{3.74165739, 0.00000000, 0.00000000, 8.69482605, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1837
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1838
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1839
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
1840
1841
static const double dmats1[10][10] = \
1842
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1843
{3.16227766, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1844
{5.47722558, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1845
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1846
{2.95803989, 5.61248608, -1.08012345, -0.76376262, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1847
{2.29128785, 7.24568837, 4.18330013, -0.59160798, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1848
{1.87082869, 0.00000000, 0.00000000, 4.34741302, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1849
{-2.64575131, 0.00000000, 9.66091783, 0.68313005, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1850
{3.24037035, 0.00000000, 0.00000000, 7.52994024, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1851
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
1852
1853
static const double dmats2[10][10] = \
1854
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1855
{3.16227766, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1856
{1.82574186, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1857
{5.16397779, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1858
{2.95803989, 5.61248608, -1.08012345, -0.76376262, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1859
{2.29128785, 1.44913767, 4.18330013, -0.59160798, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1860
{1.87082869, 7.09929574, 0.00000000, 4.34741302, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1861
{1.32287566, 0.00000000, 3.86436713, -0.34156503, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1862
{1.08012345, 0.00000000, 7.09929574, 2.50998008, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1863
{-3.81881308, 0.00000000, 0.00000000, 8.87411967, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
1864
1865
// Compute reference derivatives.
1866
// Declare pointer to array of derivatives on FIAT element.
1867
double *derivatives = new double[num_derivatives];
1868
for (unsigned int r = 0; r < num_derivatives; r++)
1869
{
1870
derivatives[r] = 0.00000000;
1871
}// end loop over 'r'
1872
1873
// Declare derivative matrix (of polynomial basis).
1874
double dmats[10][10] = \
1875
{{1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1876
{0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1877
{0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1878
{0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1879
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1880
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1881
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000},
1882
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000},
1883
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000},
1884
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000}};
1885
1886
// Declare (auxiliary) derivative matrix (of polynomial basis).
1887
double dmats_old[10][10] = \
1888
{{1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1889
{0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1890
{0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1891
{0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1892
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1893
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
1894
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000},
1895
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000},
1896
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000},
1897
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000}};
1898
1899
// Loop possible derivatives.
1900
for (unsigned int r = 0; r < num_derivatives; r++)
1901
{
1902
// Resetting dmats values to compute next derivative.
1903
for (unsigned int t = 0; t < 10; t++)
1904
{
1905
for (unsigned int u = 0; u < 10; u++)
1906
{
1907
dmats[t][u] = 0.00000000;
1908
if (t == u)
1909
{
1910
dmats[t][u] = 1.00000000;
1911
}
1912
1913
}// end loop over 'u'
1914
}// end loop over 't'
1915
1916
// Looping derivative order to generate dmats.
1917
for (unsigned int s = 0; s < n; s++)
1918
{
1919
// Updating dmats_old with new values and resetting dmats.
1920
for (unsigned int t = 0; t < 10; t++)
1921
{
1922
for (unsigned int u = 0; u < 10; u++)
1923
{
1924
dmats_old[t][u] = dmats[t][u];
1925
dmats[t][u] = 0.00000000;
1926
}// end loop over 'u'
1927
}// end loop over 't'
1928
1929
// Update dmats using an inner product.
1930
if (combinations[r][s] == 0)
1931
{
1932
for (unsigned int t = 0; t < 10; t++)
1933
{
1934
for (unsigned int u = 0; u < 10; u++)
1935
{
1936
for (unsigned int tu = 0; tu < 10; tu++)
1937
{
1938
dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
1939
}// end loop over 'tu'
1940
}// end loop over 'u'
1941
}// end loop over 't'
1942
}
1943
1944
if (combinations[r][s] == 1)
1945
{
1946
for (unsigned int t = 0; t < 10; t++)
1947
{
1948
for (unsigned int u = 0; u < 10; u++)
1949
{
1950
for (unsigned int tu = 0; tu < 10; tu++)
1951
{
1952
dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
1953
}// end loop over 'tu'
1954
}// end loop over 'u'
1955
}// end loop over 't'
1956
}
1957
1958
if (combinations[r][s] == 2)
1959
{
1960
for (unsigned int t = 0; t < 10; t++)
1961
{
1962
for (unsigned int u = 0; u < 10; u++)
1963
{
1964
for (unsigned int tu = 0; tu < 10; tu++)
1965
{
1966
dmats[t][u] += dmats2[t][tu]*dmats_old[tu][u];
1967
}// end loop over 'tu'
1968
}// end loop over 'u'
1969
}// end loop over 't'
1970
}
1971
1972
}// end loop over 's'
1973
for (unsigned int s = 0; s < 10; s++)
1974
{
1975
for (unsigned int t = 0; t < 10; t++)
1976
{
1977
derivatives[r] += coefficients0[dof][s]*dmats[s][t]*basisvalues[t];
1978
}// end loop over 't'
1979
}// end loop over 's'
1980
}// end loop over 'r'
1981
1982
// Transform derivatives back to physical element
1983
for (unsigned int r = 0; r < num_derivatives; r++)
1984
{
1985
for (unsigned int s = 0; s < num_derivatives; s++)
1986
{
1987
values[num_derivatives + r] += transform[r][s]*derivatives[s];
1988
}// end loop over 's'
1989
}// end loop over 'r'
1990
1991
// Delete pointer to array of derivatives on FIAT element
1992
delete [] derivatives;
1993
1994
// Delete pointer to array of combinations of derivatives and transform
1995
for (unsigned int r = 0; r < num_derivatives; r++)
1996
{
1997
delete [] combinations[r];
1998
}// end loop over 'r'
1999
delete [] combinations;
2000
for (unsigned int r = 0; r < num_derivatives; r++)
2001
{
2002
delete [] transform[r];
2003
}// end loop over 'r'
2004
delete [] transform;
2005
}
2006
2007
if (20 <= i && i <= 29)
2008
{
2009
// Map degree of freedom to element degree of freedom
2010
const unsigned int dof = i - 20;
2011
2012
// Array of basisvalues.
2013
double basisvalues[10] = {0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000};
2014
2015
// Declare helper variables.
2016
unsigned int rr = 0;
2017
unsigned int ss = 0;
2018
unsigned int tt = 0;
2019
double tmp5 = 0.00000000;
2020
double tmp6 = 0.00000000;
2021
double tmp7 = 0.00000000;
2022
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
2023
double tmp1 = 0.25000000*(Y + Z)*(Y + Z);
2024
double tmp2 = 0.50000000*(1.00000000 + Z + 2.00000000*Y);
2025
double tmp3 = 0.50000000*(1.00000000 - Z);
2026
double tmp4 = tmp3*tmp3;
2027
2028
// Compute basisvalues.
2029
basisvalues[0] = 1.00000000;
2030
basisvalues[1] = tmp0;
2031
for (unsigned int r = 1; r < 2; r++)
2032
{
2033
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
2034
ss = r*(r + 1)*(r + 2)/6;
2035
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
2036
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.00000000 + 2.00000000*r)/(1.00000000 + r) - basisvalues[tt]*tmp1*r/(1.00000000 + r));
2037
}// end loop over 'r'
2038
for (unsigned int r = 0; r < 2; r++)
2039
{
2040
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
2041
ss = r*(r + 1)*(r + 2)/6;
2042
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
2043
}// end loop over 'r'
2044
for (unsigned int r = 0; r < 1; r++)
2045
{
2046
for (unsigned int s = 1; s < 2 - r; s++)
2047
{
2048
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
2049
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
2050
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
2051
tmp5 = (2.00000000 + 2.00000000*r + 2.00000000*s)*(3.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
2052
tmp6 = (1.00000000 + 4.00000000*r*r + 4.00000000*r)*(2.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
2053
tmp7 = (1.00000000 + s + 2.00000000*r)*(3.00000000 + 2.00000000*r + 2.00000000*s)*s/((1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
2054
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
2055
}// end loop over 's'
2056
}// end loop over 'r'
2057
for (unsigned int r = 0; r < 2; r++)
2058
{
2059
for (unsigned int s = 0; s < 2 - r; s++)
2060
{
2061
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
2062
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
2063
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
2064
}// end loop over 's'
2065
}// end loop over 'r'
2066
for (unsigned int r = 0; r < 1; r++)
2067
{
2068
for (unsigned int s = 0; s < 1 - r; s++)
2069
{
2070
for (unsigned int t = 1; t < 2 - r - s; t++)
2071
{
2072
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
2073
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
2074
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
2075
tmp5 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)/(2.00000000*(1.00000000 + t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
2076
tmp6 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 4.00000000*r*r + 4.00000000*s*s + 8.00000000*r*s + 8.00000000*r + 8.00000000*s)/(2.00000000*(1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
2077
tmp7 = (2.00000000 + t + 2.00000000*r + 2.00000000*s)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*t/((1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
2078
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
2079
}// end loop over 't'
2080
}// end loop over 's'
2081
}// end loop over 'r'
2082
for (unsigned int r = 0; r < 3; r++)
2083
{
2084
for (unsigned int s = 0; s < 3 - r; s++)
2085
{
2086
for (unsigned int t = 0; t < 3 - r - s; t++)
2087
{
2088
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
2089
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
2090
}// end loop over 't'
2091
}// end loop over 's'
2092
}// end loop over 'r'
2093
2094
// Table(s) of coefficients.
2095
static const double coefficients0[10][10] = \
2096
{{-0.05773503, -0.06085806, -0.03513642, -0.02484520, 0.06506000, 0.05039526, 0.04114756, 0.02909572, 0.02375655, 0.01679842},
2097
{-0.05773503, 0.06085806, -0.03513642, -0.02484520, 0.06506000, -0.05039526, -0.04114756, 0.02909572, 0.02375655, 0.01679842},
2098
{-0.05773503, 0.00000000, 0.07027284, -0.02484520, 0.00000000, 0.00000000, 0.00000000, 0.08728716, -0.04751311, 0.01679842},
2099
{-0.05773503, 0.00000000, 0.00000000, 0.07453560, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.10079053},
2100
{0.23094011, 0.00000000, 0.14054567, 0.09938080, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.11878277, -0.06719368},
2101
{0.23094011, 0.12171612, -0.07027284, 0.09938080, 0.00000000, 0.00000000, 0.10286890, 0.00000000, -0.05939139, -0.06719368},
2102
{0.23094011, 0.12171612, 0.07027284, -0.09938080, 0.00000000, 0.10079053, -0.02057378, -0.08728716, -0.01187828, 0.01679842},
2103
{0.23094011, -0.12171612, -0.07027284, 0.09938080, 0.00000000, 0.00000000, -0.10286890, 0.00000000, -0.05939139, -0.06719368},
2104
{0.23094011, -0.12171612, 0.07027284, -0.09938080, 0.00000000, -0.10079053, 0.02057378, -0.08728716, -0.01187828, 0.01679842},
2105
{0.23094011, 0.00000000, -0.14054567, -0.09938080, -0.13012001, 0.00000000, 0.00000000, 0.02909572, 0.02375655, 0.01679842}};
2106
2107
// Tables of derivatives of the polynomial base (transpose).
2108
static const double dmats0[10][10] = \
2109
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2110
{6.32455532, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2111
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2112
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2113
{0.00000000, 11.22497216, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2114
{4.58257569, 0.00000000, 8.36660027, -1.18321596, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2115
{3.74165739, 0.00000000, 0.00000000, 8.69482605, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2116
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2117
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2118
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
2119
2120
static const double dmats1[10][10] = \
2121
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2122
{3.16227766, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2123
{5.47722558, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2124
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2125
{2.95803989, 5.61248608, -1.08012345, -0.76376262, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2126
{2.29128785, 7.24568837, 4.18330013, -0.59160798, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2127
{1.87082869, 0.00000000, 0.00000000, 4.34741302, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2128
{-2.64575131, 0.00000000, 9.66091783, 0.68313005, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2129
{3.24037035, 0.00000000, 0.00000000, 7.52994024, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2130
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
2131
2132
static const double dmats2[10][10] = \
2133
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2134
{3.16227766, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2135
{1.82574186, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2136
{5.16397779, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2137
{2.95803989, 5.61248608, -1.08012345, -0.76376262, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2138
{2.29128785, 1.44913767, 4.18330013, -0.59160798, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2139
{1.87082869, 7.09929574, 0.00000000, 4.34741302, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2140
{1.32287566, 0.00000000, 3.86436713, -0.34156503, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2141
{1.08012345, 0.00000000, 7.09929574, 2.50998008, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2142
{-3.81881308, 0.00000000, 0.00000000, 8.87411967, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
2143
2144
// Compute reference derivatives.
2145
// Declare pointer to array of derivatives on FIAT element.
2146
double *derivatives = new double[num_derivatives];
2147
for (unsigned int r = 0; r < num_derivatives; r++)
2148
{
2149
derivatives[r] = 0.00000000;
2150
}// end loop over 'r'
2151
2152
// Declare derivative matrix (of polynomial basis).
2153
double dmats[10][10] = \
2154
{{1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2155
{0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2156
{0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2157
{0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2158
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2159
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2160
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000},
2161
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000},
2162
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000},
2163
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000}};
2164
2165
// Declare (auxiliary) derivative matrix (of polynomial basis).
2166
double dmats_old[10][10] = \
2167
{{1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2168
{0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2169
{0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2170
{0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2171
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2172
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
2173
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000},
2174
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000},
2175
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000},
2176
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000}};
2177
2178
// Loop possible derivatives.
2179
for (unsigned int r = 0; r < num_derivatives; r++)
2180
{
2181
// Resetting dmats values to compute next derivative.
2182
for (unsigned int t = 0; t < 10; t++)
2183
{
2184
for (unsigned int u = 0; u < 10; u++)
2185
{
2186
dmats[t][u] = 0.00000000;
2187
if (t == u)
2188
{
2189
dmats[t][u] = 1.00000000;
2190
}
2191
2192
}// end loop over 'u'
2193
}// end loop over 't'
2194
2195
// Looping derivative order to generate dmats.
2196
for (unsigned int s = 0; s < n; s++)
2197
{
2198
// Updating dmats_old with new values and resetting dmats.
2199
for (unsigned int t = 0; t < 10; t++)
2200
{
2201
for (unsigned int u = 0; u < 10; u++)
2202
{
2203
dmats_old[t][u] = dmats[t][u];
2204
dmats[t][u] = 0.00000000;
2205
}// end loop over 'u'
2206
}// end loop over 't'
2207
2208
// Update dmats using an inner product.
2209
if (combinations[r][s] == 0)
2210
{
2211
for (unsigned int t = 0; t < 10; t++)
2212
{
2213
for (unsigned int u = 0; u < 10; u++)
2214
{
2215
for (unsigned int tu = 0; tu < 10; tu++)
2216
{
2217
dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
2218
}// end loop over 'tu'
2219
}// end loop over 'u'
2220
}// end loop over 't'
2221
}
2222
2223
if (combinations[r][s] == 1)
2224
{
2225
for (unsigned int t = 0; t < 10; t++)
2226
{
2227
for (unsigned int u = 0; u < 10; u++)
2228
{
2229
for (unsigned int tu = 0; tu < 10; tu++)
2230
{
2231
dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
2232
}// end loop over 'tu'
2233
}// end loop over 'u'
2234
}// end loop over 't'
2235
}
2236
2237
if (combinations[r][s] == 2)
2238
{
2239
for (unsigned int t = 0; t < 10; t++)
2240
{
2241
for (unsigned int u = 0; u < 10; u++)
2242
{
2243
for (unsigned int tu = 0; tu < 10; tu++)
2244
{
2245
dmats[t][u] += dmats2[t][tu]*dmats_old[tu][u];
2246
}// end loop over 'tu'
2247
}// end loop over 'u'
2248
}// end loop over 't'
2249
}
2250
2251
}// end loop over 's'
2252
for (unsigned int s = 0; s < 10; s++)
2253
{
2254
for (unsigned int t = 0; t < 10; t++)
2255
{
2256
derivatives[r] += coefficients0[dof][s]*dmats[s][t]*basisvalues[t];
2257
}// end loop over 't'
2258
}// end loop over 's'
2259
}// end loop over 'r'
2260
2261
// Transform derivatives back to physical element
2262
for (unsigned int r = 0; r < num_derivatives; r++)
2263
{
2264
for (unsigned int s = 0; s < num_derivatives; s++)
2265
{
2266
values[2*num_derivatives + r] += transform[r][s]*derivatives[s];
2267
}// end loop over 's'
2268
}// end loop over 'r'
2269
2270
// Delete pointer to array of derivatives on FIAT element
2271
delete [] derivatives;
2272
2273
// Delete pointer to array of combinations of derivatives and transform
2274
for (unsigned int r = 0; r < num_derivatives; r++)
2275
{
2276
delete [] combinations[r];
2277
}// end loop over 'r'
2278
delete [] combinations;
2279
for (unsigned int r = 0; r < num_derivatives; r++)
2280
{
2281
delete [] transform[r];
2282
}// end loop over 'r'
2283
delete [] transform;
7281
switch (i)
7282
{
7283
case 0:
7284
{
7285
7286
// Array of basisvalues.
7287
double basisvalues[10] = {0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000};
7288
7289
// Declare helper variables.
7290
unsigned int rr = 0;
7291
unsigned int ss = 0;
7292
unsigned int tt = 0;
7293
double tmp5 = 0.00000000;
7294
double tmp6 = 0.00000000;
7295
double tmp7 = 0.00000000;
7296
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
7297
double tmp1 = 0.25000000*(Y + Z)*(Y + Z);
7298
double tmp2 = 0.50000000*(1.00000000 + Z + 2.00000000*Y);
7299
double tmp3 = 0.50000000*(1.00000000 - Z);
7300
double tmp4 = tmp3*tmp3;
7301
7302
// Compute basisvalues.
7303
basisvalues[0] = 1.00000000;
7304
basisvalues[1] = tmp0;
7305
for (unsigned int r = 1; r < 2; r++)
7306
{
7307
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
7308
ss = r*(r + 1)*(r + 2)/6;
7309
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
7310
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.00000000 + 2.00000000*r)/(1.00000000 + r) - basisvalues[tt]*tmp1*r/(1.00000000 + r));
7311
}// end loop over 'r'
7312
for (unsigned int r = 0; r < 2; r++)
7313
{
7314
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
7315
ss = r*(r + 1)*(r + 2)/6;
7316
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
7317
}// end loop over 'r'
7318
for (unsigned int r = 0; r < 1; r++)
7319
{
7320
for (unsigned int s = 1; s < 2 - r; s++)
7321
{
7322
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
7323
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
7324
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
7325
tmp5 = (2.00000000 + 2.00000000*r + 2.00000000*s)*(3.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
7326
tmp6 = (1.00000000 + 4.00000000*r*r + 4.00000000*r)*(2.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
7327
tmp7 = (1.00000000 + s + 2.00000000*r)*(3.00000000 + 2.00000000*r + 2.00000000*s)*s/((1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
7328
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
7329
}// end loop over 's'
7330
}// end loop over 'r'
7331
for (unsigned int r = 0; r < 2; r++)
7332
{
7333
for (unsigned int s = 0; s < 2 - r; s++)
7334
{
7335
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
7336
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
7337
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
7338
}// end loop over 's'
7339
}// end loop over 'r'
7340
for (unsigned int r = 0; r < 1; r++)
7341
{
7342
for (unsigned int s = 0; s < 1 - r; s++)
7343
{
7344
for (unsigned int t = 1; t < 2 - r - s; t++)
7345
{
7346
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
7347
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
7348
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
7349
tmp5 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)/(2.00000000*(1.00000000 + t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
7350
tmp6 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 4.00000000*r*r + 4.00000000*s*s + 8.00000000*r*s + 8.00000000*r + 8.00000000*s)/(2.00000000*(1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
7351
tmp7 = (2.00000000 + t + 2.00000000*r + 2.00000000*s)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*t/((1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
7352
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
7353
}// end loop over 't'
7354
}// end loop over 's'
7355
}// end loop over 'r'
7356
for (unsigned int r = 0; r < 3; r++)
7357
{
7358
for (unsigned int s = 0; s < 3 - r; s++)
7359
{
7360
for (unsigned int t = 0; t < 3 - r - s; t++)
7361
{
7362
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
7363
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
7364
}// end loop over 't'
7365
}// end loop over 's'
7366
}// end loop over 'r'
7367
7368
// Table(s) of coefficients.
7369
static const double coefficients0[10] = \
7370
{-0.05773503, -0.06085806, -0.03513642, -0.02484520, 0.06506000, 0.05039526, 0.04114756, 0.02909572, 0.02375655, 0.01679842};
7371
7372
// Tables of derivatives of the polynomial base (transpose).
7373
static const double dmats0[10][10] = \
7374
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
7375
{6.32455532, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
7376
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
7377
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
7378
{0.00000000, 11.22497216, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
7379
{4.58257569, 0.00000000, 8.36660027, -1.18321596, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
7380
{3.74165739, 0.00000000, 0.00000000, 8.69482605, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
7381
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
7382
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
7383
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
7384
7385
static const double dmats1[10][10] = \
7386
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
7387
{3.16227766, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
7388
{5.47722558, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
7389
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
7390
{2.95803989, 5.61248608, -1.08012345, -0.76376262, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
7391
{2.29128785, 7.24568837, 4.18330013, -0.59160798, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
7392
{1.87082869, 0.00000000, 0.00000000, 4.34741302, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
7393
{-2.64575131, 0.00000000, 9.66091783, 0.68313005, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
7394
{3.24037035, 0.00000000, 0.00000000, 7.52994024, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
7395
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
7396
7397
static const double dmats2[10][10] = \
7398
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
7399
{3.16227766, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
7400
{1.82574186, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
7401
{5.16397779, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
7402
{2.95803989, 5.61248608, -1.08012345, -0.76376262, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
7403
{2.29128785, 1.44913767, 4.18330013, -0.59160798, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
7404
{1.87082869, 7.09929574, 0.00000000, 4.34741302, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
7405
{1.32287566, 0.00000000, 3.86436713, -0.34156503, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
7406
{1.08012345, 0.00000000, 7.09929574, 2.50998008, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
7407
{-3.81881308, 0.00000000, 0.00000000, 8.87411967, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
7408
7409
// Compute reference derivatives.
7410
// Declare pointer to array of derivatives on FIAT element.
7411
double *derivatives = new double[num_derivatives];
7412
for (unsigned int r = 0; r < num_derivatives; r++)
7413
{
7414
derivatives[r] = 0.00000000;
7415
}// end loop over 'r'
7416
7417
// Declare derivative matrix (of polynomial basis).
7418
double dmats[10][10] = \
7419
{{1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
7420
{0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
7421
{0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
7422
{0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
7423
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
7424
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
7425
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000},
7426
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000},
7427
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000},
7428
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000}};
7429
7430
// Declare (auxiliary) derivative matrix (of polynomial basis).
7431
double dmats_old[10][10] = \
7432
{{1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
7433
{0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
7434
{0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
7435
{0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
7436
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
7437
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
7438
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000},
7439
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000},
7440
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000},
7441
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000}};
7442
7443
// Loop possible derivatives.
7444
for (unsigned int r = 0; r < num_derivatives; r++)
7445
{
7446
// Resetting dmats values to compute next derivative.
7447
for (unsigned int t = 0; t < 10; t++)
7448
{
7449
for (unsigned int u = 0; u < 10; u++)
7450
{
7451
dmats[t][u] = 0.00000000;
7452
if (t == u)
7453
{
7454
dmats[t][u] = 1.00000000;
7455
}
7456
7457
}// end loop over 'u'
7458
}// end loop over 't'
7459
7460
// Looping derivative order to generate dmats.
7461
for (unsigned int s = 0; s < n; s++)
7462
{
7463
// Updating dmats_old with new values and resetting dmats.
7464
for (unsigned int t = 0; t < 10; t++)
7465
{
7466
for (unsigned int u = 0; u < 10; u++)
7467
{
7468
dmats_old[t][u] = dmats[t][u];
7469
dmats[t][u] = 0.00000000;
7470
}// end loop over 'u'
7471
}// end loop over 't'
7472
7473
// Update dmats using an inner product.
7474
if (combinations[r][s] == 0)
7475
{
7476
for (unsigned int t = 0; t < 10; t++)
7477
{
7478
for (unsigned int u = 0; u < 10; u++)
7479
{
7480
for (unsigned int tu = 0; tu < 10; tu++)
7481
{
7482
dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
7483
}// end loop over 'tu'
7484
}// end loop over 'u'
7485
}// end loop over 't'
7486
}
7487
7488
if (combinations[r][s] == 1)
7489
{
7490
for (unsigned int t = 0; t < 10; t++)
7491
{
7492
for (unsigned int u = 0; u < 10; u++)
7493
{
7494
for (unsigned int tu = 0; tu < 10; tu++)
7495
{
7496
dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
7497
}// end loop over 'tu'
7498
}// end loop over 'u'
7499
}// end loop over 't'
7500
}
7501
7502
if (combinations[r][s] == 2)
7503
{
7504
for (unsigned int t = 0; t < 10; t++)
7505
{
7506
for (unsigned int u = 0; u < 10; u++)
7507
{
7508
for (unsigned int tu = 0; tu < 10; tu++)
7509
{
7510
dmats[t][u] += dmats2[t][tu]*dmats_old[tu][u];
7511
}// end loop over 'tu'
7512
}// end loop over 'u'
7513
}// end loop over 't'
7514
}
7515
7516
}// end loop over 's'
7517
for (unsigned int s = 0; s < 10; s++)
7518
{
7519
for (unsigned int t = 0; t < 10; t++)
7520
{
7521
derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
7522
}// end loop over 't'
7523
}// end loop over 's'
7524
}// end loop over 'r'
7525
7526
// Transform derivatives back to physical element
7527
for (unsigned int r = 0; r < num_derivatives; r++)
7528
{
7529
for (unsigned int s = 0; s < num_derivatives; s++)
7530
{
7531
values[r] += transform[r][s]*derivatives[s];
7532
}// end loop over 's'
7533
}// end loop over 'r'
7534
7535
// Delete pointer to array of derivatives on FIAT element
7536
delete [] derivatives;
7537
7538
// Delete pointer to array of combinations of derivatives and transform
7539
for (unsigned int r = 0; r < num_derivatives; r++)
7540
{
7541
delete [] combinations[r];
7542
}// end loop over 'r'
7543
delete [] combinations;
7544
for (unsigned int r = 0; r < num_derivatives; r++)
7545
{
7546
delete [] transform[r];
7547
}// end loop over 'r'
7548
delete [] transform;
7549
break;
7550
}
7551
case 1:
7552
{
7553
7554
// Array of basisvalues.
7555
double basisvalues[10] = {0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000};
7556
7557
// Declare helper variables.
7558
unsigned int rr = 0;
7559
unsigned int ss = 0;
7560
unsigned int tt = 0;
7561
double tmp5 = 0.00000000;
7562
double tmp6 = 0.00000000;
7563
double tmp7 = 0.00000000;
7564
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
7565
double tmp1 = 0.25000000*(Y + Z)*(Y + Z);
7566
double tmp2 = 0.50000000*(1.00000000 + Z + 2.00000000*Y);
7567
double tmp3 = 0.50000000*(1.00000000 - Z);
7568
double tmp4 = tmp3*tmp3;
7569
7570
// Compute basisvalues.
7571
basisvalues[0] = 1.00000000;
7572
basisvalues[1] = tmp0;
7573
for (unsigned int r = 1; r < 2; r++)
7574
{
7575
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
7576
ss = r*(r + 1)*(r + 2)/6;
7577
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
7578
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.00000000 + 2.00000000*r)/(1.00000000 + r) - basisvalues[tt]*tmp1*r/(1.00000000 + r));
7579
}// end loop over 'r'
7580
for (unsigned int r = 0; r < 2; r++)
7581
{
7582
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
7583
ss = r*(r + 1)*(r + 2)/6;
7584
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
7585
}// end loop over 'r'
7586
for (unsigned int r = 0; r < 1; r++)
7587
{
7588
for (unsigned int s = 1; s < 2 - r; s++)
7589
{
7590
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
7591
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
7592
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
7593
tmp5 = (2.00000000 + 2.00000000*r + 2.00000000*s)*(3.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
7594
tmp6 = (1.00000000 + 4.00000000*r*r + 4.00000000*r)*(2.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
7595
tmp7 = (1.00000000 + s + 2.00000000*r)*(3.00000000 + 2.00000000*r + 2.00000000*s)*s/((1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
7596
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
7597
}// end loop over 's'
7598
}// end loop over 'r'
7599
for (unsigned int r = 0; r < 2; r++)
7600
{
7601
for (unsigned int s = 0; s < 2 - r; s++)
7602
{
7603
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
7604
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
7605
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
7606
}// end loop over 's'
7607
}// end loop over 'r'
7608
for (unsigned int r = 0; r < 1; r++)
7609
{
7610
for (unsigned int s = 0; s < 1 - r; s++)
7611
{
7612
for (unsigned int t = 1; t < 2 - r - s; t++)
7613
{
7614
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
7615
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
7616
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
7617
tmp5 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)/(2.00000000*(1.00000000 + t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
7618
tmp6 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 4.00000000*r*r + 4.00000000*s*s + 8.00000000*r*s + 8.00000000*r + 8.00000000*s)/(2.00000000*(1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
7619
tmp7 = (2.00000000 + t + 2.00000000*r + 2.00000000*s)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*t/((1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
7620
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
7621
}// end loop over 't'
7622
}// end loop over 's'
7623
}// end loop over 'r'
7624
for (unsigned int r = 0; r < 3; r++)
7625
{
7626
for (unsigned int s = 0; s < 3 - r; s++)
7627
{
7628
for (unsigned int t = 0; t < 3 - r - s; t++)
7629
{
7630
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
7631
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
7632
}// end loop over 't'
7633
}// end loop over 's'
7634
}// end loop over 'r'
7635
7636
// Table(s) of coefficients.
7637
static const double coefficients0[10] = \
7638
{-0.05773503, 0.06085806, -0.03513642, -0.02484520, 0.06506000, -0.05039526, -0.04114756, 0.02909572, 0.02375655, 0.01679842};
7639
7640
// Tables of derivatives of the polynomial base (transpose).
7641
static const double dmats0[10][10] = \
7642
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
7643
{6.32455532, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
7644
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
7645
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
7646
{0.00000000, 11.22497216, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
7647
{4.58257569, 0.00000000, 8.36660027, -1.18321596, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
7648
{3.74165739, 0.00000000, 0.00000000, 8.69482605, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
7649
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
7650
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
7651
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
7652
7653
static const double dmats1[10][10] = \
7654
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
7655
{3.16227766, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
7656
{5.47722558, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
7657
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
7658
{2.95803989, 5.61248608, -1.08012345, -0.76376262, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
7659
{2.29128785, 7.24568837, 4.18330013, -0.59160798, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
7660
{1.87082869, 0.00000000, 0.00000000, 4.34741302, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
7661
{-2.64575131, 0.00000000, 9.66091783, 0.68313005, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
7662
{3.24037035, 0.00000000, 0.00000000, 7.52994024, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
7663
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
7664
7665
static const double dmats2[10][10] = \
7666
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
7667
{3.16227766, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
7668
{1.82574186, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
7669
{5.16397779, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
7670
{2.95803989, 5.61248608, -1.08012345, -0.76376262, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
7671
{2.29128785, 1.44913767, 4.18330013, -0.59160798, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
7672
{1.87082869, 7.09929574, 0.00000000, 4.34741302, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
7673
{1.32287566, 0.00000000, 3.86436713, -0.34156503, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
7674
{1.08012345, 0.00000000, 7.09929574, 2.50998008, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
7675
{-3.81881308, 0.00000000, 0.00000000, 8.87411967, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
7676
7677
// Compute reference derivatives.
7678
// Declare pointer to array of derivatives on FIAT element.
7679
double *derivatives = new double[num_derivatives];
7680
for (unsigned int r = 0; r < num_derivatives; r++)
7681
{
7682
derivatives[r] = 0.00000000;
7683
}// end loop over 'r'
7684
7685
// Declare derivative matrix (of polynomial basis).
7686
double dmats[10][10] = \
7687
{{1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
7688
{0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
7689
{0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
7690
{0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
7691
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
7692
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
7693
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000},
7694
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000},
7695
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000},
7696
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000}};
7697
7698
// Declare (auxiliary) derivative matrix (of polynomial basis).
7699
double dmats_old[10][10] = \
7700
{{1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
7701
{0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
7702
{0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
7703
{0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
7704
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
7705
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
7706
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000},
7707
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000},
7708
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000},
7709
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000}};
7710
7711
// Loop possible derivatives.
7712
for (unsigned int r = 0; r < num_derivatives; r++)
7713
{
7714
// Resetting dmats values to compute next derivative.
7715
for (unsigned int t = 0; t < 10; t++)
7716
{
7717
for (unsigned int u = 0; u < 10; u++)
7718
{
7719
dmats[t][u] = 0.00000000;
7720
if (t == u)
7721
{
7722
dmats[t][u] = 1.00000000;
7723
}
7724
7725
}// end loop over 'u'
7726
}// end loop over 't'
7727
7728
// Looping derivative order to generate dmats.
7729
for (unsigned int s = 0; s < n; s++)
7730
{
7731
// Updating dmats_old with new values and resetting dmats.
7732
for (unsigned int t = 0; t < 10; t++)
7733
{
7734
for (unsigned int u = 0; u < 10; u++)
7735
{
7736
dmats_old[t][u] = dmats[t][u];
7737
dmats[t][u] = 0.00000000;
7738
}// end loop over 'u'
7739
}// end loop over 't'
7740
7741
// Update dmats using an inner product.
7742
if (combinations[r][s] == 0)
7743
{
7744
for (unsigned int t = 0; t < 10; t++)
7745
{
7746
for (unsigned int u = 0; u < 10; u++)
7747
{
7748
for (unsigned int tu = 0; tu < 10; tu++)
7749
{
7750
dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
7751
}// end loop over 'tu'
7752
}// end loop over 'u'
7753
}// end loop over 't'
7754
}
7755
7756
if (combinations[r][s] == 1)
7757
{
7758
for (unsigned int t = 0; t < 10; t++)
7759
{
7760
for (unsigned int u = 0; u < 10; u++)
7761
{
7762
for (unsigned int tu = 0; tu < 10; tu++)
7763
{
7764
dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
7765
}// end loop over 'tu'
7766
}// end loop over 'u'
7767
}// end loop over 't'
7768
}
7769
7770
if (combinations[r][s] == 2)
7771
{
7772
for (unsigned int t = 0; t < 10; t++)
7773
{
7774
for (unsigned int u = 0; u < 10; u++)
7775
{
7776
for (unsigned int tu = 0; tu < 10; tu++)
7777
{
7778
dmats[t][u] += dmats2[t][tu]*dmats_old[tu][u];
7779
}// end loop over 'tu'
7780
}// end loop over 'u'
7781
}// end loop over 't'
7782
}
7783
7784
}// end loop over 's'
7785
for (unsigned int s = 0; s < 10; s++)
7786
{
7787
for (unsigned int t = 0; t < 10; t++)
7788
{
7789
derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
7790
}// end loop over 't'
7791
}// end loop over 's'
7792
}// end loop over 'r'
7793
7794
// Transform derivatives back to physical element
7795
for (unsigned int r = 0; r < num_derivatives; r++)
7796
{
7797
for (unsigned int s = 0; s < num_derivatives; s++)
7798
{
7799
values[r] += transform[r][s]*derivatives[s];
7800
}// end loop over 's'
7801
}// end loop over 'r'
7802
7803
// Delete pointer to array of derivatives on FIAT element
7804
delete [] derivatives;
7805
7806
// Delete pointer to array of combinations of derivatives and transform
7807
for (unsigned int r = 0; r < num_derivatives; r++)
7808
{
7809
delete [] combinations[r];
7810
}// end loop over 'r'
7811
delete [] combinations;
7812
for (unsigned int r = 0; r < num_derivatives; r++)
7813
{
7814
delete [] transform[r];
7815
}// end loop over 'r'
7816
delete [] transform;
7817
break;
7818
}
7819
case 2:
7820
{
7821
7822
// Array of basisvalues.
7823
double basisvalues[10] = {0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000};
7824
7825
// Declare helper variables.
7826
unsigned int rr = 0;
7827
unsigned int ss = 0;
7828
unsigned int tt = 0;
7829
double tmp5 = 0.00000000;
7830
double tmp6 = 0.00000000;
7831
double tmp7 = 0.00000000;
7832
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
7833
double tmp1 = 0.25000000*(Y + Z)*(Y + Z);
7834
double tmp2 = 0.50000000*(1.00000000 + Z + 2.00000000*Y);
7835
double tmp3 = 0.50000000*(1.00000000 - Z);
7836
double tmp4 = tmp3*tmp3;
7837
7838
// Compute basisvalues.
7839
basisvalues[0] = 1.00000000;
7840
basisvalues[1] = tmp0;
7841
for (unsigned int r = 1; r < 2; r++)
7842
{
7843
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
7844
ss = r*(r + 1)*(r + 2)/6;
7845
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
7846
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.00000000 + 2.00000000*r)/(1.00000000 + r) - basisvalues[tt]*tmp1*r/(1.00000000 + r));
7847
}// end loop over 'r'
7848
for (unsigned int r = 0; r < 2; r++)
7849
{
7850
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
7851
ss = r*(r + 1)*(r + 2)/6;
7852
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
7853
}// end loop over 'r'
7854
for (unsigned int r = 0; r < 1; r++)
7855
{
7856
for (unsigned int s = 1; s < 2 - r; s++)
7857
{
7858
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
7859
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
7860
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
7861
tmp5 = (2.00000000 + 2.00000000*r + 2.00000000*s)*(3.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
7862
tmp6 = (1.00000000 + 4.00000000*r*r + 4.00000000*r)*(2.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
7863
tmp7 = (1.00000000 + s + 2.00000000*r)*(3.00000000 + 2.00000000*r + 2.00000000*s)*s/((1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
7864
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
7865
}// end loop over 's'
7866
}// end loop over 'r'
7867
for (unsigned int r = 0; r < 2; r++)
7868
{
7869
for (unsigned int s = 0; s < 2 - r; s++)
7870
{
7871
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
7872
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
7873
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
7874
}// end loop over 's'
7875
}// end loop over 'r'
7876
for (unsigned int r = 0; r < 1; r++)
7877
{
7878
for (unsigned int s = 0; s < 1 - r; s++)
7879
{
7880
for (unsigned int t = 1; t < 2 - r - s; t++)
7881
{
7882
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
7883
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
7884
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
7885
tmp5 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)/(2.00000000*(1.00000000 + t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
7886
tmp6 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 4.00000000*r*r + 4.00000000*s*s + 8.00000000*r*s + 8.00000000*r + 8.00000000*s)/(2.00000000*(1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
7887
tmp7 = (2.00000000 + t + 2.00000000*r + 2.00000000*s)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*t/((1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
7888
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
7889
}// end loop over 't'
7890
}// end loop over 's'
7891
}// end loop over 'r'
7892
for (unsigned int r = 0; r < 3; r++)
7893
{
7894
for (unsigned int s = 0; s < 3 - r; s++)
7895
{
7896
for (unsigned int t = 0; t < 3 - r - s; t++)
7897
{
7898
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
7899
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
7900
}// end loop over 't'
7901
}// end loop over 's'
7902
}// end loop over 'r'
7903
7904
// Table(s) of coefficients.
7905
static const double coefficients0[10] = \
7906
{-0.05773503, 0.00000000, 0.07027284, -0.02484520, 0.00000000, 0.00000000, 0.00000000, 0.08728716, -0.04751311, 0.01679842};
7907
7908
// Tables of derivatives of the polynomial base (transpose).
7909
static const double dmats0[10][10] = \
7910
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
7911
{6.32455532, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
7912
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
7913
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
7914
{0.00000000, 11.22497216, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
7915
{4.58257569, 0.00000000, 8.36660027, -1.18321596, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
7916
{3.74165739, 0.00000000, 0.00000000, 8.69482605, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
7917
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
7918
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
7919
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
7920
7921
static const double dmats1[10][10] = \
7922
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
7923
{3.16227766, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
7924
{5.47722558, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
7925
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
7926
{2.95803989, 5.61248608, -1.08012345, -0.76376262, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
7927
{2.29128785, 7.24568837, 4.18330013, -0.59160798, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
7928
{1.87082869, 0.00000000, 0.00000000, 4.34741302, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
7929
{-2.64575131, 0.00000000, 9.66091783, 0.68313005, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
7930
{3.24037035, 0.00000000, 0.00000000, 7.52994024, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
7931
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
7932
7933
static const double dmats2[10][10] = \
7934
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
7935
{3.16227766, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
7936
{1.82574186, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
7937
{5.16397779, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
7938
{2.95803989, 5.61248608, -1.08012345, -0.76376262, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
7939
{2.29128785, 1.44913767, 4.18330013, -0.59160798, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
7940
{1.87082869, 7.09929574, 0.00000000, 4.34741302, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
7941
{1.32287566, 0.00000000, 3.86436713, -0.34156503, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
7942
{1.08012345, 0.00000000, 7.09929574, 2.50998008, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
7943
{-3.81881308, 0.00000000, 0.00000000, 8.87411967, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
7944
7945
// Compute reference derivatives.
7946
// Declare pointer to array of derivatives on FIAT element.
7947
double *derivatives = new double[num_derivatives];
7948
for (unsigned int r = 0; r < num_derivatives; r++)
7949
{
7950
derivatives[r] = 0.00000000;
7951
}// end loop over 'r'
7952
7953
// Declare derivative matrix (of polynomial basis).
7954
double dmats[10][10] = \
7955
{{1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
7956
{0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
7957
{0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
7958
{0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
7959
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
7960
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
7961
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000},
7962
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000},
7963
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000},
7964
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000}};
7965
7966
// Declare (auxiliary) derivative matrix (of polynomial basis).
7967
double dmats_old[10][10] = \
7968
{{1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
7969
{0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
7970
{0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
7971
{0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
7972
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
7973
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
7974
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000},
7975
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000},
7976
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000},
7977
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000}};
7978
7979
// Loop possible derivatives.
7980
for (unsigned int r = 0; r < num_derivatives; r++)
7981
{
7982
// Resetting dmats values to compute next derivative.
7983
for (unsigned int t = 0; t < 10; t++)
7984
{
7985
for (unsigned int u = 0; u < 10; u++)
7986
{
7987
dmats[t][u] = 0.00000000;
7988
if (t == u)
7989
{
7990
dmats[t][u] = 1.00000000;
7991
}
7992
7993
}// end loop over 'u'
7994
}// end loop over 't'
7995
7996
// Looping derivative order to generate dmats.
7997
for (unsigned int s = 0; s < n; s++)
7998
{
7999
// Updating dmats_old with new values and resetting dmats.
8000
for (unsigned int t = 0; t < 10; t++)
8001
{
8002
for (unsigned int u = 0; u < 10; u++)
8003
{
8004
dmats_old[t][u] = dmats[t][u];
8005
dmats[t][u] = 0.00000000;
8006
}// end loop over 'u'
8007
}// end loop over 't'
8008
8009
// Update dmats using an inner product.
8010
if (combinations[r][s] == 0)
8011
{
8012
for (unsigned int t = 0; t < 10; t++)
8013
{
8014
for (unsigned int u = 0; u < 10; u++)
8015
{
8016
for (unsigned int tu = 0; tu < 10; tu++)
8017
{
8018
dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
8019
}// end loop over 'tu'
8020
}// end loop over 'u'
8021
}// end loop over 't'
8022
}
8023
8024
if (combinations[r][s] == 1)
8025
{
8026
for (unsigned int t = 0; t < 10; t++)
8027
{
8028
for (unsigned int u = 0; u < 10; u++)
8029
{
8030
for (unsigned int tu = 0; tu < 10; tu++)
8031
{
8032
dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
8033
}// end loop over 'tu'
8034
}// end loop over 'u'
8035
}// end loop over 't'
8036
}
8037
8038
if (combinations[r][s] == 2)
8039
{
8040
for (unsigned int t = 0; t < 10; t++)
8041
{
8042
for (unsigned int u = 0; u < 10; u++)
8043
{
8044
for (unsigned int tu = 0; tu < 10; tu++)
8045
{
8046
dmats[t][u] += dmats2[t][tu]*dmats_old[tu][u];
8047
}// end loop over 'tu'
8048
}// end loop over 'u'
8049
}// end loop over 't'
8050
}
8051
8052
}// end loop over 's'
8053
for (unsigned int s = 0; s < 10; s++)
8054
{
8055
for (unsigned int t = 0; t < 10; t++)
8056
{
8057
derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
8058
}// end loop over 't'
8059
}// end loop over 's'
8060
}// end loop over 'r'
8061
8062
// Transform derivatives back to physical element
8063
for (unsigned int r = 0; r < num_derivatives; r++)
8064
{
8065
for (unsigned int s = 0; s < num_derivatives; s++)
8066
{
8067
values[r] += transform[r][s]*derivatives[s];
8068
}// end loop over 's'
8069
}// end loop over 'r'
8070
8071
// Delete pointer to array of derivatives on FIAT element
8072
delete [] derivatives;
8073
8074
// Delete pointer to array of combinations of derivatives and transform
8075
for (unsigned int r = 0; r < num_derivatives; r++)
8076
{
8077
delete [] combinations[r];
8078
}// end loop over 'r'
8079
delete [] combinations;
8080
for (unsigned int r = 0; r < num_derivatives; r++)
8081
{
8082
delete [] transform[r];
8083
}// end loop over 'r'
8084
delete [] transform;
8085
break;
8086
}
8087
case 3:
8088
{
8089
8090
// Array of basisvalues.
8091
double basisvalues[10] = {0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000};
8092
8093
// Declare helper variables.
8094
unsigned int rr = 0;
8095
unsigned int ss = 0;
8096
unsigned int tt = 0;
8097
double tmp5 = 0.00000000;
8098
double tmp6 = 0.00000000;
8099
double tmp7 = 0.00000000;
8100
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
8101
double tmp1 = 0.25000000*(Y + Z)*(Y + Z);
8102
double tmp2 = 0.50000000*(1.00000000 + Z + 2.00000000*Y);
8103
double tmp3 = 0.50000000*(1.00000000 - Z);
8104
double tmp4 = tmp3*tmp3;
8105
8106
// Compute basisvalues.
8107
basisvalues[0] = 1.00000000;
8108
basisvalues[1] = tmp0;
8109
for (unsigned int r = 1; r < 2; r++)
8110
{
8111
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
8112
ss = r*(r + 1)*(r + 2)/6;
8113
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
8114
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.00000000 + 2.00000000*r)/(1.00000000 + r) - basisvalues[tt]*tmp1*r/(1.00000000 + r));
8115
}// end loop over 'r'
8116
for (unsigned int r = 0; r < 2; r++)
8117
{
8118
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
8119
ss = r*(r + 1)*(r + 2)/6;
8120
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
8121
}// end loop over 'r'
8122
for (unsigned int r = 0; r < 1; r++)
8123
{
8124
for (unsigned int s = 1; s < 2 - r; s++)
8125
{
8126
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
8127
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
8128
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
8129
tmp5 = (2.00000000 + 2.00000000*r + 2.00000000*s)*(3.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
8130
tmp6 = (1.00000000 + 4.00000000*r*r + 4.00000000*r)*(2.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
8131
tmp7 = (1.00000000 + s + 2.00000000*r)*(3.00000000 + 2.00000000*r + 2.00000000*s)*s/((1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
8132
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
8133
}// end loop over 's'
8134
}// end loop over 'r'
8135
for (unsigned int r = 0; r < 2; r++)
8136
{
8137
for (unsigned int s = 0; s < 2 - r; s++)
8138
{
8139
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
8140
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
8141
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
8142
}// end loop over 's'
8143
}// end loop over 'r'
8144
for (unsigned int r = 0; r < 1; r++)
8145
{
8146
for (unsigned int s = 0; s < 1 - r; s++)
8147
{
8148
for (unsigned int t = 1; t < 2 - r - s; t++)
8149
{
8150
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
8151
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
8152
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
8153
tmp5 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)/(2.00000000*(1.00000000 + t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
8154
tmp6 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 4.00000000*r*r + 4.00000000*s*s + 8.00000000*r*s + 8.00000000*r + 8.00000000*s)/(2.00000000*(1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
8155
tmp7 = (2.00000000 + t + 2.00000000*r + 2.00000000*s)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*t/((1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
8156
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
8157
}// end loop over 't'
8158
}// end loop over 's'
8159
}// end loop over 'r'
8160
for (unsigned int r = 0; r < 3; r++)
8161
{
8162
for (unsigned int s = 0; s < 3 - r; s++)
8163
{
8164
for (unsigned int t = 0; t < 3 - r - s; t++)
8165
{
8166
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
8167
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
8168
}// end loop over 't'
8169
}// end loop over 's'
8170
}// end loop over 'r'
8171
8172
// Table(s) of coefficients.
8173
static const double coefficients0[10] = \
8174
{-0.05773503, 0.00000000, 0.00000000, 0.07453560, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.10079053};
8175
8176
// Tables of derivatives of the polynomial base (transpose).
8177
static const double dmats0[10][10] = \
8178
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
8179
{6.32455532, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
8180
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
8181
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
8182
{0.00000000, 11.22497216, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
8183
{4.58257569, 0.00000000, 8.36660027, -1.18321596, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
8184
{3.74165739, 0.00000000, 0.00000000, 8.69482605, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
8185
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
8186
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
8187
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
8188
8189
static const double dmats1[10][10] = \
8190
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
8191
{3.16227766, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
8192
{5.47722558, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
8193
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
8194
{2.95803989, 5.61248608, -1.08012345, -0.76376262, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
8195
{2.29128785, 7.24568837, 4.18330013, -0.59160798, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
8196
{1.87082869, 0.00000000, 0.00000000, 4.34741302, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
8197
{-2.64575131, 0.00000000, 9.66091783, 0.68313005, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
8198
{3.24037035, 0.00000000, 0.00000000, 7.52994024, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
8199
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
8200
8201
static const double dmats2[10][10] = \
8202
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
8203
{3.16227766, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
8204
{1.82574186, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
8205
{5.16397779, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
8206
{2.95803989, 5.61248608, -1.08012345, -0.76376262, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
8207
{2.29128785, 1.44913767, 4.18330013, -0.59160798, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
8208
{1.87082869, 7.09929574, 0.00000000, 4.34741302, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
8209
{1.32287566, 0.00000000, 3.86436713, -0.34156503, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
8210
{1.08012345, 0.00000000, 7.09929574, 2.50998008, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
8211
{-3.81881308, 0.00000000, 0.00000000, 8.87411967, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
8212
8213
// Compute reference derivatives.
8214
// Declare pointer to array of derivatives on FIAT element.
8215
double *derivatives = new double[num_derivatives];
8216
for (unsigned int r = 0; r < num_derivatives; r++)
8217
{
8218
derivatives[r] = 0.00000000;
8219
}// end loop over 'r'
8220
8221
// Declare derivative matrix (of polynomial basis).
8222
double dmats[10][10] = \
8223
{{1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
8224
{0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
8225
{0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
8226
{0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
8227
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
8228
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
8229
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000},
8230
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000},
8231
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000},
8232
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000}};
8233
8234
// Declare (auxiliary) derivative matrix (of polynomial basis).
8235
double dmats_old[10][10] = \
8236
{{1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
8237
{0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
8238
{0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
8239
{0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
8240
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
8241
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
8242
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000},
8243
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000},
8244
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000},
8245
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000}};
8246
8247
// Loop possible derivatives.
8248
for (unsigned int r = 0; r < num_derivatives; r++)
8249
{
8250
// Resetting dmats values to compute next derivative.
8251
for (unsigned int t = 0; t < 10; t++)
8252
{
8253
for (unsigned int u = 0; u < 10; u++)
8254
{
8255
dmats[t][u] = 0.00000000;
8256
if (t == u)
8257
{
8258
dmats[t][u] = 1.00000000;
8259
}
8260
8261
}// end loop over 'u'
8262
}// end loop over 't'
8263
8264
// Looping derivative order to generate dmats.
8265
for (unsigned int s = 0; s < n; s++)
8266
{
8267
// Updating dmats_old with new values and resetting dmats.
8268
for (unsigned int t = 0; t < 10; t++)
8269
{
8270
for (unsigned int u = 0; u < 10; u++)
8271
{
8272
dmats_old[t][u] = dmats[t][u];
8273
dmats[t][u] = 0.00000000;
8274
}// end loop over 'u'
8275
}// end loop over 't'
8276
8277
// Update dmats using an inner product.
8278
if (combinations[r][s] == 0)
8279
{
8280
for (unsigned int t = 0; t < 10; t++)
8281
{
8282
for (unsigned int u = 0; u < 10; u++)
8283
{
8284
for (unsigned int tu = 0; tu < 10; tu++)
8285
{
8286
dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
8287
}// end loop over 'tu'
8288
}// end loop over 'u'
8289
}// end loop over 't'
8290
}
8291
8292
if (combinations[r][s] == 1)
8293
{
8294
for (unsigned int t = 0; t < 10; t++)
8295
{
8296
for (unsigned int u = 0; u < 10; u++)
8297
{
8298
for (unsigned int tu = 0; tu < 10; tu++)
8299
{
8300
dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
8301
}// end loop over 'tu'
8302
}// end loop over 'u'
8303
}// end loop over 't'
8304
}
8305
8306
if (combinations[r][s] == 2)
8307
{
8308
for (unsigned int t = 0; t < 10; t++)
8309
{
8310
for (unsigned int u = 0; u < 10; u++)
8311
{
8312
for (unsigned int tu = 0; tu < 10; tu++)
8313
{
8314
dmats[t][u] += dmats2[t][tu]*dmats_old[tu][u];
8315
}// end loop over 'tu'
8316
}// end loop over 'u'
8317
}// end loop over 't'
8318
}
8319
8320
}// end loop over 's'
8321
for (unsigned int s = 0; s < 10; s++)
8322
{
8323
for (unsigned int t = 0; t < 10; t++)
8324
{
8325
derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
8326
}// end loop over 't'
8327
}// end loop over 's'
8328
}// end loop over 'r'
8329
8330
// Transform derivatives back to physical element
8331
for (unsigned int r = 0; r < num_derivatives; r++)
8332
{
8333
for (unsigned int s = 0; s < num_derivatives; s++)
8334
{
8335
values[r] += transform[r][s]*derivatives[s];
8336
}// end loop over 's'
8337
}// end loop over 'r'
8338
8339
// Delete pointer to array of derivatives on FIAT element
8340
delete [] derivatives;
8341
8342
// Delete pointer to array of combinations of derivatives and transform
8343
for (unsigned int r = 0; r < num_derivatives; r++)
8344
{
8345
delete [] combinations[r];
8346
}// end loop over 'r'
8347
delete [] combinations;
8348
for (unsigned int r = 0; r < num_derivatives; r++)
8349
{
8350
delete [] transform[r];
8351
}// end loop over 'r'
8352
delete [] transform;
8353
break;
8354
}
8355
case 4:
8356
{
8357
8358
// Array of basisvalues.
8359
double basisvalues[10] = {0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000};
8360
8361
// Declare helper variables.
8362
unsigned int rr = 0;
8363
unsigned int ss = 0;
8364
unsigned int tt = 0;
8365
double tmp5 = 0.00000000;
8366
double tmp6 = 0.00000000;
8367
double tmp7 = 0.00000000;
8368
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
8369
double tmp1 = 0.25000000*(Y + Z)*(Y + Z);
8370
double tmp2 = 0.50000000*(1.00000000 + Z + 2.00000000*Y);
8371
double tmp3 = 0.50000000*(1.00000000 - Z);
8372
double tmp4 = tmp3*tmp3;
8373
8374
// Compute basisvalues.
8375
basisvalues[0] = 1.00000000;
8376
basisvalues[1] = tmp0;
8377
for (unsigned int r = 1; r < 2; r++)
8378
{
8379
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
8380
ss = r*(r + 1)*(r + 2)/6;
8381
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
8382
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.00000000 + 2.00000000*r)/(1.00000000 + r) - basisvalues[tt]*tmp1*r/(1.00000000 + r));
8383
}// end loop over 'r'
8384
for (unsigned int r = 0; r < 2; r++)
8385
{
8386
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
8387
ss = r*(r + 1)*(r + 2)/6;
8388
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
8389
}// end loop over 'r'
8390
for (unsigned int r = 0; r < 1; r++)
8391
{
8392
for (unsigned int s = 1; s < 2 - r; s++)
8393
{
8394
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
8395
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
8396
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
8397
tmp5 = (2.00000000 + 2.00000000*r + 2.00000000*s)*(3.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
8398
tmp6 = (1.00000000 + 4.00000000*r*r + 4.00000000*r)*(2.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
8399
tmp7 = (1.00000000 + s + 2.00000000*r)*(3.00000000 + 2.00000000*r + 2.00000000*s)*s/((1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
8400
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
8401
}// end loop over 's'
8402
}// end loop over 'r'
8403
for (unsigned int r = 0; r < 2; r++)
8404
{
8405
for (unsigned int s = 0; s < 2 - r; s++)
8406
{
8407
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
8408
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
8409
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
8410
}// end loop over 's'
8411
}// end loop over 'r'
8412
for (unsigned int r = 0; r < 1; r++)
8413
{
8414
for (unsigned int s = 0; s < 1 - r; s++)
8415
{
8416
for (unsigned int t = 1; t < 2 - r - s; t++)
8417
{
8418
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
8419
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
8420
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
8421
tmp5 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)/(2.00000000*(1.00000000 + t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
8422
tmp6 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 4.00000000*r*r + 4.00000000*s*s + 8.00000000*r*s + 8.00000000*r + 8.00000000*s)/(2.00000000*(1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
8423
tmp7 = (2.00000000 + t + 2.00000000*r + 2.00000000*s)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*t/((1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
8424
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
8425
}// end loop over 't'
8426
}// end loop over 's'
8427
}// end loop over 'r'
8428
for (unsigned int r = 0; r < 3; r++)
8429
{
8430
for (unsigned int s = 0; s < 3 - r; s++)
8431
{
8432
for (unsigned int t = 0; t < 3 - r - s; t++)
8433
{
8434
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
8435
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
8436
}// end loop over 't'
8437
}// end loop over 's'
8438
}// end loop over 'r'
8439
8440
// Table(s) of coefficients.
8441
static const double coefficients0[10] = \
8442
{0.23094011, 0.00000000, 0.14054567, 0.09938080, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.11878277, -0.06719368};
8443
8444
// Tables of derivatives of the polynomial base (transpose).
8445
static const double dmats0[10][10] = \
8446
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
8447
{6.32455532, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
8448
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
8449
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
8450
{0.00000000, 11.22497216, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
8451
{4.58257569, 0.00000000, 8.36660027, -1.18321596, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
8452
{3.74165739, 0.00000000, 0.00000000, 8.69482605, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
8453
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
8454
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
8455
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
8456
8457
static const double dmats1[10][10] = \
8458
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
8459
{3.16227766, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
8460
{5.47722558, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
8461
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
8462
{2.95803989, 5.61248608, -1.08012345, -0.76376262, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
8463
{2.29128785, 7.24568837, 4.18330013, -0.59160798, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
8464
{1.87082869, 0.00000000, 0.00000000, 4.34741302, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
8465
{-2.64575131, 0.00000000, 9.66091783, 0.68313005, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
8466
{3.24037035, 0.00000000, 0.00000000, 7.52994024, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
8467
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
8468
8469
static const double dmats2[10][10] = \
8470
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
8471
{3.16227766, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
8472
{1.82574186, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
8473
{5.16397779, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
8474
{2.95803989, 5.61248608, -1.08012345, -0.76376262, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
8475
{2.29128785, 1.44913767, 4.18330013, -0.59160798, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
8476
{1.87082869, 7.09929574, 0.00000000, 4.34741302, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
8477
{1.32287566, 0.00000000, 3.86436713, -0.34156503, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
8478
{1.08012345, 0.00000000, 7.09929574, 2.50998008, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
8479
{-3.81881308, 0.00000000, 0.00000000, 8.87411967, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
8480
8481
// Compute reference derivatives.
8482
// Declare pointer to array of derivatives on FIAT element.
8483
double *derivatives = new double[num_derivatives];
8484
for (unsigned int r = 0; r < num_derivatives; r++)
8485
{
8486
derivatives[r] = 0.00000000;
8487
}// end loop over 'r'
8488
8489
// Declare derivative matrix (of polynomial basis).
8490
double dmats[10][10] = \
8491
{{1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
8492
{0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
8493
{0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
8494
{0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
8495
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
8496
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
8497
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000},
8498
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000},
8499
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000},
8500
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000}};
8501
8502
// Declare (auxiliary) derivative matrix (of polynomial basis).
8503
double dmats_old[10][10] = \
8504
{{1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
8505
{0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
8506
{0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
8507
{0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
8508
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
8509
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
8510
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000},
8511
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000},
8512
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000},
8513
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000}};
8514
8515
// Loop possible derivatives.
8516
for (unsigned int r = 0; r < num_derivatives; r++)
8517
{
8518
// Resetting dmats values to compute next derivative.
8519
for (unsigned int t = 0; t < 10; t++)
8520
{
8521
for (unsigned int u = 0; u < 10; u++)
8522
{
8523
dmats[t][u] = 0.00000000;
8524
if (t == u)
8525
{
8526
dmats[t][u] = 1.00000000;
8527
}
8528
8529
}// end loop over 'u'
8530
}// end loop over 't'
8531
8532
// Looping derivative order to generate dmats.
8533
for (unsigned int s = 0; s < n; s++)
8534
{
8535
// Updating dmats_old with new values and resetting dmats.
8536
for (unsigned int t = 0; t < 10; t++)
8537
{
8538
for (unsigned int u = 0; u < 10; u++)
8539
{
8540
dmats_old[t][u] = dmats[t][u];
8541
dmats[t][u] = 0.00000000;
8542
}// end loop over 'u'
8543
}// end loop over 't'
8544
8545
// Update dmats using an inner product.
8546
if (combinations[r][s] == 0)
8547
{
8548
for (unsigned int t = 0; t < 10; t++)
8549
{
8550
for (unsigned int u = 0; u < 10; u++)
8551
{
8552
for (unsigned int tu = 0; tu < 10; tu++)
8553
{
8554
dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
8555
}// end loop over 'tu'
8556
}// end loop over 'u'
8557
}// end loop over 't'
8558
}
8559
8560
if (combinations[r][s] == 1)
8561
{
8562
for (unsigned int t = 0; t < 10; t++)
8563
{
8564
for (unsigned int u = 0; u < 10; u++)
8565
{
8566
for (unsigned int tu = 0; tu < 10; tu++)
8567
{
8568
dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
8569
}// end loop over 'tu'
8570
}// end loop over 'u'
8571
}// end loop over 't'
8572
}
8573
8574
if (combinations[r][s] == 2)
8575
{
8576
for (unsigned int t = 0; t < 10; t++)
8577
{
8578
for (unsigned int u = 0; u < 10; u++)
8579
{
8580
for (unsigned int tu = 0; tu < 10; tu++)
8581
{
8582
dmats[t][u] += dmats2[t][tu]*dmats_old[tu][u];
8583
}// end loop over 'tu'
8584
}// end loop over 'u'
8585
}// end loop over 't'
8586
}
8587
8588
}// end loop over 's'
8589
for (unsigned int s = 0; s < 10; s++)
8590
{
8591
for (unsigned int t = 0; t < 10; t++)
8592
{
8593
derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
8594
}// end loop over 't'
8595
}// end loop over 's'
8596
}// end loop over 'r'
8597
8598
// Transform derivatives back to physical element
8599
for (unsigned int r = 0; r < num_derivatives; r++)
8600
{
8601
for (unsigned int s = 0; s < num_derivatives; s++)
8602
{
8603
values[r] += transform[r][s]*derivatives[s];
8604
}// end loop over 's'
8605
}// end loop over 'r'
8606
8607
// Delete pointer to array of derivatives on FIAT element
8608
delete [] derivatives;
8609
8610
// Delete pointer to array of combinations of derivatives and transform
8611
for (unsigned int r = 0; r < num_derivatives; r++)
8612
{
8613
delete [] combinations[r];
8614
}// end loop over 'r'
8615
delete [] combinations;
8616
for (unsigned int r = 0; r < num_derivatives; r++)
8617
{
8618
delete [] transform[r];
8619
}// end loop over 'r'
8620
delete [] transform;
8621
break;
8622
}
8623
case 5:
8624
{
8625
8626
// Array of basisvalues.
8627
double basisvalues[10] = {0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000};
8628
8629
// Declare helper variables.
8630
unsigned int rr = 0;
8631
unsigned int ss = 0;
8632
unsigned int tt = 0;
8633
double tmp5 = 0.00000000;
8634
double tmp6 = 0.00000000;
8635
double tmp7 = 0.00000000;
8636
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
8637
double tmp1 = 0.25000000*(Y + Z)*(Y + Z);
8638
double tmp2 = 0.50000000*(1.00000000 + Z + 2.00000000*Y);
8639
double tmp3 = 0.50000000*(1.00000000 - Z);
8640
double tmp4 = tmp3*tmp3;
8641
8642
// Compute basisvalues.
8643
basisvalues[0] = 1.00000000;
8644
basisvalues[1] = tmp0;
8645
for (unsigned int r = 1; r < 2; r++)
8646
{
8647
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
8648
ss = r*(r + 1)*(r + 2)/6;
8649
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
8650
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.00000000 + 2.00000000*r)/(1.00000000 + r) - basisvalues[tt]*tmp1*r/(1.00000000 + r));
8651
}// end loop over 'r'
8652
for (unsigned int r = 0; r < 2; r++)
8653
{
8654
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
8655
ss = r*(r + 1)*(r + 2)/6;
8656
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
8657
}// end loop over 'r'
8658
for (unsigned int r = 0; r < 1; r++)
8659
{
8660
for (unsigned int s = 1; s < 2 - r; s++)
8661
{
8662
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
8663
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
8664
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
8665
tmp5 = (2.00000000 + 2.00000000*r + 2.00000000*s)*(3.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
8666
tmp6 = (1.00000000 + 4.00000000*r*r + 4.00000000*r)*(2.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
8667
tmp7 = (1.00000000 + s + 2.00000000*r)*(3.00000000 + 2.00000000*r + 2.00000000*s)*s/((1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
8668
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
8669
}// end loop over 's'
8670
}// end loop over 'r'
8671
for (unsigned int r = 0; r < 2; r++)
8672
{
8673
for (unsigned int s = 0; s < 2 - r; s++)
8674
{
8675
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
8676
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
8677
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
8678
}// end loop over 's'
8679
}// end loop over 'r'
8680
for (unsigned int r = 0; r < 1; r++)
8681
{
8682
for (unsigned int s = 0; s < 1 - r; s++)
8683
{
8684
for (unsigned int t = 1; t < 2 - r - s; t++)
8685
{
8686
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
8687
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
8688
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
8689
tmp5 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)/(2.00000000*(1.00000000 + t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
8690
tmp6 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 4.00000000*r*r + 4.00000000*s*s + 8.00000000*r*s + 8.00000000*r + 8.00000000*s)/(2.00000000*(1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
8691
tmp7 = (2.00000000 + t + 2.00000000*r + 2.00000000*s)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*t/((1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
8692
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
8693
}// end loop over 't'
8694
}// end loop over 's'
8695
}// end loop over 'r'
8696
for (unsigned int r = 0; r < 3; r++)
8697
{
8698
for (unsigned int s = 0; s < 3 - r; s++)
8699
{
8700
for (unsigned int t = 0; t < 3 - r - s; t++)
8701
{
8702
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
8703
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
8704
}// end loop over 't'
8705
}// end loop over 's'
8706
}// end loop over 'r'
8707
8708
// Table(s) of coefficients.
8709
static const double coefficients0[10] = \
8710
{0.23094011, 0.12171612, -0.07027284, 0.09938080, 0.00000000, 0.00000000, 0.10286890, 0.00000000, -0.05939139, -0.06719368};
8711
8712
// Tables of derivatives of the polynomial base (transpose).
8713
static const double dmats0[10][10] = \
8714
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
8715
{6.32455532, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
8716
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
8717
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
8718
{0.00000000, 11.22497216, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
8719
{4.58257569, 0.00000000, 8.36660027, -1.18321596, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
8720
{3.74165739, 0.00000000, 0.00000000, 8.69482605, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
8721
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
8722
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
8723
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
8724
8725
static const double dmats1[10][10] = \
8726
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
8727
{3.16227766, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
8728
{5.47722558, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
8729
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
8730
{2.95803989, 5.61248608, -1.08012345, -0.76376262, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
8731
{2.29128785, 7.24568837, 4.18330013, -0.59160798, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
8732
{1.87082869, 0.00000000, 0.00000000, 4.34741302, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
8733
{-2.64575131, 0.00000000, 9.66091783, 0.68313005, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
8734
{3.24037035, 0.00000000, 0.00000000, 7.52994024, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
8735
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
8736
8737
static const double dmats2[10][10] = \
8738
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
8739
{3.16227766, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
8740
{1.82574186, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
8741
{5.16397779, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
8742
{2.95803989, 5.61248608, -1.08012345, -0.76376262, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
8743
{2.29128785, 1.44913767, 4.18330013, -0.59160798, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
8744
{1.87082869, 7.09929574, 0.00000000, 4.34741302, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
8745
{1.32287566, 0.00000000, 3.86436713, -0.34156503, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
8746
{1.08012345, 0.00000000, 7.09929574, 2.50998008, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
8747
{-3.81881308, 0.00000000, 0.00000000, 8.87411967, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
8748
8749
// Compute reference derivatives.
8750
// Declare pointer to array of derivatives on FIAT element.
8751
double *derivatives = new double[num_derivatives];
8752
for (unsigned int r = 0; r < num_derivatives; r++)
8753
{
8754
derivatives[r] = 0.00000000;
8755
}// end loop over 'r'
8756
8757
// Declare derivative matrix (of polynomial basis).
8758
double dmats[10][10] = \
8759
{{1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
8760
{0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
8761
{0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
8762
{0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
8763
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
8764
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
8765
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000},
8766
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000},
8767
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000},
8768
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000}};
8769
8770
// Declare (auxiliary) derivative matrix (of polynomial basis).
8771
double dmats_old[10][10] = \
8772
{{1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
8773
{0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
8774
{0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
8775
{0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
8776
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
8777
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
8778
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000},
8779
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000},
8780
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000},
8781
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000}};
8782
8783
// Loop possible derivatives.
8784
for (unsigned int r = 0; r < num_derivatives; r++)
8785
{
8786
// Resetting dmats values to compute next derivative.
8787
for (unsigned int t = 0; t < 10; t++)
8788
{
8789
for (unsigned int u = 0; u < 10; u++)
8790
{
8791
dmats[t][u] = 0.00000000;
8792
if (t == u)
8793
{
8794
dmats[t][u] = 1.00000000;
8795
}
8796
8797
}// end loop over 'u'
8798
}// end loop over 't'
8799
8800
// Looping derivative order to generate dmats.
8801
for (unsigned int s = 0; s < n; s++)
8802
{
8803
// Updating dmats_old with new values and resetting dmats.
8804
for (unsigned int t = 0; t < 10; t++)
8805
{
8806
for (unsigned int u = 0; u < 10; u++)
8807
{
8808
dmats_old[t][u] = dmats[t][u];
8809
dmats[t][u] = 0.00000000;
8810
}// end loop over 'u'
8811
}// end loop over 't'
8812
8813
// Update dmats using an inner product.
8814
if (combinations[r][s] == 0)
8815
{
8816
for (unsigned int t = 0; t < 10; t++)
8817
{
8818
for (unsigned int u = 0; u < 10; u++)
8819
{
8820
for (unsigned int tu = 0; tu < 10; tu++)
8821
{
8822
dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
8823
}// end loop over 'tu'
8824
}// end loop over 'u'
8825
}// end loop over 't'
8826
}
8827
8828
if (combinations[r][s] == 1)
8829
{
8830
for (unsigned int t = 0; t < 10; t++)
8831
{
8832
for (unsigned int u = 0; u < 10; u++)
8833
{
8834
for (unsigned int tu = 0; tu < 10; tu++)
8835
{
8836
dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
8837
}// end loop over 'tu'
8838
}// end loop over 'u'
8839
}// end loop over 't'
8840
}
8841
8842
if (combinations[r][s] == 2)
8843
{
8844
for (unsigned int t = 0; t < 10; t++)
8845
{
8846
for (unsigned int u = 0; u < 10; u++)
8847
{
8848
for (unsigned int tu = 0; tu < 10; tu++)
8849
{
8850
dmats[t][u] += dmats2[t][tu]*dmats_old[tu][u];
8851
}// end loop over 'tu'
8852
}// end loop over 'u'
8853
}// end loop over 't'
8854
}
8855
8856
}// end loop over 's'
8857
for (unsigned int s = 0; s < 10; s++)
8858
{
8859
for (unsigned int t = 0; t < 10; t++)
8860
{
8861
derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
8862
}// end loop over 't'
8863
}// end loop over 's'
8864
}// end loop over 'r'
8865
8866
// Transform derivatives back to physical element
8867
for (unsigned int r = 0; r < num_derivatives; r++)
8868
{
8869
for (unsigned int s = 0; s < num_derivatives; s++)
8870
{
8871
values[r] += transform[r][s]*derivatives[s];
8872
}// end loop over 's'
8873
}// end loop over 'r'
8874
8875
// Delete pointer to array of derivatives on FIAT element
8876
delete [] derivatives;
8877
8878
// Delete pointer to array of combinations of derivatives and transform
8879
for (unsigned int r = 0; r < num_derivatives; r++)
8880
{
8881
delete [] combinations[r];
8882
}// end loop over 'r'
8883
delete [] combinations;
8884
for (unsigned int r = 0; r < num_derivatives; r++)
8885
{
8886
delete [] transform[r];
8887
}// end loop over 'r'
8888
delete [] transform;
8889
break;
8890
}
8891
case 6:
8892
{
8893
8894
// Array of basisvalues.
8895
double basisvalues[10] = {0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000};
8896
8897
// Declare helper variables.
8898
unsigned int rr = 0;
8899
unsigned int ss = 0;
8900
unsigned int tt = 0;
8901
double tmp5 = 0.00000000;
8902
double tmp6 = 0.00000000;
8903
double tmp7 = 0.00000000;
8904
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
8905
double tmp1 = 0.25000000*(Y + Z)*(Y + Z);
8906
double tmp2 = 0.50000000*(1.00000000 + Z + 2.00000000*Y);
8907
double tmp3 = 0.50000000*(1.00000000 - Z);
8908
double tmp4 = tmp3*tmp3;
8909
8910
// Compute basisvalues.
8911
basisvalues[0] = 1.00000000;
8912
basisvalues[1] = tmp0;
8913
for (unsigned int r = 1; r < 2; r++)
8914
{
8915
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
8916
ss = r*(r + 1)*(r + 2)/6;
8917
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
8918
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.00000000 + 2.00000000*r)/(1.00000000 + r) - basisvalues[tt]*tmp1*r/(1.00000000 + r));
8919
}// end loop over 'r'
8920
for (unsigned int r = 0; r < 2; r++)
8921
{
8922
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
8923
ss = r*(r + 1)*(r + 2)/6;
8924
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
8925
}// end loop over 'r'
8926
for (unsigned int r = 0; r < 1; r++)
8927
{
8928
for (unsigned int s = 1; s < 2 - r; s++)
8929
{
8930
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
8931
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
8932
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
8933
tmp5 = (2.00000000 + 2.00000000*r + 2.00000000*s)*(3.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
8934
tmp6 = (1.00000000 + 4.00000000*r*r + 4.00000000*r)*(2.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
8935
tmp7 = (1.00000000 + s + 2.00000000*r)*(3.00000000 + 2.00000000*r + 2.00000000*s)*s/((1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
8936
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
8937
}// end loop over 's'
8938
}// end loop over 'r'
8939
for (unsigned int r = 0; r < 2; r++)
8940
{
8941
for (unsigned int s = 0; s < 2 - r; s++)
8942
{
8943
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
8944
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
8945
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
8946
}// end loop over 's'
8947
}// end loop over 'r'
8948
for (unsigned int r = 0; r < 1; r++)
8949
{
8950
for (unsigned int s = 0; s < 1 - r; s++)
8951
{
8952
for (unsigned int t = 1; t < 2 - r - s; t++)
8953
{
8954
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
8955
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
8956
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
8957
tmp5 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)/(2.00000000*(1.00000000 + t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
8958
tmp6 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 4.00000000*r*r + 4.00000000*s*s + 8.00000000*r*s + 8.00000000*r + 8.00000000*s)/(2.00000000*(1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
8959
tmp7 = (2.00000000 + t + 2.00000000*r + 2.00000000*s)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*t/((1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
8960
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
8961
}// end loop over 't'
8962
}// end loop over 's'
8963
}// end loop over 'r'
8964
for (unsigned int r = 0; r < 3; r++)
8965
{
8966
for (unsigned int s = 0; s < 3 - r; s++)
8967
{
8968
for (unsigned int t = 0; t < 3 - r - s; t++)
8969
{
8970
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
8971
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
8972
}// end loop over 't'
8973
}// end loop over 's'
8974
}// end loop over 'r'
8975
8976
// Table(s) of coefficients.
8977
static const double coefficients0[10] = \
8978
{0.23094011, 0.12171612, 0.07027284, -0.09938080, 0.00000000, 0.10079053, -0.02057378, -0.08728716, -0.01187828, 0.01679842};
8979
8980
// Tables of derivatives of the polynomial base (transpose).
8981
static const double dmats0[10][10] = \
8982
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
8983
{6.32455532, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
8984
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
8985
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
8986
{0.00000000, 11.22497216, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
8987
{4.58257569, 0.00000000, 8.36660027, -1.18321596, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
8988
{3.74165739, 0.00000000, 0.00000000, 8.69482605, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
8989
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
8990
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
8991
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
8992
8993
static const double dmats1[10][10] = \
8994
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
8995
{3.16227766, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
8996
{5.47722558, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
8997
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
8998
{2.95803989, 5.61248608, -1.08012345, -0.76376262, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
8999
{2.29128785, 7.24568837, 4.18330013, -0.59160798, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9000
{1.87082869, 0.00000000, 0.00000000, 4.34741302, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9001
{-2.64575131, 0.00000000, 9.66091783, 0.68313005, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9002
{3.24037035, 0.00000000, 0.00000000, 7.52994024, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9003
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
9004
9005
static const double dmats2[10][10] = \
9006
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9007
{3.16227766, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9008
{1.82574186, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9009
{5.16397779, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9010
{2.95803989, 5.61248608, -1.08012345, -0.76376262, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9011
{2.29128785, 1.44913767, 4.18330013, -0.59160798, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9012
{1.87082869, 7.09929574, 0.00000000, 4.34741302, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9013
{1.32287566, 0.00000000, 3.86436713, -0.34156503, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9014
{1.08012345, 0.00000000, 7.09929574, 2.50998008, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9015
{-3.81881308, 0.00000000, 0.00000000, 8.87411967, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
9016
9017
// Compute reference derivatives.
9018
// Declare pointer to array of derivatives on FIAT element.
9019
double *derivatives = new double[num_derivatives];
9020
for (unsigned int r = 0; r < num_derivatives; r++)
9021
{
9022
derivatives[r] = 0.00000000;
9023
}// end loop over 'r'
9024
9025
// Declare derivative matrix (of polynomial basis).
9026
double dmats[10][10] = \
9027
{{1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9028
{0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9029
{0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9030
{0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9031
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9032
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9033
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000},
9034
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000},
9035
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000},
9036
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000}};
9037
9038
// Declare (auxiliary) derivative matrix (of polynomial basis).
9039
double dmats_old[10][10] = \
9040
{{1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9041
{0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9042
{0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9043
{0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9044
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9045
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9046
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000},
9047
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000},
9048
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000},
9049
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000}};
9050
9051
// Loop possible derivatives.
9052
for (unsigned int r = 0; r < num_derivatives; r++)
9053
{
9054
// Resetting dmats values to compute next derivative.
9055
for (unsigned int t = 0; t < 10; t++)
9056
{
9057
for (unsigned int u = 0; u < 10; u++)
9058
{
9059
dmats[t][u] = 0.00000000;
9060
if (t == u)
9061
{
9062
dmats[t][u] = 1.00000000;
9063
}
9064
9065
}// end loop over 'u'
9066
}// end loop over 't'
9067
9068
// Looping derivative order to generate dmats.
9069
for (unsigned int s = 0; s < n; s++)
9070
{
9071
// Updating dmats_old with new values and resetting dmats.
9072
for (unsigned int t = 0; t < 10; t++)
9073
{
9074
for (unsigned int u = 0; u < 10; u++)
9075
{
9076
dmats_old[t][u] = dmats[t][u];
9077
dmats[t][u] = 0.00000000;
9078
}// end loop over 'u'
9079
}// end loop over 't'
9080
9081
// Update dmats using an inner product.
9082
if (combinations[r][s] == 0)
9083
{
9084
for (unsigned int t = 0; t < 10; t++)
9085
{
9086
for (unsigned int u = 0; u < 10; u++)
9087
{
9088
for (unsigned int tu = 0; tu < 10; tu++)
9089
{
9090
dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
9091
}// end loop over 'tu'
9092
}// end loop over 'u'
9093
}// end loop over 't'
9094
}
9095
9096
if (combinations[r][s] == 1)
9097
{
9098
for (unsigned int t = 0; t < 10; t++)
9099
{
9100
for (unsigned int u = 0; u < 10; u++)
9101
{
9102
for (unsigned int tu = 0; tu < 10; tu++)
9103
{
9104
dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
9105
}// end loop over 'tu'
9106
}// end loop over 'u'
9107
}// end loop over 't'
9108
}
9109
9110
if (combinations[r][s] == 2)
9111
{
9112
for (unsigned int t = 0; t < 10; t++)
9113
{
9114
for (unsigned int u = 0; u < 10; u++)
9115
{
9116
for (unsigned int tu = 0; tu < 10; tu++)
9117
{
9118
dmats[t][u] += dmats2[t][tu]*dmats_old[tu][u];
9119
}// end loop over 'tu'
9120
}// end loop over 'u'
9121
}// end loop over 't'
9122
}
9123
9124
}// end loop over 's'
9125
for (unsigned int s = 0; s < 10; s++)
9126
{
9127
for (unsigned int t = 0; t < 10; t++)
9128
{
9129
derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
9130
}// end loop over 't'
9131
}// end loop over 's'
9132
}// end loop over 'r'
9133
9134
// Transform derivatives back to physical element
9135
for (unsigned int r = 0; r < num_derivatives; r++)
9136
{
9137
for (unsigned int s = 0; s < num_derivatives; s++)
9138
{
9139
values[r] += transform[r][s]*derivatives[s];
9140
}// end loop over 's'
9141
}// end loop over 'r'
9142
9143
// Delete pointer to array of derivatives on FIAT element
9144
delete [] derivatives;
9145
9146
// Delete pointer to array of combinations of derivatives and transform
9147
for (unsigned int r = 0; r < num_derivatives; r++)
9148
{
9149
delete [] combinations[r];
9150
}// end loop over 'r'
9151
delete [] combinations;
9152
for (unsigned int r = 0; r < num_derivatives; r++)
9153
{
9154
delete [] transform[r];
9155
}// end loop over 'r'
9156
delete [] transform;
9157
break;
9158
}
9159
case 7:
9160
{
9161
9162
// Array of basisvalues.
9163
double basisvalues[10] = {0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000};
9164
9165
// Declare helper variables.
9166
unsigned int rr = 0;
9167
unsigned int ss = 0;
9168
unsigned int tt = 0;
9169
double tmp5 = 0.00000000;
9170
double tmp6 = 0.00000000;
9171
double tmp7 = 0.00000000;
9172
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
9173
double tmp1 = 0.25000000*(Y + Z)*(Y + Z);
9174
double tmp2 = 0.50000000*(1.00000000 + Z + 2.00000000*Y);
9175
double tmp3 = 0.50000000*(1.00000000 - Z);
9176
double tmp4 = tmp3*tmp3;
9177
9178
// Compute basisvalues.
9179
basisvalues[0] = 1.00000000;
9180
basisvalues[1] = tmp0;
9181
for (unsigned int r = 1; r < 2; r++)
9182
{
9183
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
9184
ss = r*(r + 1)*(r + 2)/6;
9185
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
9186
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.00000000 + 2.00000000*r)/(1.00000000 + r) - basisvalues[tt]*tmp1*r/(1.00000000 + r));
9187
}// end loop over 'r'
9188
for (unsigned int r = 0; r < 2; r++)
9189
{
9190
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
9191
ss = r*(r + 1)*(r + 2)/6;
9192
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
9193
}// end loop over 'r'
9194
for (unsigned int r = 0; r < 1; r++)
9195
{
9196
for (unsigned int s = 1; s < 2 - r; s++)
9197
{
9198
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
9199
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
9200
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
9201
tmp5 = (2.00000000 + 2.00000000*r + 2.00000000*s)*(3.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
9202
tmp6 = (1.00000000 + 4.00000000*r*r + 4.00000000*r)*(2.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
9203
tmp7 = (1.00000000 + s + 2.00000000*r)*(3.00000000 + 2.00000000*r + 2.00000000*s)*s/((1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
9204
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
9205
}// end loop over 's'
9206
}// end loop over 'r'
9207
for (unsigned int r = 0; r < 2; r++)
9208
{
9209
for (unsigned int s = 0; s < 2 - r; s++)
9210
{
9211
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
9212
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
9213
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
9214
}// end loop over 's'
9215
}// end loop over 'r'
9216
for (unsigned int r = 0; r < 1; r++)
9217
{
9218
for (unsigned int s = 0; s < 1 - r; s++)
9219
{
9220
for (unsigned int t = 1; t < 2 - r - s; t++)
9221
{
9222
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
9223
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
9224
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
9225
tmp5 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)/(2.00000000*(1.00000000 + t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
9226
tmp6 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 4.00000000*r*r + 4.00000000*s*s + 8.00000000*r*s + 8.00000000*r + 8.00000000*s)/(2.00000000*(1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
9227
tmp7 = (2.00000000 + t + 2.00000000*r + 2.00000000*s)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*t/((1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
9228
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
9229
}// end loop over 't'
9230
}// end loop over 's'
9231
}// end loop over 'r'
9232
for (unsigned int r = 0; r < 3; r++)
9233
{
9234
for (unsigned int s = 0; s < 3 - r; s++)
9235
{
9236
for (unsigned int t = 0; t < 3 - r - s; t++)
9237
{
9238
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
9239
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
9240
}// end loop over 't'
9241
}// end loop over 's'
9242
}// end loop over 'r'
9243
9244
// Table(s) of coefficients.
9245
static const double coefficients0[10] = \
9246
{0.23094011, -0.12171612, -0.07027284, 0.09938080, 0.00000000, 0.00000000, -0.10286890, 0.00000000, -0.05939139, -0.06719368};
9247
9248
// Tables of derivatives of the polynomial base (transpose).
9249
static const double dmats0[10][10] = \
9250
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9251
{6.32455532, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9252
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9253
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9254
{0.00000000, 11.22497216, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9255
{4.58257569, 0.00000000, 8.36660027, -1.18321596, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9256
{3.74165739, 0.00000000, 0.00000000, 8.69482605, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9257
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9258
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9259
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
9260
9261
static const double dmats1[10][10] = \
9262
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9263
{3.16227766, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9264
{5.47722558, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9265
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9266
{2.95803989, 5.61248608, -1.08012345, -0.76376262, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9267
{2.29128785, 7.24568837, 4.18330013, -0.59160798, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9268
{1.87082869, 0.00000000, 0.00000000, 4.34741302, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9269
{-2.64575131, 0.00000000, 9.66091783, 0.68313005, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9270
{3.24037035, 0.00000000, 0.00000000, 7.52994024, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9271
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
9272
9273
static const double dmats2[10][10] = \
9274
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9275
{3.16227766, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9276
{1.82574186, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9277
{5.16397779, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9278
{2.95803989, 5.61248608, -1.08012345, -0.76376262, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9279
{2.29128785, 1.44913767, 4.18330013, -0.59160798, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9280
{1.87082869, 7.09929574, 0.00000000, 4.34741302, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9281
{1.32287566, 0.00000000, 3.86436713, -0.34156503, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9282
{1.08012345, 0.00000000, 7.09929574, 2.50998008, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9283
{-3.81881308, 0.00000000, 0.00000000, 8.87411967, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
9284
9285
// Compute reference derivatives.
9286
// Declare pointer to array of derivatives on FIAT element.
9287
double *derivatives = new double[num_derivatives];
9288
for (unsigned int r = 0; r < num_derivatives; r++)
9289
{
9290
derivatives[r] = 0.00000000;
9291
}// end loop over 'r'
9292
9293
// Declare derivative matrix (of polynomial basis).
9294
double dmats[10][10] = \
9295
{{1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9296
{0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9297
{0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9298
{0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9299
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9300
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9301
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000},
9302
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000},
9303
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000},
9304
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000}};
9305
9306
// Declare (auxiliary) derivative matrix (of polynomial basis).
9307
double dmats_old[10][10] = \
9308
{{1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9309
{0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9310
{0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9311
{0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9312
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9313
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9314
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000},
9315
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000},
9316
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000},
9317
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000}};
9318
9319
// Loop possible derivatives.
9320
for (unsigned int r = 0; r < num_derivatives; r++)
9321
{
9322
// Resetting dmats values to compute next derivative.
9323
for (unsigned int t = 0; t < 10; t++)
9324
{
9325
for (unsigned int u = 0; u < 10; u++)
9326
{
9327
dmats[t][u] = 0.00000000;
9328
if (t == u)
9329
{
9330
dmats[t][u] = 1.00000000;
9331
}
9332
9333
}// end loop over 'u'
9334
}// end loop over 't'
9335
9336
// Looping derivative order to generate dmats.
9337
for (unsigned int s = 0; s < n; s++)
9338
{
9339
// Updating dmats_old with new values and resetting dmats.
9340
for (unsigned int t = 0; t < 10; t++)
9341
{
9342
for (unsigned int u = 0; u < 10; u++)
9343
{
9344
dmats_old[t][u] = dmats[t][u];
9345
dmats[t][u] = 0.00000000;
9346
}// end loop over 'u'
9347
}// end loop over 't'
9348
9349
// Update dmats using an inner product.
9350
if (combinations[r][s] == 0)
9351
{
9352
for (unsigned int t = 0; t < 10; t++)
9353
{
9354
for (unsigned int u = 0; u < 10; u++)
9355
{
9356
for (unsigned int tu = 0; tu < 10; tu++)
9357
{
9358
dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
9359
}// end loop over 'tu'
9360
}// end loop over 'u'
9361
}// end loop over 't'
9362
}
9363
9364
if (combinations[r][s] == 1)
9365
{
9366
for (unsigned int t = 0; t < 10; t++)
9367
{
9368
for (unsigned int u = 0; u < 10; u++)
9369
{
9370
for (unsigned int tu = 0; tu < 10; tu++)
9371
{
9372
dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
9373
}// end loop over 'tu'
9374
}// end loop over 'u'
9375
}// end loop over 't'
9376
}
9377
9378
if (combinations[r][s] == 2)
9379
{
9380
for (unsigned int t = 0; t < 10; t++)
9381
{
9382
for (unsigned int u = 0; u < 10; u++)
9383
{
9384
for (unsigned int tu = 0; tu < 10; tu++)
9385
{
9386
dmats[t][u] += dmats2[t][tu]*dmats_old[tu][u];
9387
}// end loop over 'tu'
9388
}// end loop over 'u'
9389
}// end loop over 't'
9390
}
9391
9392
}// end loop over 's'
9393
for (unsigned int s = 0; s < 10; s++)
9394
{
9395
for (unsigned int t = 0; t < 10; t++)
9396
{
9397
derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
9398
}// end loop over 't'
9399
}// end loop over 's'
9400
}// end loop over 'r'
9401
9402
// Transform derivatives back to physical element
9403
for (unsigned int r = 0; r < num_derivatives; r++)
9404
{
9405
for (unsigned int s = 0; s < num_derivatives; s++)
9406
{
9407
values[r] += transform[r][s]*derivatives[s];
9408
}// end loop over 's'
9409
}// end loop over 'r'
9410
9411
// Delete pointer to array of derivatives on FIAT element
9412
delete [] derivatives;
9413
9414
// Delete pointer to array of combinations of derivatives and transform
9415
for (unsigned int r = 0; r < num_derivatives; r++)
9416
{
9417
delete [] combinations[r];
9418
}// end loop over 'r'
9419
delete [] combinations;
9420
for (unsigned int r = 0; r < num_derivatives; r++)
9421
{
9422
delete [] transform[r];
9423
}// end loop over 'r'
9424
delete [] transform;
9425
break;
9426
}
9427
case 8:
9428
{
9429
9430
// Array of basisvalues.
9431
double basisvalues[10] = {0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000};
9432
9433
// Declare helper variables.
9434
unsigned int rr = 0;
9435
unsigned int ss = 0;
9436
unsigned int tt = 0;
9437
double tmp5 = 0.00000000;
9438
double tmp6 = 0.00000000;
9439
double tmp7 = 0.00000000;
9440
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
9441
double tmp1 = 0.25000000*(Y + Z)*(Y + Z);
9442
double tmp2 = 0.50000000*(1.00000000 + Z + 2.00000000*Y);
9443
double tmp3 = 0.50000000*(1.00000000 - Z);
9444
double tmp4 = tmp3*tmp3;
9445
9446
// Compute basisvalues.
9447
basisvalues[0] = 1.00000000;
9448
basisvalues[1] = tmp0;
9449
for (unsigned int r = 1; r < 2; r++)
9450
{
9451
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
9452
ss = r*(r + 1)*(r + 2)/6;
9453
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
9454
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.00000000 + 2.00000000*r)/(1.00000000 + r) - basisvalues[tt]*tmp1*r/(1.00000000 + r));
9455
}// end loop over 'r'
9456
for (unsigned int r = 0; r < 2; r++)
9457
{
9458
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
9459
ss = r*(r + 1)*(r + 2)/6;
9460
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
9461
}// end loop over 'r'
9462
for (unsigned int r = 0; r < 1; r++)
9463
{
9464
for (unsigned int s = 1; s < 2 - r; s++)
9465
{
9466
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
9467
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
9468
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
9469
tmp5 = (2.00000000 + 2.00000000*r + 2.00000000*s)*(3.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
9470
tmp6 = (1.00000000 + 4.00000000*r*r + 4.00000000*r)*(2.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
9471
tmp7 = (1.00000000 + s + 2.00000000*r)*(3.00000000 + 2.00000000*r + 2.00000000*s)*s/((1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
9472
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
9473
}// end loop over 's'
9474
}// end loop over 'r'
9475
for (unsigned int r = 0; r < 2; r++)
9476
{
9477
for (unsigned int s = 0; s < 2 - r; s++)
9478
{
9479
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
9480
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
9481
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
9482
}// end loop over 's'
9483
}// end loop over 'r'
9484
for (unsigned int r = 0; r < 1; r++)
9485
{
9486
for (unsigned int s = 0; s < 1 - r; s++)
9487
{
9488
for (unsigned int t = 1; t < 2 - r - s; t++)
9489
{
9490
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
9491
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
9492
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
9493
tmp5 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)/(2.00000000*(1.00000000 + t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
9494
tmp6 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 4.00000000*r*r + 4.00000000*s*s + 8.00000000*r*s + 8.00000000*r + 8.00000000*s)/(2.00000000*(1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
9495
tmp7 = (2.00000000 + t + 2.00000000*r + 2.00000000*s)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*t/((1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
9496
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
9497
}// end loop over 't'
9498
}// end loop over 's'
9499
}// end loop over 'r'
9500
for (unsigned int r = 0; r < 3; r++)
9501
{
9502
for (unsigned int s = 0; s < 3 - r; s++)
9503
{
9504
for (unsigned int t = 0; t < 3 - r - s; t++)
9505
{
9506
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
9507
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
9508
}// end loop over 't'
9509
}// end loop over 's'
9510
}// end loop over 'r'
9511
9512
// Table(s) of coefficients.
9513
static const double coefficients0[10] = \
9514
{0.23094011, -0.12171612, 0.07027284, -0.09938080, 0.00000000, -0.10079053, 0.02057378, -0.08728716, -0.01187828, 0.01679842};
9515
9516
// Tables of derivatives of the polynomial base (transpose).
9517
static const double dmats0[10][10] = \
9518
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9519
{6.32455532, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9520
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9521
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9522
{0.00000000, 11.22497216, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9523
{4.58257569, 0.00000000, 8.36660027, -1.18321596, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9524
{3.74165739, 0.00000000, 0.00000000, 8.69482605, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9525
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9526
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9527
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
9528
9529
static const double dmats1[10][10] = \
9530
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9531
{3.16227766, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9532
{5.47722558, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9533
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9534
{2.95803989, 5.61248608, -1.08012345, -0.76376262, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9535
{2.29128785, 7.24568837, 4.18330013, -0.59160798, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9536
{1.87082869, 0.00000000, 0.00000000, 4.34741302, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9537
{-2.64575131, 0.00000000, 9.66091783, 0.68313005, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9538
{3.24037035, 0.00000000, 0.00000000, 7.52994024, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9539
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
9540
9541
static const double dmats2[10][10] = \
9542
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9543
{3.16227766, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9544
{1.82574186, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9545
{5.16397779, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9546
{2.95803989, 5.61248608, -1.08012345, -0.76376262, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9547
{2.29128785, 1.44913767, 4.18330013, -0.59160798, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9548
{1.87082869, 7.09929574, 0.00000000, 4.34741302, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9549
{1.32287566, 0.00000000, 3.86436713, -0.34156503, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9550
{1.08012345, 0.00000000, 7.09929574, 2.50998008, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9551
{-3.81881308, 0.00000000, 0.00000000, 8.87411967, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
9552
9553
// Compute reference derivatives.
9554
// Declare pointer to array of derivatives on FIAT element.
9555
double *derivatives = new double[num_derivatives];
9556
for (unsigned int r = 0; r < num_derivatives; r++)
9557
{
9558
derivatives[r] = 0.00000000;
9559
}// end loop over 'r'
9560
9561
// Declare derivative matrix (of polynomial basis).
9562
double dmats[10][10] = \
9563
{{1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9564
{0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9565
{0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9566
{0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9567
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9568
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9569
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000},
9570
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000},
9571
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000},
9572
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000}};
9573
9574
// Declare (auxiliary) derivative matrix (of polynomial basis).
9575
double dmats_old[10][10] = \
9576
{{1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9577
{0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9578
{0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9579
{0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9580
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9581
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9582
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000},
9583
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000},
9584
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000},
9585
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000}};
9586
9587
// Loop possible derivatives.
9588
for (unsigned int r = 0; r < num_derivatives; r++)
9589
{
9590
// Resetting dmats values to compute next derivative.
9591
for (unsigned int t = 0; t < 10; t++)
9592
{
9593
for (unsigned int u = 0; u < 10; u++)
9594
{
9595
dmats[t][u] = 0.00000000;
9596
if (t == u)
9597
{
9598
dmats[t][u] = 1.00000000;
9599
}
9600
9601
}// end loop over 'u'
9602
}// end loop over 't'
9603
9604
// Looping derivative order to generate dmats.
9605
for (unsigned int s = 0; s < n; s++)
9606
{
9607
// Updating dmats_old with new values and resetting dmats.
9608
for (unsigned int t = 0; t < 10; t++)
9609
{
9610
for (unsigned int u = 0; u < 10; u++)
9611
{
9612
dmats_old[t][u] = dmats[t][u];
9613
dmats[t][u] = 0.00000000;
9614
}// end loop over 'u'
9615
}// end loop over 't'
9616
9617
// Update dmats using an inner product.
9618
if (combinations[r][s] == 0)
9619
{
9620
for (unsigned int t = 0; t < 10; t++)
9621
{
9622
for (unsigned int u = 0; u < 10; u++)
9623
{
9624
for (unsigned int tu = 0; tu < 10; tu++)
9625
{
9626
dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
9627
}// end loop over 'tu'
9628
}// end loop over 'u'
9629
}// end loop over 't'
9630
}
9631
9632
if (combinations[r][s] == 1)
9633
{
9634
for (unsigned int t = 0; t < 10; t++)
9635
{
9636
for (unsigned int u = 0; u < 10; u++)
9637
{
9638
for (unsigned int tu = 0; tu < 10; tu++)
9639
{
9640
dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
9641
}// end loop over 'tu'
9642
}// end loop over 'u'
9643
}// end loop over 't'
9644
}
9645
9646
if (combinations[r][s] == 2)
9647
{
9648
for (unsigned int t = 0; t < 10; t++)
9649
{
9650
for (unsigned int u = 0; u < 10; u++)
9651
{
9652
for (unsigned int tu = 0; tu < 10; tu++)
9653
{
9654
dmats[t][u] += dmats2[t][tu]*dmats_old[tu][u];
9655
}// end loop over 'tu'
9656
}// end loop over 'u'
9657
}// end loop over 't'
9658
}
9659
9660
}// end loop over 's'
9661
for (unsigned int s = 0; s < 10; s++)
9662
{
9663
for (unsigned int t = 0; t < 10; t++)
9664
{
9665
derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
9666
}// end loop over 't'
9667
}// end loop over 's'
9668
}// end loop over 'r'
9669
9670
// Transform derivatives back to physical element
9671
for (unsigned int r = 0; r < num_derivatives; r++)
9672
{
9673
for (unsigned int s = 0; s < num_derivatives; s++)
9674
{
9675
values[r] += transform[r][s]*derivatives[s];
9676
}// end loop over 's'
9677
}// end loop over 'r'
9678
9679
// Delete pointer to array of derivatives on FIAT element
9680
delete [] derivatives;
9681
9682
// Delete pointer to array of combinations of derivatives and transform
9683
for (unsigned int r = 0; r < num_derivatives; r++)
9684
{
9685
delete [] combinations[r];
9686
}// end loop over 'r'
9687
delete [] combinations;
9688
for (unsigned int r = 0; r < num_derivatives; r++)
9689
{
9690
delete [] transform[r];
9691
}// end loop over 'r'
9692
delete [] transform;
9693
break;
9694
}
9695
case 9:
9696
{
9697
9698
// Array of basisvalues.
9699
double basisvalues[10] = {0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000};
9700
9701
// Declare helper variables.
9702
unsigned int rr = 0;
9703
unsigned int ss = 0;
9704
unsigned int tt = 0;
9705
double tmp5 = 0.00000000;
9706
double tmp6 = 0.00000000;
9707
double tmp7 = 0.00000000;
9708
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
9709
double tmp1 = 0.25000000*(Y + Z)*(Y + Z);
9710
double tmp2 = 0.50000000*(1.00000000 + Z + 2.00000000*Y);
9711
double tmp3 = 0.50000000*(1.00000000 - Z);
9712
double tmp4 = tmp3*tmp3;
9713
9714
// Compute basisvalues.
9715
basisvalues[0] = 1.00000000;
9716
basisvalues[1] = tmp0;
9717
for (unsigned int r = 1; r < 2; r++)
9718
{
9719
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
9720
ss = r*(r + 1)*(r + 2)/6;
9721
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
9722
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.00000000 + 2.00000000*r)/(1.00000000 + r) - basisvalues[tt]*tmp1*r/(1.00000000 + r));
9723
}// end loop over 'r'
9724
for (unsigned int r = 0; r < 2; r++)
9725
{
9726
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
9727
ss = r*(r + 1)*(r + 2)/6;
9728
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
9729
}// end loop over 'r'
9730
for (unsigned int r = 0; r < 1; r++)
9731
{
9732
for (unsigned int s = 1; s < 2 - r; s++)
9733
{
9734
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
9735
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
9736
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
9737
tmp5 = (2.00000000 + 2.00000000*r + 2.00000000*s)*(3.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
9738
tmp6 = (1.00000000 + 4.00000000*r*r + 4.00000000*r)*(2.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
9739
tmp7 = (1.00000000 + s + 2.00000000*r)*(3.00000000 + 2.00000000*r + 2.00000000*s)*s/((1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
9740
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
9741
}// end loop over 's'
9742
}// end loop over 'r'
9743
for (unsigned int r = 0; r < 2; r++)
9744
{
9745
for (unsigned int s = 0; s < 2 - r; s++)
9746
{
9747
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
9748
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
9749
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
9750
}// end loop over 's'
9751
}// end loop over 'r'
9752
for (unsigned int r = 0; r < 1; r++)
9753
{
9754
for (unsigned int s = 0; s < 1 - r; s++)
9755
{
9756
for (unsigned int t = 1; t < 2 - r - s; t++)
9757
{
9758
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
9759
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
9760
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
9761
tmp5 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)/(2.00000000*(1.00000000 + t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
9762
tmp6 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 4.00000000*r*r + 4.00000000*s*s + 8.00000000*r*s + 8.00000000*r + 8.00000000*s)/(2.00000000*(1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
9763
tmp7 = (2.00000000 + t + 2.00000000*r + 2.00000000*s)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*t/((1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
9764
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
9765
}// end loop over 't'
9766
}// end loop over 's'
9767
}// end loop over 'r'
9768
for (unsigned int r = 0; r < 3; r++)
9769
{
9770
for (unsigned int s = 0; s < 3 - r; s++)
9771
{
9772
for (unsigned int t = 0; t < 3 - r - s; t++)
9773
{
9774
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
9775
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
9776
}// end loop over 't'
9777
}// end loop over 's'
9778
}// end loop over 'r'
9779
9780
// Table(s) of coefficients.
9781
static const double coefficients0[10] = \
9782
{0.23094011, 0.00000000, -0.14054567, -0.09938080, -0.13012001, 0.00000000, 0.00000000, 0.02909572, 0.02375655, 0.01679842};
9783
9784
// Tables of derivatives of the polynomial base (transpose).
9785
static const double dmats0[10][10] = \
9786
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9787
{6.32455532, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9788
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9789
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9790
{0.00000000, 11.22497216, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9791
{4.58257569, 0.00000000, 8.36660027, -1.18321596, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9792
{3.74165739, 0.00000000, 0.00000000, 8.69482605, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9793
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9794
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9795
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
9796
9797
static const double dmats1[10][10] = \
9798
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9799
{3.16227766, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9800
{5.47722558, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9801
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9802
{2.95803989, 5.61248608, -1.08012345, -0.76376262, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9803
{2.29128785, 7.24568837, 4.18330013, -0.59160798, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9804
{1.87082869, 0.00000000, 0.00000000, 4.34741302, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9805
{-2.64575131, 0.00000000, 9.66091783, 0.68313005, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9806
{3.24037035, 0.00000000, 0.00000000, 7.52994024, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9807
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
9808
9809
static const double dmats2[10][10] = \
9810
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9811
{3.16227766, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9812
{1.82574186, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9813
{5.16397779, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9814
{2.95803989, 5.61248608, -1.08012345, -0.76376262, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9815
{2.29128785, 1.44913767, 4.18330013, -0.59160798, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9816
{1.87082869, 7.09929574, 0.00000000, 4.34741302, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9817
{1.32287566, 0.00000000, 3.86436713, -0.34156503, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9818
{1.08012345, 0.00000000, 7.09929574, 2.50998008, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9819
{-3.81881308, 0.00000000, 0.00000000, 8.87411967, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
9820
9821
// Compute reference derivatives.
9822
// Declare pointer to array of derivatives on FIAT element.
9823
double *derivatives = new double[num_derivatives];
9824
for (unsigned int r = 0; r < num_derivatives; r++)
9825
{
9826
derivatives[r] = 0.00000000;
9827
}// end loop over 'r'
9828
9829
// Declare derivative matrix (of polynomial basis).
9830
double dmats[10][10] = \
9831
{{1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9832
{0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9833
{0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9834
{0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9835
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9836
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9837
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000},
9838
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000},
9839
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000},
9840
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000}};
9841
9842
// Declare (auxiliary) derivative matrix (of polynomial basis).
9843
double dmats_old[10][10] = \
9844
{{1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9845
{0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9846
{0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9847
{0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9848
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9849
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
9850
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000},
9851
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000},
9852
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000},
9853
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000}};
9854
9855
// Loop possible derivatives.
9856
for (unsigned int r = 0; r < num_derivatives; r++)
9857
{
9858
// Resetting dmats values to compute next derivative.
9859
for (unsigned int t = 0; t < 10; t++)
9860
{
9861
for (unsigned int u = 0; u < 10; u++)
9862
{
9863
dmats[t][u] = 0.00000000;
9864
if (t == u)
9865
{
9866
dmats[t][u] = 1.00000000;
9867
}
9868
9869
}// end loop over 'u'
9870
}// end loop over 't'
9871
9872
// Looping derivative order to generate dmats.
9873
for (unsigned int s = 0; s < n; s++)
9874
{
9875
// Updating dmats_old with new values and resetting dmats.
9876
for (unsigned int t = 0; t < 10; t++)
9877
{
9878
for (unsigned int u = 0; u < 10; u++)
9879
{
9880
dmats_old[t][u] = dmats[t][u];
9881
dmats[t][u] = 0.00000000;
9882
}// end loop over 'u'
9883
}// end loop over 't'
9884
9885
// Update dmats using an inner product.
9886
if (combinations[r][s] == 0)
9887
{
9888
for (unsigned int t = 0; t < 10; t++)
9889
{
9890
for (unsigned int u = 0; u < 10; u++)
9891
{
9892
for (unsigned int tu = 0; tu < 10; tu++)
9893
{
9894
dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
9895
}// end loop over 'tu'
9896
}// end loop over 'u'
9897
}// end loop over 't'
9898
}
9899
9900
if (combinations[r][s] == 1)
9901
{
9902
for (unsigned int t = 0; t < 10; t++)
9903
{
9904
for (unsigned int u = 0; u < 10; u++)
9905
{
9906
for (unsigned int tu = 0; tu < 10; tu++)
9907
{
9908
dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
9909
}// end loop over 'tu'
9910
}// end loop over 'u'
9911
}// end loop over 't'
9912
}
9913
9914
if (combinations[r][s] == 2)
9915
{
9916
for (unsigned int t = 0; t < 10; t++)
9917
{
9918
for (unsigned int u = 0; u < 10; u++)
9919
{
9920
for (unsigned int tu = 0; tu < 10; tu++)
9921
{
9922
dmats[t][u] += dmats2[t][tu]*dmats_old[tu][u];
9923
}// end loop over 'tu'
9924
}// end loop over 'u'
9925
}// end loop over 't'
9926
}
9927
9928
}// end loop over 's'
9929
for (unsigned int s = 0; s < 10; s++)
9930
{
9931
for (unsigned int t = 0; t < 10; t++)
9932
{
9933
derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
9934
}// end loop over 't'
9935
}// end loop over 's'
9936
}// end loop over 'r'
9937
9938
// Transform derivatives back to physical element
9939
for (unsigned int r = 0; r < num_derivatives; r++)
9940
{
9941
for (unsigned int s = 0; s < num_derivatives; s++)
9942
{
9943
values[r] += transform[r][s]*derivatives[s];
9944
}// end loop over 's'
9945
}// end loop over 'r'
9946
9947
// Delete pointer to array of derivatives on FIAT element
9948
delete [] derivatives;
9949
9950
// Delete pointer to array of combinations of derivatives and transform
9951
for (unsigned int r = 0; r < num_derivatives; r++)
9952
{
9953
delete [] combinations[r];
9954
}// end loop over 'r'
9955
delete [] combinations;
9956
for (unsigned int r = 0; r < num_derivatives; r++)
9957
{
9958
delete [] transform[r];
9959
}// end loop over 'r'
9960
delete [] transform;
9961
break;
9962
}
9963
case 10:
9964
{
9965
9966
// Array of basisvalues.
9967
double basisvalues[10] = {0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000};
9968
9969
// Declare helper variables.
9970
unsigned int rr = 0;
9971
unsigned int ss = 0;
9972
unsigned int tt = 0;
9973
double tmp5 = 0.00000000;
9974
double tmp6 = 0.00000000;
9975
double tmp7 = 0.00000000;
9976
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
9977
double tmp1 = 0.25000000*(Y + Z)*(Y + Z);
9978
double tmp2 = 0.50000000*(1.00000000 + Z + 2.00000000*Y);
9979
double tmp3 = 0.50000000*(1.00000000 - Z);
9980
double tmp4 = tmp3*tmp3;
9981
9982
// Compute basisvalues.
9983
basisvalues[0] = 1.00000000;
9984
basisvalues[1] = tmp0;
9985
for (unsigned int r = 1; r < 2; r++)
9986
{
9987
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
9988
ss = r*(r + 1)*(r + 2)/6;
9989
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
9990
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.00000000 + 2.00000000*r)/(1.00000000 + r) - basisvalues[tt]*tmp1*r/(1.00000000 + r));
9991
}// end loop over 'r'
9992
for (unsigned int r = 0; r < 2; r++)
9993
{
9994
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
9995
ss = r*(r + 1)*(r + 2)/6;
9996
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
9997
}// end loop over 'r'
9998
for (unsigned int r = 0; r < 1; r++)
9999
{
10000
for (unsigned int s = 1; s < 2 - r; s++)
10001
{
10002
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
10003
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
10004
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
10005
tmp5 = (2.00000000 + 2.00000000*r + 2.00000000*s)*(3.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
10006
tmp6 = (1.00000000 + 4.00000000*r*r + 4.00000000*r)*(2.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
10007
tmp7 = (1.00000000 + s + 2.00000000*r)*(3.00000000 + 2.00000000*r + 2.00000000*s)*s/((1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
10008
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
10009
}// end loop over 's'
10010
}// end loop over 'r'
10011
for (unsigned int r = 0; r < 2; r++)
10012
{
10013
for (unsigned int s = 0; s < 2 - r; s++)
10014
{
10015
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
10016
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
10017
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
10018
}// end loop over 's'
10019
}// end loop over 'r'
10020
for (unsigned int r = 0; r < 1; r++)
10021
{
10022
for (unsigned int s = 0; s < 1 - r; s++)
10023
{
10024
for (unsigned int t = 1; t < 2 - r - s; t++)
10025
{
10026
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
10027
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
10028
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
10029
tmp5 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)/(2.00000000*(1.00000000 + t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
10030
tmp6 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 4.00000000*r*r + 4.00000000*s*s + 8.00000000*r*s + 8.00000000*r + 8.00000000*s)/(2.00000000*(1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
10031
tmp7 = (2.00000000 + t + 2.00000000*r + 2.00000000*s)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*t/((1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
10032
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
10033
}// end loop over 't'
10034
}// end loop over 's'
10035
}// end loop over 'r'
10036
for (unsigned int r = 0; r < 3; r++)
10037
{
10038
for (unsigned int s = 0; s < 3 - r; s++)
10039
{
10040
for (unsigned int t = 0; t < 3 - r - s; t++)
10041
{
10042
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
10043
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
10044
}// end loop over 't'
10045
}// end loop over 's'
10046
}// end loop over 'r'
10047
10048
// Table(s) of coefficients.
10049
static const double coefficients0[10] = \
10050
{-0.05773503, -0.06085806, -0.03513642, -0.02484520, 0.06506000, 0.05039526, 0.04114756, 0.02909572, 0.02375655, 0.01679842};
10051
10052
// Tables of derivatives of the polynomial base (transpose).
10053
static const double dmats0[10][10] = \
10054
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10055
{6.32455532, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10056
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10057
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10058
{0.00000000, 11.22497216, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10059
{4.58257569, 0.00000000, 8.36660027, -1.18321596, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10060
{3.74165739, 0.00000000, 0.00000000, 8.69482605, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10061
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10062
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10063
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
10064
10065
static const double dmats1[10][10] = \
10066
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10067
{3.16227766, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10068
{5.47722558, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10069
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10070
{2.95803989, 5.61248608, -1.08012345, -0.76376262, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10071
{2.29128785, 7.24568837, 4.18330013, -0.59160798, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10072
{1.87082869, 0.00000000, 0.00000000, 4.34741302, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10073
{-2.64575131, 0.00000000, 9.66091783, 0.68313005, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10074
{3.24037035, 0.00000000, 0.00000000, 7.52994024, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10075
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
10076
10077
static const double dmats2[10][10] = \
10078
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10079
{3.16227766, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10080
{1.82574186, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10081
{5.16397779, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10082
{2.95803989, 5.61248608, -1.08012345, -0.76376262, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10083
{2.29128785, 1.44913767, 4.18330013, -0.59160798, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10084
{1.87082869, 7.09929574, 0.00000000, 4.34741302, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10085
{1.32287566, 0.00000000, 3.86436713, -0.34156503, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10086
{1.08012345, 0.00000000, 7.09929574, 2.50998008, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10087
{-3.81881308, 0.00000000, 0.00000000, 8.87411967, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
10088
10089
// Compute reference derivatives.
10090
// Declare pointer to array of derivatives on FIAT element.
10091
double *derivatives = new double[num_derivatives];
10092
for (unsigned int r = 0; r < num_derivatives; r++)
10093
{
10094
derivatives[r] = 0.00000000;
10095
}// end loop over 'r'
10096
10097
// Declare derivative matrix (of polynomial basis).
10098
double dmats[10][10] = \
10099
{{1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10100
{0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10101
{0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10102
{0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10103
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10104
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10105
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000},
10106
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000},
10107
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000},
10108
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000}};
10109
10110
// Declare (auxiliary) derivative matrix (of polynomial basis).
10111
double dmats_old[10][10] = \
10112
{{1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10113
{0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10114
{0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10115
{0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10116
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10117
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10118
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000},
10119
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000},
10120
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000},
10121
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000}};
10122
10123
// Loop possible derivatives.
10124
for (unsigned int r = 0; r < num_derivatives; r++)
10125
{
10126
// Resetting dmats values to compute next derivative.
10127
for (unsigned int t = 0; t < 10; t++)
10128
{
10129
for (unsigned int u = 0; u < 10; u++)
10130
{
10131
dmats[t][u] = 0.00000000;
10132
if (t == u)
10133
{
10134
dmats[t][u] = 1.00000000;
10135
}
10136
10137
}// end loop over 'u'
10138
}// end loop over 't'
10139
10140
// Looping derivative order to generate dmats.
10141
for (unsigned int s = 0; s < n; s++)
10142
{
10143
// Updating dmats_old with new values and resetting dmats.
10144
for (unsigned int t = 0; t < 10; t++)
10145
{
10146
for (unsigned int u = 0; u < 10; u++)
10147
{
10148
dmats_old[t][u] = dmats[t][u];
10149
dmats[t][u] = 0.00000000;
10150
}// end loop over 'u'
10151
}// end loop over 't'
10152
10153
// Update dmats using an inner product.
10154
if (combinations[r][s] == 0)
10155
{
10156
for (unsigned int t = 0; t < 10; t++)
10157
{
10158
for (unsigned int u = 0; u < 10; u++)
10159
{
10160
for (unsigned int tu = 0; tu < 10; tu++)
10161
{
10162
dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
10163
}// end loop over 'tu'
10164
}// end loop over 'u'
10165
}// end loop over 't'
10166
}
10167
10168
if (combinations[r][s] == 1)
10169
{
10170
for (unsigned int t = 0; t < 10; t++)
10171
{
10172
for (unsigned int u = 0; u < 10; u++)
10173
{
10174
for (unsigned int tu = 0; tu < 10; tu++)
10175
{
10176
dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
10177
}// end loop over 'tu'
10178
}// end loop over 'u'
10179
}// end loop over 't'
10180
}
10181
10182
if (combinations[r][s] == 2)
10183
{
10184
for (unsigned int t = 0; t < 10; t++)
10185
{
10186
for (unsigned int u = 0; u < 10; u++)
10187
{
10188
for (unsigned int tu = 0; tu < 10; tu++)
10189
{
10190
dmats[t][u] += dmats2[t][tu]*dmats_old[tu][u];
10191
}// end loop over 'tu'
10192
}// end loop over 'u'
10193
}// end loop over 't'
10194
}
10195
10196
}// end loop over 's'
10197
for (unsigned int s = 0; s < 10; s++)
10198
{
10199
for (unsigned int t = 0; t < 10; t++)
10200
{
10201
derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
10202
}// end loop over 't'
10203
}// end loop over 's'
10204
}// end loop over 'r'
10205
10206
// Transform derivatives back to physical element
10207
for (unsigned int r = 0; r < num_derivatives; r++)
10208
{
10209
for (unsigned int s = 0; s < num_derivatives; s++)
10210
{
10211
values[num_derivatives + r] += transform[r][s]*derivatives[s];
10212
}// end loop over 's'
10213
}// end loop over 'r'
10214
10215
// Delete pointer to array of derivatives on FIAT element
10216
delete [] derivatives;
10217
10218
// Delete pointer to array of combinations of derivatives and transform
10219
for (unsigned int r = 0; r < num_derivatives; r++)
10220
{
10221
delete [] combinations[r];
10222
}// end loop over 'r'
10223
delete [] combinations;
10224
for (unsigned int r = 0; r < num_derivatives; r++)
10225
{
10226
delete [] transform[r];
10227
}// end loop over 'r'
10228
delete [] transform;
10229
break;
10230
}
10231
case 11:
10232
{
10233
10234
// Array of basisvalues.
10235
double basisvalues[10] = {0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000};
10236
10237
// Declare helper variables.
10238
unsigned int rr = 0;
10239
unsigned int ss = 0;
10240
unsigned int tt = 0;
10241
double tmp5 = 0.00000000;
10242
double tmp6 = 0.00000000;
10243
double tmp7 = 0.00000000;
10244
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
10245
double tmp1 = 0.25000000*(Y + Z)*(Y + Z);
10246
double tmp2 = 0.50000000*(1.00000000 + Z + 2.00000000*Y);
10247
double tmp3 = 0.50000000*(1.00000000 - Z);
10248
double tmp4 = tmp3*tmp3;
10249
10250
// Compute basisvalues.
10251
basisvalues[0] = 1.00000000;
10252
basisvalues[1] = tmp0;
10253
for (unsigned int r = 1; r < 2; r++)
10254
{
10255
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
10256
ss = r*(r + 1)*(r + 2)/6;
10257
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
10258
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.00000000 + 2.00000000*r)/(1.00000000 + r) - basisvalues[tt]*tmp1*r/(1.00000000 + r));
10259
}// end loop over 'r'
10260
for (unsigned int r = 0; r < 2; r++)
10261
{
10262
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
10263
ss = r*(r + 1)*(r + 2)/6;
10264
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
10265
}// end loop over 'r'
10266
for (unsigned int r = 0; r < 1; r++)
10267
{
10268
for (unsigned int s = 1; s < 2 - r; s++)
10269
{
10270
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
10271
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
10272
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
10273
tmp5 = (2.00000000 + 2.00000000*r + 2.00000000*s)*(3.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
10274
tmp6 = (1.00000000 + 4.00000000*r*r + 4.00000000*r)*(2.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
10275
tmp7 = (1.00000000 + s + 2.00000000*r)*(3.00000000 + 2.00000000*r + 2.00000000*s)*s/((1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
10276
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
10277
}// end loop over 's'
10278
}// end loop over 'r'
10279
for (unsigned int r = 0; r < 2; r++)
10280
{
10281
for (unsigned int s = 0; s < 2 - r; s++)
10282
{
10283
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
10284
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
10285
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
10286
}// end loop over 's'
10287
}// end loop over 'r'
10288
for (unsigned int r = 0; r < 1; r++)
10289
{
10290
for (unsigned int s = 0; s < 1 - r; s++)
10291
{
10292
for (unsigned int t = 1; t < 2 - r - s; t++)
10293
{
10294
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
10295
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
10296
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
10297
tmp5 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)/(2.00000000*(1.00000000 + t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
10298
tmp6 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 4.00000000*r*r + 4.00000000*s*s + 8.00000000*r*s + 8.00000000*r + 8.00000000*s)/(2.00000000*(1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
10299
tmp7 = (2.00000000 + t + 2.00000000*r + 2.00000000*s)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*t/((1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
10300
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
10301
}// end loop over 't'
10302
}// end loop over 's'
10303
}// end loop over 'r'
10304
for (unsigned int r = 0; r < 3; r++)
10305
{
10306
for (unsigned int s = 0; s < 3 - r; s++)
10307
{
10308
for (unsigned int t = 0; t < 3 - r - s; t++)
10309
{
10310
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
10311
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
10312
}// end loop over 't'
10313
}// end loop over 's'
10314
}// end loop over 'r'
10315
10316
// Table(s) of coefficients.
10317
static const double coefficients0[10] = \
10318
{-0.05773503, 0.06085806, -0.03513642, -0.02484520, 0.06506000, -0.05039526, -0.04114756, 0.02909572, 0.02375655, 0.01679842};
10319
10320
// Tables of derivatives of the polynomial base (transpose).
10321
static const double dmats0[10][10] = \
10322
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10323
{6.32455532, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10324
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10325
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10326
{0.00000000, 11.22497216, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10327
{4.58257569, 0.00000000, 8.36660027, -1.18321596, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10328
{3.74165739, 0.00000000, 0.00000000, 8.69482605, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10329
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10330
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10331
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
10332
10333
static const double dmats1[10][10] = \
10334
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10335
{3.16227766, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10336
{5.47722558, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10337
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10338
{2.95803989, 5.61248608, -1.08012345, -0.76376262, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10339
{2.29128785, 7.24568837, 4.18330013, -0.59160798, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10340
{1.87082869, 0.00000000, 0.00000000, 4.34741302, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10341
{-2.64575131, 0.00000000, 9.66091783, 0.68313005, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10342
{3.24037035, 0.00000000, 0.00000000, 7.52994024, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10343
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
10344
10345
static const double dmats2[10][10] = \
10346
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10347
{3.16227766, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10348
{1.82574186, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10349
{5.16397779, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10350
{2.95803989, 5.61248608, -1.08012345, -0.76376262, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10351
{2.29128785, 1.44913767, 4.18330013, -0.59160798, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10352
{1.87082869, 7.09929574, 0.00000000, 4.34741302, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10353
{1.32287566, 0.00000000, 3.86436713, -0.34156503, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10354
{1.08012345, 0.00000000, 7.09929574, 2.50998008, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10355
{-3.81881308, 0.00000000, 0.00000000, 8.87411967, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
10356
10357
// Compute reference derivatives.
10358
// Declare pointer to array of derivatives on FIAT element.
10359
double *derivatives = new double[num_derivatives];
10360
for (unsigned int r = 0; r < num_derivatives; r++)
10361
{
10362
derivatives[r] = 0.00000000;
10363
}// end loop over 'r'
10364
10365
// Declare derivative matrix (of polynomial basis).
10366
double dmats[10][10] = \
10367
{{1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10368
{0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10369
{0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10370
{0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10371
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10372
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10373
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000},
10374
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000},
10375
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000},
10376
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000}};
10377
10378
// Declare (auxiliary) derivative matrix (of polynomial basis).
10379
double dmats_old[10][10] = \
10380
{{1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10381
{0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10382
{0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10383
{0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10384
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10385
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10386
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000},
10387
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000},
10388
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000},
10389
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000}};
10390
10391
// Loop possible derivatives.
10392
for (unsigned int r = 0; r < num_derivatives; r++)
10393
{
10394
// Resetting dmats values to compute next derivative.
10395
for (unsigned int t = 0; t < 10; t++)
10396
{
10397
for (unsigned int u = 0; u < 10; u++)
10398
{
10399
dmats[t][u] = 0.00000000;
10400
if (t == u)
10401
{
10402
dmats[t][u] = 1.00000000;
10403
}
10404
10405
}// end loop over 'u'
10406
}// end loop over 't'
10407
10408
// Looping derivative order to generate dmats.
10409
for (unsigned int s = 0; s < n; s++)
10410
{
10411
// Updating dmats_old with new values and resetting dmats.
10412
for (unsigned int t = 0; t < 10; t++)
10413
{
10414
for (unsigned int u = 0; u < 10; u++)
10415
{
10416
dmats_old[t][u] = dmats[t][u];
10417
dmats[t][u] = 0.00000000;
10418
}// end loop over 'u'
10419
}// end loop over 't'
10420
10421
// Update dmats using an inner product.
10422
if (combinations[r][s] == 0)
10423
{
10424
for (unsigned int t = 0; t < 10; t++)
10425
{
10426
for (unsigned int u = 0; u < 10; u++)
10427
{
10428
for (unsigned int tu = 0; tu < 10; tu++)
10429
{
10430
dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
10431
}// end loop over 'tu'
10432
}// end loop over 'u'
10433
}// end loop over 't'
10434
}
10435
10436
if (combinations[r][s] == 1)
10437
{
10438
for (unsigned int t = 0; t < 10; t++)
10439
{
10440
for (unsigned int u = 0; u < 10; u++)
10441
{
10442
for (unsigned int tu = 0; tu < 10; tu++)
10443
{
10444
dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
10445
}// end loop over 'tu'
10446
}// end loop over 'u'
10447
}// end loop over 't'
10448
}
10449
10450
if (combinations[r][s] == 2)
10451
{
10452
for (unsigned int t = 0; t < 10; t++)
10453
{
10454
for (unsigned int u = 0; u < 10; u++)
10455
{
10456
for (unsigned int tu = 0; tu < 10; tu++)
10457
{
10458
dmats[t][u] += dmats2[t][tu]*dmats_old[tu][u];
10459
}// end loop over 'tu'
10460
}// end loop over 'u'
10461
}// end loop over 't'
10462
}
10463
10464
}// end loop over 's'
10465
for (unsigned int s = 0; s < 10; s++)
10466
{
10467
for (unsigned int t = 0; t < 10; t++)
10468
{
10469
derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
10470
}// end loop over 't'
10471
}// end loop over 's'
10472
}// end loop over 'r'
10473
10474
// Transform derivatives back to physical element
10475
for (unsigned int r = 0; r < num_derivatives; r++)
10476
{
10477
for (unsigned int s = 0; s < num_derivatives; s++)
10478
{
10479
values[num_derivatives + r] += transform[r][s]*derivatives[s];
10480
}// end loop over 's'
10481
}// end loop over 'r'
10482
10483
// Delete pointer to array of derivatives on FIAT element
10484
delete [] derivatives;
10485
10486
// Delete pointer to array of combinations of derivatives and transform
10487
for (unsigned int r = 0; r < num_derivatives; r++)
10488
{
10489
delete [] combinations[r];
10490
}// end loop over 'r'
10491
delete [] combinations;
10492
for (unsigned int r = 0; r < num_derivatives; r++)
10493
{
10494
delete [] transform[r];
10495
}// end loop over 'r'
10496
delete [] transform;
10497
break;
10498
}
10499
case 12:
10500
{
10501
10502
// Array of basisvalues.
10503
double basisvalues[10] = {0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000};
10504
10505
// Declare helper variables.
10506
unsigned int rr = 0;
10507
unsigned int ss = 0;
10508
unsigned int tt = 0;
10509
double tmp5 = 0.00000000;
10510
double tmp6 = 0.00000000;
10511
double tmp7 = 0.00000000;
10512
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
10513
double tmp1 = 0.25000000*(Y + Z)*(Y + Z);
10514
double tmp2 = 0.50000000*(1.00000000 + Z + 2.00000000*Y);
10515
double tmp3 = 0.50000000*(1.00000000 - Z);
10516
double tmp4 = tmp3*tmp3;
10517
10518
// Compute basisvalues.
10519
basisvalues[0] = 1.00000000;
10520
basisvalues[1] = tmp0;
10521
for (unsigned int r = 1; r < 2; r++)
10522
{
10523
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
10524
ss = r*(r + 1)*(r + 2)/6;
10525
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
10526
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.00000000 + 2.00000000*r)/(1.00000000 + r) - basisvalues[tt]*tmp1*r/(1.00000000 + r));
10527
}// end loop over 'r'
10528
for (unsigned int r = 0; r < 2; r++)
10529
{
10530
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
10531
ss = r*(r + 1)*(r + 2)/6;
10532
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
10533
}// end loop over 'r'
10534
for (unsigned int r = 0; r < 1; r++)
10535
{
10536
for (unsigned int s = 1; s < 2 - r; s++)
10537
{
10538
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
10539
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
10540
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
10541
tmp5 = (2.00000000 + 2.00000000*r + 2.00000000*s)*(3.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
10542
tmp6 = (1.00000000 + 4.00000000*r*r + 4.00000000*r)*(2.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
10543
tmp7 = (1.00000000 + s + 2.00000000*r)*(3.00000000 + 2.00000000*r + 2.00000000*s)*s/((1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
10544
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
10545
}// end loop over 's'
10546
}// end loop over 'r'
10547
for (unsigned int r = 0; r < 2; r++)
10548
{
10549
for (unsigned int s = 0; s < 2 - r; s++)
10550
{
10551
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
10552
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
10553
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
10554
}// end loop over 's'
10555
}// end loop over 'r'
10556
for (unsigned int r = 0; r < 1; r++)
10557
{
10558
for (unsigned int s = 0; s < 1 - r; s++)
10559
{
10560
for (unsigned int t = 1; t < 2 - r - s; t++)
10561
{
10562
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
10563
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
10564
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
10565
tmp5 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)/(2.00000000*(1.00000000 + t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
10566
tmp6 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 4.00000000*r*r + 4.00000000*s*s + 8.00000000*r*s + 8.00000000*r + 8.00000000*s)/(2.00000000*(1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
10567
tmp7 = (2.00000000 + t + 2.00000000*r + 2.00000000*s)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*t/((1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
10568
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
10569
}// end loop over 't'
10570
}// end loop over 's'
10571
}// end loop over 'r'
10572
for (unsigned int r = 0; r < 3; r++)
10573
{
10574
for (unsigned int s = 0; s < 3 - r; s++)
10575
{
10576
for (unsigned int t = 0; t < 3 - r - s; t++)
10577
{
10578
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
10579
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
10580
}// end loop over 't'
10581
}// end loop over 's'
10582
}// end loop over 'r'
10583
10584
// Table(s) of coefficients.
10585
static const double coefficients0[10] = \
10586
{-0.05773503, 0.00000000, 0.07027284, -0.02484520, 0.00000000, 0.00000000, 0.00000000, 0.08728716, -0.04751311, 0.01679842};
10587
10588
// Tables of derivatives of the polynomial base (transpose).
10589
static const double dmats0[10][10] = \
10590
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10591
{6.32455532, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10592
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10593
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10594
{0.00000000, 11.22497216, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10595
{4.58257569, 0.00000000, 8.36660027, -1.18321596, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10596
{3.74165739, 0.00000000, 0.00000000, 8.69482605, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10597
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10598
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10599
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
10600
10601
static const double dmats1[10][10] = \
10602
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10603
{3.16227766, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10604
{5.47722558, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10605
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10606
{2.95803989, 5.61248608, -1.08012345, -0.76376262, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10607
{2.29128785, 7.24568837, 4.18330013, -0.59160798, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10608
{1.87082869, 0.00000000, 0.00000000, 4.34741302, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10609
{-2.64575131, 0.00000000, 9.66091783, 0.68313005, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10610
{3.24037035, 0.00000000, 0.00000000, 7.52994024, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10611
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
10612
10613
static const double dmats2[10][10] = \
10614
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10615
{3.16227766, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10616
{1.82574186, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10617
{5.16397779, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10618
{2.95803989, 5.61248608, -1.08012345, -0.76376262, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10619
{2.29128785, 1.44913767, 4.18330013, -0.59160798, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10620
{1.87082869, 7.09929574, 0.00000000, 4.34741302, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10621
{1.32287566, 0.00000000, 3.86436713, -0.34156503, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10622
{1.08012345, 0.00000000, 7.09929574, 2.50998008, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10623
{-3.81881308, 0.00000000, 0.00000000, 8.87411967, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
10624
10625
// Compute reference derivatives.
10626
// Declare pointer to array of derivatives on FIAT element.
10627
double *derivatives = new double[num_derivatives];
10628
for (unsigned int r = 0; r < num_derivatives; r++)
10629
{
10630
derivatives[r] = 0.00000000;
10631
}// end loop over 'r'
10632
10633
// Declare derivative matrix (of polynomial basis).
10634
double dmats[10][10] = \
10635
{{1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10636
{0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10637
{0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10638
{0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10639
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10640
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10641
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000},
10642
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000},
10643
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000},
10644
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000}};
10645
10646
// Declare (auxiliary) derivative matrix (of polynomial basis).
10647
double dmats_old[10][10] = \
10648
{{1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10649
{0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10650
{0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10651
{0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10652
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10653
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10654
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000},
10655
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000},
10656
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000},
10657
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000}};
10658
10659
// Loop possible derivatives.
10660
for (unsigned int r = 0; r < num_derivatives; r++)
10661
{
10662
// Resetting dmats values to compute next derivative.
10663
for (unsigned int t = 0; t < 10; t++)
10664
{
10665
for (unsigned int u = 0; u < 10; u++)
10666
{
10667
dmats[t][u] = 0.00000000;
10668
if (t == u)
10669
{
10670
dmats[t][u] = 1.00000000;
10671
}
10672
10673
}// end loop over 'u'
10674
}// end loop over 't'
10675
10676
// Looping derivative order to generate dmats.
10677
for (unsigned int s = 0; s < n; s++)
10678
{
10679
// Updating dmats_old with new values and resetting dmats.
10680
for (unsigned int t = 0; t < 10; t++)
10681
{
10682
for (unsigned int u = 0; u < 10; u++)
10683
{
10684
dmats_old[t][u] = dmats[t][u];
10685
dmats[t][u] = 0.00000000;
10686
}// end loop over 'u'
10687
}// end loop over 't'
10688
10689
// Update dmats using an inner product.
10690
if (combinations[r][s] == 0)
10691
{
10692
for (unsigned int t = 0; t < 10; t++)
10693
{
10694
for (unsigned int u = 0; u < 10; u++)
10695
{
10696
for (unsigned int tu = 0; tu < 10; tu++)
10697
{
10698
dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
10699
}// end loop over 'tu'
10700
}// end loop over 'u'
10701
}// end loop over 't'
10702
}
10703
10704
if (combinations[r][s] == 1)
10705
{
10706
for (unsigned int t = 0; t < 10; t++)
10707
{
10708
for (unsigned int u = 0; u < 10; u++)
10709
{
10710
for (unsigned int tu = 0; tu < 10; tu++)
10711
{
10712
dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
10713
}// end loop over 'tu'
10714
}// end loop over 'u'
10715
}// end loop over 't'
10716
}
10717
10718
if (combinations[r][s] == 2)
10719
{
10720
for (unsigned int t = 0; t < 10; t++)
10721
{
10722
for (unsigned int u = 0; u < 10; u++)
10723
{
10724
for (unsigned int tu = 0; tu < 10; tu++)
10725
{
10726
dmats[t][u] += dmats2[t][tu]*dmats_old[tu][u];
10727
}// end loop over 'tu'
10728
}// end loop over 'u'
10729
}// end loop over 't'
10730
}
10731
10732
}// end loop over 's'
10733
for (unsigned int s = 0; s < 10; s++)
10734
{
10735
for (unsigned int t = 0; t < 10; t++)
10736
{
10737
derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
10738
}// end loop over 't'
10739
}// end loop over 's'
10740
}// end loop over 'r'
10741
10742
// Transform derivatives back to physical element
10743
for (unsigned int r = 0; r < num_derivatives; r++)
10744
{
10745
for (unsigned int s = 0; s < num_derivatives; s++)
10746
{
10747
values[num_derivatives + r] += transform[r][s]*derivatives[s];
10748
}// end loop over 's'
10749
}// end loop over 'r'
10750
10751
// Delete pointer to array of derivatives on FIAT element
10752
delete [] derivatives;
10753
10754
// Delete pointer to array of combinations of derivatives and transform
10755
for (unsigned int r = 0; r < num_derivatives; r++)
10756
{
10757
delete [] combinations[r];
10758
}// end loop over 'r'
10759
delete [] combinations;
10760
for (unsigned int r = 0; r < num_derivatives; r++)
10761
{
10762
delete [] transform[r];
10763
}// end loop over 'r'
10764
delete [] transform;
10765
break;
10766
}
10767
case 13:
10768
{
10769
10770
// Array of basisvalues.
10771
double basisvalues[10] = {0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000};
10772
10773
// Declare helper variables.
10774
unsigned int rr = 0;
10775
unsigned int ss = 0;
10776
unsigned int tt = 0;
10777
double tmp5 = 0.00000000;
10778
double tmp6 = 0.00000000;
10779
double tmp7 = 0.00000000;
10780
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
10781
double tmp1 = 0.25000000*(Y + Z)*(Y + Z);
10782
double tmp2 = 0.50000000*(1.00000000 + Z + 2.00000000*Y);
10783
double tmp3 = 0.50000000*(1.00000000 - Z);
10784
double tmp4 = tmp3*tmp3;
10785
10786
// Compute basisvalues.
10787
basisvalues[0] = 1.00000000;
10788
basisvalues[1] = tmp0;
10789
for (unsigned int r = 1; r < 2; r++)
10790
{
10791
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
10792
ss = r*(r + 1)*(r + 2)/6;
10793
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
10794
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.00000000 + 2.00000000*r)/(1.00000000 + r) - basisvalues[tt]*tmp1*r/(1.00000000 + r));
10795
}// end loop over 'r'
10796
for (unsigned int r = 0; r < 2; r++)
10797
{
10798
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
10799
ss = r*(r + 1)*(r + 2)/6;
10800
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
10801
}// end loop over 'r'
10802
for (unsigned int r = 0; r < 1; r++)
10803
{
10804
for (unsigned int s = 1; s < 2 - r; s++)
10805
{
10806
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
10807
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
10808
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
10809
tmp5 = (2.00000000 + 2.00000000*r + 2.00000000*s)*(3.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
10810
tmp6 = (1.00000000 + 4.00000000*r*r + 4.00000000*r)*(2.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
10811
tmp7 = (1.00000000 + s + 2.00000000*r)*(3.00000000 + 2.00000000*r + 2.00000000*s)*s/((1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
10812
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
10813
}// end loop over 's'
10814
}// end loop over 'r'
10815
for (unsigned int r = 0; r < 2; r++)
10816
{
10817
for (unsigned int s = 0; s < 2 - r; s++)
10818
{
10819
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
10820
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
10821
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
10822
}// end loop over 's'
10823
}// end loop over 'r'
10824
for (unsigned int r = 0; r < 1; r++)
10825
{
10826
for (unsigned int s = 0; s < 1 - r; s++)
10827
{
10828
for (unsigned int t = 1; t < 2 - r - s; t++)
10829
{
10830
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
10831
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
10832
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
10833
tmp5 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)/(2.00000000*(1.00000000 + t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
10834
tmp6 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 4.00000000*r*r + 4.00000000*s*s + 8.00000000*r*s + 8.00000000*r + 8.00000000*s)/(2.00000000*(1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
10835
tmp7 = (2.00000000 + t + 2.00000000*r + 2.00000000*s)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*t/((1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
10836
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
10837
}// end loop over 't'
10838
}// end loop over 's'
10839
}// end loop over 'r'
10840
for (unsigned int r = 0; r < 3; r++)
10841
{
10842
for (unsigned int s = 0; s < 3 - r; s++)
10843
{
10844
for (unsigned int t = 0; t < 3 - r - s; t++)
10845
{
10846
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
10847
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
10848
}// end loop over 't'
10849
}// end loop over 's'
10850
}// end loop over 'r'
10851
10852
// Table(s) of coefficients.
10853
static const double coefficients0[10] = \
10854
{-0.05773503, 0.00000000, 0.00000000, 0.07453560, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.10079053};
10855
10856
// Tables of derivatives of the polynomial base (transpose).
10857
static const double dmats0[10][10] = \
10858
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10859
{6.32455532, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10860
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10861
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10862
{0.00000000, 11.22497216, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10863
{4.58257569, 0.00000000, 8.36660027, -1.18321596, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10864
{3.74165739, 0.00000000, 0.00000000, 8.69482605, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10865
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10866
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10867
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
10868
10869
static const double dmats1[10][10] = \
10870
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10871
{3.16227766, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10872
{5.47722558, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10873
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10874
{2.95803989, 5.61248608, -1.08012345, -0.76376262, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10875
{2.29128785, 7.24568837, 4.18330013, -0.59160798, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10876
{1.87082869, 0.00000000, 0.00000000, 4.34741302, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10877
{-2.64575131, 0.00000000, 9.66091783, 0.68313005, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10878
{3.24037035, 0.00000000, 0.00000000, 7.52994024, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10879
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
10880
10881
static const double dmats2[10][10] = \
10882
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10883
{3.16227766, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10884
{1.82574186, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10885
{5.16397779, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10886
{2.95803989, 5.61248608, -1.08012345, -0.76376262, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10887
{2.29128785, 1.44913767, 4.18330013, -0.59160798, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10888
{1.87082869, 7.09929574, 0.00000000, 4.34741302, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10889
{1.32287566, 0.00000000, 3.86436713, -0.34156503, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10890
{1.08012345, 0.00000000, 7.09929574, 2.50998008, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10891
{-3.81881308, 0.00000000, 0.00000000, 8.87411967, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
10892
10893
// Compute reference derivatives.
10894
// Declare pointer to array of derivatives on FIAT element.
10895
double *derivatives = new double[num_derivatives];
10896
for (unsigned int r = 0; r < num_derivatives; r++)
10897
{
10898
derivatives[r] = 0.00000000;
10899
}// end loop over 'r'
10900
10901
// Declare derivative matrix (of polynomial basis).
10902
double dmats[10][10] = \
10903
{{1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10904
{0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10905
{0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10906
{0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10907
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10908
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10909
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000},
10910
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000},
10911
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000},
10912
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000}};
10913
10914
// Declare (auxiliary) derivative matrix (of polynomial basis).
10915
double dmats_old[10][10] = \
10916
{{1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10917
{0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10918
{0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10919
{0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10920
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10921
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
10922
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000},
10923
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000},
10924
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000},
10925
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000}};
10926
10927
// Loop possible derivatives.
10928
for (unsigned int r = 0; r < num_derivatives; r++)
10929
{
10930
// Resetting dmats values to compute next derivative.
10931
for (unsigned int t = 0; t < 10; t++)
10932
{
10933
for (unsigned int u = 0; u < 10; u++)
10934
{
10935
dmats[t][u] = 0.00000000;
10936
if (t == u)
10937
{
10938
dmats[t][u] = 1.00000000;
10939
}
10940
10941
}// end loop over 'u'
10942
}// end loop over 't'
10943
10944
// Looping derivative order to generate dmats.
10945
for (unsigned int s = 0; s < n; s++)
10946
{
10947
// Updating dmats_old with new values and resetting dmats.
10948
for (unsigned int t = 0; t < 10; t++)
10949
{
10950
for (unsigned int u = 0; u < 10; u++)
10951
{
10952
dmats_old[t][u] = dmats[t][u];
10953
dmats[t][u] = 0.00000000;
10954
}// end loop over 'u'
10955
}// end loop over 't'
10956
10957
// Update dmats using an inner product.
10958
if (combinations[r][s] == 0)
10959
{
10960
for (unsigned int t = 0; t < 10; t++)
10961
{
10962
for (unsigned int u = 0; u < 10; u++)
10963
{
10964
for (unsigned int tu = 0; tu < 10; tu++)
10965
{
10966
dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
10967
}// end loop over 'tu'
10968
}// end loop over 'u'
10969
}// end loop over 't'
10970
}
10971
10972
if (combinations[r][s] == 1)
10973
{
10974
for (unsigned int t = 0; t < 10; t++)
10975
{
10976
for (unsigned int u = 0; u < 10; u++)
10977
{
10978
for (unsigned int tu = 0; tu < 10; tu++)
10979
{
10980
dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
10981
}// end loop over 'tu'
10982
}// end loop over 'u'
10983
}// end loop over 't'
10984
}
10985
10986
if (combinations[r][s] == 2)
10987
{
10988
for (unsigned int t = 0; t < 10; t++)
10989
{
10990
for (unsigned int u = 0; u < 10; u++)
10991
{
10992
for (unsigned int tu = 0; tu < 10; tu++)
10993
{
10994
dmats[t][u] += dmats2[t][tu]*dmats_old[tu][u];
10995
}// end loop over 'tu'
10996
}// end loop over 'u'
10997
}// end loop over 't'
10998
}
10999
11000
}// end loop over 's'
11001
for (unsigned int s = 0; s < 10; s++)
11002
{
11003
for (unsigned int t = 0; t < 10; t++)
11004
{
11005
derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
11006
}// end loop over 't'
11007
}// end loop over 's'
11008
}// end loop over 'r'
11009
11010
// Transform derivatives back to physical element
11011
for (unsigned int r = 0; r < num_derivatives; r++)
11012
{
11013
for (unsigned int s = 0; s < num_derivatives; s++)
11014
{
11015
values[num_derivatives + r] += transform[r][s]*derivatives[s];
11016
}// end loop over 's'
11017
}// end loop over 'r'
11018
11019
// Delete pointer to array of derivatives on FIAT element
11020
delete [] derivatives;
11021
11022
// Delete pointer to array of combinations of derivatives and transform
11023
for (unsigned int r = 0; r < num_derivatives; r++)
11024
{
11025
delete [] combinations[r];
11026
}// end loop over 'r'
11027
delete [] combinations;
11028
for (unsigned int r = 0; r < num_derivatives; r++)
11029
{
11030
delete [] transform[r];
11031
}// end loop over 'r'
11032
delete [] transform;
11033
break;
11034
}
11035
case 14:
11036
{
11037
11038
// Array of basisvalues.
11039
double basisvalues[10] = {0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000};
11040
11041
// Declare helper variables.
11042
unsigned int rr = 0;
11043
unsigned int ss = 0;
11044
unsigned int tt = 0;
11045
double tmp5 = 0.00000000;
11046
double tmp6 = 0.00000000;
11047
double tmp7 = 0.00000000;
11048
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
11049
double tmp1 = 0.25000000*(Y + Z)*(Y + Z);
11050
double tmp2 = 0.50000000*(1.00000000 + Z + 2.00000000*Y);
11051
double tmp3 = 0.50000000*(1.00000000 - Z);
11052
double tmp4 = tmp3*tmp3;
11053
11054
// Compute basisvalues.
11055
basisvalues[0] = 1.00000000;
11056
basisvalues[1] = tmp0;
11057
for (unsigned int r = 1; r < 2; r++)
11058
{
11059
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
11060
ss = r*(r + 1)*(r + 2)/6;
11061
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
11062
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.00000000 + 2.00000000*r)/(1.00000000 + r) - basisvalues[tt]*tmp1*r/(1.00000000 + r));
11063
}// end loop over 'r'
11064
for (unsigned int r = 0; r < 2; r++)
11065
{
11066
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
11067
ss = r*(r + 1)*(r + 2)/6;
11068
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
11069
}// end loop over 'r'
11070
for (unsigned int r = 0; r < 1; r++)
11071
{
11072
for (unsigned int s = 1; s < 2 - r; s++)
11073
{
11074
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
11075
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
11076
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
11077
tmp5 = (2.00000000 + 2.00000000*r + 2.00000000*s)*(3.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
11078
tmp6 = (1.00000000 + 4.00000000*r*r + 4.00000000*r)*(2.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
11079
tmp7 = (1.00000000 + s + 2.00000000*r)*(3.00000000 + 2.00000000*r + 2.00000000*s)*s/((1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
11080
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
11081
}// end loop over 's'
11082
}// end loop over 'r'
11083
for (unsigned int r = 0; r < 2; r++)
11084
{
11085
for (unsigned int s = 0; s < 2 - r; s++)
11086
{
11087
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
11088
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
11089
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
11090
}// end loop over 's'
11091
}// end loop over 'r'
11092
for (unsigned int r = 0; r < 1; r++)
11093
{
11094
for (unsigned int s = 0; s < 1 - r; s++)
11095
{
11096
for (unsigned int t = 1; t < 2 - r - s; t++)
11097
{
11098
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
11099
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
11100
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
11101
tmp5 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)/(2.00000000*(1.00000000 + t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
11102
tmp6 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 4.00000000*r*r + 4.00000000*s*s + 8.00000000*r*s + 8.00000000*r + 8.00000000*s)/(2.00000000*(1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
11103
tmp7 = (2.00000000 + t + 2.00000000*r + 2.00000000*s)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*t/((1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
11104
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
11105
}// end loop over 't'
11106
}// end loop over 's'
11107
}// end loop over 'r'
11108
for (unsigned int r = 0; r < 3; r++)
11109
{
11110
for (unsigned int s = 0; s < 3 - r; s++)
11111
{
11112
for (unsigned int t = 0; t < 3 - r - s; t++)
11113
{
11114
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
11115
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
11116
}// end loop over 't'
11117
}// end loop over 's'
11118
}// end loop over 'r'
11119
11120
// Table(s) of coefficients.
11121
static const double coefficients0[10] = \
11122
{0.23094011, 0.00000000, 0.14054567, 0.09938080, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.11878277, -0.06719368};
11123
11124
// Tables of derivatives of the polynomial base (transpose).
11125
static const double dmats0[10][10] = \
11126
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11127
{6.32455532, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11128
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11129
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11130
{0.00000000, 11.22497216, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11131
{4.58257569, 0.00000000, 8.36660027, -1.18321596, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11132
{3.74165739, 0.00000000, 0.00000000, 8.69482605, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11133
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11134
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11135
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
11136
11137
static const double dmats1[10][10] = \
11138
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11139
{3.16227766, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11140
{5.47722558, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11141
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11142
{2.95803989, 5.61248608, -1.08012345, -0.76376262, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11143
{2.29128785, 7.24568837, 4.18330013, -0.59160798, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11144
{1.87082869, 0.00000000, 0.00000000, 4.34741302, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11145
{-2.64575131, 0.00000000, 9.66091783, 0.68313005, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11146
{3.24037035, 0.00000000, 0.00000000, 7.52994024, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11147
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
11148
11149
static const double dmats2[10][10] = \
11150
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11151
{3.16227766, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11152
{1.82574186, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11153
{5.16397779, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11154
{2.95803989, 5.61248608, -1.08012345, -0.76376262, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11155
{2.29128785, 1.44913767, 4.18330013, -0.59160798, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11156
{1.87082869, 7.09929574, 0.00000000, 4.34741302, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11157
{1.32287566, 0.00000000, 3.86436713, -0.34156503, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11158
{1.08012345, 0.00000000, 7.09929574, 2.50998008, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11159
{-3.81881308, 0.00000000, 0.00000000, 8.87411967, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
11160
11161
// Compute reference derivatives.
11162
// Declare pointer to array of derivatives on FIAT element.
11163
double *derivatives = new double[num_derivatives];
11164
for (unsigned int r = 0; r < num_derivatives; r++)
11165
{
11166
derivatives[r] = 0.00000000;
11167
}// end loop over 'r'
11168
11169
// Declare derivative matrix (of polynomial basis).
11170
double dmats[10][10] = \
11171
{{1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11172
{0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11173
{0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11174
{0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11175
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11176
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11177
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000},
11178
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000},
11179
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000},
11180
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000}};
11181
11182
// Declare (auxiliary) derivative matrix (of polynomial basis).
11183
double dmats_old[10][10] = \
11184
{{1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11185
{0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11186
{0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11187
{0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11188
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11189
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11190
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000},
11191
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000},
11192
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000},
11193
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000}};
11194
11195
// Loop possible derivatives.
11196
for (unsigned int r = 0; r < num_derivatives; r++)
11197
{
11198
// Resetting dmats values to compute next derivative.
11199
for (unsigned int t = 0; t < 10; t++)
11200
{
11201
for (unsigned int u = 0; u < 10; u++)
11202
{
11203
dmats[t][u] = 0.00000000;
11204
if (t == u)
11205
{
11206
dmats[t][u] = 1.00000000;
11207
}
11208
11209
}// end loop over 'u'
11210
}// end loop over 't'
11211
11212
// Looping derivative order to generate dmats.
11213
for (unsigned int s = 0; s < n; s++)
11214
{
11215
// Updating dmats_old with new values and resetting dmats.
11216
for (unsigned int t = 0; t < 10; t++)
11217
{
11218
for (unsigned int u = 0; u < 10; u++)
11219
{
11220
dmats_old[t][u] = dmats[t][u];
11221
dmats[t][u] = 0.00000000;
11222
}// end loop over 'u'
11223
}// end loop over 't'
11224
11225
// Update dmats using an inner product.
11226
if (combinations[r][s] == 0)
11227
{
11228
for (unsigned int t = 0; t < 10; t++)
11229
{
11230
for (unsigned int u = 0; u < 10; u++)
11231
{
11232
for (unsigned int tu = 0; tu < 10; tu++)
11233
{
11234
dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
11235
}// end loop over 'tu'
11236
}// end loop over 'u'
11237
}// end loop over 't'
11238
}
11239
11240
if (combinations[r][s] == 1)
11241
{
11242
for (unsigned int t = 0; t < 10; t++)
11243
{
11244
for (unsigned int u = 0; u < 10; u++)
11245
{
11246
for (unsigned int tu = 0; tu < 10; tu++)
11247
{
11248
dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
11249
}// end loop over 'tu'
11250
}// end loop over 'u'
11251
}// end loop over 't'
11252
}
11253
11254
if (combinations[r][s] == 2)
11255
{
11256
for (unsigned int t = 0; t < 10; t++)
11257
{
11258
for (unsigned int u = 0; u < 10; u++)
11259
{
11260
for (unsigned int tu = 0; tu < 10; tu++)
11261
{
11262
dmats[t][u] += dmats2[t][tu]*dmats_old[tu][u];
11263
}// end loop over 'tu'
11264
}// end loop over 'u'
11265
}// end loop over 't'
11266
}
11267
11268
}// end loop over 's'
11269
for (unsigned int s = 0; s < 10; s++)
11270
{
11271
for (unsigned int t = 0; t < 10; t++)
11272
{
11273
derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
11274
}// end loop over 't'
11275
}// end loop over 's'
11276
}// end loop over 'r'
11277
11278
// Transform derivatives back to physical element
11279
for (unsigned int r = 0; r < num_derivatives; r++)
11280
{
11281
for (unsigned int s = 0; s < num_derivatives; s++)
11282
{
11283
values[num_derivatives + r] += transform[r][s]*derivatives[s];
11284
}// end loop over 's'
11285
}// end loop over 'r'
11286
11287
// Delete pointer to array of derivatives on FIAT element
11288
delete [] derivatives;
11289
11290
// Delete pointer to array of combinations of derivatives and transform
11291
for (unsigned int r = 0; r < num_derivatives; r++)
11292
{
11293
delete [] combinations[r];
11294
}// end loop over 'r'
11295
delete [] combinations;
11296
for (unsigned int r = 0; r < num_derivatives; r++)
11297
{
11298
delete [] transform[r];
11299
}// end loop over 'r'
11300
delete [] transform;
11301
break;
11302
}
11303
case 15:
11304
{
11305
11306
// Array of basisvalues.
11307
double basisvalues[10] = {0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000};
11308
11309
// Declare helper variables.
11310
unsigned int rr = 0;
11311
unsigned int ss = 0;
11312
unsigned int tt = 0;
11313
double tmp5 = 0.00000000;
11314
double tmp6 = 0.00000000;
11315
double tmp7 = 0.00000000;
11316
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
11317
double tmp1 = 0.25000000*(Y + Z)*(Y + Z);
11318
double tmp2 = 0.50000000*(1.00000000 + Z + 2.00000000*Y);
11319
double tmp3 = 0.50000000*(1.00000000 - Z);
11320
double tmp4 = tmp3*tmp3;
11321
11322
// Compute basisvalues.
11323
basisvalues[0] = 1.00000000;
11324
basisvalues[1] = tmp0;
11325
for (unsigned int r = 1; r < 2; r++)
11326
{
11327
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
11328
ss = r*(r + 1)*(r + 2)/6;
11329
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
11330
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.00000000 + 2.00000000*r)/(1.00000000 + r) - basisvalues[tt]*tmp1*r/(1.00000000 + r));
11331
}// end loop over 'r'
11332
for (unsigned int r = 0; r < 2; r++)
11333
{
11334
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
11335
ss = r*(r + 1)*(r + 2)/6;
11336
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
11337
}// end loop over 'r'
11338
for (unsigned int r = 0; r < 1; r++)
11339
{
11340
for (unsigned int s = 1; s < 2 - r; s++)
11341
{
11342
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
11343
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
11344
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
11345
tmp5 = (2.00000000 + 2.00000000*r + 2.00000000*s)*(3.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
11346
tmp6 = (1.00000000 + 4.00000000*r*r + 4.00000000*r)*(2.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
11347
tmp7 = (1.00000000 + s + 2.00000000*r)*(3.00000000 + 2.00000000*r + 2.00000000*s)*s/((1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
11348
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
11349
}// end loop over 's'
11350
}// end loop over 'r'
11351
for (unsigned int r = 0; r < 2; r++)
11352
{
11353
for (unsigned int s = 0; s < 2 - r; s++)
11354
{
11355
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
11356
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
11357
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
11358
}// end loop over 's'
11359
}// end loop over 'r'
11360
for (unsigned int r = 0; r < 1; r++)
11361
{
11362
for (unsigned int s = 0; s < 1 - r; s++)
11363
{
11364
for (unsigned int t = 1; t < 2 - r - s; t++)
11365
{
11366
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
11367
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
11368
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
11369
tmp5 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)/(2.00000000*(1.00000000 + t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
11370
tmp6 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 4.00000000*r*r + 4.00000000*s*s + 8.00000000*r*s + 8.00000000*r + 8.00000000*s)/(2.00000000*(1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
11371
tmp7 = (2.00000000 + t + 2.00000000*r + 2.00000000*s)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*t/((1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
11372
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
11373
}// end loop over 't'
11374
}// end loop over 's'
11375
}// end loop over 'r'
11376
for (unsigned int r = 0; r < 3; r++)
11377
{
11378
for (unsigned int s = 0; s < 3 - r; s++)
11379
{
11380
for (unsigned int t = 0; t < 3 - r - s; t++)
11381
{
11382
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
11383
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
11384
}// end loop over 't'
11385
}// end loop over 's'
11386
}// end loop over 'r'
11387
11388
// Table(s) of coefficients.
11389
static const double coefficients0[10] = \
11390
{0.23094011, 0.12171612, -0.07027284, 0.09938080, 0.00000000, 0.00000000, 0.10286890, 0.00000000, -0.05939139, -0.06719368};
11391
11392
// Tables of derivatives of the polynomial base (transpose).
11393
static const double dmats0[10][10] = \
11394
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11395
{6.32455532, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11396
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11397
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11398
{0.00000000, 11.22497216, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11399
{4.58257569, 0.00000000, 8.36660027, -1.18321596, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11400
{3.74165739, 0.00000000, 0.00000000, 8.69482605, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11401
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11402
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11403
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
11404
11405
static const double dmats1[10][10] = \
11406
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11407
{3.16227766, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11408
{5.47722558, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11409
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11410
{2.95803989, 5.61248608, -1.08012345, -0.76376262, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11411
{2.29128785, 7.24568837, 4.18330013, -0.59160798, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11412
{1.87082869, 0.00000000, 0.00000000, 4.34741302, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11413
{-2.64575131, 0.00000000, 9.66091783, 0.68313005, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11414
{3.24037035, 0.00000000, 0.00000000, 7.52994024, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11415
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
11416
11417
static const double dmats2[10][10] = \
11418
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11419
{3.16227766, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11420
{1.82574186, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11421
{5.16397779, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11422
{2.95803989, 5.61248608, -1.08012345, -0.76376262, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11423
{2.29128785, 1.44913767, 4.18330013, -0.59160798, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11424
{1.87082869, 7.09929574, 0.00000000, 4.34741302, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11425
{1.32287566, 0.00000000, 3.86436713, -0.34156503, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11426
{1.08012345, 0.00000000, 7.09929574, 2.50998008, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11427
{-3.81881308, 0.00000000, 0.00000000, 8.87411967, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
11428
11429
// Compute reference derivatives.
11430
// Declare pointer to array of derivatives on FIAT element.
11431
double *derivatives = new double[num_derivatives];
11432
for (unsigned int r = 0; r < num_derivatives; r++)
11433
{
11434
derivatives[r] = 0.00000000;
11435
}// end loop over 'r'
11436
11437
// Declare derivative matrix (of polynomial basis).
11438
double dmats[10][10] = \
11439
{{1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11440
{0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11441
{0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11442
{0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11443
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11444
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11445
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000},
11446
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000},
11447
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000},
11448
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000}};
11449
11450
// Declare (auxiliary) derivative matrix (of polynomial basis).
11451
double dmats_old[10][10] = \
11452
{{1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11453
{0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11454
{0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11455
{0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11456
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11457
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11458
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000},
11459
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000},
11460
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000},
11461
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000}};
11462
11463
// Loop possible derivatives.
11464
for (unsigned int r = 0; r < num_derivatives; r++)
11465
{
11466
// Resetting dmats values to compute next derivative.
11467
for (unsigned int t = 0; t < 10; t++)
11468
{
11469
for (unsigned int u = 0; u < 10; u++)
11470
{
11471
dmats[t][u] = 0.00000000;
11472
if (t == u)
11473
{
11474
dmats[t][u] = 1.00000000;
11475
}
11476
11477
}// end loop over 'u'
11478
}// end loop over 't'
11479
11480
// Looping derivative order to generate dmats.
11481
for (unsigned int s = 0; s < n; s++)
11482
{
11483
// Updating dmats_old with new values and resetting dmats.
11484
for (unsigned int t = 0; t < 10; t++)
11485
{
11486
for (unsigned int u = 0; u < 10; u++)
11487
{
11488
dmats_old[t][u] = dmats[t][u];
11489
dmats[t][u] = 0.00000000;
11490
}// end loop over 'u'
11491
}// end loop over 't'
11492
11493
// Update dmats using an inner product.
11494
if (combinations[r][s] == 0)
11495
{
11496
for (unsigned int t = 0; t < 10; t++)
11497
{
11498
for (unsigned int u = 0; u < 10; u++)
11499
{
11500
for (unsigned int tu = 0; tu < 10; tu++)
11501
{
11502
dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
11503
}// end loop over 'tu'
11504
}// end loop over 'u'
11505
}// end loop over 't'
11506
}
11507
11508
if (combinations[r][s] == 1)
11509
{
11510
for (unsigned int t = 0; t < 10; t++)
11511
{
11512
for (unsigned int u = 0; u < 10; u++)
11513
{
11514
for (unsigned int tu = 0; tu < 10; tu++)
11515
{
11516
dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
11517
}// end loop over 'tu'
11518
}// end loop over 'u'
11519
}// end loop over 't'
11520
}
11521
11522
if (combinations[r][s] == 2)
11523
{
11524
for (unsigned int t = 0; t < 10; t++)
11525
{
11526
for (unsigned int u = 0; u < 10; u++)
11527
{
11528
for (unsigned int tu = 0; tu < 10; tu++)
11529
{
11530
dmats[t][u] += dmats2[t][tu]*dmats_old[tu][u];
11531
}// end loop over 'tu'
11532
}// end loop over 'u'
11533
}// end loop over 't'
11534
}
11535
11536
}// end loop over 's'
11537
for (unsigned int s = 0; s < 10; s++)
11538
{
11539
for (unsigned int t = 0; t < 10; t++)
11540
{
11541
derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
11542
}// end loop over 't'
11543
}// end loop over 's'
11544
}// end loop over 'r'
11545
11546
// Transform derivatives back to physical element
11547
for (unsigned int r = 0; r < num_derivatives; r++)
11548
{
11549
for (unsigned int s = 0; s < num_derivatives; s++)
11550
{
11551
values[num_derivatives + r] += transform[r][s]*derivatives[s];
11552
}// end loop over 's'
11553
}// end loop over 'r'
11554
11555
// Delete pointer to array of derivatives on FIAT element
11556
delete [] derivatives;
11557
11558
// Delete pointer to array of combinations of derivatives and transform
11559
for (unsigned int r = 0; r < num_derivatives; r++)
11560
{
11561
delete [] combinations[r];
11562
}// end loop over 'r'
11563
delete [] combinations;
11564
for (unsigned int r = 0; r < num_derivatives; r++)
11565
{
11566
delete [] transform[r];
11567
}// end loop over 'r'
11568
delete [] transform;
11569
break;
11570
}
11571
case 16:
11572
{
11573
11574
// Array of basisvalues.
11575
double basisvalues[10] = {0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000};
11576
11577
// Declare helper variables.
11578
unsigned int rr = 0;
11579
unsigned int ss = 0;
11580
unsigned int tt = 0;
11581
double tmp5 = 0.00000000;
11582
double tmp6 = 0.00000000;
11583
double tmp7 = 0.00000000;
11584
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
11585
double tmp1 = 0.25000000*(Y + Z)*(Y + Z);
11586
double tmp2 = 0.50000000*(1.00000000 + Z + 2.00000000*Y);
11587
double tmp3 = 0.50000000*(1.00000000 - Z);
11588
double tmp4 = tmp3*tmp3;
11589
11590
// Compute basisvalues.
11591
basisvalues[0] = 1.00000000;
11592
basisvalues[1] = tmp0;
11593
for (unsigned int r = 1; r < 2; r++)
11594
{
11595
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
11596
ss = r*(r + 1)*(r + 2)/6;
11597
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
11598
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.00000000 + 2.00000000*r)/(1.00000000 + r) - basisvalues[tt]*tmp1*r/(1.00000000 + r));
11599
}// end loop over 'r'
11600
for (unsigned int r = 0; r < 2; r++)
11601
{
11602
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
11603
ss = r*(r + 1)*(r + 2)/6;
11604
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
11605
}// end loop over 'r'
11606
for (unsigned int r = 0; r < 1; r++)
11607
{
11608
for (unsigned int s = 1; s < 2 - r; s++)
11609
{
11610
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
11611
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
11612
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
11613
tmp5 = (2.00000000 + 2.00000000*r + 2.00000000*s)*(3.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
11614
tmp6 = (1.00000000 + 4.00000000*r*r + 4.00000000*r)*(2.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
11615
tmp7 = (1.00000000 + s + 2.00000000*r)*(3.00000000 + 2.00000000*r + 2.00000000*s)*s/((1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
11616
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
11617
}// end loop over 's'
11618
}// end loop over 'r'
11619
for (unsigned int r = 0; r < 2; r++)
11620
{
11621
for (unsigned int s = 0; s < 2 - r; s++)
11622
{
11623
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
11624
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
11625
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
11626
}// end loop over 's'
11627
}// end loop over 'r'
11628
for (unsigned int r = 0; r < 1; r++)
11629
{
11630
for (unsigned int s = 0; s < 1 - r; s++)
11631
{
11632
for (unsigned int t = 1; t < 2 - r - s; t++)
11633
{
11634
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
11635
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
11636
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
11637
tmp5 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)/(2.00000000*(1.00000000 + t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
11638
tmp6 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 4.00000000*r*r + 4.00000000*s*s + 8.00000000*r*s + 8.00000000*r + 8.00000000*s)/(2.00000000*(1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
11639
tmp7 = (2.00000000 + t + 2.00000000*r + 2.00000000*s)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*t/((1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
11640
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
11641
}// end loop over 't'
11642
}// end loop over 's'
11643
}// end loop over 'r'
11644
for (unsigned int r = 0; r < 3; r++)
11645
{
11646
for (unsigned int s = 0; s < 3 - r; s++)
11647
{
11648
for (unsigned int t = 0; t < 3 - r - s; t++)
11649
{
11650
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
11651
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
11652
}// end loop over 't'
11653
}// end loop over 's'
11654
}// end loop over 'r'
11655
11656
// Table(s) of coefficients.
11657
static const double coefficients0[10] = \
11658
{0.23094011, 0.12171612, 0.07027284, -0.09938080, 0.00000000, 0.10079053, -0.02057378, -0.08728716, -0.01187828, 0.01679842};
11659
11660
// Tables of derivatives of the polynomial base (transpose).
11661
static const double dmats0[10][10] = \
11662
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11663
{6.32455532, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11664
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11665
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11666
{0.00000000, 11.22497216, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11667
{4.58257569, 0.00000000, 8.36660027, -1.18321596, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11668
{3.74165739, 0.00000000, 0.00000000, 8.69482605, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11669
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11670
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11671
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
11672
11673
static const double dmats1[10][10] = \
11674
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11675
{3.16227766, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11676
{5.47722558, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11677
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11678
{2.95803989, 5.61248608, -1.08012345, -0.76376262, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11679
{2.29128785, 7.24568837, 4.18330013, -0.59160798, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11680
{1.87082869, 0.00000000, 0.00000000, 4.34741302, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11681
{-2.64575131, 0.00000000, 9.66091783, 0.68313005, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11682
{3.24037035, 0.00000000, 0.00000000, 7.52994024, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11683
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
11684
11685
static const double dmats2[10][10] = \
11686
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11687
{3.16227766, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11688
{1.82574186, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11689
{5.16397779, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11690
{2.95803989, 5.61248608, -1.08012345, -0.76376262, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11691
{2.29128785, 1.44913767, 4.18330013, -0.59160798, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11692
{1.87082869, 7.09929574, 0.00000000, 4.34741302, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11693
{1.32287566, 0.00000000, 3.86436713, -0.34156503, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11694
{1.08012345, 0.00000000, 7.09929574, 2.50998008, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11695
{-3.81881308, 0.00000000, 0.00000000, 8.87411967, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
11696
11697
// Compute reference derivatives.
11698
// Declare pointer to array of derivatives on FIAT element.
11699
double *derivatives = new double[num_derivatives];
11700
for (unsigned int r = 0; r < num_derivatives; r++)
11701
{
11702
derivatives[r] = 0.00000000;
11703
}// end loop over 'r'
11704
11705
// Declare derivative matrix (of polynomial basis).
11706
double dmats[10][10] = \
11707
{{1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11708
{0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11709
{0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11710
{0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11711
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11712
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11713
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000},
11714
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000},
11715
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000},
11716
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000}};
11717
11718
// Declare (auxiliary) derivative matrix (of polynomial basis).
11719
double dmats_old[10][10] = \
11720
{{1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11721
{0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11722
{0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11723
{0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11724
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11725
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11726
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000},
11727
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000},
11728
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000},
11729
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000}};
11730
11731
// Loop possible derivatives.
11732
for (unsigned int r = 0; r < num_derivatives; r++)
11733
{
11734
// Resetting dmats values to compute next derivative.
11735
for (unsigned int t = 0; t < 10; t++)
11736
{
11737
for (unsigned int u = 0; u < 10; u++)
11738
{
11739
dmats[t][u] = 0.00000000;
11740
if (t == u)
11741
{
11742
dmats[t][u] = 1.00000000;
11743
}
11744
11745
}// end loop over 'u'
11746
}// end loop over 't'
11747
11748
// Looping derivative order to generate dmats.
11749
for (unsigned int s = 0; s < n; s++)
11750
{
11751
// Updating dmats_old with new values and resetting dmats.
11752
for (unsigned int t = 0; t < 10; t++)
11753
{
11754
for (unsigned int u = 0; u < 10; u++)
11755
{
11756
dmats_old[t][u] = dmats[t][u];
11757
dmats[t][u] = 0.00000000;
11758
}// end loop over 'u'
11759
}// end loop over 't'
11760
11761
// Update dmats using an inner product.
11762
if (combinations[r][s] == 0)
11763
{
11764
for (unsigned int t = 0; t < 10; t++)
11765
{
11766
for (unsigned int u = 0; u < 10; u++)
11767
{
11768
for (unsigned int tu = 0; tu < 10; tu++)
11769
{
11770
dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
11771
}// end loop over 'tu'
11772
}// end loop over 'u'
11773
}// end loop over 't'
11774
}
11775
11776
if (combinations[r][s] == 1)
11777
{
11778
for (unsigned int t = 0; t < 10; t++)
11779
{
11780
for (unsigned int u = 0; u < 10; u++)
11781
{
11782
for (unsigned int tu = 0; tu < 10; tu++)
11783
{
11784
dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
11785
}// end loop over 'tu'
11786
}// end loop over 'u'
11787
}// end loop over 't'
11788
}
11789
11790
if (combinations[r][s] == 2)
11791
{
11792
for (unsigned int t = 0; t < 10; t++)
11793
{
11794
for (unsigned int u = 0; u < 10; u++)
11795
{
11796
for (unsigned int tu = 0; tu < 10; tu++)
11797
{
11798
dmats[t][u] += dmats2[t][tu]*dmats_old[tu][u];
11799
}// end loop over 'tu'
11800
}// end loop over 'u'
11801
}// end loop over 't'
11802
}
11803
11804
}// end loop over 's'
11805
for (unsigned int s = 0; s < 10; s++)
11806
{
11807
for (unsigned int t = 0; t < 10; t++)
11808
{
11809
derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
11810
}// end loop over 't'
11811
}// end loop over 's'
11812
}// end loop over 'r'
11813
11814
// Transform derivatives back to physical element
11815
for (unsigned int r = 0; r < num_derivatives; r++)
11816
{
11817
for (unsigned int s = 0; s < num_derivatives; s++)
11818
{
11819
values[num_derivatives + r] += transform[r][s]*derivatives[s];
11820
}// end loop over 's'
11821
}// end loop over 'r'
11822
11823
// Delete pointer to array of derivatives on FIAT element
11824
delete [] derivatives;
11825
11826
// Delete pointer to array of combinations of derivatives and transform
11827
for (unsigned int r = 0; r < num_derivatives; r++)
11828
{
11829
delete [] combinations[r];
11830
}// end loop over 'r'
11831
delete [] combinations;
11832
for (unsigned int r = 0; r < num_derivatives; r++)
11833
{
11834
delete [] transform[r];
11835
}// end loop over 'r'
11836
delete [] transform;
11837
break;
11838
}
11839
case 17:
11840
{
11841
11842
// Array of basisvalues.
11843
double basisvalues[10] = {0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000};
11844
11845
// Declare helper variables.
11846
unsigned int rr = 0;
11847
unsigned int ss = 0;
11848
unsigned int tt = 0;
11849
double tmp5 = 0.00000000;
11850
double tmp6 = 0.00000000;
11851
double tmp7 = 0.00000000;
11852
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
11853
double tmp1 = 0.25000000*(Y + Z)*(Y + Z);
11854
double tmp2 = 0.50000000*(1.00000000 + Z + 2.00000000*Y);
11855
double tmp3 = 0.50000000*(1.00000000 - Z);
11856
double tmp4 = tmp3*tmp3;
11857
11858
// Compute basisvalues.
11859
basisvalues[0] = 1.00000000;
11860
basisvalues[1] = tmp0;
11861
for (unsigned int r = 1; r < 2; r++)
11862
{
11863
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
11864
ss = r*(r + 1)*(r + 2)/6;
11865
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
11866
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.00000000 + 2.00000000*r)/(1.00000000 + r) - basisvalues[tt]*tmp1*r/(1.00000000 + r));
11867
}// end loop over 'r'
11868
for (unsigned int r = 0; r < 2; r++)
11869
{
11870
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
11871
ss = r*(r + 1)*(r + 2)/6;
11872
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
11873
}// end loop over 'r'
11874
for (unsigned int r = 0; r < 1; r++)
11875
{
11876
for (unsigned int s = 1; s < 2 - r; s++)
11877
{
11878
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
11879
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
11880
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
11881
tmp5 = (2.00000000 + 2.00000000*r + 2.00000000*s)*(3.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
11882
tmp6 = (1.00000000 + 4.00000000*r*r + 4.00000000*r)*(2.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
11883
tmp7 = (1.00000000 + s + 2.00000000*r)*(3.00000000 + 2.00000000*r + 2.00000000*s)*s/((1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
11884
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
11885
}// end loop over 's'
11886
}// end loop over 'r'
11887
for (unsigned int r = 0; r < 2; r++)
11888
{
11889
for (unsigned int s = 0; s < 2 - r; s++)
11890
{
11891
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
11892
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
11893
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
11894
}// end loop over 's'
11895
}// end loop over 'r'
11896
for (unsigned int r = 0; r < 1; r++)
11897
{
11898
for (unsigned int s = 0; s < 1 - r; s++)
11899
{
11900
for (unsigned int t = 1; t < 2 - r - s; t++)
11901
{
11902
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
11903
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
11904
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
11905
tmp5 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)/(2.00000000*(1.00000000 + t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
11906
tmp6 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 4.00000000*r*r + 4.00000000*s*s + 8.00000000*r*s + 8.00000000*r + 8.00000000*s)/(2.00000000*(1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
11907
tmp7 = (2.00000000 + t + 2.00000000*r + 2.00000000*s)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*t/((1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
11908
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
11909
}// end loop over 't'
11910
}// end loop over 's'
11911
}// end loop over 'r'
11912
for (unsigned int r = 0; r < 3; r++)
11913
{
11914
for (unsigned int s = 0; s < 3 - r; s++)
11915
{
11916
for (unsigned int t = 0; t < 3 - r - s; t++)
11917
{
11918
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
11919
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
11920
}// end loop over 't'
11921
}// end loop over 's'
11922
}// end loop over 'r'
11923
11924
// Table(s) of coefficients.
11925
static const double coefficients0[10] = \
11926
{0.23094011, -0.12171612, -0.07027284, 0.09938080, 0.00000000, 0.00000000, -0.10286890, 0.00000000, -0.05939139, -0.06719368};
11927
11928
// Tables of derivatives of the polynomial base (transpose).
11929
static const double dmats0[10][10] = \
11930
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11931
{6.32455532, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11932
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11933
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11934
{0.00000000, 11.22497216, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11935
{4.58257569, 0.00000000, 8.36660027, -1.18321596, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11936
{3.74165739, 0.00000000, 0.00000000, 8.69482605, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11937
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11938
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11939
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
11940
11941
static const double dmats1[10][10] = \
11942
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11943
{3.16227766, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11944
{5.47722558, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11945
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11946
{2.95803989, 5.61248608, -1.08012345, -0.76376262, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11947
{2.29128785, 7.24568837, 4.18330013, -0.59160798, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11948
{1.87082869, 0.00000000, 0.00000000, 4.34741302, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11949
{-2.64575131, 0.00000000, 9.66091783, 0.68313005, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11950
{3.24037035, 0.00000000, 0.00000000, 7.52994024, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11951
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
11952
11953
static const double dmats2[10][10] = \
11954
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11955
{3.16227766, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11956
{1.82574186, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11957
{5.16397779, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11958
{2.95803989, 5.61248608, -1.08012345, -0.76376262, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11959
{2.29128785, 1.44913767, 4.18330013, -0.59160798, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11960
{1.87082869, 7.09929574, 0.00000000, 4.34741302, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11961
{1.32287566, 0.00000000, 3.86436713, -0.34156503, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11962
{1.08012345, 0.00000000, 7.09929574, 2.50998008, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11963
{-3.81881308, 0.00000000, 0.00000000, 8.87411967, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
11964
11965
// Compute reference derivatives.
11966
// Declare pointer to array of derivatives on FIAT element.
11967
double *derivatives = new double[num_derivatives];
11968
for (unsigned int r = 0; r < num_derivatives; r++)
11969
{
11970
derivatives[r] = 0.00000000;
11971
}// end loop over 'r'
11972
11973
// Declare derivative matrix (of polynomial basis).
11974
double dmats[10][10] = \
11975
{{1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11976
{0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11977
{0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11978
{0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11979
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11980
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11981
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000},
11982
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000},
11983
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000},
11984
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000}};
11985
11986
// Declare (auxiliary) derivative matrix (of polynomial basis).
11987
double dmats_old[10][10] = \
11988
{{1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11989
{0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11990
{0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11991
{0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11992
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11993
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
11994
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000},
11995
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000},
11996
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000},
11997
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000}};
11998
11999
// Loop possible derivatives.
12000
for (unsigned int r = 0; r < num_derivatives; r++)
12001
{
12002
// Resetting dmats values to compute next derivative.
12003
for (unsigned int t = 0; t < 10; t++)
12004
{
12005
for (unsigned int u = 0; u < 10; u++)
12006
{
12007
dmats[t][u] = 0.00000000;
12008
if (t == u)
12009
{
12010
dmats[t][u] = 1.00000000;
12011
}
12012
12013
}// end loop over 'u'
12014
}// end loop over 't'
12015
12016
// Looping derivative order to generate dmats.
12017
for (unsigned int s = 0; s < n; s++)
12018
{
12019
// Updating dmats_old with new values and resetting dmats.
12020
for (unsigned int t = 0; t < 10; t++)
12021
{
12022
for (unsigned int u = 0; u < 10; u++)
12023
{
12024
dmats_old[t][u] = dmats[t][u];
12025
dmats[t][u] = 0.00000000;
12026
}// end loop over 'u'
12027
}// end loop over 't'
12028
12029
// Update dmats using an inner product.
12030
if (combinations[r][s] == 0)
12031
{
12032
for (unsigned int t = 0; t < 10; t++)
12033
{
12034
for (unsigned int u = 0; u < 10; u++)
12035
{
12036
for (unsigned int tu = 0; tu < 10; tu++)
12037
{
12038
dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
12039
}// end loop over 'tu'
12040
}// end loop over 'u'
12041
}// end loop over 't'
12042
}
12043
12044
if (combinations[r][s] == 1)
12045
{
12046
for (unsigned int t = 0; t < 10; t++)
12047
{
12048
for (unsigned int u = 0; u < 10; u++)
12049
{
12050
for (unsigned int tu = 0; tu < 10; tu++)
12051
{
12052
dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
12053
}// end loop over 'tu'
12054
}// end loop over 'u'
12055
}// end loop over 't'
12056
}
12057
12058
if (combinations[r][s] == 2)
12059
{
12060
for (unsigned int t = 0; t < 10; t++)
12061
{
12062
for (unsigned int u = 0; u < 10; u++)
12063
{
12064
for (unsigned int tu = 0; tu < 10; tu++)
12065
{
12066
dmats[t][u] += dmats2[t][tu]*dmats_old[tu][u];
12067
}// end loop over 'tu'
12068
}// end loop over 'u'
12069
}// end loop over 't'
12070
}
12071
12072
}// end loop over 's'
12073
for (unsigned int s = 0; s < 10; s++)
12074
{
12075
for (unsigned int t = 0; t < 10; t++)
12076
{
12077
derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
12078
}// end loop over 't'
12079
}// end loop over 's'
12080
}// end loop over 'r'
12081
12082
// Transform derivatives back to physical element
12083
for (unsigned int r = 0; r < num_derivatives; r++)
12084
{
12085
for (unsigned int s = 0; s < num_derivatives; s++)
12086
{
12087
values[num_derivatives + r] += transform[r][s]*derivatives[s];
12088
}// end loop over 's'
12089
}// end loop over 'r'
12090
12091
// Delete pointer to array of derivatives on FIAT element
12092
delete [] derivatives;
12093
12094
// Delete pointer to array of combinations of derivatives and transform
12095
for (unsigned int r = 0; r < num_derivatives; r++)
12096
{
12097
delete [] combinations[r];
12098
}// end loop over 'r'
12099
delete [] combinations;
12100
for (unsigned int r = 0; r < num_derivatives; r++)
12101
{
12102
delete [] transform[r];
12103
}// end loop over 'r'
12104
delete [] transform;
12105
break;
12106
}
12107
case 18:
12108
{
12109
12110
// Array of basisvalues.
12111
double basisvalues[10] = {0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000};
12112
12113
// Declare helper variables.
12114
unsigned int rr = 0;
12115
unsigned int ss = 0;
12116
unsigned int tt = 0;
12117
double tmp5 = 0.00000000;
12118
double tmp6 = 0.00000000;
12119
double tmp7 = 0.00000000;
12120
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
12121
double tmp1 = 0.25000000*(Y + Z)*(Y + Z);
12122
double tmp2 = 0.50000000*(1.00000000 + Z + 2.00000000*Y);
12123
double tmp3 = 0.50000000*(1.00000000 - Z);
12124
double tmp4 = tmp3*tmp3;
12125
12126
// Compute basisvalues.
12127
basisvalues[0] = 1.00000000;
12128
basisvalues[1] = tmp0;
12129
for (unsigned int r = 1; r < 2; r++)
12130
{
12131
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
12132
ss = r*(r + 1)*(r + 2)/6;
12133
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
12134
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.00000000 + 2.00000000*r)/(1.00000000 + r) - basisvalues[tt]*tmp1*r/(1.00000000 + r));
12135
}// end loop over 'r'
12136
for (unsigned int r = 0; r < 2; r++)
12137
{
12138
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
12139
ss = r*(r + 1)*(r + 2)/6;
12140
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
12141
}// end loop over 'r'
12142
for (unsigned int r = 0; r < 1; r++)
12143
{
12144
for (unsigned int s = 1; s < 2 - r; s++)
12145
{
12146
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
12147
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
12148
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
12149
tmp5 = (2.00000000 + 2.00000000*r + 2.00000000*s)*(3.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
12150
tmp6 = (1.00000000 + 4.00000000*r*r + 4.00000000*r)*(2.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
12151
tmp7 = (1.00000000 + s + 2.00000000*r)*(3.00000000 + 2.00000000*r + 2.00000000*s)*s/((1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
12152
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
12153
}// end loop over 's'
12154
}// end loop over 'r'
12155
for (unsigned int r = 0; r < 2; r++)
12156
{
12157
for (unsigned int s = 0; s < 2 - r; s++)
12158
{
12159
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
12160
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
12161
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
12162
}// end loop over 's'
12163
}// end loop over 'r'
12164
for (unsigned int r = 0; r < 1; r++)
12165
{
12166
for (unsigned int s = 0; s < 1 - r; s++)
12167
{
12168
for (unsigned int t = 1; t < 2 - r - s; t++)
12169
{
12170
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
12171
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
12172
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
12173
tmp5 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)/(2.00000000*(1.00000000 + t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
12174
tmp6 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 4.00000000*r*r + 4.00000000*s*s + 8.00000000*r*s + 8.00000000*r + 8.00000000*s)/(2.00000000*(1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
12175
tmp7 = (2.00000000 + t + 2.00000000*r + 2.00000000*s)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*t/((1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
12176
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
12177
}// end loop over 't'
12178
}// end loop over 's'
12179
}// end loop over 'r'
12180
for (unsigned int r = 0; r < 3; r++)
12181
{
12182
for (unsigned int s = 0; s < 3 - r; s++)
12183
{
12184
for (unsigned int t = 0; t < 3 - r - s; t++)
12185
{
12186
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
12187
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
12188
}// end loop over 't'
12189
}// end loop over 's'
12190
}// end loop over 'r'
12191
12192
// Table(s) of coefficients.
12193
static const double coefficients0[10] = \
12194
{0.23094011, -0.12171612, 0.07027284, -0.09938080, 0.00000000, -0.10079053, 0.02057378, -0.08728716, -0.01187828, 0.01679842};
12195
12196
// Tables of derivatives of the polynomial base (transpose).
12197
static const double dmats0[10][10] = \
12198
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
12199
{6.32455532, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
12200
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
12201
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
12202
{0.00000000, 11.22497216, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
12203
{4.58257569, 0.00000000, 8.36660027, -1.18321596, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
12204
{3.74165739, 0.00000000, 0.00000000, 8.69482605, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
12205
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
12206
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
12207
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
12208
12209
static const double dmats1[10][10] = \
12210
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
12211
{3.16227766, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
12212
{5.47722558, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
12213
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
12214
{2.95803989, 5.61248608, -1.08012345, -0.76376262, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
12215
{2.29128785, 7.24568837, 4.18330013, -0.59160798, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
12216
{1.87082869, 0.00000000, 0.00000000, 4.34741302, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
12217
{-2.64575131, 0.00000000, 9.66091783, 0.68313005, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
12218
{3.24037035, 0.00000000, 0.00000000, 7.52994024, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
12219
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
12220
12221
static const double dmats2[10][10] = \
12222
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
12223
{3.16227766, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
12224
{1.82574186, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
12225
{5.16397779, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
12226
{2.95803989, 5.61248608, -1.08012345, -0.76376262, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
12227
{2.29128785, 1.44913767, 4.18330013, -0.59160798, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
12228
{1.87082869, 7.09929574, 0.00000000, 4.34741302, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
12229
{1.32287566, 0.00000000, 3.86436713, -0.34156503, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
12230
{1.08012345, 0.00000000, 7.09929574, 2.50998008, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
12231
{-3.81881308, 0.00000000, 0.00000000, 8.87411967, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
12232
12233
// Compute reference derivatives.
12234
// Declare pointer to array of derivatives on FIAT element.
12235
double *derivatives = new double[num_derivatives];
12236
for (unsigned int r = 0; r < num_derivatives; r++)
12237
{
12238
derivatives[r] = 0.00000000;
12239
}// end loop over 'r'
12240
12241
// Declare derivative matrix (of polynomial basis).
12242
double dmats[10][10] = \
12243
{{1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
12244
{0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
12245
{0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
12246
{0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
12247
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
12248
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
12249
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000},
12250
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000},
12251
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000},
12252
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000}};
12253
12254
// Declare (auxiliary) derivative matrix (of polynomial basis).
12255
double dmats_old[10][10] = \
12256
{{1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
12257
{0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
12258
{0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
12259
{0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
12260
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
12261
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
12262
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000},
12263
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000},
12264
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000},
12265
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000}};
12266
12267
// Loop possible derivatives.
12268
for (unsigned int r = 0; r < num_derivatives; r++)
12269
{
12270
// Resetting dmats values to compute next derivative.
12271
for (unsigned int t = 0; t < 10; t++)
12272
{
12273
for (unsigned int u = 0; u < 10; u++)
12274
{
12275
dmats[t][u] = 0.00000000;
12276
if (t == u)
12277
{
12278
dmats[t][u] = 1.00000000;
12279
}
12280
12281
}// end loop over 'u'
12282
}// end loop over 't'
12283
12284
// Looping derivative order to generate dmats.
12285
for (unsigned int s = 0; s < n; s++)
12286
{
12287
// Updating dmats_old with new values and resetting dmats.
12288
for (unsigned int t = 0; t < 10; t++)
12289
{
12290
for (unsigned int u = 0; u < 10; u++)
12291
{
12292
dmats_old[t][u] = dmats[t][u];
12293
dmats[t][u] = 0.00000000;
12294
}// end loop over 'u'
12295
}// end loop over 't'
12296
12297
// Update dmats using an inner product.
12298
if (combinations[r][s] == 0)
12299
{
12300
for (unsigned int t = 0; t < 10; t++)
12301
{
12302
for (unsigned int u = 0; u < 10; u++)
12303
{
12304
for (unsigned int tu = 0; tu < 10; tu++)
12305
{
12306
dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
12307
}// end loop over 'tu'
12308
}// end loop over 'u'
12309
}// end loop over 't'
12310
}
12311
12312
if (combinations[r][s] == 1)
12313
{
12314
for (unsigned int t = 0; t < 10; t++)
12315
{
12316
for (unsigned int u = 0; u < 10; u++)
12317
{
12318
for (unsigned int tu = 0; tu < 10; tu++)
12319
{
12320
dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
12321
}// end loop over 'tu'
12322
}// end loop over 'u'
12323
}// end loop over 't'
12324
}
12325
12326
if (combinations[r][s] == 2)
12327
{
12328
for (unsigned int t = 0; t < 10; t++)
12329
{
12330
for (unsigned int u = 0; u < 10; u++)
12331
{
12332
for (unsigned int tu = 0; tu < 10; tu++)
12333
{
12334
dmats[t][u] += dmats2[t][tu]*dmats_old[tu][u];
12335
}// end loop over 'tu'
12336
}// end loop over 'u'
12337
}// end loop over 't'
12338
}
12339
12340
}// end loop over 's'
12341
for (unsigned int s = 0; s < 10; s++)
12342
{
12343
for (unsigned int t = 0; t < 10; t++)
12344
{
12345
derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
12346
}// end loop over 't'
12347
}// end loop over 's'
12348
}// end loop over 'r'
12349
12350
// Transform derivatives back to physical element
12351
for (unsigned int r = 0; r < num_derivatives; r++)
12352
{
12353
for (unsigned int s = 0; s < num_derivatives; s++)
12354
{
12355
values[num_derivatives + r] += transform[r][s]*derivatives[s];
12356
}// end loop over 's'
12357
}// end loop over 'r'
12358
12359
// Delete pointer to array of derivatives on FIAT element
12360
delete [] derivatives;
12361
12362
// Delete pointer to array of combinations of derivatives and transform
12363
for (unsigned int r = 0; r < num_derivatives; r++)
12364
{
12365
delete [] combinations[r];
12366
}// end loop over 'r'
12367
delete [] combinations;
12368
for (unsigned int r = 0; r < num_derivatives; r++)
12369
{
12370
delete [] transform[r];
12371
}// end loop over 'r'
12372
delete [] transform;
12373
break;
12374
}
12375
case 19:
12376
{
12377
12378
// Array of basisvalues.
12379
double basisvalues[10] = {0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000};
12380
12381
// Declare helper variables.
12382
unsigned int rr = 0;
12383
unsigned int ss = 0;
12384
unsigned int tt = 0;
12385
double tmp5 = 0.00000000;
12386
double tmp6 = 0.00000000;
12387
double tmp7 = 0.00000000;
12388
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
12389
double tmp1 = 0.25000000*(Y + Z)*(Y + Z);
12390
double tmp2 = 0.50000000*(1.00000000 + Z + 2.00000000*Y);
12391
double tmp3 = 0.50000000*(1.00000000 - Z);
12392
double tmp4 = tmp3*tmp3;
12393
12394
// Compute basisvalues.
12395
basisvalues[0] = 1.00000000;
12396
basisvalues[1] = tmp0;
12397
for (unsigned int r = 1; r < 2; r++)
12398
{
12399
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
12400
ss = r*(r + 1)*(r + 2)/6;
12401
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
12402
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.00000000 + 2.00000000*r)/(1.00000000 + r) - basisvalues[tt]*tmp1*r/(1.00000000 + r));
12403
}// end loop over 'r'
12404
for (unsigned int r = 0; r < 2; r++)
12405
{
12406
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
12407
ss = r*(r + 1)*(r + 2)/6;
12408
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
12409
}// end loop over 'r'
12410
for (unsigned int r = 0; r < 1; r++)
12411
{
12412
for (unsigned int s = 1; s < 2 - r; s++)
12413
{
12414
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
12415
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
12416
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
12417
tmp5 = (2.00000000 + 2.00000000*r + 2.00000000*s)*(3.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
12418
tmp6 = (1.00000000 + 4.00000000*r*r + 4.00000000*r)*(2.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
12419
tmp7 = (1.00000000 + s + 2.00000000*r)*(3.00000000 + 2.00000000*r + 2.00000000*s)*s/((1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
12420
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
12421
}// end loop over 's'
12422
}// end loop over 'r'
12423
for (unsigned int r = 0; r < 2; r++)
12424
{
12425
for (unsigned int s = 0; s < 2 - r; s++)
12426
{
12427
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
12428
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
12429
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
12430
}// end loop over 's'
12431
}// end loop over 'r'
12432
for (unsigned int r = 0; r < 1; r++)
12433
{
12434
for (unsigned int s = 0; s < 1 - r; s++)
12435
{
12436
for (unsigned int t = 1; t < 2 - r - s; t++)
12437
{
12438
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
12439
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
12440
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
12441
tmp5 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)/(2.00000000*(1.00000000 + t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
12442
tmp6 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 4.00000000*r*r + 4.00000000*s*s + 8.00000000*r*s + 8.00000000*r + 8.00000000*s)/(2.00000000*(1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
12443
tmp7 = (2.00000000 + t + 2.00000000*r + 2.00000000*s)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*t/((1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
12444
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
12445
}// end loop over 't'
12446
}// end loop over 's'
12447
}// end loop over 'r'
12448
for (unsigned int r = 0; r < 3; r++)
12449
{
12450
for (unsigned int s = 0; s < 3 - r; s++)
12451
{
12452
for (unsigned int t = 0; t < 3 - r - s; t++)
12453
{
12454
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
12455
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
12456
}// end loop over 't'
12457
}// end loop over 's'
12458
}// end loop over 'r'
12459
12460
// Table(s) of coefficients.
12461
static const double coefficients0[10] = \
12462
{0.23094011, 0.00000000, -0.14054567, -0.09938080, -0.13012001, 0.00000000, 0.00000000, 0.02909572, 0.02375655, 0.01679842};
12463
12464
// Tables of derivatives of the polynomial base (transpose).
12465
static const double dmats0[10][10] = \
12466
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
12467
{6.32455532, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
12468
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
12469
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
12470
{0.00000000, 11.22497216, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
12471
{4.58257569, 0.00000000, 8.36660027, -1.18321596, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
12472
{3.74165739, 0.00000000, 0.00000000, 8.69482605, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
12473
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
12474
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
12475
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
12476
12477
static const double dmats1[10][10] = \
12478
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
12479
{3.16227766, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
12480
{5.47722558, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
12481
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
12482
{2.95803989, 5.61248608, -1.08012345, -0.76376262, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
12483
{2.29128785, 7.24568837, 4.18330013, -0.59160798, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
12484
{1.87082869, 0.00000000, 0.00000000, 4.34741302, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
12485
{-2.64575131, 0.00000000, 9.66091783, 0.68313005, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
12486
{3.24037035, 0.00000000, 0.00000000, 7.52994024, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
12487
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
12488
12489
static const double dmats2[10][10] = \
12490
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
12491
{3.16227766, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
12492
{1.82574186, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
12493
{5.16397779, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
12494
{2.95803989, 5.61248608, -1.08012345, -0.76376262, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
12495
{2.29128785, 1.44913767, 4.18330013, -0.59160798, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
12496
{1.87082869, 7.09929574, 0.00000000, 4.34741302, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
12497
{1.32287566, 0.00000000, 3.86436713, -0.34156503, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
12498
{1.08012345, 0.00000000, 7.09929574, 2.50998008, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
12499
{-3.81881308, 0.00000000, 0.00000000, 8.87411967, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
12500
12501
// Compute reference derivatives.
12502
// Declare pointer to array of derivatives on FIAT element.
12503
double *derivatives = new double[num_derivatives];
12504
for (unsigned int r = 0; r < num_derivatives; r++)
12505
{
12506
derivatives[r] = 0.00000000;
12507
}// end loop over 'r'
12508
12509
// Declare derivative matrix (of polynomial basis).
12510
double dmats[10][10] = \
12511
{{1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
12512
{0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
12513
{0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
12514
{0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
12515
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
12516
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
12517
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000},
12518
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000},
12519
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000},
12520
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000}};
12521
12522
// Declare (auxiliary) derivative matrix (of polynomial basis).
12523
double dmats_old[10][10] = \
12524
{{1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
12525
{0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
12526
{0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
12527
{0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
12528
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
12529
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
12530
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000},
12531
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000},
12532
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000},
12533
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000}};
12534
12535
// Loop possible derivatives.
12536
for (unsigned int r = 0; r < num_derivatives; r++)
12537
{
12538
// Resetting dmats values to compute next derivative.
12539
for (unsigned int t = 0; t < 10; t++)
12540
{
12541
for (unsigned int u = 0; u < 10; u++)
12542
{
12543
dmats[t][u] = 0.00000000;
12544
if (t == u)
12545
{
12546
dmats[t][u] = 1.00000000;
12547
}
12548
12549
}// end loop over 'u'
12550
}// end loop over 't'
12551
12552
// Looping derivative order to generate dmats.
12553
for (unsigned int s = 0; s < n; s++)
12554
{
12555
// Updating dmats_old with new values and resetting dmats.
12556
for (unsigned int t = 0; t < 10; t++)
12557
{
12558
for (unsigned int u = 0; u < 10; u++)
12559
{
12560
dmats_old[t][u] = dmats[t][u];
12561
dmats[t][u] = 0.00000000;
12562
}// end loop over 'u'
12563
}// end loop over 't'
12564
12565
// Update dmats using an inner product.
12566
if (combinations[r][s] == 0)
12567
{
12568
for (unsigned int t = 0; t < 10; t++)
12569
{
12570
for (unsigned int u = 0; u < 10; u++)
12571
{
12572
for (unsigned int tu = 0; tu < 10; tu++)
12573
{
12574
dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
12575
}// end loop over 'tu'
12576
}// end loop over 'u'
12577
}// end loop over 't'
12578
}
12579
12580
if (combinations[r][s] == 1)
12581
{
12582
for (unsigned int t = 0; t < 10; t++)
12583
{
12584
for (unsigned int u = 0; u < 10; u++)
12585
{
12586
for (unsigned int tu = 0; tu < 10; tu++)
12587
{
12588
dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
12589
}// end loop over 'tu'
12590
}// end loop over 'u'
12591
}// end loop over 't'
12592
}
12593
12594
if (combinations[r][s] == 2)
12595
{
12596
for (unsigned int t = 0; t < 10; t++)
12597
{
12598
for (unsigned int u = 0; u < 10; u++)
12599
{
12600
for (unsigned int tu = 0; tu < 10; tu++)
12601
{
12602
dmats[t][u] += dmats2[t][tu]*dmats_old[tu][u];
12603
}// end loop over 'tu'
12604
}// end loop over 'u'
12605
}// end loop over 't'
12606
}
12607
12608
}// end loop over 's'
12609
for (unsigned int s = 0; s < 10; s++)
12610
{
12611
for (unsigned int t = 0; t < 10; t++)
12612
{
12613
derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
12614
}// end loop over 't'
12615
}// end loop over 's'
12616
}// end loop over 'r'
12617
12618
// Transform derivatives back to physical element
12619
for (unsigned int r = 0; r < num_derivatives; r++)
12620
{
12621
for (unsigned int s = 0; s < num_derivatives; s++)
12622
{
12623
values[num_derivatives + r] += transform[r][s]*derivatives[s];
12624
}// end loop over 's'
12625
}// end loop over 'r'
12626
12627
// Delete pointer to array of derivatives on FIAT element
12628
delete [] derivatives;
12629
12630
// Delete pointer to array of combinations of derivatives and transform
12631
for (unsigned int r = 0; r < num_derivatives; r++)
12632
{
12633
delete [] combinations[r];
12634
}// end loop over 'r'
12635
delete [] combinations;
12636
for (unsigned int r = 0; r < num_derivatives; r++)
12637
{
12638
delete [] transform[r];
12639
}// end loop over 'r'
12640
delete [] transform;
12641
break;
12642
}
12643
case 20:
12644
{
12645
12646
// Array of basisvalues.
12647
double basisvalues[10] = {0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000};
12648
12649
// Declare helper variables.
12650
unsigned int rr = 0;
12651
unsigned int ss = 0;
12652
unsigned int tt = 0;
12653
double tmp5 = 0.00000000;
12654
double tmp6 = 0.00000000;
12655
double tmp7 = 0.00000000;
12656
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
12657
double tmp1 = 0.25000000*(Y + Z)*(Y + Z);
12658
double tmp2 = 0.50000000*(1.00000000 + Z + 2.00000000*Y);
12659
double tmp3 = 0.50000000*(1.00000000 - Z);
12660
double tmp4 = tmp3*tmp3;
12661
12662
// Compute basisvalues.
12663
basisvalues[0] = 1.00000000;
12664
basisvalues[1] = tmp0;
12665
for (unsigned int r = 1; r < 2; r++)
12666
{
12667
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
12668
ss = r*(r + 1)*(r + 2)/6;
12669
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
12670
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.00000000 + 2.00000000*r)/(1.00000000 + r) - basisvalues[tt]*tmp1*r/(1.00000000 + r));
12671
}// end loop over 'r'
12672
for (unsigned int r = 0; r < 2; r++)
12673
{
12674
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
12675
ss = r*(r + 1)*(r + 2)/6;
12676
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
12677
}// end loop over 'r'
12678
for (unsigned int r = 0; r < 1; r++)
12679
{
12680
for (unsigned int s = 1; s < 2 - r; s++)
12681
{
12682
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
12683
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
12684
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
12685
tmp5 = (2.00000000 + 2.00000000*r + 2.00000000*s)*(3.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
12686
tmp6 = (1.00000000 + 4.00000000*r*r + 4.00000000*r)*(2.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
12687
tmp7 = (1.00000000 + s + 2.00000000*r)*(3.00000000 + 2.00000000*r + 2.00000000*s)*s/((1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
12688
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
12689
}// end loop over 's'
12690
}// end loop over 'r'
12691
for (unsigned int r = 0; r < 2; r++)
12692
{
12693
for (unsigned int s = 0; s < 2 - r; s++)
12694
{
12695
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
12696
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
12697
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
12698
}// end loop over 's'
12699
}// end loop over 'r'
12700
for (unsigned int r = 0; r < 1; r++)
12701
{
12702
for (unsigned int s = 0; s < 1 - r; s++)
12703
{
12704
for (unsigned int t = 1; t < 2 - r - s; t++)
12705
{
12706
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
12707
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
12708
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
12709
tmp5 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)/(2.00000000*(1.00000000 + t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
12710
tmp6 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 4.00000000*r*r + 4.00000000*s*s + 8.00000000*r*s + 8.00000000*r + 8.00000000*s)/(2.00000000*(1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
12711
tmp7 = (2.00000000 + t + 2.00000000*r + 2.00000000*s)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*t/((1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
12712
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
12713
}// end loop over 't'
12714
}// end loop over 's'
12715
}// end loop over 'r'
12716
for (unsigned int r = 0; r < 3; r++)
12717
{
12718
for (unsigned int s = 0; s < 3 - r; s++)
12719
{
12720
for (unsigned int t = 0; t < 3 - r - s; t++)
12721
{
12722
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
12723
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
12724
}// end loop over 't'
12725
}// end loop over 's'
12726
}// end loop over 'r'
12727
12728
// Table(s) of coefficients.
12729
static const double coefficients0[10] = \
12730
{-0.05773503, -0.06085806, -0.03513642, -0.02484520, 0.06506000, 0.05039526, 0.04114756, 0.02909572, 0.02375655, 0.01679842};
12731
12732
// Tables of derivatives of the polynomial base (transpose).
12733
static const double dmats0[10][10] = \
12734
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
12735
{6.32455532, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
12736
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
12737
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
12738
{0.00000000, 11.22497216, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
12739
{4.58257569, 0.00000000, 8.36660027, -1.18321596, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
12740
{3.74165739, 0.00000000, 0.00000000, 8.69482605, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
12741
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
12742
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
12743
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
12744
12745
static const double dmats1[10][10] = \
12746
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
12747
{3.16227766, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
12748
{5.47722558, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
12749
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
12750
{2.95803989, 5.61248608, -1.08012345, -0.76376262, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
12751
{2.29128785, 7.24568837, 4.18330013, -0.59160798, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
12752
{1.87082869, 0.00000000, 0.00000000, 4.34741302, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
12753
{-2.64575131, 0.00000000, 9.66091783, 0.68313005, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
12754
{3.24037035, 0.00000000, 0.00000000, 7.52994024, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
12755
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
12756
12757
static const double dmats2[10][10] = \
12758
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
12759
{3.16227766, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
12760
{1.82574186, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
12761
{5.16397779, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
12762
{2.95803989, 5.61248608, -1.08012345, -0.76376262, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
12763
{2.29128785, 1.44913767, 4.18330013, -0.59160798, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
12764
{1.87082869, 7.09929574, 0.00000000, 4.34741302, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
12765
{1.32287566, 0.00000000, 3.86436713, -0.34156503, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
12766
{1.08012345, 0.00000000, 7.09929574, 2.50998008, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
12767
{-3.81881308, 0.00000000, 0.00000000, 8.87411967, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
12768
12769
// Compute reference derivatives.
12770
// Declare pointer to array of derivatives on FIAT element.
12771
double *derivatives = new double[num_derivatives];
12772
for (unsigned int r = 0; r < num_derivatives; r++)
12773
{
12774
derivatives[r] = 0.00000000;
12775
}// end loop over 'r'
12776
12777
// Declare derivative matrix (of polynomial basis).
12778
double dmats[10][10] = \
12779
{{1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
12780
{0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
12781
{0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
12782
{0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
12783
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
12784
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
12785
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000},
12786
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000},
12787
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000},
12788
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000}};
12789
12790
// Declare (auxiliary) derivative matrix (of polynomial basis).
12791
double dmats_old[10][10] = \
12792
{{1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
12793
{0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
12794
{0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
12795
{0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
12796
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
12797
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
12798
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000},
12799
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000},
12800
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000},
12801
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000}};
12802
12803
// Loop possible derivatives.
12804
for (unsigned int r = 0; r < num_derivatives; r++)
12805
{
12806
// Resetting dmats values to compute next derivative.
12807
for (unsigned int t = 0; t < 10; t++)
12808
{
12809
for (unsigned int u = 0; u < 10; u++)
12810
{
12811
dmats[t][u] = 0.00000000;
12812
if (t == u)
12813
{
12814
dmats[t][u] = 1.00000000;
12815
}
12816
12817
}// end loop over 'u'
12818
}// end loop over 't'
12819
12820
// Looping derivative order to generate dmats.
12821
for (unsigned int s = 0; s < n; s++)
12822
{
12823
// Updating dmats_old with new values and resetting dmats.
12824
for (unsigned int t = 0; t < 10; t++)
12825
{
12826
for (unsigned int u = 0; u < 10; u++)
12827
{
12828
dmats_old[t][u] = dmats[t][u];
12829
dmats[t][u] = 0.00000000;
12830
}// end loop over 'u'
12831
}// end loop over 't'
12832
12833
// Update dmats using an inner product.
12834
if (combinations[r][s] == 0)
12835
{
12836
for (unsigned int t = 0; t < 10; t++)
12837
{
12838
for (unsigned int u = 0; u < 10; u++)
12839
{
12840
for (unsigned int tu = 0; tu < 10; tu++)
12841
{
12842
dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
12843
}// end loop over 'tu'
12844
}// end loop over 'u'
12845
}// end loop over 't'
12846
}
12847
12848
if (combinations[r][s] == 1)
12849
{
12850
for (unsigned int t = 0; t < 10; t++)
12851
{
12852
for (unsigned int u = 0; u < 10; u++)
12853
{
12854
for (unsigned int tu = 0; tu < 10; tu++)
12855
{
12856
dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
12857
}// end loop over 'tu'
12858
}// end loop over 'u'
12859
}// end loop over 't'
12860
}
12861
12862
if (combinations[r][s] == 2)
12863
{
12864
for (unsigned int t = 0; t < 10; t++)
12865
{
12866
for (unsigned int u = 0; u < 10; u++)
12867
{
12868
for (unsigned int tu = 0; tu < 10; tu++)
12869
{
12870
dmats[t][u] += dmats2[t][tu]*dmats_old[tu][u];
12871
}// end loop over 'tu'
12872
}// end loop over 'u'
12873
}// end loop over 't'
12874
}
12875
12876
}// end loop over 's'
12877
for (unsigned int s = 0; s < 10; s++)
12878
{
12879
for (unsigned int t = 0; t < 10; t++)
12880
{
12881
derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
12882
}// end loop over 't'
12883
}// end loop over 's'
12884
}// end loop over 'r'
12885
12886
// Transform derivatives back to physical element
12887
for (unsigned int r = 0; r < num_derivatives; r++)
12888
{
12889
for (unsigned int s = 0; s < num_derivatives; s++)
12890
{
12891
values[2*num_derivatives + r] += transform[r][s]*derivatives[s];
12892
}// end loop over 's'
12893
}// end loop over 'r'
12894
12895
// Delete pointer to array of derivatives on FIAT element
12896
delete [] derivatives;
12897
12898
// Delete pointer to array of combinations of derivatives and transform
12899
for (unsigned int r = 0; r < num_derivatives; r++)
12900
{
12901
delete [] combinations[r];
12902
}// end loop over 'r'
12903
delete [] combinations;
12904
for (unsigned int r = 0; r < num_derivatives; r++)
12905
{
12906
delete [] transform[r];
12907
}// end loop over 'r'
12908
delete [] transform;
12909
break;
12910
}
12911
case 21:
12912
{
12913
12914
// Array of basisvalues.
12915
double basisvalues[10] = {0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000};
12916
12917
// Declare helper variables.
12918
unsigned int rr = 0;
12919
unsigned int ss = 0;
12920
unsigned int tt = 0;
12921
double tmp5 = 0.00000000;
12922
double tmp6 = 0.00000000;
12923
double tmp7 = 0.00000000;
12924
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
12925
double tmp1 = 0.25000000*(Y + Z)*(Y + Z);
12926
double tmp2 = 0.50000000*(1.00000000 + Z + 2.00000000*Y);
12927
double tmp3 = 0.50000000*(1.00000000 - Z);
12928
double tmp4 = tmp3*tmp3;
12929
12930
// Compute basisvalues.
12931
basisvalues[0] = 1.00000000;
12932
basisvalues[1] = tmp0;
12933
for (unsigned int r = 1; r < 2; r++)
12934
{
12935
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
12936
ss = r*(r + 1)*(r + 2)/6;
12937
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
12938
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.00000000 + 2.00000000*r)/(1.00000000 + r) - basisvalues[tt]*tmp1*r/(1.00000000 + r));
12939
}// end loop over 'r'
12940
for (unsigned int r = 0; r < 2; r++)
12941
{
12942
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
12943
ss = r*(r + 1)*(r + 2)/6;
12944
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
12945
}// end loop over 'r'
12946
for (unsigned int r = 0; r < 1; r++)
12947
{
12948
for (unsigned int s = 1; s < 2 - r; s++)
12949
{
12950
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
12951
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
12952
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
12953
tmp5 = (2.00000000 + 2.00000000*r + 2.00000000*s)*(3.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
12954
tmp6 = (1.00000000 + 4.00000000*r*r + 4.00000000*r)*(2.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
12955
tmp7 = (1.00000000 + s + 2.00000000*r)*(3.00000000 + 2.00000000*r + 2.00000000*s)*s/((1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
12956
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
12957
}// end loop over 's'
12958
}// end loop over 'r'
12959
for (unsigned int r = 0; r < 2; r++)
12960
{
12961
for (unsigned int s = 0; s < 2 - r; s++)
12962
{
12963
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
12964
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
12965
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
12966
}// end loop over 's'
12967
}// end loop over 'r'
12968
for (unsigned int r = 0; r < 1; r++)
12969
{
12970
for (unsigned int s = 0; s < 1 - r; s++)
12971
{
12972
for (unsigned int t = 1; t < 2 - r - s; t++)
12973
{
12974
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
12975
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
12976
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
12977
tmp5 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)/(2.00000000*(1.00000000 + t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
12978
tmp6 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 4.00000000*r*r + 4.00000000*s*s + 8.00000000*r*s + 8.00000000*r + 8.00000000*s)/(2.00000000*(1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
12979
tmp7 = (2.00000000 + t + 2.00000000*r + 2.00000000*s)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*t/((1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
12980
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
12981
}// end loop over 't'
12982
}// end loop over 's'
12983
}// end loop over 'r'
12984
for (unsigned int r = 0; r < 3; r++)
12985
{
12986
for (unsigned int s = 0; s < 3 - r; s++)
12987
{
12988
for (unsigned int t = 0; t < 3 - r - s; t++)
12989
{
12990
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
12991
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
12992
}// end loop over 't'
12993
}// end loop over 's'
12994
}// end loop over 'r'
12995
12996
// Table(s) of coefficients.
12997
static const double coefficients0[10] = \
12998
{-0.05773503, 0.06085806, -0.03513642, -0.02484520, 0.06506000, -0.05039526, -0.04114756, 0.02909572, 0.02375655, 0.01679842};
12999
13000
// Tables of derivatives of the polynomial base (transpose).
13001
static const double dmats0[10][10] = \
13002
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13003
{6.32455532, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13004
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13005
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13006
{0.00000000, 11.22497216, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13007
{4.58257569, 0.00000000, 8.36660027, -1.18321596, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13008
{3.74165739, 0.00000000, 0.00000000, 8.69482605, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13009
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13010
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13011
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
13012
13013
static const double dmats1[10][10] = \
13014
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13015
{3.16227766, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13016
{5.47722558, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13017
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13018
{2.95803989, 5.61248608, -1.08012345, -0.76376262, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13019
{2.29128785, 7.24568837, 4.18330013, -0.59160798, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13020
{1.87082869, 0.00000000, 0.00000000, 4.34741302, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13021
{-2.64575131, 0.00000000, 9.66091783, 0.68313005, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13022
{3.24037035, 0.00000000, 0.00000000, 7.52994024, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13023
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
13024
13025
static const double dmats2[10][10] = \
13026
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13027
{3.16227766, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13028
{1.82574186, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13029
{5.16397779, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13030
{2.95803989, 5.61248608, -1.08012345, -0.76376262, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13031
{2.29128785, 1.44913767, 4.18330013, -0.59160798, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13032
{1.87082869, 7.09929574, 0.00000000, 4.34741302, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13033
{1.32287566, 0.00000000, 3.86436713, -0.34156503, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13034
{1.08012345, 0.00000000, 7.09929574, 2.50998008, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13035
{-3.81881308, 0.00000000, 0.00000000, 8.87411967, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
13036
13037
// Compute reference derivatives.
13038
// Declare pointer to array of derivatives on FIAT element.
13039
double *derivatives = new double[num_derivatives];
13040
for (unsigned int r = 0; r < num_derivatives; r++)
13041
{
13042
derivatives[r] = 0.00000000;
13043
}// end loop over 'r'
13044
13045
// Declare derivative matrix (of polynomial basis).
13046
double dmats[10][10] = \
13047
{{1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13048
{0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13049
{0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13050
{0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13051
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13052
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13053
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000},
13054
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000},
13055
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000},
13056
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000}};
13057
13058
// Declare (auxiliary) derivative matrix (of polynomial basis).
13059
double dmats_old[10][10] = \
13060
{{1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13061
{0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13062
{0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13063
{0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13064
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13065
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13066
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000},
13067
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000},
13068
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000},
13069
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000}};
13070
13071
// Loop possible derivatives.
13072
for (unsigned int r = 0; r < num_derivatives; r++)
13073
{
13074
// Resetting dmats values to compute next derivative.
13075
for (unsigned int t = 0; t < 10; t++)
13076
{
13077
for (unsigned int u = 0; u < 10; u++)
13078
{
13079
dmats[t][u] = 0.00000000;
13080
if (t == u)
13081
{
13082
dmats[t][u] = 1.00000000;
13083
}
13084
13085
}// end loop over 'u'
13086
}// end loop over 't'
13087
13088
// Looping derivative order to generate dmats.
13089
for (unsigned int s = 0; s < n; s++)
13090
{
13091
// Updating dmats_old with new values and resetting dmats.
13092
for (unsigned int t = 0; t < 10; t++)
13093
{
13094
for (unsigned int u = 0; u < 10; u++)
13095
{
13096
dmats_old[t][u] = dmats[t][u];
13097
dmats[t][u] = 0.00000000;
13098
}// end loop over 'u'
13099
}// end loop over 't'
13100
13101
// Update dmats using an inner product.
13102
if (combinations[r][s] == 0)
13103
{
13104
for (unsigned int t = 0; t < 10; t++)
13105
{
13106
for (unsigned int u = 0; u < 10; u++)
13107
{
13108
for (unsigned int tu = 0; tu < 10; tu++)
13109
{
13110
dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
13111
}// end loop over 'tu'
13112
}// end loop over 'u'
13113
}// end loop over 't'
13114
}
13115
13116
if (combinations[r][s] == 1)
13117
{
13118
for (unsigned int t = 0; t < 10; t++)
13119
{
13120
for (unsigned int u = 0; u < 10; u++)
13121
{
13122
for (unsigned int tu = 0; tu < 10; tu++)
13123
{
13124
dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
13125
}// end loop over 'tu'
13126
}// end loop over 'u'
13127
}// end loop over 't'
13128
}
13129
13130
if (combinations[r][s] == 2)
13131
{
13132
for (unsigned int t = 0; t < 10; t++)
13133
{
13134
for (unsigned int u = 0; u < 10; u++)
13135
{
13136
for (unsigned int tu = 0; tu < 10; tu++)
13137
{
13138
dmats[t][u] += dmats2[t][tu]*dmats_old[tu][u];
13139
}// end loop over 'tu'
13140
}// end loop over 'u'
13141
}// end loop over 't'
13142
}
13143
13144
}// end loop over 's'
13145
for (unsigned int s = 0; s < 10; s++)
13146
{
13147
for (unsigned int t = 0; t < 10; t++)
13148
{
13149
derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
13150
}// end loop over 't'
13151
}// end loop over 's'
13152
}// end loop over 'r'
13153
13154
// Transform derivatives back to physical element
13155
for (unsigned int r = 0; r < num_derivatives; r++)
13156
{
13157
for (unsigned int s = 0; s < num_derivatives; s++)
13158
{
13159
values[2*num_derivatives + r] += transform[r][s]*derivatives[s];
13160
}// end loop over 's'
13161
}// end loop over 'r'
13162
13163
// Delete pointer to array of derivatives on FIAT element
13164
delete [] derivatives;
13165
13166
// Delete pointer to array of combinations of derivatives and transform
13167
for (unsigned int r = 0; r < num_derivatives; r++)
13168
{
13169
delete [] combinations[r];
13170
}// end loop over 'r'
13171
delete [] combinations;
13172
for (unsigned int r = 0; r < num_derivatives; r++)
13173
{
13174
delete [] transform[r];
13175
}// end loop over 'r'
13176
delete [] transform;
13177
break;
13178
}
13179
case 22:
13180
{
13181
13182
// Array of basisvalues.
13183
double basisvalues[10] = {0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000};
13184
13185
// Declare helper variables.
13186
unsigned int rr = 0;
13187
unsigned int ss = 0;
13188
unsigned int tt = 0;
13189
double tmp5 = 0.00000000;
13190
double tmp6 = 0.00000000;
13191
double tmp7 = 0.00000000;
13192
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
13193
double tmp1 = 0.25000000*(Y + Z)*(Y + Z);
13194
double tmp2 = 0.50000000*(1.00000000 + Z + 2.00000000*Y);
13195
double tmp3 = 0.50000000*(1.00000000 - Z);
13196
double tmp4 = tmp3*tmp3;
13197
13198
// Compute basisvalues.
13199
basisvalues[0] = 1.00000000;
13200
basisvalues[1] = tmp0;
13201
for (unsigned int r = 1; r < 2; r++)
13202
{
13203
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
13204
ss = r*(r + 1)*(r + 2)/6;
13205
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
13206
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.00000000 + 2.00000000*r)/(1.00000000 + r) - basisvalues[tt]*tmp1*r/(1.00000000 + r));
13207
}// end loop over 'r'
13208
for (unsigned int r = 0; r < 2; r++)
13209
{
13210
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
13211
ss = r*(r + 1)*(r + 2)/6;
13212
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
13213
}// end loop over 'r'
13214
for (unsigned int r = 0; r < 1; r++)
13215
{
13216
for (unsigned int s = 1; s < 2 - r; s++)
13217
{
13218
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
13219
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
13220
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
13221
tmp5 = (2.00000000 + 2.00000000*r + 2.00000000*s)*(3.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
13222
tmp6 = (1.00000000 + 4.00000000*r*r + 4.00000000*r)*(2.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
13223
tmp7 = (1.00000000 + s + 2.00000000*r)*(3.00000000 + 2.00000000*r + 2.00000000*s)*s/((1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
13224
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
13225
}// end loop over 's'
13226
}// end loop over 'r'
13227
for (unsigned int r = 0; r < 2; r++)
13228
{
13229
for (unsigned int s = 0; s < 2 - r; s++)
13230
{
13231
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
13232
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
13233
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
13234
}// end loop over 's'
13235
}// end loop over 'r'
13236
for (unsigned int r = 0; r < 1; r++)
13237
{
13238
for (unsigned int s = 0; s < 1 - r; s++)
13239
{
13240
for (unsigned int t = 1; t < 2 - r - s; t++)
13241
{
13242
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
13243
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
13244
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
13245
tmp5 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)/(2.00000000*(1.00000000 + t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
13246
tmp6 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 4.00000000*r*r + 4.00000000*s*s + 8.00000000*r*s + 8.00000000*r + 8.00000000*s)/(2.00000000*(1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
13247
tmp7 = (2.00000000 + t + 2.00000000*r + 2.00000000*s)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*t/((1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
13248
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
13249
}// end loop over 't'
13250
}// end loop over 's'
13251
}// end loop over 'r'
13252
for (unsigned int r = 0; r < 3; r++)
13253
{
13254
for (unsigned int s = 0; s < 3 - r; s++)
13255
{
13256
for (unsigned int t = 0; t < 3 - r - s; t++)
13257
{
13258
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
13259
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
13260
}// end loop over 't'
13261
}// end loop over 's'
13262
}// end loop over 'r'
13263
13264
// Table(s) of coefficients.
13265
static const double coefficients0[10] = \
13266
{-0.05773503, 0.00000000, 0.07027284, -0.02484520, 0.00000000, 0.00000000, 0.00000000, 0.08728716, -0.04751311, 0.01679842};
13267
13268
// Tables of derivatives of the polynomial base (transpose).
13269
static const double dmats0[10][10] = \
13270
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13271
{6.32455532, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13272
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13273
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13274
{0.00000000, 11.22497216, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13275
{4.58257569, 0.00000000, 8.36660027, -1.18321596, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13276
{3.74165739, 0.00000000, 0.00000000, 8.69482605, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13277
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13278
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13279
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
13280
13281
static const double dmats1[10][10] = \
13282
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13283
{3.16227766, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13284
{5.47722558, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13285
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13286
{2.95803989, 5.61248608, -1.08012345, -0.76376262, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13287
{2.29128785, 7.24568837, 4.18330013, -0.59160798, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13288
{1.87082869, 0.00000000, 0.00000000, 4.34741302, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13289
{-2.64575131, 0.00000000, 9.66091783, 0.68313005, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13290
{3.24037035, 0.00000000, 0.00000000, 7.52994024, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13291
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
13292
13293
static const double dmats2[10][10] = \
13294
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13295
{3.16227766, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13296
{1.82574186, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13297
{5.16397779, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13298
{2.95803989, 5.61248608, -1.08012345, -0.76376262, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13299
{2.29128785, 1.44913767, 4.18330013, -0.59160798, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13300
{1.87082869, 7.09929574, 0.00000000, 4.34741302, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13301
{1.32287566, 0.00000000, 3.86436713, -0.34156503, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13302
{1.08012345, 0.00000000, 7.09929574, 2.50998008, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13303
{-3.81881308, 0.00000000, 0.00000000, 8.87411967, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
13304
13305
// Compute reference derivatives.
13306
// Declare pointer to array of derivatives on FIAT element.
13307
double *derivatives = new double[num_derivatives];
13308
for (unsigned int r = 0; r < num_derivatives; r++)
13309
{
13310
derivatives[r] = 0.00000000;
13311
}// end loop over 'r'
13312
13313
// Declare derivative matrix (of polynomial basis).
13314
double dmats[10][10] = \
13315
{{1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13316
{0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13317
{0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13318
{0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13319
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13320
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13321
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000},
13322
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000},
13323
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000},
13324
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000}};
13325
13326
// Declare (auxiliary) derivative matrix (of polynomial basis).
13327
double dmats_old[10][10] = \
13328
{{1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13329
{0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13330
{0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13331
{0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13332
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13333
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13334
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000},
13335
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000},
13336
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000},
13337
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000}};
13338
13339
// Loop possible derivatives.
13340
for (unsigned int r = 0; r < num_derivatives; r++)
13341
{
13342
// Resetting dmats values to compute next derivative.
13343
for (unsigned int t = 0; t < 10; t++)
13344
{
13345
for (unsigned int u = 0; u < 10; u++)
13346
{
13347
dmats[t][u] = 0.00000000;
13348
if (t == u)
13349
{
13350
dmats[t][u] = 1.00000000;
13351
}
13352
13353
}// end loop over 'u'
13354
}// end loop over 't'
13355
13356
// Looping derivative order to generate dmats.
13357
for (unsigned int s = 0; s < n; s++)
13358
{
13359
// Updating dmats_old with new values and resetting dmats.
13360
for (unsigned int t = 0; t < 10; t++)
13361
{
13362
for (unsigned int u = 0; u < 10; u++)
13363
{
13364
dmats_old[t][u] = dmats[t][u];
13365
dmats[t][u] = 0.00000000;
13366
}// end loop over 'u'
13367
}// end loop over 't'
13368
13369
// Update dmats using an inner product.
13370
if (combinations[r][s] == 0)
13371
{
13372
for (unsigned int t = 0; t < 10; t++)
13373
{
13374
for (unsigned int u = 0; u < 10; u++)
13375
{
13376
for (unsigned int tu = 0; tu < 10; tu++)
13377
{
13378
dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
13379
}// end loop over 'tu'
13380
}// end loop over 'u'
13381
}// end loop over 't'
13382
}
13383
13384
if (combinations[r][s] == 1)
13385
{
13386
for (unsigned int t = 0; t < 10; t++)
13387
{
13388
for (unsigned int u = 0; u < 10; u++)
13389
{
13390
for (unsigned int tu = 0; tu < 10; tu++)
13391
{
13392
dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
13393
}// end loop over 'tu'
13394
}// end loop over 'u'
13395
}// end loop over 't'
13396
}
13397
13398
if (combinations[r][s] == 2)
13399
{
13400
for (unsigned int t = 0; t < 10; t++)
13401
{
13402
for (unsigned int u = 0; u < 10; u++)
13403
{
13404
for (unsigned int tu = 0; tu < 10; tu++)
13405
{
13406
dmats[t][u] += dmats2[t][tu]*dmats_old[tu][u];
13407
}// end loop over 'tu'
13408
}// end loop over 'u'
13409
}// end loop over 't'
13410
}
13411
13412
}// end loop over 's'
13413
for (unsigned int s = 0; s < 10; s++)
13414
{
13415
for (unsigned int t = 0; t < 10; t++)
13416
{
13417
derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
13418
}// end loop over 't'
13419
}// end loop over 's'
13420
}// end loop over 'r'
13421
13422
// Transform derivatives back to physical element
13423
for (unsigned int r = 0; r < num_derivatives; r++)
13424
{
13425
for (unsigned int s = 0; s < num_derivatives; s++)
13426
{
13427
values[2*num_derivatives + r] += transform[r][s]*derivatives[s];
13428
}// end loop over 's'
13429
}// end loop over 'r'
13430
13431
// Delete pointer to array of derivatives on FIAT element
13432
delete [] derivatives;
13433
13434
// Delete pointer to array of combinations of derivatives and transform
13435
for (unsigned int r = 0; r < num_derivatives; r++)
13436
{
13437
delete [] combinations[r];
13438
}// end loop over 'r'
13439
delete [] combinations;
13440
for (unsigned int r = 0; r < num_derivatives; r++)
13441
{
13442
delete [] transform[r];
13443
}// end loop over 'r'
13444
delete [] transform;
13445
break;
13446
}
13447
case 23:
13448
{
13449
13450
// Array of basisvalues.
13451
double basisvalues[10] = {0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000};
13452
13453
// Declare helper variables.
13454
unsigned int rr = 0;
13455
unsigned int ss = 0;
13456
unsigned int tt = 0;
13457
double tmp5 = 0.00000000;
13458
double tmp6 = 0.00000000;
13459
double tmp7 = 0.00000000;
13460
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
13461
double tmp1 = 0.25000000*(Y + Z)*(Y + Z);
13462
double tmp2 = 0.50000000*(1.00000000 + Z + 2.00000000*Y);
13463
double tmp3 = 0.50000000*(1.00000000 - Z);
13464
double tmp4 = tmp3*tmp3;
13465
13466
// Compute basisvalues.
13467
basisvalues[0] = 1.00000000;
13468
basisvalues[1] = tmp0;
13469
for (unsigned int r = 1; r < 2; r++)
13470
{
13471
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
13472
ss = r*(r + 1)*(r + 2)/6;
13473
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
13474
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.00000000 + 2.00000000*r)/(1.00000000 + r) - basisvalues[tt]*tmp1*r/(1.00000000 + r));
13475
}// end loop over 'r'
13476
for (unsigned int r = 0; r < 2; r++)
13477
{
13478
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
13479
ss = r*(r + 1)*(r + 2)/6;
13480
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
13481
}// end loop over 'r'
13482
for (unsigned int r = 0; r < 1; r++)
13483
{
13484
for (unsigned int s = 1; s < 2 - r; s++)
13485
{
13486
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
13487
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
13488
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
13489
tmp5 = (2.00000000 + 2.00000000*r + 2.00000000*s)*(3.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
13490
tmp6 = (1.00000000 + 4.00000000*r*r + 4.00000000*r)*(2.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
13491
tmp7 = (1.00000000 + s + 2.00000000*r)*(3.00000000 + 2.00000000*r + 2.00000000*s)*s/((1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
13492
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
13493
}// end loop over 's'
13494
}// end loop over 'r'
13495
for (unsigned int r = 0; r < 2; r++)
13496
{
13497
for (unsigned int s = 0; s < 2 - r; s++)
13498
{
13499
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
13500
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
13501
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
13502
}// end loop over 's'
13503
}// end loop over 'r'
13504
for (unsigned int r = 0; r < 1; r++)
13505
{
13506
for (unsigned int s = 0; s < 1 - r; s++)
13507
{
13508
for (unsigned int t = 1; t < 2 - r - s; t++)
13509
{
13510
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
13511
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
13512
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
13513
tmp5 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)/(2.00000000*(1.00000000 + t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
13514
tmp6 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 4.00000000*r*r + 4.00000000*s*s + 8.00000000*r*s + 8.00000000*r + 8.00000000*s)/(2.00000000*(1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
13515
tmp7 = (2.00000000 + t + 2.00000000*r + 2.00000000*s)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*t/((1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
13516
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
13517
}// end loop over 't'
13518
}// end loop over 's'
13519
}// end loop over 'r'
13520
for (unsigned int r = 0; r < 3; r++)
13521
{
13522
for (unsigned int s = 0; s < 3 - r; s++)
13523
{
13524
for (unsigned int t = 0; t < 3 - r - s; t++)
13525
{
13526
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
13527
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
13528
}// end loop over 't'
13529
}// end loop over 's'
13530
}// end loop over 'r'
13531
13532
// Table(s) of coefficients.
13533
static const double coefficients0[10] = \
13534
{-0.05773503, 0.00000000, 0.00000000, 0.07453560, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.10079053};
13535
13536
// Tables of derivatives of the polynomial base (transpose).
13537
static const double dmats0[10][10] = \
13538
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13539
{6.32455532, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13540
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13541
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13542
{0.00000000, 11.22497216, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13543
{4.58257569, 0.00000000, 8.36660027, -1.18321596, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13544
{3.74165739, 0.00000000, 0.00000000, 8.69482605, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13545
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13546
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13547
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
13548
13549
static const double dmats1[10][10] = \
13550
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13551
{3.16227766, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13552
{5.47722558, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13553
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13554
{2.95803989, 5.61248608, -1.08012345, -0.76376262, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13555
{2.29128785, 7.24568837, 4.18330013, -0.59160798, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13556
{1.87082869, 0.00000000, 0.00000000, 4.34741302, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13557
{-2.64575131, 0.00000000, 9.66091783, 0.68313005, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13558
{3.24037035, 0.00000000, 0.00000000, 7.52994024, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13559
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
13560
13561
static const double dmats2[10][10] = \
13562
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13563
{3.16227766, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13564
{1.82574186, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13565
{5.16397779, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13566
{2.95803989, 5.61248608, -1.08012345, -0.76376262, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13567
{2.29128785, 1.44913767, 4.18330013, -0.59160798, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13568
{1.87082869, 7.09929574, 0.00000000, 4.34741302, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13569
{1.32287566, 0.00000000, 3.86436713, -0.34156503, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13570
{1.08012345, 0.00000000, 7.09929574, 2.50998008, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13571
{-3.81881308, 0.00000000, 0.00000000, 8.87411967, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
13572
13573
// Compute reference derivatives.
13574
// Declare pointer to array of derivatives on FIAT element.
13575
double *derivatives = new double[num_derivatives];
13576
for (unsigned int r = 0; r < num_derivatives; r++)
13577
{
13578
derivatives[r] = 0.00000000;
13579
}// end loop over 'r'
13580
13581
// Declare derivative matrix (of polynomial basis).
13582
double dmats[10][10] = \
13583
{{1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13584
{0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13585
{0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13586
{0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13587
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13588
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13589
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000},
13590
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000},
13591
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000},
13592
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000}};
13593
13594
// Declare (auxiliary) derivative matrix (of polynomial basis).
13595
double dmats_old[10][10] = \
13596
{{1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13597
{0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13598
{0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13599
{0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13600
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13601
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13602
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000},
13603
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000},
13604
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000},
13605
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000}};
13606
13607
// Loop possible derivatives.
13608
for (unsigned int r = 0; r < num_derivatives; r++)
13609
{
13610
// Resetting dmats values to compute next derivative.
13611
for (unsigned int t = 0; t < 10; t++)
13612
{
13613
for (unsigned int u = 0; u < 10; u++)
13614
{
13615
dmats[t][u] = 0.00000000;
13616
if (t == u)
13617
{
13618
dmats[t][u] = 1.00000000;
13619
}
13620
13621
}// end loop over 'u'
13622
}// end loop over 't'
13623
13624
// Looping derivative order to generate dmats.
13625
for (unsigned int s = 0; s < n; s++)
13626
{
13627
// Updating dmats_old with new values and resetting dmats.
13628
for (unsigned int t = 0; t < 10; t++)
13629
{
13630
for (unsigned int u = 0; u < 10; u++)
13631
{
13632
dmats_old[t][u] = dmats[t][u];
13633
dmats[t][u] = 0.00000000;
13634
}// end loop over 'u'
13635
}// end loop over 't'
13636
13637
// Update dmats using an inner product.
13638
if (combinations[r][s] == 0)
13639
{
13640
for (unsigned int t = 0; t < 10; t++)
13641
{
13642
for (unsigned int u = 0; u < 10; u++)
13643
{
13644
for (unsigned int tu = 0; tu < 10; tu++)
13645
{
13646
dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
13647
}// end loop over 'tu'
13648
}// end loop over 'u'
13649
}// end loop over 't'
13650
}
13651
13652
if (combinations[r][s] == 1)
13653
{
13654
for (unsigned int t = 0; t < 10; t++)
13655
{
13656
for (unsigned int u = 0; u < 10; u++)
13657
{
13658
for (unsigned int tu = 0; tu < 10; tu++)
13659
{
13660
dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
13661
}// end loop over 'tu'
13662
}// end loop over 'u'
13663
}// end loop over 't'
13664
}
13665
13666
if (combinations[r][s] == 2)
13667
{
13668
for (unsigned int t = 0; t < 10; t++)
13669
{
13670
for (unsigned int u = 0; u < 10; u++)
13671
{
13672
for (unsigned int tu = 0; tu < 10; tu++)
13673
{
13674
dmats[t][u] += dmats2[t][tu]*dmats_old[tu][u];
13675
}// end loop over 'tu'
13676
}// end loop over 'u'
13677
}// end loop over 't'
13678
}
13679
13680
}// end loop over 's'
13681
for (unsigned int s = 0; s < 10; s++)
13682
{
13683
for (unsigned int t = 0; t < 10; t++)
13684
{
13685
derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
13686
}// end loop over 't'
13687
}// end loop over 's'
13688
}// end loop over 'r'
13689
13690
// Transform derivatives back to physical element
13691
for (unsigned int r = 0; r < num_derivatives; r++)
13692
{
13693
for (unsigned int s = 0; s < num_derivatives; s++)
13694
{
13695
values[2*num_derivatives + r] += transform[r][s]*derivatives[s];
13696
}// end loop over 's'
13697
}// end loop over 'r'
13698
13699
// Delete pointer to array of derivatives on FIAT element
13700
delete [] derivatives;
13701
13702
// Delete pointer to array of combinations of derivatives and transform
13703
for (unsigned int r = 0; r < num_derivatives; r++)
13704
{
13705
delete [] combinations[r];
13706
}// end loop over 'r'
13707
delete [] combinations;
13708
for (unsigned int r = 0; r < num_derivatives; r++)
13709
{
13710
delete [] transform[r];
13711
}// end loop over 'r'
13712
delete [] transform;
13713
break;
13714
}
13715
case 24:
13716
{
13717
13718
// Array of basisvalues.
13719
double basisvalues[10] = {0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000};
13720
13721
// Declare helper variables.
13722
unsigned int rr = 0;
13723
unsigned int ss = 0;
13724
unsigned int tt = 0;
13725
double tmp5 = 0.00000000;
13726
double tmp6 = 0.00000000;
13727
double tmp7 = 0.00000000;
13728
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
13729
double tmp1 = 0.25000000*(Y + Z)*(Y + Z);
13730
double tmp2 = 0.50000000*(1.00000000 + Z + 2.00000000*Y);
13731
double tmp3 = 0.50000000*(1.00000000 - Z);
13732
double tmp4 = tmp3*tmp3;
13733
13734
// Compute basisvalues.
13735
basisvalues[0] = 1.00000000;
13736
basisvalues[1] = tmp0;
13737
for (unsigned int r = 1; r < 2; r++)
13738
{
13739
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
13740
ss = r*(r + 1)*(r + 2)/6;
13741
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
13742
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.00000000 + 2.00000000*r)/(1.00000000 + r) - basisvalues[tt]*tmp1*r/(1.00000000 + r));
13743
}// end loop over 'r'
13744
for (unsigned int r = 0; r < 2; r++)
13745
{
13746
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
13747
ss = r*(r + 1)*(r + 2)/6;
13748
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
13749
}// end loop over 'r'
13750
for (unsigned int r = 0; r < 1; r++)
13751
{
13752
for (unsigned int s = 1; s < 2 - r; s++)
13753
{
13754
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
13755
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
13756
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
13757
tmp5 = (2.00000000 + 2.00000000*r + 2.00000000*s)*(3.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
13758
tmp6 = (1.00000000 + 4.00000000*r*r + 4.00000000*r)*(2.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
13759
tmp7 = (1.00000000 + s + 2.00000000*r)*(3.00000000 + 2.00000000*r + 2.00000000*s)*s/((1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
13760
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
13761
}// end loop over 's'
13762
}// end loop over 'r'
13763
for (unsigned int r = 0; r < 2; r++)
13764
{
13765
for (unsigned int s = 0; s < 2 - r; s++)
13766
{
13767
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
13768
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
13769
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
13770
}// end loop over 's'
13771
}// end loop over 'r'
13772
for (unsigned int r = 0; r < 1; r++)
13773
{
13774
for (unsigned int s = 0; s < 1 - r; s++)
13775
{
13776
for (unsigned int t = 1; t < 2 - r - s; t++)
13777
{
13778
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
13779
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
13780
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
13781
tmp5 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)/(2.00000000*(1.00000000 + t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
13782
tmp6 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 4.00000000*r*r + 4.00000000*s*s + 8.00000000*r*s + 8.00000000*r + 8.00000000*s)/(2.00000000*(1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
13783
tmp7 = (2.00000000 + t + 2.00000000*r + 2.00000000*s)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*t/((1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
13784
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
13785
}// end loop over 't'
13786
}// end loop over 's'
13787
}// end loop over 'r'
13788
for (unsigned int r = 0; r < 3; r++)
13789
{
13790
for (unsigned int s = 0; s < 3 - r; s++)
13791
{
13792
for (unsigned int t = 0; t < 3 - r - s; t++)
13793
{
13794
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
13795
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
13796
}// end loop over 't'
13797
}// end loop over 's'
13798
}// end loop over 'r'
13799
13800
// Table(s) of coefficients.
13801
static const double coefficients0[10] = \
13802
{0.23094011, 0.00000000, 0.14054567, 0.09938080, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.11878277, -0.06719368};
13803
13804
// Tables of derivatives of the polynomial base (transpose).
13805
static const double dmats0[10][10] = \
13806
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13807
{6.32455532, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13808
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13809
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13810
{0.00000000, 11.22497216, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13811
{4.58257569, 0.00000000, 8.36660027, -1.18321596, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13812
{3.74165739, 0.00000000, 0.00000000, 8.69482605, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13813
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13814
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13815
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
13816
13817
static const double dmats1[10][10] = \
13818
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13819
{3.16227766, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13820
{5.47722558, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13821
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13822
{2.95803989, 5.61248608, -1.08012345, -0.76376262, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13823
{2.29128785, 7.24568837, 4.18330013, -0.59160798, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13824
{1.87082869, 0.00000000, 0.00000000, 4.34741302, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13825
{-2.64575131, 0.00000000, 9.66091783, 0.68313005, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13826
{3.24037035, 0.00000000, 0.00000000, 7.52994024, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13827
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
13828
13829
static const double dmats2[10][10] = \
13830
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13831
{3.16227766, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13832
{1.82574186, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13833
{5.16397779, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13834
{2.95803989, 5.61248608, -1.08012345, -0.76376262, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13835
{2.29128785, 1.44913767, 4.18330013, -0.59160798, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13836
{1.87082869, 7.09929574, 0.00000000, 4.34741302, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13837
{1.32287566, 0.00000000, 3.86436713, -0.34156503, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13838
{1.08012345, 0.00000000, 7.09929574, 2.50998008, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13839
{-3.81881308, 0.00000000, 0.00000000, 8.87411967, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
13840
13841
// Compute reference derivatives.
13842
// Declare pointer to array of derivatives on FIAT element.
13843
double *derivatives = new double[num_derivatives];
13844
for (unsigned int r = 0; r < num_derivatives; r++)
13845
{
13846
derivatives[r] = 0.00000000;
13847
}// end loop over 'r'
13848
13849
// Declare derivative matrix (of polynomial basis).
13850
double dmats[10][10] = \
13851
{{1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13852
{0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13853
{0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13854
{0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13855
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13856
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13857
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000},
13858
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000},
13859
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000},
13860
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000}};
13861
13862
// Declare (auxiliary) derivative matrix (of polynomial basis).
13863
double dmats_old[10][10] = \
13864
{{1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13865
{0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13866
{0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13867
{0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13868
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13869
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
13870
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000},
13871
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000},
13872
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000},
13873
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000}};
13874
13875
// Loop possible derivatives.
13876
for (unsigned int r = 0; r < num_derivatives; r++)
13877
{
13878
// Resetting dmats values to compute next derivative.
13879
for (unsigned int t = 0; t < 10; t++)
13880
{
13881
for (unsigned int u = 0; u < 10; u++)
13882
{
13883
dmats[t][u] = 0.00000000;
13884
if (t == u)
13885
{
13886
dmats[t][u] = 1.00000000;
13887
}
13888
13889
}// end loop over 'u'
13890
}// end loop over 't'
13891
13892
// Looping derivative order to generate dmats.
13893
for (unsigned int s = 0; s < n; s++)
13894
{
13895
// Updating dmats_old with new values and resetting dmats.
13896
for (unsigned int t = 0; t < 10; t++)
13897
{
13898
for (unsigned int u = 0; u < 10; u++)
13899
{
13900
dmats_old[t][u] = dmats[t][u];
13901
dmats[t][u] = 0.00000000;
13902
}// end loop over 'u'
13903
}// end loop over 't'
13904
13905
// Update dmats using an inner product.
13906
if (combinations[r][s] == 0)
13907
{
13908
for (unsigned int t = 0; t < 10; t++)
13909
{
13910
for (unsigned int u = 0; u < 10; u++)
13911
{
13912
for (unsigned int tu = 0; tu < 10; tu++)
13913
{
13914
dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
13915
}// end loop over 'tu'
13916
}// end loop over 'u'
13917
}// end loop over 't'
13918
}
13919
13920
if (combinations[r][s] == 1)
13921
{
13922
for (unsigned int t = 0; t < 10; t++)
13923
{
13924
for (unsigned int u = 0; u < 10; u++)
13925
{
13926
for (unsigned int tu = 0; tu < 10; tu++)
13927
{
13928
dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
13929
}// end loop over 'tu'
13930
}// end loop over 'u'
13931
}// end loop over 't'
13932
}
13933
13934
if (combinations[r][s] == 2)
13935
{
13936
for (unsigned int t = 0; t < 10; t++)
13937
{
13938
for (unsigned int u = 0; u < 10; u++)
13939
{
13940
for (unsigned int tu = 0; tu < 10; tu++)
13941
{
13942
dmats[t][u] += dmats2[t][tu]*dmats_old[tu][u];
13943
}// end loop over 'tu'
13944
}// end loop over 'u'
13945
}// end loop over 't'
13946
}
13947
13948
}// end loop over 's'
13949
for (unsigned int s = 0; s < 10; s++)
13950
{
13951
for (unsigned int t = 0; t < 10; t++)
13952
{
13953
derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
13954
}// end loop over 't'
13955
}// end loop over 's'
13956
}// end loop over 'r'
13957
13958
// Transform derivatives back to physical element
13959
for (unsigned int r = 0; r < num_derivatives; r++)
13960
{
13961
for (unsigned int s = 0; s < num_derivatives; s++)
13962
{
13963
values[2*num_derivatives + r] += transform[r][s]*derivatives[s];
13964
}// end loop over 's'
13965
}// end loop over 'r'
13966
13967
// Delete pointer to array of derivatives on FIAT element
13968
delete [] derivatives;
13969
13970
// Delete pointer to array of combinations of derivatives and transform
13971
for (unsigned int r = 0; r < num_derivatives; r++)
13972
{
13973
delete [] combinations[r];
13974
}// end loop over 'r'
13975
delete [] combinations;
13976
for (unsigned int r = 0; r < num_derivatives; r++)
13977
{
13978
delete [] transform[r];
13979
}// end loop over 'r'
13980
delete [] transform;
13981
break;
13982
}
13983
case 25:
13984
{
13985
13986
// Array of basisvalues.
13987
double basisvalues[10] = {0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000};
13988
13989
// Declare helper variables.
13990
unsigned int rr = 0;
13991
unsigned int ss = 0;
13992
unsigned int tt = 0;
13993
double tmp5 = 0.00000000;
13994
double tmp6 = 0.00000000;
13995
double tmp7 = 0.00000000;
13996
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
13997
double tmp1 = 0.25000000*(Y + Z)*(Y + Z);
13998
double tmp2 = 0.50000000*(1.00000000 + Z + 2.00000000*Y);
13999
double tmp3 = 0.50000000*(1.00000000 - Z);
14000
double tmp4 = tmp3*tmp3;
14001
14002
// Compute basisvalues.
14003
basisvalues[0] = 1.00000000;
14004
basisvalues[1] = tmp0;
14005
for (unsigned int r = 1; r < 2; r++)
14006
{
14007
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
14008
ss = r*(r + 1)*(r + 2)/6;
14009
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
14010
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.00000000 + 2.00000000*r)/(1.00000000 + r) - basisvalues[tt]*tmp1*r/(1.00000000 + r));
14011
}// end loop over 'r'
14012
for (unsigned int r = 0; r < 2; r++)
14013
{
14014
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
14015
ss = r*(r + 1)*(r + 2)/6;
14016
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
14017
}// end loop over 'r'
14018
for (unsigned int r = 0; r < 1; r++)
14019
{
14020
for (unsigned int s = 1; s < 2 - r; s++)
14021
{
14022
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
14023
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
14024
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
14025
tmp5 = (2.00000000 + 2.00000000*r + 2.00000000*s)*(3.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
14026
tmp6 = (1.00000000 + 4.00000000*r*r + 4.00000000*r)*(2.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
14027
tmp7 = (1.00000000 + s + 2.00000000*r)*(3.00000000 + 2.00000000*r + 2.00000000*s)*s/((1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
14028
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
14029
}// end loop over 's'
14030
}// end loop over 'r'
14031
for (unsigned int r = 0; r < 2; r++)
14032
{
14033
for (unsigned int s = 0; s < 2 - r; s++)
14034
{
14035
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
14036
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
14037
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
14038
}// end loop over 's'
14039
}// end loop over 'r'
14040
for (unsigned int r = 0; r < 1; r++)
14041
{
14042
for (unsigned int s = 0; s < 1 - r; s++)
14043
{
14044
for (unsigned int t = 1; t < 2 - r - s; t++)
14045
{
14046
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
14047
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
14048
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
14049
tmp5 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)/(2.00000000*(1.00000000 + t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
14050
tmp6 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 4.00000000*r*r + 4.00000000*s*s + 8.00000000*r*s + 8.00000000*r + 8.00000000*s)/(2.00000000*(1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
14051
tmp7 = (2.00000000 + t + 2.00000000*r + 2.00000000*s)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*t/((1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
14052
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
14053
}// end loop over 't'
14054
}// end loop over 's'
14055
}// end loop over 'r'
14056
for (unsigned int r = 0; r < 3; r++)
14057
{
14058
for (unsigned int s = 0; s < 3 - r; s++)
14059
{
14060
for (unsigned int t = 0; t < 3 - r - s; t++)
14061
{
14062
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
14063
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
14064
}// end loop over 't'
14065
}// end loop over 's'
14066
}// end loop over 'r'
14067
14068
// Table(s) of coefficients.
14069
static const double coefficients0[10] = \
14070
{0.23094011, 0.12171612, -0.07027284, 0.09938080, 0.00000000, 0.00000000, 0.10286890, 0.00000000, -0.05939139, -0.06719368};
14071
14072
// Tables of derivatives of the polynomial base (transpose).
14073
static const double dmats0[10][10] = \
14074
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14075
{6.32455532, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14076
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14077
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14078
{0.00000000, 11.22497216, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14079
{4.58257569, 0.00000000, 8.36660027, -1.18321596, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14080
{3.74165739, 0.00000000, 0.00000000, 8.69482605, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14081
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14082
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14083
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
14084
14085
static const double dmats1[10][10] = \
14086
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14087
{3.16227766, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14088
{5.47722558, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14089
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14090
{2.95803989, 5.61248608, -1.08012345, -0.76376262, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14091
{2.29128785, 7.24568837, 4.18330013, -0.59160798, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14092
{1.87082869, 0.00000000, 0.00000000, 4.34741302, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14093
{-2.64575131, 0.00000000, 9.66091783, 0.68313005, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14094
{3.24037035, 0.00000000, 0.00000000, 7.52994024, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14095
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
14096
14097
static const double dmats2[10][10] = \
14098
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14099
{3.16227766, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14100
{1.82574186, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14101
{5.16397779, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14102
{2.95803989, 5.61248608, -1.08012345, -0.76376262, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14103
{2.29128785, 1.44913767, 4.18330013, -0.59160798, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14104
{1.87082869, 7.09929574, 0.00000000, 4.34741302, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14105
{1.32287566, 0.00000000, 3.86436713, -0.34156503, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14106
{1.08012345, 0.00000000, 7.09929574, 2.50998008, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14107
{-3.81881308, 0.00000000, 0.00000000, 8.87411967, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
14108
14109
// Compute reference derivatives.
14110
// Declare pointer to array of derivatives on FIAT element.
14111
double *derivatives = new double[num_derivatives];
14112
for (unsigned int r = 0; r < num_derivatives; r++)
14113
{
14114
derivatives[r] = 0.00000000;
14115
}// end loop over 'r'
14116
14117
// Declare derivative matrix (of polynomial basis).
14118
double dmats[10][10] = \
14119
{{1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14120
{0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14121
{0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14122
{0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14123
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14124
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14125
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000},
14126
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000},
14127
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000},
14128
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000}};
14129
14130
// Declare (auxiliary) derivative matrix (of polynomial basis).
14131
double dmats_old[10][10] = \
14132
{{1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14133
{0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14134
{0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14135
{0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14136
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14137
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14138
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000},
14139
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000},
14140
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000},
14141
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000}};
14142
14143
// Loop possible derivatives.
14144
for (unsigned int r = 0; r < num_derivatives; r++)
14145
{
14146
// Resetting dmats values to compute next derivative.
14147
for (unsigned int t = 0; t < 10; t++)
14148
{
14149
for (unsigned int u = 0; u < 10; u++)
14150
{
14151
dmats[t][u] = 0.00000000;
14152
if (t == u)
14153
{
14154
dmats[t][u] = 1.00000000;
14155
}
14156
14157
}// end loop over 'u'
14158
}// end loop over 't'
14159
14160
// Looping derivative order to generate dmats.
14161
for (unsigned int s = 0; s < n; s++)
14162
{
14163
// Updating dmats_old with new values and resetting dmats.
14164
for (unsigned int t = 0; t < 10; t++)
14165
{
14166
for (unsigned int u = 0; u < 10; u++)
14167
{
14168
dmats_old[t][u] = dmats[t][u];
14169
dmats[t][u] = 0.00000000;
14170
}// end loop over 'u'
14171
}// end loop over 't'
14172
14173
// Update dmats using an inner product.
14174
if (combinations[r][s] == 0)
14175
{
14176
for (unsigned int t = 0; t < 10; t++)
14177
{
14178
for (unsigned int u = 0; u < 10; u++)
14179
{
14180
for (unsigned int tu = 0; tu < 10; tu++)
14181
{
14182
dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
14183
}// end loop over 'tu'
14184
}// end loop over 'u'
14185
}// end loop over 't'
14186
}
14187
14188
if (combinations[r][s] == 1)
14189
{
14190
for (unsigned int t = 0; t < 10; t++)
14191
{
14192
for (unsigned int u = 0; u < 10; u++)
14193
{
14194
for (unsigned int tu = 0; tu < 10; tu++)
14195
{
14196
dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
14197
}// end loop over 'tu'
14198
}// end loop over 'u'
14199
}// end loop over 't'
14200
}
14201
14202
if (combinations[r][s] == 2)
14203
{
14204
for (unsigned int t = 0; t < 10; t++)
14205
{
14206
for (unsigned int u = 0; u < 10; u++)
14207
{
14208
for (unsigned int tu = 0; tu < 10; tu++)
14209
{
14210
dmats[t][u] += dmats2[t][tu]*dmats_old[tu][u];
14211
}// end loop over 'tu'
14212
}// end loop over 'u'
14213
}// end loop over 't'
14214
}
14215
14216
}// end loop over 's'
14217
for (unsigned int s = 0; s < 10; s++)
14218
{
14219
for (unsigned int t = 0; t < 10; t++)
14220
{
14221
derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
14222
}// end loop over 't'
14223
}// end loop over 's'
14224
}// end loop over 'r'
14225
14226
// Transform derivatives back to physical element
14227
for (unsigned int r = 0; r < num_derivatives; r++)
14228
{
14229
for (unsigned int s = 0; s < num_derivatives; s++)
14230
{
14231
values[2*num_derivatives + r] += transform[r][s]*derivatives[s];
14232
}// end loop over 's'
14233
}// end loop over 'r'
14234
14235
// Delete pointer to array of derivatives on FIAT element
14236
delete [] derivatives;
14237
14238
// Delete pointer to array of combinations of derivatives and transform
14239
for (unsigned int r = 0; r < num_derivatives; r++)
14240
{
14241
delete [] combinations[r];
14242
}// end loop over 'r'
14243
delete [] combinations;
14244
for (unsigned int r = 0; r < num_derivatives; r++)
14245
{
14246
delete [] transform[r];
14247
}// end loop over 'r'
14248
delete [] transform;
14249
break;
14250
}
14251
case 26:
14252
{
14253
14254
// Array of basisvalues.
14255
double basisvalues[10] = {0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000};
14256
14257
// Declare helper variables.
14258
unsigned int rr = 0;
14259
unsigned int ss = 0;
14260
unsigned int tt = 0;
14261
double tmp5 = 0.00000000;
14262
double tmp6 = 0.00000000;
14263
double tmp7 = 0.00000000;
14264
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
14265
double tmp1 = 0.25000000*(Y + Z)*(Y + Z);
14266
double tmp2 = 0.50000000*(1.00000000 + Z + 2.00000000*Y);
14267
double tmp3 = 0.50000000*(1.00000000 - Z);
14268
double tmp4 = tmp3*tmp3;
14269
14270
// Compute basisvalues.
14271
basisvalues[0] = 1.00000000;
14272
basisvalues[1] = tmp0;
14273
for (unsigned int r = 1; r < 2; r++)
14274
{
14275
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
14276
ss = r*(r + 1)*(r + 2)/6;
14277
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
14278
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.00000000 + 2.00000000*r)/(1.00000000 + r) - basisvalues[tt]*tmp1*r/(1.00000000 + r));
14279
}// end loop over 'r'
14280
for (unsigned int r = 0; r < 2; r++)
14281
{
14282
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
14283
ss = r*(r + 1)*(r + 2)/6;
14284
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
14285
}// end loop over 'r'
14286
for (unsigned int r = 0; r < 1; r++)
14287
{
14288
for (unsigned int s = 1; s < 2 - r; s++)
14289
{
14290
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
14291
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
14292
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
14293
tmp5 = (2.00000000 + 2.00000000*r + 2.00000000*s)*(3.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
14294
tmp6 = (1.00000000 + 4.00000000*r*r + 4.00000000*r)*(2.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
14295
tmp7 = (1.00000000 + s + 2.00000000*r)*(3.00000000 + 2.00000000*r + 2.00000000*s)*s/((1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
14296
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
14297
}// end loop over 's'
14298
}// end loop over 'r'
14299
for (unsigned int r = 0; r < 2; r++)
14300
{
14301
for (unsigned int s = 0; s < 2 - r; s++)
14302
{
14303
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
14304
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
14305
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
14306
}// end loop over 's'
14307
}// end loop over 'r'
14308
for (unsigned int r = 0; r < 1; r++)
14309
{
14310
for (unsigned int s = 0; s < 1 - r; s++)
14311
{
14312
for (unsigned int t = 1; t < 2 - r - s; t++)
14313
{
14314
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
14315
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
14316
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
14317
tmp5 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)/(2.00000000*(1.00000000 + t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
14318
tmp6 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 4.00000000*r*r + 4.00000000*s*s + 8.00000000*r*s + 8.00000000*r + 8.00000000*s)/(2.00000000*(1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
14319
tmp7 = (2.00000000 + t + 2.00000000*r + 2.00000000*s)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*t/((1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
14320
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
14321
}// end loop over 't'
14322
}// end loop over 's'
14323
}// end loop over 'r'
14324
for (unsigned int r = 0; r < 3; r++)
14325
{
14326
for (unsigned int s = 0; s < 3 - r; s++)
14327
{
14328
for (unsigned int t = 0; t < 3 - r - s; t++)
14329
{
14330
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
14331
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
14332
}// end loop over 't'
14333
}// end loop over 's'
14334
}// end loop over 'r'
14335
14336
// Table(s) of coefficients.
14337
static const double coefficients0[10] = \
14338
{0.23094011, 0.12171612, 0.07027284, -0.09938080, 0.00000000, 0.10079053, -0.02057378, -0.08728716, -0.01187828, 0.01679842};
14339
14340
// Tables of derivatives of the polynomial base (transpose).
14341
static const double dmats0[10][10] = \
14342
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14343
{6.32455532, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14344
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14345
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14346
{0.00000000, 11.22497216, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14347
{4.58257569, 0.00000000, 8.36660027, -1.18321596, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14348
{3.74165739, 0.00000000, 0.00000000, 8.69482605, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14349
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14350
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14351
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
14352
14353
static const double dmats1[10][10] = \
14354
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14355
{3.16227766, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14356
{5.47722558, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14357
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14358
{2.95803989, 5.61248608, -1.08012345, -0.76376262, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14359
{2.29128785, 7.24568837, 4.18330013, -0.59160798, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14360
{1.87082869, 0.00000000, 0.00000000, 4.34741302, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14361
{-2.64575131, 0.00000000, 9.66091783, 0.68313005, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14362
{3.24037035, 0.00000000, 0.00000000, 7.52994024, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14363
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
14364
14365
static const double dmats2[10][10] = \
14366
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14367
{3.16227766, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14368
{1.82574186, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14369
{5.16397779, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14370
{2.95803989, 5.61248608, -1.08012345, -0.76376262, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14371
{2.29128785, 1.44913767, 4.18330013, -0.59160798, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14372
{1.87082869, 7.09929574, 0.00000000, 4.34741302, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14373
{1.32287566, 0.00000000, 3.86436713, -0.34156503, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14374
{1.08012345, 0.00000000, 7.09929574, 2.50998008, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14375
{-3.81881308, 0.00000000, 0.00000000, 8.87411967, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
14376
14377
// Compute reference derivatives.
14378
// Declare pointer to array of derivatives on FIAT element.
14379
double *derivatives = new double[num_derivatives];
14380
for (unsigned int r = 0; r < num_derivatives; r++)
14381
{
14382
derivatives[r] = 0.00000000;
14383
}// end loop over 'r'
14384
14385
// Declare derivative matrix (of polynomial basis).
14386
double dmats[10][10] = \
14387
{{1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14388
{0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14389
{0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14390
{0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14391
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14392
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14393
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000},
14394
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000},
14395
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000},
14396
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000}};
14397
14398
// Declare (auxiliary) derivative matrix (of polynomial basis).
14399
double dmats_old[10][10] = \
14400
{{1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14401
{0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14402
{0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14403
{0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14404
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14405
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14406
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000},
14407
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000},
14408
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000},
14409
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000}};
14410
14411
// Loop possible derivatives.
14412
for (unsigned int r = 0; r < num_derivatives; r++)
14413
{
14414
// Resetting dmats values to compute next derivative.
14415
for (unsigned int t = 0; t < 10; t++)
14416
{
14417
for (unsigned int u = 0; u < 10; u++)
14418
{
14419
dmats[t][u] = 0.00000000;
14420
if (t == u)
14421
{
14422
dmats[t][u] = 1.00000000;
14423
}
14424
14425
}// end loop over 'u'
14426
}// end loop over 't'
14427
14428
// Looping derivative order to generate dmats.
14429
for (unsigned int s = 0; s < n; s++)
14430
{
14431
// Updating dmats_old with new values and resetting dmats.
14432
for (unsigned int t = 0; t < 10; t++)
14433
{
14434
for (unsigned int u = 0; u < 10; u++)
14435
{
14436
dmats_old[t][u] = dmats[t][u];
14437
dmats[t][u] = 0.00000000;
14438
}// end loop over 'u'
14439
}// end loop over 't'
14440
14441
// Update dmats using an inner product.
14442
if (combinations[r][s] == 0)
14443
{
14444
for (unsigned int t = 0; t < 10; t++)
14445
{
14446
for (unsigned int u = 0; u < 10; u++)
14447
{
14448
for (unsigned int tu = 0; tu < 10; tu++)
14449
{
14450
dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
14451
}// end loop over 'tu'
14452
}// end loop over 'u'
14453
}// end loop over 't'
14454
}
14455
14456
if (combinations[r][s] == 1)
14457
{
14458
for (unsigned int t = 0; t < 10; t++)
14459
{
14460
for (unsigned int u = 0; u < 10; u++)
14461
{
14462
for (unsigned int tu = 0; tu < 10; tu++)
14463
{
14464
dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
14465
}// end loop over 'tu'
14466
}// end loop over 'u'
14467
}// end loop over 't'
14468
}
14469
14470
if (combinations[r][s] == 2)
14471
{
14472
for (unsigned int t = 0; t < 10; t++)
14473
{
14474
for (unsigned int u = 0; u < 10; u++)
14475
{
14476
for (unsigned int tu = 0; tu < 10; tu++)
14477
{
14478
dmats[t][u] += dmats2[t][tu]*dmats_old[tu][u];
14479
}// end loop over 'tu'
14480
}// end loop over 'u'
14481
}// end loop over 't'
14482
}
14483
14484
}// end loop over 's'
14485
for (unsigned int s = 0; s < 10; s++)
14486
{
14487
for (unsigned int t = 0; t < 10; t++)
14488
{
14489
derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
14490
}// end loop over 't'
14491
}// end loop over 's'
14492
}// end loop over 'r'
14493
14494
// Transform derivatives back to physical element
14495
for (unsigned int r = 0; r < num_derivatives; r++)
14496
{
14497
for (unsigned int s = 0; s < num_derivatives; s++)
14498
{
14499
values[2*num_derivatives + r] += transform[r][s]*derivatives[s];
14500
}// end loop over 's'
14501
}// end loop over 'r'
14502
14503
// Delete pointer to array of derivatives on FIAT element
14504
delete [] derivatives;
14505
14506
// Delete pointer to array of combinations of derivatives and transform
14507
for (unsigned int r = 0; r < num_derivatives; r++)
14508
{
14509
delete [] combinations[r];
14510
}// end loop over 'r'
14511
delete [] combinations;
14512
for (unsigned int r = 0; r < num_derivatives; r++)
14513
{
14514
delete [] transform[r];
14515
}// end loop over 'r'
14516
delete [] transform;
14517
break;
14518
}
14519
case 27:
14520
{
14521
14522
// Array of basisvalues.
14523
double basisvalues[10] = {0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000};
14524
14525
// Declare helper variables.
14526
unsigned int rr = 0;
14527
unsigned int ss = 0;
14528
unsigned int tt = 0;
14529
double tmp5 = 0.00000000;
14530
double tmp6 = 0.00000000;
14531
double tmp7 = 0.00000000;
14532
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
14533
double tmp1 = 0.25000000*(Y + Z)*(Y + Z);
14534
double tmp2 = 0.50000000*(1.00000000 + Z + 2.00000000*Y);
14535
double tmp3 = 0.50000000*(1.00000000 - Z);
14536
double tmp4 = tmp3*tmp3;
14537
14538
// Compute basisvalues.
14539
basisvalues[0] = 1.00000000;
14540
basisvalues[1] = tmp0;
14541
for (unsigned int r = 1; r < 2; r++)
14542
{
14543
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
14544
ss = r*(r + 1)*(r + 2)/6;
14545
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
14546
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.00000000 + 2.00000000*r)/(1.00000000 + r) - basisvalues[tt]*tmp1*r/(1.00000000 + r));
14547
}// end loop over 'r'
14548
for (unsigned int r = 0; r < 2; r++)
14549
{
14550
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
14551
ss = r*(r + 1)*(r + 2)/6;
14552
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
14553
}// end loop over 'r'
14554
for (unsigned int r = 0; r < 1; r++)
14555
{
14556
for (unsigned int s = 1; s < 2 - r; s++)
14557
{
14558
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
14559
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
14560
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
14561
tmp5 = (2.00000000 + 2.00000000*r + 2.00000000*s)*(3.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
14562
tmp6 = (1.00000000 + 4.00000000*r*r + 4.00000000*r)*(2.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
14563
tmp7 = (1.00000000 + s + 2.00000000*r)*(3.00000000 + 2.00000000*r + 2.00000000*s)*s/((1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
14564
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
14565
}// end loop over 's'
14566
}// end loop over 'r'
14567
for (unsigned int r = 0; r < 2; r++)
14568
{
14569
for (unsigned int s = 0; s < 2 - r; s++)
14570
{
14571
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
14572
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
14573
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
14574
}// end loop over 's'
14575
}// end loop over 'r'
14576
for (unsigned int r = 0; r < 1; r++)
14577
{
14578
for (unsigned int s = 0; s < 1 - r; s++)
14579
{
14580
for (unsigned int t = 1; t < 2 - r - s; t++)
14581
{
14582
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
14583
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
14584
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
14585
tmp5 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)/(2.00000000*(1.00000000 + t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
14586
tmp6 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 4.00000000*r*r + 4.00000000*s*s + 8.00000000*r*s + 8.00000000*r + 8.00000000*s)/(2.00000000*(1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
14587
tmp7 = (2.00000000 + t + 2.00000000*r + 2.00000000*s)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*t/((1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
14588
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
14589
}// end loop over 't'
14590
}// end loop over 's'
14591
}// end loop over 'r'
14592
for (unsigned int r = 0; r < 3; r++)
14593
{
14594
for (unsigned int s = 0; s < 3 - r; s++)
14595
{
14596
for (unsigned int t = 0; t < 3 - r - s; t++)
14597
{
14598
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
14599
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
14600
}// end loop over 't'
14601
}// end loop over 's'
14602
}// end loop over 'r'
14603
14604
// Table(s) of coefficients.
14605
static const double coefficients0[10] = \
14606
{0.23094011, -0.12171612, -0.07027284, 0.09938080, 0.00000000, 0.00000000, -0.10286890, 0.00000000, -0.05939139, -0.06719368};
14607
14608
// Tables of derivatives of the polynomial base (transpose).
14609
static const double dmats0[10][10] = \
14610
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14611
{6.32455532, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14612
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14613
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14614
{0.00000000, 11.22497216, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14615
{4.58257569, 0.00000000, 8.36660027, -1.18321596, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14616
{3.74165739, 0.00000000, 0.00000000, 8.69482605, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14617
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14618
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14619
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
14620
14621
static const double dmats1[10][10] = \
14622
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14623
{3.16227766, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14624
{5.47722558, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14625
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14626
{2.95803989, 5.61248608, -1.08012345, -0.76376262, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14627
{2.29128785, 7.24568837, 4.18330013, -0.59160798, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14628
{1.87082869, 0.00000000, 0.00000000, 4.34741302, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14629
{-2.64575131, 0.00000000, 9.66091783, 0.68313005, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14630
{3.24037035, 0.00000000, 0.00000000, 7.52994024, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14631
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
14632
14633
static const double dmats2[10][10] = \
14634
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14635
{3.16227766, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14636
{1.82574186, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14637
{5.16397779, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14638
{2.95803989, 5.61248608, -1.08012345, -0.76376262, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14639
{2.29128785, 1.44913767, 4.18330013, -0.59160798, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14640
{1.87082869, 7.09929574, 0.00000000, 4.34741302, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14641
{1.32287566, 0.00000000, 3.86436713, -0.34156503, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14642
{1.08012345, 0.00000000, 7.09929574, 2.50998008, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14643
{-3.81881308, 0.00000000, 0.00000000, 8.87411967, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
14644
14645
// Compute reference derivatives.
14646
// Declare pointer to array of derivatives on FIAT element.
14647
double *derivatives = new double[num_derivatives];
14648
for (unsigned int r = 0; r < num_derivatives; r++)
14649
{
14650
derivatives[r] = 0.00000000;
14651
}// end loop over 'r'
14652
14653
// Declare derivative matrix (of polynomial basis).
14654
double dmats[10][10] = \
14655
{{1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14656
{0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14657
{0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14658
{0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14659
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14660
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14661
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000},
14662
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000},
14663
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000},
14664
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000}};
14665
14666
// Declare (auxiliary) derivative matrix (of polynomial basis).
14667
double dmats_old[10][10] = \
14668
{{1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14669
{0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14670
{0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14671
{0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14672
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14673
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14674
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000},
14675
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000},
14676
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000},
14677
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000}};
14678
14679
// Loop possible derivatives.
14680
for (unsigned int r = 0; r < num_derivatives; r++)
14681
{
14682
// Resetting dmats values to compute next derivative.
14683
for (unsigned int t = 0; t < 10; t++)
14684
{
14685
for (unsigned int u = 0; u < 10; u++)
14686
{
14687
dmats[t][u] = 0.00000000;
14688
if (t == u)
14689
{
14690
dmats[t][u] = 1.00000000;
14691
}
14692
14693
}// end loop over 'u'
14694
}// end loop over 't'
14695
14696
// Looping derivative order to generate dmats.
14697
for (unsigned int s = 0; s < n; s++)
14698
{
14699
// Updating dmats_old with new values and resetting dmats.
14700
for (unsigned int t = 0; t < 10; t++)
14701
{
14702
for (unsigned int u = 0; u < 10; u++)
14703
{
14704
dmats_old[t][u] = dmats[t][u];
14705
dmats[t][u] = 0.00000000;
14706
}// end loop over 'u'
14707
}// end loop over 't'
14708
14709
// Update dmats using an inner product.
14710
if (combinations[r][s] == 0)
14711
{
14712
for (unsigned int t = 0; t < 10; t++)
14713
{
14714
for (unsigned int u = 0; u < 10; u++)
14715
{
14716
for (unsigned int tu = 0; tu < 10; tu++)
14717
{
14718
dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
14719
}// end loop over 'tu'
14720
}// end loop over 'u'
14721
}// end loop over 't'
14722
}
14723
14724
if (combinations[r][s] == 1)
14725
{
14726
for (unsigned int t = 0; t < 10; t++)
14727
{
14728
for (unsigned int u = 0; u < 10; u++)
14729
{
14730
for (unsigned int tu = 0; tu < 10; tu++)
14731
{
14732
dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
14733
}// end loop over 'tu'
14734
}// end loop over 'u'
14735
}// end loop over 't'
14736
}
14737
14738
if (combinations[r][s] == 2)
14739
{
14740
for (unsigned int t = 0; t < 10; t++)
14741
{
14742
for (unsigned int u = 0; u < 10; u++)
14743
{
14744
for (unsigned int tu = 0; tu < 10; tu++)
14745
{
14746
dmats[t][u] += dmats2[t][tu]*dmats_old[tu][u];
14747
}// end loop over 'tu'
14748
}// end loop over 'u'
14749
}// end loop over 't'
14750
}
14751
14752
}// end loop over 's'
14753
for (unsigned int s = 0; s < 10; s++)
14754
{
14755
for (unsigned int t = 0; t < 10; t++)
14756
{
14757
derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
14758
}// end loop over 't'
14759
}// end loop over 's'
14760
}// end loop over 'r'
14761
14762
// Transform derivatives back to physical element
14763
for (unsigned int r = 0; r < num_derivatives; r++)
14764
{
14765
for (unsigned int s = 0; s < num_derivatives; s++)
14766
{
14767
values[2*num_derivatives + r] += transform[r][s]*derivatives[s];
14768
}// end loop over 's'
14769
}// end loop over 'r'
14770
14771
// Delete pointer to array of derivatives on FIAT element
14772
delete [] derivatives;
14773
14774
// Delete pointer to array of combinations of derivatives and transform
14775
for (unsigned int r = 0; r < num_derivatives; r++)
14776
{
14777
delete [] combinations[r];
14778
}// end loop over 'r'
14779
delete [] combinations;
14780
for (unsigned int r = 0; r < num_derivatives; r++)
14781
{
14782
delete [] transform[r];
14783
}// end loop over 'r'
14784
delete [] transform;
14785
break;
14786
}
14787
case 28:
14788
{
14789
14790
// Array of basisvalues.
14791
double basisvalues[10] = {0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000};
14792
14793
// Declare helper variables.
14794
unsigned int rr = 0;
14795
unsigned int ss = 0;
14796
unsigned int tt = 0;
14797
double tmp5 = 0.00000000;
14798
double tmp6 = 0.00000000;
14799
double tmp7 = 0.00000000;
14800
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
14801
double tmp1 = 0.25000000*(Y + Z)*(Y + Z);
14802
double tmp2 = 0.50000000*(1.00000000 + Z + 2.00000000*Y);
14803
double tmp3 = 0.50000000*(1.00000000 - Z);
14804
double tmp4 = tmp3*tmp3;
14805
14806
// Compute basisvalues.
14807
basisvalues[0] = 1.00000000;
14808
basisvalues[1] = tmp0;
14809
for (unsigned int r = 1; r < 2; r++)
14810
{
14811
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
14812
ss = r*(r + 1)*(r + 2)/6;
14813
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
14814
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.00000000 + 2.00000000*r)/(1.00000000 + r) - basisvalues[tt]*tmp1*r/(1.00000000 + r));
14815
}// end loop over 'r'
14816
for (unsigned int r = 0; r < 2; r++)
14817
{
14818
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
14819
ss = r*(r + 1)*(r + 2)/6;
14820
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
14821
}// end loop over 'r'
14822
for (unsigned int r = 0; r < 1; r++)
14823
{
14824
for (unsigned int s = 1; s < 2 - r; s++)
14825
{
14826
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
14827
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
14828
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
14829
tmp5 = (2.00000000 + 2.00000000*r + 2.00000000*s)*(3.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
14830
tmp6 = (1.00000000 + 4.00000000*r*r + 4.00000000*r)*(2.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
14831
tmp7 = (1.00000000 + s + 2.00000000*r)*(3.00000000 + 2.00000000*r + 2.00000000*s)*s/((1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
14832
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
14833
}// end loop over 's'
14834
}// end loop over 'r'
14835
for (unsigned int r = 0; r < 2; r++)
14836
{
14837
for (unsigned int s = 0; s < 2 - r; s++)
14838
{
14839
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
14840
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
14841
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
14842
}// end loop over 's'
14843
}// end loop over 'r'
14844
for (unsigned int r = 0; r < 1; r++)
14845
{
14846
for (unsigned int s = 0; s < 1 - r; s++)
14847
{
14848
for (unsigned int t = 1; t < 2 - r - s; t++)
14849
{
14850
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
14851
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
14852
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
14853
tmp5 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)/(2.00000000*(1.00000000 + t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
14854
tmp6 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 4.00000000*r*r + 4.00000000*s*s + 8.00000000*r*s + 8.00000000*r + 8.00000000*s)/(2.00000000*(1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
14855
tmp7 = (2.00000000 + t + 2.00000000*r + 2.00000000*s)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*t/((1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
14856
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
14857
}// end loop over 't'
14858
}// end loop over 's'
14859
}// end loop over 'r'
14860
for (unsigned int r = 0; r < 3; r++)
14861
{
14862
for (unsigned int s = 0; s < 3 - r; s++)
14863
{
14864
for (unsigned int t = 0; t < 3 - r - s; t++)
14865
{
14866
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
14867
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
14868
}// end loop over 't'
14869
}// end loop over 's'
14870
}// end loop over 'r'
14871
14872
// Table(s) of coefficients.
14873
static const double coefficients0[10] = \
14874
{0.23094011, -0.12171612, 0.07027284, -0.09938080, 0.00000000, -0.10079053, 0.02057378, -0.08728716, -0.01187828, 0.01679842};
14875
14876
// Tables of derivatives of the polynomial base (transpose).
14877
static const double dmats0[10][10] = \
14878
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14879
{6.32455532, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14880
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14881
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14882
{0.00000000, 11.22497216, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14883
{4.58257569, 0.00000000, 8.36660027, -1.18321596, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14884
{3.74165739, 0.00000000, 0.00000000, 8.69482605, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14885
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14886
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14887
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
14888
14889
static const double dmats1[10][10] = \
14890
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14891
{3.16227766, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14892
{5.47722558, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14893
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14894
{2.95803989, 5.61248608, -1.08012345, -0.76376262, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14895
{2.29128785, 7.24568837, 4.18330013, -0.59160798, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14896
{1.87082869, 0.00000000, 0.00000000, 4.34741302, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14897
{-2.64575131, 0.00000000, 9.66091783, 0.68313005, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14898
{3.24037035, 0.00000000, 0.00000000, 7.52994024, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14899
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
14900
14901
static const double dmats2[10][10] = \
14902
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14903
{3.16227766, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14904
{1.82574186, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14905
{5.16397779, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14906
{2.95803989, 5.61248608, -1.08012345, -0.76376262, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14907
{2.29128785, 1.44913767, 4.18330013, -0.59160798, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14908
{1.87082869, 7.09929574, 0.00000000, 4.34741302, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14909
{1.32287566, 0.00000000, 3.86436713, -0.34156503, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14910
{1.08012345, 0.00000000, 7.09929574, 2.50998008, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14911
{-3.81881308, 0.00000000, 0.00000000, 8.87411967, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
14912
14913
// Compute reference derivatives.
14914
// Declare pointer to array of derivatives on FIAT element.
14915
double *derivatives = new double[num_derivatives];
14916
for (unsigned int r = 0; r < num_derivatives; r++)
14917
{
14918
derivatives[r] = 0.00000000;
14919
}// end loop over 'r'
14920
14921
// Declare derivative matrix (of polynomial basis).
14922
double dmats[10][10] = \
14923
{{1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14924
{0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14925
{0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14926
{0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14927
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14928
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14929
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000},
14930
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000},
14931
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000},
14932
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000}};
14933
14934
// Declare (auxiliary) derivative matrix (of polynomial basis).
14935
double dmats_old[10][10] = \
14936
{{1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14937
{0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14938
{0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14939
{0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14940
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14941
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
14942
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000},
14943
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000},
14944
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000},
14945
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000}};
14946
14947
// Loop possible derivatives.
14948
for (unsigned int r = 0; r < num_derivatives; r++)
14949
{
14950
// Resetting dmats values to compute next derivative.
14951
for (unsigned int t = 0; t < 10; t++)
14952
{
14953
for (unsigned int u = 0; u < 10; u++)
14954
{
14955
dmats[t][u] = 0.00000000;
14956
if (t == u)
14957
{
14958
dmats[t][u] = 1.00000000;
14959
}
14960
14961
}// end loop over 'u'
14962
}// end loop over 't'
14963
14964
// Looping derivative order to generate dmats.
14965
for (unsigned int s = 0; s < n; s++)
14966
{
14967
// Updating dmats_old with new values and resetting dmats.
14968
for (unsigned int t = 0; t < 10; t++)
14969
{
14970
for (unsigned int u = 0; u < 10; u++)
14971
{
14972
dmats_old[t][u] = dmats[t][u];
14973
dmats[t][u] = 0.00000000;
14974
}// end loop over 'u'
14975
}// end loop over 't'
14976
14977
// Update dmats using an inner product.
14978
if (combinations[r][s] == 0)
14979
{
14980
for (unsigned int t = 0; t < 10; t++)
14981
{
14982
for (unsigned int u = 0; u < 10; u++)
14983
{
14984
for (unsigned int tu = 0; tu < 10; tu++)
14985
{
14986
dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
14987
}// end loop over 'tu'
14988
}// end loop over 'u'
14989
}// end loop over 't'
14990
}
14991
14992
if (combinations[r][s] == 1)
14993
{
14994
for (unsigned int t = 0; t < 10; t++)
14995
{
14996
for (unsigned int u = 0; u < 10; u++)
14997
{
14998
for (unsigned int tu = 0; tu < 10; tu++)
14999
{
15000
dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
15001
}// end loop over 'tu'
15002
}// end loop over 'u'
15003
}// end loop over 't'
15004
}
15005
15006
if (combinations[r][s] == 2)
15007
{
15008
for (unsigned int t = 0; t < 10; t++)
15009
{
15010
for (unsigned int u = 0; u < 10; u++)
15011
{
15012
for (unsigned int tu = 0; tu < 10; tu++)
15013
{
15014
dmats[t][u] += dmats2[t][tu]*dmats_old[tu][u];
15015
}// end loop over 'tu'
15016
}// end loop over 'u'
15017
}// end loop over 't'
15018
}
15019
15020
}// end loop over 's'
15021
for (unsigned int s = 0; s < 10; s++)
15022
{
15023
for (unsigned int t = 0; t < 10; t++)
15024
{
15025
derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
15026
}// end loop over 't'
15027
}// end loop over 's'
15028
}// end loop over 'r'
15029
15030
// Transform derivatives back to physical element
15031
for (unsigned int r = 0; r < num_derivatives; r++)
15032
{
15033
for (unsigned int s = 0; s < num_derivatives; s++)
15034
{
15035
values[2*num_derivatives + r] += transform[r][s]*derivatives[s];
15036
}// end loop over 's'
15037
}// end loop over 'r'
15038
15039
// Delete pointer to array of derivatives on FIAT element
15040
delete [] derivatives;
15041
15042
// Delete pointer to array of combinations of derivatives and transform
15043
for (unsigned int r = 0; r < num_derivatives; r++)
15044
{
15045
delete [] combinations[r];
15046
}// end loop over 'r'
15047
delete [] combinations;
15048
for (unsigned int r = 0; r < num_derivatives; r++)
15049
{
15050
delete [] transform[r];
15051
}// end loop over 'r'
15052
delete [] transform;
15053
break;
15054
}
15055
case 29:
15056
{
15057
15058
// Array of basisvalues.
15059
double basisvalues[10] = {0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000};
15060
15061
// Declare helper variables.
15062
unsigned int rr = 0;
15063
unsigned int ss = 0;
15064
unsigned int tt = 0;
15065
double tmp5 = 0.00000000;
15066
double tmp6 = 0.00000000;
15067
double tmp7 = 0.00000000;
15068
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
15069
double tmp1 = 0.25000000*(Y + Z)*(Y + Z);
15070
double tmp2 = 0.50000000*(1.00000000 + Z + 2.00000000*Y);
15071
double tmp3 = 0.50000000*(1.00000000 - Z);
15072
double tmp4 = tmp3*tmp3;
15073
15074
// Compute basisvalues.
15075
basisvalues[0] = 1.00000000;
15076
basisvalues[1] = tmp0;
15077
for (unsigned int r = 1; r < 2; r++)
15078
{
15079
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
15080
ss = r*(r + 1)*(r + 2)/6;
15081
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
15082
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.00000000 + 2.00000000*r)/(1.00000000 + r) - basisvalues[tt]*tmp1*r/(1.00000000 + r));
15083
}// end loop over 'r'
15084
for (unsigned int r = 0; r < 2; r++)
15085
{
15086
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
15087
ss = r*(r + 1)*(r + 2)/6;
15088
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
15089
}// end loop over 'r'
15090
for (unsigned int r = 0; r < 1; r++)
15091
{
15092
for (unsigned int s = 1; s < 2 - r; s++)
15093
{
15094
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
15095
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
15096
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
15097
tmp5 = (2.00000000 + 2.00000000*r + 2.00000000*s)*(3.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
15098
tmp6 = (1.00000000 + 4.00000000*r*r + 4.00000000*r)*(2.00000000 + 2.00000000*r + 2.00000000*s)/(2.00000000*(1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
15099
tmp7 = (1.00000000 + s + 2.00000000*r)*(3.00000000 + 2.00000000*r + 2.00000000*s)*s/((1.00000000 + 2.00000000*r + 2.00000000*s)*(1.00000000 + s)*(2.00000000 + s + 2.00000000*r));
15100
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
15101
}// end loop over 's'
15102
}// end loop over 'r'
15103
for (unsigned int r = 0; r < 2; r++)
15104
{
15105
for (unsigned int s = 0; s < 2 - r; s++)
15106
{
15107
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
15108
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
15109
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
15110
}// end loop over 's'
15111
}// end loop over 'r'
15112
for (unsigned int r = 0; r < 1; r++)
15113
{
15114
for (unsigned int s = 0; s < 1 - r; s++)
15115
{
15116
for (unsigned int t = 1; t < 2 - r - s; t++)
15117
{
15118
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
15119
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
15120
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
15121
tmp5 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)/(2.00000000*(1.00000000 + t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
15122
tmp6 = (3.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(4.00000000 + 4.00000000*r*r + 4.00000000*s*s + 8.00000000*r*s + 8.00000000*r + 8.00000000*s)/(2.00000000*(1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
15123
tmp7 = (2.00000000 + t + 2.00000000*r + 2.00000000*s)*(4.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*t/((1.00000000 + t)*(2.00000000 + 2.00000000*r + 2.00000000*s + 2.00000000*t)*(3.00000000 + t + 2.00000000*r + 2.00000000*s));
15124
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
15125
}// end loop over 't'
15126
}// end loop over 's'
15127
}// end loop over 'r'
15128
for (unsigned int r = 0; r < 3; r++)
15129
{
15130
for (unsigned int s = 0; s < 3 - r; s++)
15131
{
15132
for (unsigned int t = 0; t < 3 - r - s; t++)
15133
{
15134
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
15135
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
15136
}// end loop over 't'
15137
}// end loop over 's'
15138
}// end loop over 'r'
15139
15140
// Table(s) of coefficients.
15141
static const double coefficients0[10] = \
15142
{0.23094011, 0.00000000, -0.14054567, -0.09938080, -0.13012001, 0.00000000, 0.00000000, 0.02909572, 0.02375655, 0.01679842};
15143
15144
// Tables of derivatives of the polynomial base (transpose).
15145
static const double dmats0[10][10] = \
15146
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
15147
{6.32455532, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
15148
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
15149
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
15150
{0.00000000, 11.22497216, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
15151
{4.58257569, 0.00000000, 8.36660027, -1.18321596, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
15152
{3.74165739, 0.00000000, 0.00000000, 8.69482605, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
15153
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
15154
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
15155
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
15156
15157
static const double dmats1[10][10] = \
15158
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
15159
{3.16227766, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
15160
{5.47722558, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
15161
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
15162
{2.95803989, 5.61248608, -1.08012345, -0.76376262, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
15163
{2.29128785, 7.24568837, 4.18330013, -0.59160798, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
15164
{1.87082869, 0.00000000, 0.00000000, 4.34741302, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
15165
{-2.64575131, 0.00000000, 9.66091783, 0.68313005, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
15166
{3.24037035, 0.00000000, 0.00000000, 7.52994024, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
15167
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
15168
15169
static const double dmats2[10][10] = \
15170
{{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
15171
{3.16227766, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
15172
{1.82574186, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
15173
{5.16397779, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
15174
{2.95803989, 5.61248608, -1.08012345, -0.76376262, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
15175
{2.29128785, 1.44913767, 4.18330013, -0.59160798, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
15176
{1.87082869, 7.09929574, 0.00000000, 4.34741302, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
15177
{1.32287566, 0.00000000, 3.86436713, -0.34156503, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
15178
{1.08012345, 0.00000000, 7.09929574, 2.50998008, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
15179
{-3.81881308, 0.00000000, 0.00000000, 8.87411967, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000}};
15180
15181
// Compute reference derivatives.
15182
// Declare pointer to array of derivatives on FIAT element.
15183
double *derivatives = new double[num_derivatives];
15184
for (unsigned int r = 0; r < num_derivatives; r++)
15185
{
15186
derivatives[r] = 0.00000000;
15187
}// end loop over 'r'
15188
15189
// Declare derivative matrix (of polynomial basis).
15190
double dmats[10][10] = \
15191
{{1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
15192
{0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
15193
{0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
15194
{0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
15195
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
15196
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
15197
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000},
15198
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000},
15199
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000},
15200
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000}};
15201
15202
// Declare (auxiliary) derivative matrix (of polynomial basis).
15203
double dmats_old[10][10] = \
15204
{{1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
15205
{0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
15206
{0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
15207
{0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
15208
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
15209
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000},
15210
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000, 0.00000000},
15211
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000, 0.00000000},
15212
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 0.00000000},
15213
{0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 1.00000000}};
15214
15215
// Loop possible derivatives.
15216
for (unsigned int r = 0; r < num_derivatives; r++)
15217
{
15218
// Resetting dmats values to compute next derivative.
15219
for (unsigned int t = 0; t < 10; t++)
15220
{
15221
for (unsigned int u = 0; u < 10; u++)
15222
{
15223
dmats[t][u] = 0.00000000;
15224
if (t == u)
15225
{
15226
dmats[t][u] = 1.00000000;
15227
}
15228
15229
}// end loop over 'u'
15230
}// end loop over 't'
15231
15232
// Looping derivative order to generate dmats.
15233
for (unsigned int s = 0; s < n; s++)
15234
{
15235
// Updating dmats_old with new values and resetting dmats.
15236
for (unsigned int t = 0; t < 10; t++)
15237
{
15238
for (unsigned int u = 0; u < 10; u++)
15239
{
15240
dmats_old[t][u] = dmats[t][u];
15241
dmats[t][u] = 0.00000000;
15242
}// end loop over 'u'
15243
}// end loop over 't'
15244
15245
// Update dmats using an inner product.
15246
if (combinations[r][s] == 0)
15247
{
15248
for (unsigned int t = 0; t < 10; t++)
15249
{
15250
for (unsigned int u = 0; u < 10; u++)
15251
{
15252
for (unsigned int tu = 0; tu < 10; tu++)
15253
{
15254
dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
15255
}// end loop over 'tu'
15256
}// end loop over 'u'
15257
}// end loop over 't'
15258
}
15259
15260
if (combinations[r][s] == 1)
15261
{
15262
for (unsigned int t = 0; t < 10; t++)
15263
{
15264
for (unsigned int u = 0; u < 10; u++)
15265
{
15266
for (unsigned int tu = 0; tu < 10; tu++)
15267
{
15268
dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
15269
}// end loop over 'tu'
15270
}// end loop over 'u'
15271
}// end loop over 't'
15272
}
15273
15274
if (combinations[r][s] == 2)
15275
{
15276
for (unsigned int t = 0; t < 10; t++)
15277
{
15278
for (unsigned int u = 0; u < 10; u++)
15279
{
15280
for (unsigned int tu = 0; tu < 10; tu++)
15281
{
15282
dmats[t][u] += dmats2[t][tu]*dmats_old[tu][u];
15283
}// end loop over 'tu'
15284
}// end loop over 'u'
15285
}// end loop over 't'
15286
}
15287
15288
}// end loop over 's'
15289
for (unsigned int s = 0; s < 10; s++)
15290
{
15291
for (unsigned int t = 0; t < 10; t++)
15292
{
15293
derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
15294
}// end loop over 't'
15295
}// end loop over 's'
15296
}// end loop over 'r'
15297
15298
// Transform derivatives back to physical element
15299
for (unsigned int r = 0; r < num_derivatives; r++)
15300
{
15301
for (unsigned int s = 0; s < num_derivatives; s++)
15302
{
15303
values[2*num_derivatives + r] += transform[r][s]*derivatives[s];
15304
}// end loop over 's'
15305
}// end loop over 'r'
15306
15307
// Delete pointer to array of derivatives on FIAT element
15308
delete [] derivatives;
15309
15310
// Delete pointer to array of combinations of derivatives and transform
15311
for (unsigned int r = 0; r < num_derivatives; r++)
15312
{
15313
delete [] combinations[r];
15314
}// end loop over 'r'
15315
delete [] combinations;
15316
for (unsigned int r = 0; r < num_derivatives; r++)
15317
{
15318
delete [] transform[r];
15319
}// end loop over 'r'
15320
delete [] transform;
15321
break;
15322
}
2284
15323
}
2285
15324
2286
15325
}
2922
15961
2923
15962
// Reset values.
2924
15963
*values = 0.00000000;
2925
2926
// Map degree of freedom to element degree of freedom
2927
const unsigned int dof = i;
2928
2929
// Array of basisvalues.
2930
double basisvalues[4] = {0.00000000, 0.00000000, 0.00000000, 0.00000000};
2931
2932
// Declare helper variables.
2933
unsigned int rr = 0;
2934
unsigned int ss = 0;
2935
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
2936
2937
// Compute basisvalues.
2938
basisvalues[0] = 1.00000000;
2939
basisvalues[1] = tmp0;
2940
for (unsigned int r = 0; r < 1; r++)
2941
{
2942
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
2943
ss = r*(r + 1)*(r + 2)/6;
2944
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
2945
}// end loop over 'r'
2946
for (unsigned int r = 0; r < 1; r++)
2947
{
2948
for (unsigned int s = 0; s < 1 - r; s++)
2949
{
2950
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
2951
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
2952
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
2953
}// end loop over 's'
2954
}// end loop over 'r'
2955
for (unsigned int r = 0; r < 2; r++)
2956
{
2957
for (unsigned int s = 0; s < 2 - r; s++)
2958
{
2959
for (unsigned int t = 0; t < 2 - r - s; t++)
2960
{
2961
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
2962
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
2963
}// end loop over 't'
2964
}// end loop over 's'
2965
}// end loop over 'r'
2966
2967
// Table(s) of coefficients.
2968
static const double coefficients0[4][4] = \
2969
{{0.28867513, -0.18257419, -0.10540926, -0.07453560},
2970
{0.28867513, 0.18257419, -0.10540926, -0.07453560},
2971
{0.28867513, 0.00000000, 0.21081851, -0.07453560},
2972
{0.28867513, 0.00000000, 0.00000000, 0.22360680}};
2973
2974
// Compute value(s).
2975
for (unsigned int r = 0; r < 4; r++)
2976
{
2977
*values += coefficients0[dof][r]*basisvalues[r];
2978
}// end loop over 'r'
15964
switch (i)
15965
{
15966
case 0:
15967
{
15968
15969
// Array of basisvalues.
15970
double basisvalues[4] = {0.00000000, 0.00000000, 0.00000000, 0.00000000};
15971
15972
// Declare helper variables.
15973
unsigned int rr = 0;
15974
unsigned int ss = 0;
15975
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
15976
15977
// Compute basisvalues.
15978
basisvalues[0] = 1.00000000;
15979
basisvalues[1] = tmp0;
15980
for (unsigned int r = 0; r < 1; r++)
15981
{
15982
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
15983
ss = r*(r + 1)*(r + 2)/6;
15984
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
15985
}// end loop over 'r'
15986
for (unsigned int r = 0; r < 1; r++)
15987
{
15988
for (unsigned int s = 0; s < 1 - r; s++)
15989
{
15990
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
15991
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
15992
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
15993
}// end loop over 's'
15994
}// end loop over 'r'
15995
for (unsigned int r = 0; r < 2; r++)
15996
{
15997
for (unsigned int s = 0; s < 2 - r; s++)
15998
{
15999
for (unsigned int t = 0; t < 2 - r - s; t++)
16000
{
16001
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
16002
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
16003
}// end loop over 't'
16004
}// end loop over 's'
16005
}// end loop over 'r'
16006
16007
// Table(s) of coefficients.
16008
static const double coefficients0[4] = \
16009
{0.28867513, -0.18257419, -0.10540926, -0.07453560};
16010
16011
// Compute value(s).
16012
for (unsigned int r = 0; r < 4; r++)
16013
{
16014
*values += coefficients0[r]*basisvalues[r];
16015
}// end loop over 'r'
16016
break;
16017
}
16018
case 1:
16019
{
16020
16021
// Array of basisvalues.
16022
double basisvalues[4] = {0.00000000, 0.00000000, 0.00000000, 0.00000000};
16023
16024
// Declare helper variables.
16025
unsigned int rr = 0;
16026
unsigned int ss = 0;
16027
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
16028
16029
// Compute basisvalues.
16030
basisvalues[0] = 1.00000000;
16031
basisvalues[1] = tmp0;
16032
for (unsigned int r = 0; r < 1; r++)
16033
{
16034
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
16035
ss = r*(r + 1)*(r + 2)/6;
16036
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
16037
}// end loop over 'r'
16038
for (unsigned int r = 0; r < 1; r++)
16039
{
16040
for (unsigned int s = 0; s < 1 - r; s++)
16041
{
16042
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
16043
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
16044
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
16045
}// end loop over 's'
16046
}// end loop over 'r'
16047
for (unsigned int r = 0; r < 2; r++)
16048
{
16049
for (unsigned int s = 0; s < 2 - r; s++)
16050
{
16051
for (unsigned int t = 0; t < 2 - r - s; t++)
16052
{
16053
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
16054
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
16055
}// end loop over 't'
16056
}// end loop over 's'
16057
}// end loop over 'r'
16058
16059
// Table(s) of coefficients.
16060
static const double coefficients0[4] = \
16061
{0.28867513, 0.18257419, -0.10540926, -0.07453560};
16062
16063
// Compute value(s).
16064
for (unsigned int r = 0; r < 4; r++)
16065
{
16066
*values += coefficients0[r]*basisvalues[r];
16067
}// end loop over 'r'
16068
break;
16069
}
16070
case 2:
16071
{
16072
16073
// Array of basisvalues.
16074
double basisvalues[4] = {0.00000000, 0.00000000, 0.00000000, 0.00000000};
16075
16076
// Declare helper variables.
16077
unsigned int rr = 0;
16078
unsigned int ss = 0;
16079
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
16080
16081
// Compute basisvalues.
16082
basisvalues[0] = 1.00000000;
16083
basisvalues[1] = tmp0;
16084
for (unsigned int r = 0; r < 1; r++)
16085
{
16086
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
16087
ss = r*(r + 1)*(r + 2)/6;
16088
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
16089
}// end loop over 'r'
16090
for (unsigned int r = 0; r < 1; r++)
16091
{
16092
for (unsigned int s = 0; s < 1 - r; s++)
16093
{
16094
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
16095
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
16096
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
16097
}// end loop over 's'
16098
}// end loop over 'r'
16099
for (unsigned int r = 0; r < 2; r++)
16100
{
16101
for (unsigned int s = 0; s < 2 - r; s++)
16102
{
16103
for (unsigned int t = 0; t < 2 - r - s; t++)
16104
{
16105
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
16106
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
16107
}// end loop over 't'
16108
}// end loop over 's'
16109
}// end loop over 'r'
16110
16111
// Table(s) of coefficients.
16112
static const double coefficients0[4] = \
16113
{0.28867513, 0.00000000, 0.21081851, -0.07453560};
16114
16115
// Compute value(s).
16116
for (unsigned int r = 0; r < 4; r++)
16117
{
16118
*values += coefficients0[r]*basisvalues[r];
16119
}// end loop over 'r'
16120
break;
16121
}
16122
case 3:
16123
{
16124
16125
// Array of basisvalues.
16126
double basisvalues[4] = {0.00000000, 0.00000000, 0.00000000, 0.00000000};
16127
16128
// Declare helper variables.
16129
unsigned int rr = 0;
16130
unsigned int ss = 0;
16131
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
16132
16133
// Compute basisvalues.
16134
basisvalues[0] = 1.00000000;
16135
basisvalues[1] = tmp0;
16136
for (unsigned int r = 0; r < 1; r++)
16137
{
16138
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
16139
ss = r*(r + 1)*(r + 2)/6;
16140
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
16141
}// end loop over 'r'
16142
for (unsigned int r = 0; r < 1; r++)
16143
{
16144
for (unsigned int s = 0; s < 1 - r; s++)
16145
{
16146
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
16147
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
16148
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
16149
}// end loop over 's'
16150
}// end loop over 'r'
16151
for (unsigned int r = 0; r < 2; r++)
16152
{
16153
for (unsigned int s = 0; s < 2 - r; s++)
16154
{
16155
for (unsigned int t = 0; t < 2 - r - s; t++)
16156
{
16157
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
16158
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
16159
}// end loop over 't'
16160
}// end loop over 's'
16161
}// end loop over 'r'
16162
16163
// Table(s) of coefficients.
16164
static const double coefficients0[4] = \
16165
{0.28867513, 0.00000000, 0.00000000, 0.22360680};
16166
16167
// Compute value(s).
16168
for (unsigned int r = 0; r < 4; r++)
16169
{
16170
*values += coefficients0[r]*basisvalues[r];
16171
}// end loop over 'r'
16172
break;
16173
}
16174
}
16175
2979
16176
}
2980
16177
2981
16178
/// Evaluate all basis functions at given point in cell
3115
16312
values[r] = 0.00000000;
3116
16313
}// end loop over 'r'
3117
16314
3118
// Map degree of freedom to element degree of freedom
3119
const unsigned int dof = i;
3120
3121
// Array of basisvalues.
3122
double basisvalues[4] = {0.00000000, 0.00000000, 0.00000000, 0.00000000};
3123
3124
// Declare helper variables.
3125
unsigned int rr = 0;
3126
unsigned int ss = 0;
3127
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
3128
3129
// Compute basisvalues.
3130
basisvalues[0] = 1.00000000;
3131
basisvalues[1] = tmp0;
3132
for (unsigned int r = 0; r < 1; r++)
3133
{
3134
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
3135
ss = r*(r + 1)*(r + 2)/6;
3136
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
3137
}// end loop over 'r'
3138
for (unsigned int r = 0; r < 1; r++)
3139
{
3140
for (unsigned int s = 0; s < 1 - r; s++)
3141
{
3142
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
3143
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
3144
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
3145
}// end loop over 's'
3146
}// end loop over 'r'
3147
for (unsigned int r = 0; r < 2; r++)
3148
{
3149
for (unsigned int s = 0; s < 2 - r; s++)
3150
{
3151
for (unsigned int t = 0; t < 2 - r - s; t++)
3152
{
3153
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
3154
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
3155
}// end loop over 't'
3156
}// end loop over 's'
3157
}// end loop over 'r'
3158
3159
// Table(s) of coefficients.
3160
static const double coefficients0[4][4] = \
3161
{{0.28867513, -0.18257419, -0.10540926, -0.07453560},
3162
{0.28867513, 0.18257419, -0.10540926, -0.07453560},
3163
{0.28867513, 0.00000000, 0.21081851, -0.07453560},
3164
{0.28867513, 0.00000000, 0.00000000, 0.22360680}};
3165
3166
// Tables of derivatives of the polynomial base (transpose).
3167
static const double dmats0[4][4] = \
3168
{{0.00000000, 0.00000000, 0.00000000, 0.00000000},
3169
{6.32455532, 0.00000000, 0.00000000, 0.00000000},
3170
{0.00000000, 0.00000000, 0.00000000, 0.00000000},
3171
{0.00000000, 0.00000000, 0.00000000, 0.00000000}};
3172
3173
static const double dmats1[4][4] = \
3174
{{0.00000000, 0.00000000, 0.00000000, 0.00000000},
3175
{3.16227766, 0.00000000, 0.00000000, 0.00000000},
3176
{5.47722558, 0.00000000, 0.00000000, 0.00000000},
3177
{0.00000000, 0.00000000, 0.00000000, 0.00000000}};
3178
3179
static const double dmats2[4][4] = \
3180
{{0.00000000, 0.00000000, 0.00000000, 0.00000000},
3181
{3.16227766, 0.00000000, 0.00000000, 0.00000000},
3182
{1.82574186, 0.00000000, 0.00000000, 0.00000000},
3183
{5.16397779, 0.00000000, 0.00000000, 0.00000000}};
3184
3185
// Compute reference derivatives.
3186
// Declare pointer to array of derivatives on FIAT element.
3187
double *derivatives = new double[num_derivatives];
3188
for (unsigned int r = 0; r < num_derivatives; r++)
3189
{
3190
derivatives[r] = 0.00000000;
3191
}// end loop over 'r'
3192
3193
// Declare derivative matrix (of polynomial basis).
3194
double dmats[4][4] = \
3195
{{1.00000000, 0.00000000, 0.00000000, 0.00000000},
3196
{0.00000000, 1.00000000, 0.00000000, 0.00000000},
3197
{0.00000000, 0.00000000, 1.00000000, 0.00000000},
3198
{0.00000000, 0.00000000, 0.00000000, 1.00000000}};
3199
3200
// Declare (auxiliary) derivative matrix (of polynomial basis).
3201
double dmats_old[4][4] = \
3202
{{1.00000000, 0.00000000, 0.00000000, 0.00000000},
3203
{0.00000000, 1.00000000, 0.00000000, 0.00000000},
3204
{0.00000000, 0.00000000, 1.00000000, 0.00000000},
3205
{0.00000000, 0.00000000, 0.00000000, 1.00000000}};
3206
3207
// Loop possible derivatives.
3208
for (unsigned int r = 0; r < num_derivatives; r++)
3209
{
3210
// Resetting dmats values to compute next derivative.
3211
for (unsigned int t = 0; t < 4; t++)
3212
{
3213
for (unsigned int u = 0; u < 4; u++)
3214
{
3215
dmats[t][u] = 0.00000000;
3216
if (t == u)
3217
{
3218
dmats[t][u] = 1.00000000;
3219
}
3220
3221
}// end loop over 'u'
3222
}// end loop over 't'
3223
3224
// Looping derivative order to generate dmats.
3225
for (unsigned int s = 0; s < n; s++)
3226
{
3227
// Updating dmats_old with new values and resetting dmats.
3228
for (unsigned int t = 0; t < 4; t++)
3229
{
3230
for (unsigned int u = 0; u < 4; u++)
3231
{
3232
dmats_old[t][u] = dmats[t][u];
3233
dmats[t][u] = 0.00000000;
3234
}// end loop over 'u'
3235
}// end loop over 't'
3236
3237
// Update dmats using an inner product.
3238
if (combinations[r][s] == 0)
3239
{
3240
for (unsigned int t = 0; t < 4; t++)
3241
{
3242
for (unsigned int u = 0; u < 4; u++)
3243
{
3244
for (unsigned int tu = 0; tu < 4; tu++)
3245
{
3246
dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
3247
}// end loop over 'tu'
3248
}// end loop over 'u'
3249
}// end loop over 't'
3250
}
3251
3252
if (combinations[r][s] == 1)
3253
{
3254
for (unsigned int t = 0; t < 4; t++)
3255
{
3256
for (unsigned int u = 0; u < 4; u++)
3257
{
3258
for (unsigned int tu = 0; tu < 4; tu++)
3259
{
3260
dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
3261
}// end loop over 'tu'
3262
}// end loop over 'u'
3263
}// end loop over 't'
3264
}
3265
3266
if (combinations[r][s] == 2)
3267
{
3268
for (unsigned int t = 0; t < 4; t++)
3269
{
3270
for (unsigned int u = 0; u < 4; u++)
3271
{
3272
for (unsigned int tu = 0; tu < 4; tu++)
3273
{
3274
dmats[t][u] += dmats2[t][tu]*dmats_old[tu][u];
3275
}// end loop over 'tu'
3276
}// end loop over 'u'
3277
}// end loop over 't'
3278
}
3279
3280
}// end loop over 's'
3281
for (unsigned int s = 0; s < 4; s++)
3282
{
3283
for (unsigned int t = 0; t < 4; t++)
3284
{
3285
derivatives[r] += coefficients0[dof][s]*dmats[s][t]*basisvalues[t];
3286
}// end loop over 't'
3287
}// end loop over 's'
3288
}// end loop over 'r'
3289
3290
// Transform derivatives back to physical element
3291
for (unsigned int r = 0; r < num_derivatives; r++)
3292
{
3293
for (unsigned int s = 0; s < num_derivatives; s++)
3294
{
3295
values[r] += transform[r][s]*derivatives[s];
3296
}// end loop over 's'
3297
}// end loop over 'r'
3298
3299
// Delete pointer to array of derivatives on FIAT element
3300
delete [] derivatives;
3301
3302
// Delete pointer to array of combinations of derivatives and transform
3303
for (unsigned int r = 0; r < num_derivatives; r++)
3304
{
3305
delete [] combinations[r];
3306
}// end loop over 'r'
3307
delete [] combinations;
3308
for (unsigned int r = 0; r < num_derivatives; r++)
3309
{
3310
delete [] transform[r];
3311
}// end loop over 'r'
3312
delete [] transform;
16315
switch (i)
16316
{
16317
case 0:
16318
{
16319
16320
// Array of basisvalues.
16321
double basisvalues[4] = {0.00000000, 0.00000000, 0.00000000, 0.00000000};
16322
16323
// Declare helper variables.
16324
unsigned int rr = 0;
16325
unsigned int ss = 0;
16326
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
16327
16328
// Compute basisvalues.
16329
basisvalues[0] = 1.00000000;
16330
basisvalues[1] = tmp0;
16331
for (unsigned int r = 0; r < 1; r++)
16332
{
16333
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
16334
ss = r*(r + 1)*(r + 2)/6;
16335
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
16336
}// end loop over 'r'
16337
for (unsigned int r = 0; r < 1; r++)
16338
{
16339
for (unsigned int s = 0; s < 1 - r; s++)
16340
{
16341
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
16342
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
16343
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
16344
}// end loop over 's'
16345
}// end loop over 'r'
16346
for (unsigned int r = 0; r < 2; r++)
16347
{
16348
for (unsigned int s = 0; s < 2 - r; s++)
16349
{
16350
for (unsigned int t = 0; t < 2 - r - s; t++)
16351
{
16352
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
16353
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
16354
}// end loop over 't'
16355
}// end loop over 's'
16356
}// end loop over 'r'
16357
16358
// Table(s) of coefficients.
16359
static const double coefficients0[4] = \
16360
{0.28867513, -0.18257419, -0.10540926, -0.07453560};
16361
16362
// Tables of derivatives of the polynomial base (transpose).
16363
static const double dmats0[4][4] = \
16364
{{0.00000000, 0.00000000, 0.00000000, 0.00000000},
16365
{6.32455532, 0.00000000, 0.00000000, 0.00000000},
16366
{0.00000000, 0.00000000, 0.00000000, 0.00000000},
16367
{0.00000000, 0.00000000, 0.00000000, 0.00000000}};
16368
16369
static const double dmats1[4][4] = \
16370
{{0.00000000, 0.00000000, 0.00000000, 0.00000000},
16371
{3.16227766, 0.00000000, 0.00000000, 0.00000000},
16372
{5.47722558, 0.00000000, 0.00000000, 0.00000000},
16373
{0.00000000, 0.00000000, 0.00000000, 0.00000000}};
16374
16375
static const double dmats2[4][4] = \
16376
{{0.00000000, 0.00000000, 0.00000000, 0.00000000},
16377
{3.16227766, 0.00000000, 0.00000000, 0.00000000},
16378
{1.82574186, 0.00000000, 0.00000000, 0.00000000},
16379
{5.16397779, 0.00000000, 0.00000000, 0.00000000}};
16380
16381
// Compute reference derivatives.
16382
// Declare pointer to array of derivatives on FIAT element.
16383
double *derivatives = new double[num_derivatives];
16384
for (unsigned int r = 0; r < num_derivatives; r++)
16385
{
16386
derivatives[r] = 0.00000000;
16387
}// end loop over 'r'
16388
16389
// Declare derivative matrix (of polynomial basis).
16390
double dmats[4][4] = \
16391
{{1.00000000, 0.00000000, 0.00000000, 0.00000000},
16392
{0.00000000, 1.00000000, 0.00000000, 0.00000000},
16393
{0.00000000, 0.00000000, 1.00000000, 0.00000000},
16394
{0.00000000, 0.00000000, 0.00000000, 1.00000000}};
16395
16396
// Declare (auxiliary) derivative matrix (of polynomial basis).
16397
double dmats_old[4][4] = \
16398
{{1.00000000, 0.00000000, 0.00000000, 0.00000000},
16399
{0.00000000, 1.00000000, 0.00000000, 0.00000000},
16400
{0.00000000, 0.00000000, 1.00000000, 0.00000000},
16401
{0.00000000, 0.00000000, 0.00000000, 1.00000000}};
16402
16403
// Loop possible derivatives.
16404
for (unsigned int r = 0; r < num_derivatives; r++)
16405
{
16406
// Resetting dmats values to compute next derivative.
16407
for (unsigned int t = 0; t < 4; t++)
16408
{
16409
for (unsigned int u = 0; u < 4; u++)
16410
{
16411
dmats[t][u] = 0.00000000;
16412
if (t == u)
16413
{
16414
dmats[t][u] = 1.00000000;
16415
}
16416
16417
}// end loop over 'u'
16418
}// end loop over 't'
16419
16420
// Looping derivative order to generate dmats.
16421
for (unsigned int s = 0; s < n; s++)
16422
{
16423
// Updating dmats_old with new values and resetting dmats.
16424
for (unsigned int t = 0; t < 4; t++)
16425
{
16426
for (unsigned int u = 0; u < 4; u++)
16427
{
16428
dmats_old[t][u] = dmats[t][u];
16429
dmats[t][u] = 0.00000000;
16430
}// end loop over 'u'
16431
}// end loop over 't'
16432
16433
// Update dmats using an inner product.
16434
if (combinations[r][s] == 0)
16435
{
16436
for (unsigned int t = 0; t < 4; t++)
16437
{
16438
for (unsigned int u = 0; u < 4; u++)
16439
{
16440
for (unsigned int tu = 0; tu < 4; tu++)
16441
{
16442
dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
16443
}// end loop over 'tu'
16444
}// end loop over 'u'
16445
}// end loop over 't'
16446
}
16447
16448
if (combinations[r][s] == 1)
16449
{
16450
for (unsigned int t = 0; t < 4; t++)
16451
{
16452
for (unsigned int u = 0; u < 4; u++)
16453
{
16454
for (unsigned int tu = 0; tu < 4; tu++)
16455
{
16456
dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
16457
}// end loop over 'tu'
16458
}// end loop over 'u'
16459
}// end loop over 't'
16460
}
16461
16462
if (combinations[r][s] == 2)
16463
{
16464
for (unsigned int t = 0; t < 4; t++)
16465
{
16466
for (unsigned int u = 0; u < 4; u++)
16467
{
16468
for (unsigned int tu = 0; tu < 4; tu++)
16469
{
16470
dmats[t][u] += dmats2[t][tu]*dmats_old[tu][u];
16471
}// end loop over 'tu'
16472
}// end loop over 'u'
16473
}// end loop over 't'
16474
}
16475
16476
}// end loop over 's'
16477
for (unsigned int s = 0; s < 4; s++)
16478
{
16479
for (unsigned int t = 0; t < 4; t++)
16480
{
16481
derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
16482
}// end loop over 't'
16483
}// end loop over 's'
16484
}// end loop over 'r'
16485
16486
// Transform derivatives back to physical element
16487
for (unsigned int r = 0; r < num_derivatives; r++)
16488
{
16489
for (unsigned int s = 0; s < num_derivatives; s++)
16490
{
16491
values[r] += transform[r][s]*derivatives[s];
16492
}// end loop over 's'
16493
}// end loop over 'r'
16494
16495
// Delete pointer to array of derivatives on FIAT element
16496
delete [] derivatives;
16497
16498
// Delete pointer to array of combinations of derivatives and transform
16499
for (unsigned int r = 0; r < num_derivatives; r++)
16500
{
16501
delete [] combinations[r];
16502
}// end loop over 'r'
16503
delete [] combinations;
16504
for (unsigned int r = 0; r < num_derivatives; r++)
16505
{
16506
delete [] transform[r];
16507
}// end loop over 'r'
16508
delete [] transform;
16509
break;
16510
}
16511
case 1:
16512
{
16513
16514
// Array of basisvalues.
16515
double basisvalues[4] = {0.00000000, 0.00000000, 0.00000000, 0.00000000};
16516
16517
// Declare helper variables.
16518
unsigned int rr = 0;
16519
unsigned int ss = 0;
16520
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
16521
16522
// Compute basisvalues.
16523
basisvalues[0] = 1.00000000;
16524
basisvalues[1] = tmp0;
16525
for (unsigned int r = 0; r < 1; r++)
16526
{
16527
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
16528
ss = r*(r + 1)*(r + 2)/6;
16529
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
16530
}// end loop over 'r'
16531
for (unsigned int r = 0; r < 1; r++)
16532
{
16533
for (unsigned int s = 0; s < 1 - r; s++)
16534
{
16535
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
16536
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
16537
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
16538
}// end loop over 's'
16539
}// end loop over 'r'
16540
for (unsigned int r = 0; r < 2; r++)
16541
{
16542
for (unsigned int s = 0; s < 2 - r; s++)
16543
{
16544
for (unsigned int t = 0; t < 2 - r - s; t++)
16545
{
16546
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
16547
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
16548
}// end loop over 't'
16549
}// end loop over 's'
16550
}// end loop over 'r'
16551
16552
// Table(s) of coefficients.
16553
static const double coefficients0[4] = \
16554
{0.28867513, 0.18257419, -0.10540926, -0.07453560};
16555
16556
// Tables of derivatives of the polynomial base (transpose).
16557
static const double dmats0[4][4] = \
16558
{{0.00000000, 0.00000000, 0.00000000, 0.00000000},
16559
{6.32455532, 0.00000000, 0.00000000, 0.00000000},
16560
{0.00000000, 0.00000000, 0.00000000, 0.00000000},
16561
{0.00000000, 0.00000000, 0.00000000, 0.00000000}};
16562
16563
static const double dmats1[4][4] = \
16564
{{0.00000000, 0.00000000, 0.00000000, 0.00000000},
16565
{3.16227766, 0.00000000, 0.00000000, 0.00000000},
16566
{5.47722558, 0.00000000, 0.00000000, 0.00000000},
16567
{0.00000000, 0.00000000, 0.00000000, 0.00000000}};
16568
16569
static const double dmats2[4][4] = \
16570
{{0.00000000, 0.00000000, 0.00000000, 0.00000000},
16571
{3.16227766, 0.00000000, 0.00000000, 0.00000000},
16572
{1.82574186, 0.00000000, 0.00000000, 0.00000000},
16573
{5.16397779, 0.00000000, 0.00000000, 0.00000000}};
16574
16575
// Compute reference derivatives.
16576
// Declare pointer to array of derivatives on FIAT element.
16577
double *derivatives = new double[num_derivatives];
16578
for (unsigned int r = 0; r < num_derivatives; r++)
16579
{
16580
derivatives[r] = 0.00000000;
16581
}// end loop over 'r'
16582
16583
// Declare derivative matrix (of polynomial basis).
16584
double dmats[4][4] = \
16585
{{1.00000000, 0.00000000, 0.00000000, 0.00000000},
16586
{0.00000000, 1.00000000, 0.00000000, 0.00000000},
16587
{0.00000000, 0.00000000, 1.00000000, 0.00000000},
16588
{0.00000000, 0.00000000, 0.00000000, 1.00000000}};
16589
16590
// Declare (auxiliary) derivative matrix (of polynomial basis).
16591
double dmats_old[4][4] = \
16592
{{1.00000000, 0.00000000, 0.00000000, 0.00000000},
16593
{0.00000000, 1.00000000, 0.00000000, 0.00000000},
16594
{0.00000000, 0.00000000, 1.00000000, 0.00000000},
16595
{0.00000000, 0.00000000, 0.00000000, 1.00000000}};
16596
16597
// Loop possible derivatives.
16598
for (unsigned int r = 0; r < num_derivatives; r++)
16599
{
16600
// Resetting dmats values to compute next derivative.
16601
for (unsigned int t = 0; t < 4; t++)
16602
{
16603
for (unsigned int u = 0; u < 4; u++)
16604
{
16605
dmats[t][u] = 0.00000000;
16606
if (t == u)
16607
{
16608
dmats[t][u] = 1.00000000;
16609
}
16610
16611
}// end loop over 'u'
16612
}// end loop over 't'
16613
16614
// Looping derivative order to generate dmats.
16615
for (unsigned int s = 0; s < n; s++)
16616
{
16617
// Updating dmats_old with new values and resetting dmats.
16618
for (unsigned int t = 0; t < 4; t++)
16619
{
16620
for (unsigned int u = 0; u < 4; u++)
16621
{
16622
dmats_old[t][u] = dmats[t][u];
16623
dmats[t][u] = 0.00000000;
16624
}// end loop over 'u'
16625
}// end loop over 't'
16626
16627
// Update dmats using an inner product.
16628
if (combinations[r][s] == 0)
16629
{
16630
for (unsigned int t = 0; t < 4; t++)
16631
{
16632
for (unsigned int u = 0; u < 4; u++)
16633
{
16634
for (unsigned int tu = 0; tu < 4; tu++)
16635
{
16636
dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
16637
}// end loop over 'tu'
16638
}// end loop over 'u'
16639
}// end loop over 't'
16640
}
16641
16642
if (combinations[r][s] == 1)
16643
{
16644
for (unsigned int t = 0; t < 4; t++)
16645
{
16646
for (unsigned int u = 0; u < 4; u++)
16647
{
16648
for (unsigned int tu = 0; tu < 4; tu++)
16649
{
16650
dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
16651
}// end loop over 'tu'
16652
}// end loop over 'u'
16653
}// end loop over 't'
16654
}
16655
16656
if (combinations[r][s] == 2)
16657
{
16658
for (unsigned int t = 0; t < 4; t++)
16659
{
16660
for (unsigned int u = 0; u < 4; u++)
16661
{
16662
for (unsigned int tu = 0; tu < 4; tu++)
16663
{
16664
dmats[t][u] += dmats2[t][tu]*dmats_old[tu][u];
16665
}// end loop over 'tu'
16666
}// end loop over 'u'
16667
}// end loop over 't'
16668
}
16669
16670
}// end loop over 's'
16671
for (unsigned int s = 0; s < 4; s++)
16672
{
16673
for (unsigned int t = 0; t < 4; t++)
16674
{
16675
derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
16676
}// end loop over 't'
16677
}// end loop over 's'
16678
}// end loop over 'r'
16679
16680
// Transform derivatives back to physical element
16681
for (unsigned int r = 0; r < num_derivatives; r++)
16682
{
16683
for (unsigned int s = 0; s < num_derivatives; s++)
16684
{
16685
values[r] += transform[r][s]*derivatives[s];
16686
}// end loop over 's'
16687
}// end loop over 'r'
16688
16689
// Delete pointer to array of derivatives on FIAT element
16690
delete [] derivatives;
16691
16692
// Delete pointer to array of combinations of derivatives and transform
16693
for (unsigned int r = 0; r < num_derivatives; r++)
16694
{
16695
delete [] combinations[r];
16696
}// end loop over 'r'
16697
delete [] combinations;
16698
for (unsigned int r = 0; r < num_derivatives; r++)
16699
{
16700
delete [] transform[r];
16701
}// end loop over 'r'
16702
delete [] transform;
16703
break;
16704
}
16705
case 2:
16706
{
16707
16708
// Array of basisvalues.
16709
double basisvalues[4] = {0.00000000, 0.00000000, 0.00000000, 0.00000000};
16710
16711
// Declare helper variables.
16712
unsigned int rr = 0;
16713
unsigned int ss = 0;
16714
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
16715
16716
// Compute basisvalues.
16717
basisvalues[0] = 1.00000000;
16718
basisvalues[1] = tmp0;
16719
for (unsigned int r = 0; r < 1; r++)
16720
{
16721
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
16722
ss = r*(r + 1)*(r + 2)/6;
16723
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
16724
}// end loop over 'r'
16725
for (unsigned int r = 0; r < 1; r++)
16726
{
16727
for (unsigned int s = 0; s < 1 - r; s++)
16728
{
16729
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
16730
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
16731
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
16732
}// end loop over 's'
16733
}// end loop over 'r'
16734
for (unsigned int r = 0; r < 2; r++)
16735
{
16736
for (unsigned int s = 0; s < 2 - r; s++)
16737
{
16738
for (unsigned int t = 0; t < 2 - r - s; t++)
16739
{
16740
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
16741
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
16742
}// end loop over 't'
16743
}// end loop over 's'
16744
}// end loop over 'r'
16745
16746
// Table(s) of coefficients.
16747
static const double coefficients0[4] = \
16748
{0.28867513, 0.00000000, 0.21081851, -0.07453560};
16749
16750
// Tables of derivatives of the polynomial base (transpose).
16751
static const double dmats0[4][4] = \
16752
{{0.00000000, 0.00000000, 0.00000000, 0.00000000},
16753
{6.32455532, 0.00000000, 0.00000000, 0.00000000},
16754
{0.00000000, 0.00000000, 0.00000000, 0.00000000},
16755
{0.00000000, 0.00000000, 0.00000000, 0.00000000}};
16756
16757
static const double dmats1[4][4] = \
16758
{{0.00000000, 0.00000000, 0.00000000, 0.00000000},
16759
{3.16227766, 0.00000000, 0.00000000, 0.00000000},
16760
{5.47722558, 0.00000000, 0.00000000, 0.00000000},
16761
{0.00000000, 0.00000000, 0.00000000, 0.00000000}};
16762
16763
static const double dmats2[4][4] = \
16764
{{0.00000000, 0.00000000, 0.00000000, 0.00000000},
16765
{3.16227766, 0.00000000, 0.00000000, 0.00000000},
16766
{1.82574186, 0.00000000, 0.00000000, 0.00000000},
16767
{5.16397779, 0.00000000, 0.00000000, 0.00000000}};
16768
16769
// Compute reference derivatives.
16770
// Declare pointer to array of derivatives on FIAT element.
16771
double *derivatives = new double[num_derivatives];
16772
for (unsigned int r = 0; r < num_derivatives; r++)
16773
{
16774
derivatives[r] = 0.00000000;
16775
}// end loop over 'r'
16776
16777
// Declare derivative matrix (of polynomial basis).
16778
double dmats[4][4] = \
16779
{{1.00000000, 0.00000000, 0.00000000, 0.00000000},
16780
{0.00000000, 1.00000000, 0.00000000, 0.00000000},
16781
{0.00000000, 0.00000000, 1.00000000, 0.00000000},
16782
{0.00000000, 0.00000000, 0.00000000, 1.00000000}};
16783
16784
// Declare (auxiliary) derivative matrix (of polynomial basis).
16785
double dmats_old[4][4] = \
16786
{{1.00000000, 0.00000000, 0.00000000, 0.00000000},
16787
{0.00000000, 1.00000000, 0.00000000, 0.00000000},
16788
{0.00000000, 0.00000000, 1.00000000, 0.00000000},
16789
{0.00000000, 0.00000000, 0.00000000, 1.00000000}};
16790
16791
// Loop possible derivatives.
16792
for (unsigned int r = 0; r < num_derivatives; r++)
16793
{
16794
// Resetting dmats values to compute next derivative.
16795
for (unsigned int t = 0; t < 4; t++)
16796
{
16797
for (unsigned int u = 0; u < 4; u++)
16798
{
16799
dmats[t][u] = 0.00000000;
16800
if (t == u)
16801
{
16802
dmats[t][u] = 1.00000000;
16803
}
16804
16805
}// end loop over 'u'
16806
}// end loop over 't'
16807
16808
// Looping derivative order to generate dmats.
16809
for (unsigned int s = 0; s < n; s++)
16810
{
16811
// Updating dmats_old with new values and resetting dmats.
16812
for (unsigned int t = 0; t < 4; t++)
16813
{
16814
for (unsigned int u = 0; u < 4; u++)
16815
{
16816
dmats_old[t][u] = dmats[t][u];
16817
dmats[t][u] = 0.00000000;
16818
}// end loop over 'u'
16819
}// end loop over 't'
16820
16821
// Update dmats using an inner product.
16822
if (combinations[r][s] == 0)
16823
{
16824
for (unsigned int t = 0; t < 4; t++)
16825
{
16826
for (unsigned int u = 0; u < 4; u++)
16827
{
16828
for (unsigned int tu = 0; tu < 4; tu++)
16829
{
16830
dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
16831
}// end loop over 'tu'
16832
}// end loop over 'u'
16833
}// end loop over 't'
16834
}
16835
16836
if (combinations[r][s] == 1)
16837
{
16838
for (unsigned int t = 0; t < 4; t++)
16839
{
16840
for (unsigned int u = 0; u < 4; u++)
16841
{
16842
for (unsigned int tu = 0; tu < 4; tu++)
16843
{
16844
dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
16845
}// end loop over 'tu'
16846
}// end loop over 'u'
16847
}// end loop over 't'
16848
}
16849
16850
if (combinations[r][s] == 2)
16851
{
16852
for (unsigned int t = 0; t < 4; t++)
16853
{
16854
for (unsigned int u = 0; u < 4; u++)
16855
{
16856
for (unsigned int tu = 0; tu < 4; tu++)
16857
{
16858
dmats[t][u] += dmats2[t][tu]*dmats_old[tu][u];
16859
}// end loop over 'tu'
16860
}// end loop over 'u'
16861
}// end loop over 't'
16862
}
16863
16864
}// end loop over 's'
16865
for (unsigned int s = 0; s < 4; s++)
16866
{
16867
for (unsigned int t = 0; t < 4; t++)
16868
{
16869
derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
16870
}// end loop over 't'
16871
}// end loop over 's'
16872
}// end loop over 'r'
16873
16874
// Transform derivatives back to physical element
16875
for (unsigned int r = 0; r < num_derivatives; r++)
16876
{
16877
for (unsigned int s = 0; s < num_derivatives; s++)
16878
{
16879
values[r] += transform[r][s]*derivatives[s];
16880
}// end loop over 's'
16881
}// end loop over 'r'
16882
16883
// Delete pointer to array of derivatives on FIAT element
16884
delete [] derivatives;
16885
16886
// Delete pointer to array of combinations of derivatives and transform
16887
for (unsigned int r = 0; r < num_derivatives; r++)
16888
{
16889
delete [] combinations[r];
16890
}// end loop over 'r'
16891
delete [] combinations;
16892
for (unsigned int r = 0; r < num_derivatives; r++)
16893
{
16894
delete [] transform[r];
16895
}// end loop over 'r'
16896
delete [] transform;
16897
break;
16898
}
16899
case 3:
16900
{
16901
16902
// Array of basisvalues.
16903
double basisvalues[4] = {0.00000000, 0.00000000, 0.00000000, 0.00000000};
16904
16905
// Declare helper variables.
16906
unsigned int rr = 0;
16907
unsigned int ss = 0;
16908
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
16909
16910
// Compute basisvalues.
16911
basisvalues[0] = 1.00000000;
16912
basisvalues[1] = tmp0;
16913
for (unsigned int r = 0; r < 1; r++)
16914
{
16915
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
16916
ss = r*(r + 1)*(r + 2)/6;
16917
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
16918
}// end loop over 'r'
16919
for (unsigned int r = 0; r < 1; r++)
16920
{
16921
for (unsigned int s = 0; s < 1 - r; s++)
16922
{
16923
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
16924
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
16925
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
16926
}// end loop over 's'
16927
}// end loop over 'r'
16928
for (unsigned int r = 0; r < 2; r++)
16929
{
16930
for (unsigned int s = 0; s < 2 - r; s++)
16931
{
16932
for (unsigned int t = 0; t < 2 - r - s; t++)
16933
{
16934
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
16935
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
16936
}// end loop over 't'
16937
}// end loop over 's'
16938
}// end loop over 'r'
16939
16940
// Table(s) of coefficients.
16941
static const double coefficients0[4] = \
16942
{0.28867513, 0.00000000, 0.00000000, 0.22360680};
16943
16944
// Tables of derivatives of the polynomial base (transpose).
16945
static const double dmats0[4][4] = \
16946
{{0.00000000, 0.00000000, 0.00000000, 0.00000000},
16947
{6.32455532, 0.00000000, 0.00000000, 0.00000000},
16948
{0.00000000, 0.00000000, 0.00000000, 0.00000000},
16949
{0.00000000, 0.00000000, 0.00000000, 0.00000000}};
16950
16951
static const double dmats1[4][4] = \
16952
{{0.00000000, 0.00000000, 0.00000000, 0.00000000},
16953
{3.16227766, 0.00000000, 0.00000000, 0.00000000},
16954
{5.47722558, 0.00000000, 0.00000000, 0.00000000},
16955
{0.00000000, 0.00000000, 0.00000000, 0.00000000}};
16956
16957
static const double dmats2[4][4] = \
16958
{{0.00000000, 0.00000000, 0.00000000, 0.00000000},
16959
{3.16227766, 0.00000000, 0.00000000, 0.00000000},
16960
{1.82574186, 0.00000000, 0.00000000, 0.00000000},
16961
{5.16397779, 0.00000000, 0.00000000, 0.00000000}};
16962
16963
// Compute reference derivatives.
16964
// Declare pointer to array of derivatives on FIAT element.
16965
double *derivatives = new double[num_derivatives];
16966
for (unsigned int r = 0; r < num_derivatives; r++)
16967
{
16968
derivatives[r] = 0.00000000;
16969
}// end loop over 'r'
16970
16971
// Declare derivative matrix (of polynomial basis).
16972
double dmats[4][4] = \
16973
{{1.00000000, 0.00000000, 0.00000000, 0.00000000},
16974
{0.00000000, 1.00000000, 0.00000000, 0.00000000},
16975
{0.00000000, 0.00000000, 1.00000000, 0.00000000},
16976
{0.00000000, 0.00000000, 0.00000000, 1.00000000}};
16977
16978
// Declare (auxiliary) derivative matrix (of polynomial basis).
16979
double dmats_old[4][4] = \
16980
{{1.00000000, 0.00000000, 0.00000000, 0.00000000},
16981
{0.00000000, 1.00000000, 0.00000000, 0.00000000},
16982
{0.00000000, 0.00000000, 1.00000000, 0.00000000},
16983
{0.00000000, 0.00000000, 0.00000000, 1.00000000}};
16984
16985
// Loop possible derivatives.
16986
for (unsigned int r = 0; r < num_derivatives; r++)
16987
{
16988
// Resetting dmats values to compute next derivative.
16989
for (unsigned int t = 0; t < 4; t++)
16990
{
16991
for (unsigned int u = 0; u < 4; u++)
16992
{
16993
dmats[t][u] = 0.00000000;
16994
if (t == u)
16995
{
16996
dmats[t][u] = 1.00000000;
16997
}
16998
16999
}// end loop over 'u'
17000
}// end loop over 't'
17001
17002
// Looping derivative order to generate dmats.
17003
for (unsigned int s = 0; s < n; s++)
17004
{
17005
// Updating dmats_old with new values and resetting dmats.
17006
for (unsigned int t = 0; t < 4; t++)
17007
{
17008
for (unsigned int u = 0; u < 4; u++)
17009
{
17010
dmats_old[t][u] = dmats[t][u];
17011
dmats[t][u] = 0.00000000;
17012
}// end loop over 'u'
17013
}// end loop over 't'
17014
17015
// Update dmats using an inner product.
17016
if (combinations[r][s] == 0)
17017
{
17018
for (unsigned int t = 0; t < 4; t++)
17019
{
17020
for (unsigned int u = 0; u < 4; u++)
17021
{
17022
for (unsigned int tu = 0; tu < 4; tu++)
17023
{
17024
dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
17025
}// end loop over 'tu'
17026
}// end loop over 'u'
17027
}// end loop over 't'
17028
}
17029
17030
if (combinations[r][s] == 1)
17031
{
17032
for (unsigned int t = 0; t < 4; t++)
17033
{
17034
for (unsigned int u = 0; u < 4; u++)
17035
{
17036
for (unsigned int tu = 0; tu < 4; tu++)
17037
{
17038
dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
17039
}// end loop over 'tu'
17040
}// end loop over 'u'
17041
}// end loop over 't'
17042
}
17043
17044
if (combinations[r][s] == 2)
17045
{
17046
for (unsigned int t = 0; t < 4; t++)
17047
{
17048
for (unsigned int u = 0; u < 4; u++)
17049
{
17050
for (unsigned int tu = 0; tu < 4; tu++)
17051
{
17052
dmats[t][u] += dmats2[t][tu]*dmats_old[tu][u];
17053
}// end loop over 'tu'
17054
}// end loop over 'u'
17055
}// end loop over 't'
17056
}
17057
17058
}// end loop over 's'
17059
for (unsigned int s = 0; s < 4; s++)
17060
{
17061
for (unsigned int t = 0; t < 4; t++)
17062
{
17063
derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
17064
}// end loop over 't'
17065
}// end loop over 's'
17066
}// end loop over 'r'
17067
17068
// Transform derivatives back to physical element
17069
for (unsigned int r = 0; r < num_derivatives; r++)
17070
{
17071
for (unsigned int s = 0; s < num_derivatives; s++)
17072
{
17073
values[r] += transform[r][s]*derivatives[s];
17074
}// end loop over 's'
17075
}// end loop over 'r'
17076
17077
// Delete pointer to array of derivatives on FIAT element
17078
delete [] derivatives;
17079
17080
// Delete pointer to array of combinations of derivatives and transform
17081
for (unsigned int r = 0; r < num_derivatives; r++)
17082
{
17083
delete [] combinations[r];
17084
}// end loop over 'r'
17085
delete [] combinations;
17086
for (unsigned int r = 0; r < num_derivatives; r++)
17087
{
17088
delete [] transform[r];
17089
}// end loop over 'r'
17090
delete [] transform;
17091
break;
17092
}
17093
}
17094
3313
17095
}
3314
17096
3315
17097
/// Evaluate order n derivatives of all basis functions at given point in cell
3576
17358
values[0] = 0.00000000;
3577
17359
values[1] = 0.00000000;
3578
17360
values[2] = 0.00000000;
3579
3580
// Map degree of freedom to element degree of freedom
3581
const unsigned int dof = i;
3582
3583
// Array of basisvalues.
3584
double basisvalues[4] = {0.00000000, 0.00000000, 0.00000000, 0.00000000};
3585
3586
// Declare helper variables.
3587
unsigned int rr = 0;
3588
unsigned int ss = 0;
3589
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
3590
3591
// Compute basisvalues.
3592
basisvalues[0] = 1.00000000;
3593
basisvalues[1] = tmp0;
3594
for (unsigned int r = 0; r < 1; r++)
3595
{
3596
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
3597
ss = r*(r + 1)*(r + 2)/6;
3598
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
3599
}// end loop over 'r'
3600
for (unsigned int r = 0; r < 1; r++)
3601
{
3602
for (unsigned int s = 0; s < 1 - r; s++)
3603
{
3604
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
3605
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
3606
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
3607
}// end loop over 's'
3608
}// end loop over 'r'
3609
for (unsigned int r = 0; r < 2; r++)
3610
{
3611
for (unsigned int s = 0; s < 2 - r; s++)
3612
{
3613
for (unsigned int t = 0; t < 2 - r - s; t++)
3614
{
3615
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
3616
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
3617
}// end loop over 't'
3618
}// end loop over 's'
3619
}// end loop over 'r'
3620
3621
// Table(s) of coefficients.
3622
static const double coefficients0[6][4] = \
3623
{{0.00000000, 0.00000000, 0.00000000, 0.00000000},
3624
{-0.28867513, 0.00000000, 0.00000000, -0.22360680},
3625
{-0.28867513, 0.00000000, -0.21081851, 0.07453560},
3626
{0.28867513, 0.00000000, 0.00000000, 0.22360680},
3627
{0.28867513, 0.00000000, 0.21081851, -0.07453560},
3628
{0.57735027, 0.00000000, -0.21081851, -0.14907120}};
3629
3630
static const double coefficients1[6][4] = \
3631
{{-0.28867513, 0.00000000, 0.00000000, -0.22360680},
3632
{0.00000000, 0.00000000, 0.00000000, 0.00000000},
3633
{0.28867513, 0.18257419, -0.10540926, -0.07453560},
3634
{0.28867513, 0.00000000, 0.00000000, 0.22360680},
3635
{0.57735027, -0.18257419, 0.10540926, -0.14907120},
3636
{0.28867513, 0.18257419, -0.10540926, -0.07453560}};
3637
3638
static const double coefficients2[6][4] = \
3639
{{0.28867513, 0.00000000, 0.21081851, -0.07453560},
3640
{0.28867513, 0.18257419, -0.10540926, -0.07453560},
3641
{0.00000000, 0.00000000, 0.00000000, 0.00000000},
3642
{0.57735027, -0.18257419, -0.10540926, 0.14907120},
3643
{0.28867513, 0.00000000, 0.21081851, -0.07453560},
3644
{0.28867513, 0.18257419, -0.10540926, -0.07453560}};
3645
3646
// Compute value(s).
3647
for (unsigned int r = 0; r < 4; r++)
3648
{
3649
values[0] += coefficients0[dof][r]*basisvalues[r];
3650
values[1] += coefficients1[dof][r]*basisvalues[r];
3651
values[2] += coefficients2[dof][r]*basisvalues[r];
3652
}// end loop over 'r'
3653
3654
// Using covariant Piola transform to map values back to the physical element.
3655
const double tmp_ref0 = values[0];
3656
const double tmp_ref1 = values[1];
3657
const double tmp_ref2 = values[2];
3658
values[0] = (K_00*tmp_ref0 + K_10*tmp_ref1 + K_20*tmp_ref2);
3659
values[1] = (K_01*tmp_ref0 + K_11*tmp_ref1 + K_21*tmp_ref2);
3660
values[2] = (K_02*tmp_ref0 + K_12*tmp_ref1 + K_22*tmp_ref2);
17361
switch (i)
17362
{
17363
case 0:
17364
{
17365
17366
// Array of basisvalues.
17367
double basisvalues[4] = {0.00000000, 0.00000000, 0.00000000, 0.00000000};
17368
17369
// Declare helper variables.
17370
unsigned int rr = 0;
17371
unsigned int ss = 0;
17372
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
17373
17374
// Compute basisvalues.
17375
basisvalues[0] = 1.00000000;
17376
basisvalues[1] = tmp0;
17377
for (unsigned int r = 0; r < 1; r++)
17378
{
17379
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
17380
ss = r*(r + 1)*(r + 2)/6;
17381
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
17382
}// end loop over 'r'
17383
for (unsigned int r = 0; r < 1; r++)
17384
{
17385
for (unsigned int s = 0; s < 1 - r; s++)
17386
{
17387
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
17388
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
17389
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
17390
}// end loop over 's'
17391
}// end loop over 'r'
17392
for (unsigned int r = 0; r < 2; r++)
17393
{
17394
for (unsigned int s = 0; s < 2 - r; s++)
17395
{
17396
for (unsigned int t = 0; t < 2 - r - s; t++)
17397
{
17398
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
17399
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
17400
}// end loop over 't'
17401
}// end loop over 's'
17402
}// end loop over 'r'
17403
17404
// Table(s) of coefficients.
17405
static const double coefficients0[4] = \
17406
{0.00000000, 0.00000000, 0.00000000, 0.00000000};
17407
17408
static const double coefficients1[4] = \
17409
{-0.28867513, 0.00000000, 0.00000000, -0.22360680};
17410
17411
static const double coefficients2[4] = \
17412
{0.28867513, 0.00000000, 0.21081851, -0.07453560};
17413
17414
// Compute value(s).
17415
for (unsigned int r = 0; r < 4; r++)
17416
{
17417
values[0] += coefficients0[r]*basisvalues[r];
17418
values[1] += coefficients1[r]*basisvalues[r];
17419
values[2] += coefficients2[r]*basisvalues[r];
17420
}// end loop over 'r'
17421
17422
// Using covariant Piola transform to map values back to the physical element.
17423
const double tmp_ref0 = values[0];
17424
const double tmp_ref1 = values[1];
17425
const double tmp_ref2 = values[2];
17426
values[0] = (K_00*tmp_ref0 + K_10*tmp_ref1 + K_20*tmp_ref2);
17427
values[1] = (K_01*tmp_ref0 + K_11*tmp_ref1 + K_21*tmp_ref2);
17428
values[2] = (K_02*tmp_ref0 + K_12*tmp_ref1 + K_22*tmp_ref2);
17429
break;
17430
}
17431
case 1:
17432
{
17433
17434
// Array of basisvalues.
17435
double basisvalues[4] = {0.00000000, 0.00000000, 0.00000000, 0.00000000};
17436
17437
// Declare helper variables.
17438
unsigned int rr = 0;
17439
unsigned int ss = 0;
17440
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
17441
17442
// Compute basisvalues.
17443
basisvalues[0] = 1.00000000;
17444
basisvalues[1] = tmp0;
17445
for (unsigned int r = 0; r < 1; r++)
17446
{
17447
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
17448
ss = r*(r + 1)*(r + 2)/6;
17449
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
17450
}// end loop over 'r'
17451
for (unsigned int r = 0; r < 1; r++)
17452
{
17453
for (unsigned int s = 0; s < 1 - r; s++)
17454
{
17455
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
17456
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
17457
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
17458
}// end loop over 's'
17459
}// end loop over 'r'
17460
for (unsigned int r = 0; r < 2; r++)
17461
{
17462
for (unsigned int s = 0; s < 2 - r; s++)
17463
{
17464
for (unsigned int t = 0; t < 2 - r - s; t++)
17465
{
17466
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
17467
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
17468
}// end loop over 't'
17469
}// end loop over 's'
17470
}// end loop over 'r'
17471
17472
// Table(s) of coefficients.
17473
static const double coefficients0[4] = \
17474
{-0.28867513, 0.00000000, 0.00000000, -0.22360680};
17475
17476
static const double coefficients1[4] = \
17477
{0.00000000, 0.00000000, 0.00000000, 0.00000000};
17478
17479
static const double coefficients2[4] = \
17480
{0.28867513, 0.18257419, -0.10540926, -0.07453560};
17481
17482
// Compute value(s).
17483
for (unsigned int r = 0; r < 4; r++)
17484
{
17485
values[0] += coefficients0[r]*basisvalues[r];
17486
values[1] += coefficients1[r]*basisvalues[r];
17487
values[2] += coefficients2[r]*basisvalues[r];
17488
}// end loop over 'r'
17489
17490
// Using covariant Piola transform to map values back to the physical element.
17491
const double tmp_ref0 = values[0];
17492
const double tmp_ref1 = values[1];
17493
const double tmp_ref2 = values[2];
17494
values[0] = (K_00*tmp_ref0 + K_10*tmp_ref1 + K_20*tmp_ref2);
17495
values[1] = (K_01*tmp_ref0 + K_11*tmp_ref1 + K_21*tmp_ref2);
17496
values[2] = (K_02*tmp_ref0 + K_12*tmp_ref1 + K_22*tmp_ref2);
17497
break;
17498
}
17499
case 2:
17500
{
17501
17502
// Array of basisvalues.
17503
double basisvalues[4] = {0.00000000, 0.00000000, 0.00000000, 0.00000000};
17504
17505
// Declare helper variables.
17506
unsigned int rr = 0;
17507
unsigned int ss = 0;
17508
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
17509
17510
// Compute basisvalues.
17511
basisvalues[0] = 1.00000000;
17512
basisvalues[1] = tmp0;
17513
for (unsigned int r = 0; r < 1; r++)
17514
{
17515
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
17516
ss = r*(r + 1)*(r + 2)/6;
17517
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
17518
}// end loop over 'r'
17519
for (unsigned int r = 0; r < 1; r++)
17520
{
17521
for (unsigned int s = 0; s < 1 - r; s++)
17522
{
17523
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
17524
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
17525
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
17526
}// end loop over 's'
17527
}// end loop over 'r'
17528
for (unsigned int r = 0; r < 2; r++)
17529
{
17530
for (unsigned int s = 0; s < 2 - r; s++)
17531
{
17532
for (unsigned int t = 0; t < 2 - r - s; t++)
17533
{
17534
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
17535
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
17536
}// end loop over 't'
17537
}// end loop over 's'
17538
}// end loop over 'r'
17539
17540
// Table(s) of coefficients.
17541
static const double coefficients0[4] = \
17542
{-0.28867513, 0.00000000, -0.21081851, 0.07453560};
17543
17544
static const double coefficients1[4] = \
17545
{0.28867513, 0.18257419, -0.10540926, -0.07453560};
17546
17547
static const double coefficients2[4] = \
17548
{0.00000000, 0.00000000, 0.00000000, 0.00000000};
17549
17550
// Compute value(s).
17551
for (unsigned int r = 0; r < 4; r++)
17552
{
17553
values[0] += coefficients0[r]*basisvalues[r];
17554
values[1] += coefficients1[r]*basisvalues[r];
17555
values[2] += coefficients2[r]*basisvalues[r];
17556
}// end loop over 'r'
17557
17558
// Using covariant Piola transform to map values back to the physical element.
17559
const double tmp_ref0 = values[0];
17560
const double tmp_ref1 = values[1];
17561
const double tmp_ref2 = values[2];
17562
values[0] = (K_00*tmp_ref0 + K_10*tmp_ref1 + K_20*tmp_ref2);
17563
values[1] = (K_01*tmp_ref0 + K_11*tmp_ref1 + K_21*tmp_ref2);
17564
values[2] = (K_02*tmp_ref0 + K_12*tmp_ref1 + K_22*tmp_ref2);
17565
break;
17566
}
17567
case 3:
17568
{
17569
17570
// Array of basisvalues.
17571
double basisvalues[4] = {0.00000000, 0.00000000, 0.00000000, 0.00000000};
17572
17573
// Declare helper variables.
17574
unsigned int rr = 0;
17575
unsigned int ss = 0;
17576
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
17577
17578
// Compute basisvalues.
17579
basisvalues[0] = 1.00000000;
17580
basisvalues[1] = tmp0;
17581
for (unsigned int r = 0; r < 1; r++)
17582
{
17583
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
17584
ss = r*(r + 1)*(r + 2)/6;
17585
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
17586
}// end loop over 'r'
17587
for (unsigned int r = 0; r < 1; r++)
17588
{
17589
for (unsigned int s = 0; s < 1 - r; s++)
17590
{
17591
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
17592
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
17593
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
17594
}// end loop over 's'
17595
}// end loop over 'r'
17596
for (unsigned int r = 0; r < 2; r++)
17597
{
17598
for (unsigned int s = 0; s < 2 - r; s++)
17599
{
17600
for (unsigned int t = 0; t < 2 - r - s; t++)
17601
{
17602
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
17603
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
17604
}// end loop over 't'
17605
}// end loop over 's'
17606
}// end loop over 'r'
17607
17608
// Table(s) of coefficients.
17609
static const double coefficients0[4] = \
17610
{0.28867513, 0.00000000, 0.00000000, 0.22360680};
17611
17612
static const double coefficients1[4] = \
17613
{0.28867513, 0.00000000, 0.00000000, 0.22360680};
17614
17615
static const double coefficients2[4] = \
17616
{0.57735027, -0.18257419, -0.10540926, 0.14907120};
17617
17618
// Compute value(s).
17619
for (unsigned int r = 0; r < 4; r++)
17620
{
17621
values[0] += coefficients0[r]*basisvalues[r];
17622
values[1] += coefficients1[r]*basisvalues[r];
17623
values[2] += coefficients2[r]*basisvalues[r];
17624
}// end loop over 'r'
17625
17626
// Using covariant Piola transform to map values back to the physical element.
17627
const double tmp_ref0 = values[0];
17628
const double tmp_ref1 = values[1];
17629
const double tmp_ref2 = values[2];
17630
values[0] = (K_00*tmp_ref0 + K_10*tmp_ref1 + K_20*tmp_ref2);
17631
values[1] = (K_01*tmp_ref0 + K_11*tmp_ref1 + K_21*tmp_ref2);
17632
values[2] = (K_02*tmp_ref0 + K_12*tmp_ref1 + K_22*tmp_ref2);
17633
break;
17634
}
17635
case 4:
17636
{
17637
17638
// Array of basisvalues.
17639
double basisvalues[4] = {0.00000000, 0.00000000, 0.00000000, 0.00000000};
17640
17641
// Declare helper variables.
17642
unsigned int rr = 0;
17643
unsigned int ss = 0;
17644
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
17645
17646
// Compute basisvalues.
17647
basisvalues[0] = 1.00000000;
17648
basisvalues[1] = tmp0;
17649
for (unsigned int r = 0; r < 1; r++)
17650
{
17651
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
17652
ss = r*(r + 1)*(r + 2)/6;
17653
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
17654
}// end loop over 'r'
17655
for (unsigned int r = 0; r < 1; r++)
17656
{
17657
for (unsigned int s = 0; s < 1 - r; s++)
17658
{
17659
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
17660
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
17661
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
17662
}// end loop over 's'
17663
}// end loop over 'r'
17664
for (unsigned int r = 0; r < 2; r++)
17665
{
17666
for (unsigned int s = 0; s < 2 - r; s++)
17667
{
17668
for (unsigned int t = 0; t < 2 - r - s; t++)
17669
{
17670
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
17671
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
17672
}// end loop over 't'
17673
}// end loop over 's'
17674
}// end loop over 'r'
17675
17676
// Table(s) of coefficients.
17677
static const double coefficients0[4] = \
17678
{0.28867513, 0.00000000, 0.21081851, -0.07453560};
17679
17680
static const double coefficients1[4] = \
17681
{0.57735027, -0.18257419, 0.10540926, -0.14907120};
17682
17683
static const double coefficients2[4] = \
17684
{0.28867513, 0.00000000, 0.21081851, -0.07453560};
17685
17686
// Compute value(s).
17687
for (unsigned int r = 0; r < 4; r++)
17688
{
17689
values[0] += coefficients0[r]*basisvalues[r];
17690
values[1] += coefficients1[r]*basisvalues[r];
17691
values[2] += coefficients2[r]*basisvalues[r];
17692
}// end loop over 'r'
17693
17694
// Using covariant Piola transform to map values back to the physical element.
17695
const double tmp_ref0 = values[0];
17696
const double tmp_ref1 = values[1];
17697
const double tmp_ref2 = values[2];
17698
values[0] = (K_00*tmp_ref0 + K_10*tmp_ref1 + K_20*tmp_ref2);
17699
values[1] = (K_01*tmp_ref0 + K_11*tmp_ref1 + K_21*tmp_ref2);
17700
values[2] = (K_02*tmp_ref0 + K_12*tmp_ref1 + K_22*tmp_ref2);
17701
break;
17702
}
17703
case 5:
17704
{
17705
17706
// Array of basisvalues.
17707
double basisvalues[4] = {0.00000000, 0.00000000, 0.00000000, 0.00000000};
17708
17709
// Declare helper variables.
17710
unsigned int rr = 0;
17711
unsigned int ss = 0;
17712
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
17713
17714
// Compute basisvalues.
17715
basisvalues[0] = 1.00000000;
17716
basisvalues[1] = tmp0;
17717
for (unsigned int r = 0; r < 1; r++)
17718
{
17719
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
17720
ss = r*(r + 1)*(r + 2)/6;
17721
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
17722
}// end loop over 'r'
17723
for (unsigned int r = 0; r < 1; r++)
17724
{
17725
for (unsigned int s = 0; s < 1 - r; s++)
17726
{
17727
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
17728
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
17729
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
17730
}// end loop over 's'
17731
}// end loop over 'r'
17732
for (unsigned int r = 0; r < 2; r++)
17733
{
17734
for (unsigned int s = 0; s < 2 - r; s++)
17735
{
17736
for (unsigned int t = 0; t < 2 - r - s; t++)
17737
{
17738
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
17739
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
17740
}// end loop over 't'
17741
}// end loop over 's'
17742
}// end loop over 'r'
17743
17744
// Table(s) of coefficients.
17745
static const double coefficients0[4] = \
17746
{0.57735027, 0.00000000, -0.21081851, -0.14907120};
17747
17748
static const double coefficients1[4] = \
17749
{0.28867513, 0.18257419, -0.10540926, -0.07453560};
17750
17751
static const double coefficients2[4] = \
17752
{0.28867513, 0.18257419, -0.10540926, -0.07453560};
17753
17754
// Compute value(s).
17755
for (unsigned int r = 0; r < 4; r++)
17756
{
17757
values[0] += coefficients0[r]*basisvalues[r];
17758
values[1] += coefficients1[r]*basisvalues[r];
17759
values[2] += coefficients2[r]*basisvalues[r];
17760
}// end loop over 'r'
17761
17762
// Using covariant Piola transform to map values back to the physical element.
17763
const double tmp_ref0 = values[0];
17764
const double tmp_ref1 = values[1];
17765
const double tmp_ref2 = values[2];
17766
values[0] = (K_00*tmp_ref0 + K_10*tmp_ref1 + K_20*tmp_ref2);
17767
values[1] = (K_01*tmp_ref0 + K_11*tmp_ref1 + K_21*tmp_ref2);
17768
values[2] = (K_02*tmp_ref0 + K_12*tmp_ref1 + K_22*tmp_ref2);
17769
break;
17770
}
17771
}
17772
3661
17773
}
3662
17774
3663
17775
/// Evaluate all basis functions at given point in cell
3800
17912
values[r] = 0.00000000;
3801
17913
}// end loop over 'r'
3802
17914
3803
// Map degree of freedom to element degree of freedom
3804
const unsigned int dof = i;
3805
3806
// Array of basisvalues.
3807
double basisvalues[4] = {0.00000000, 0.00000000, 0.00000000, 0.00000000};
3808
3809
// Declare helper variables.
3810
unsigned int rr = 0;
3811
unsigned int ss = 0;
3812
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
3813
3814
// Compute basisvalues.
3815
basisvalues[0] = 1.00000000;
3816
basisvalues[1] = tmp0;
3817
for (unsigned int r = 0; r < 1; r++)
3818
{
3819
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
3820
ss = r*(r + 1)*(r + 2)/6;
3821
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
3822
}// end loop over 'r'
3823
for (unsigned int r = 0; r < 1; r++)
3824
{
3825
for (unsigned int s = 0; s < 1 - r; s++)
3826
{
3827
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
3828
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
3829
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
3830
}// end loop over 's'
3831
}// end loop over 'r'
3832
for (unsigned int r = 0; r < 2; r++)
3833
{
3834
for (unsigned int s = 0; s < 2 - r; s++)
3835
{
3836
for (unsigned int t = 0; t < 2 - r - s; t++)
3837
{
3838
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
3839
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
3840
}// end loop over 't'
3841
}// end loop over 's'
3842
}// end loop over 'r'
3843
3844
// Table(s) of coefficients.
3845
static const double coefficients0[6][4] = \
3846
{{0.00000000, 0.00000000, 0.00000000, 0.00000000},
3847
{-0.28867513, 0.00000000, 0.00000000, -0.22360680},
3848
{-0.28867513, 0.00000000, -0.21081851, 0.07453560},
3849
{0.28867513, 0.00000000, 0.00000000, 0.22360680},
3850
{0.28867513, 0.00000000, 0.21081851, -0.07453560},
3851
{0.57735027, 0.00000000, -0.21081851, -0.14907120}};
3852
3853
static const double coefficients1[6][4] = \
3854
{{-0.28867513, 0.00000000, 0.00000000, -0.22360680},
3855
{0.00000000, 0.00000000, 0.00000000, 0.00000000},
3856
{0.28867513, 0.18257419, -0.10540926, -0.07453560},
3857
{0.28867513, 0.00000000, 0.00000000, 0.22360680},
3858
{0.57735027, -0.18257419, 0.10540926, -0.14907120},
3859
{0.28867513, 0.18257419, -0.10540926, -0.07453560}};
3860
3861
static const double coefficients2[6][4] = \
3862
{{0.28867513, 0.00000000, 0.21081851, -0.07453560},
3863
{0.28867513, 0.18257419, -0.10540926, -0.07453560},
3864
{0.00000000, 0.00000000, 0.00000000, 0.00000000},
3865
{0.57735027, -0.18257419, -0.10540926, 0.14907120},
3866
{0.28867513, 0.00000000, 0.21081851, -0.07453560},
3867
{0.28867513, 0.18257419, -0.10540926, -0.07453560}};
3868
3869
// Tables of derivatives of the polynomial base (transpose).
3870
static const double dmats0[4][4] = \
3871
{{0.00000000, 0.00000000, 0.00000000, 0.00000000},
3872
{6.32455532, 0.00000000, 0.00000000, 0.00000000},
3873
{0.00000000, 0.00000000, 0.00000000, 0.00000000},
3874
{0.00000000, 0.00000000, 0.00000000, 0.00000000}};
3875
3876
static const double dmats1[4][4] = \
3877
{{0.00000000, 0.00000000, 0.00000000, 0.00000000},
3878
{3.16227766, 0.00000000, 0.00000000, 0.00000000},
3879
{5.47722558, 0.00000000, 0.00000000, 0.00000000},
3880
{0.00000000, 0.00000000, 0.00000000, 0.00000000}};
3881
3882
static const double dmats2[4][4] = \
3883
{{0.00000000, 0.00000000, 0.00000000, 0.00000000},
3884
{3.16227766, 0.00000000, 0.00000000, 0.00000000},
3885
{1.82574186, 0.00000000, 0.00000000, 0.00000000},
3886
{5.16397779, 0.00000000, 0.00000000, 0.00000000}};
3887
3888
// Compute reference derivatives.
3889
// Declare pointer to array of derivatives on FIAT element.
3890
double *derivatives = new double[3*num_derivatives];
3891
for (unsigned int r = 0; r < 3*num_derivatives; r++)
3892
{
3893
derivatives[r] = 0.00000000;
3894
}// end loop over 'r'
3895
3896
// Declare derivative matrix (of polynomial basis).
3897
double dmats[4][4] = \
3898
{{1.00000000, 0.00000000, 0.00000000, 0.00000000},
3899
{0.00000000, 1.00000000, 0.00000000, 0.00000000},
3900
{0.00000000, 0.00000000, 1.00000000, 0.00000000},
3901
{0.00000000, 0.00000000, 0.00000000, 1.00000000}};
3902
3903
// Declare (auxiliary) derivative matrix (of polynomial basis).
3904
double dmats_old[4][4] = \
3905
{{1.00000000, 0.00000000, 0.00000000, 0.00000000},
3906
{0.00000000, 1.00000000, 0.00000000, 0.00000000},
3907
{0.00000000, 0.00000000, 1.00000000, 0.00000000},
3908
{0.00000000, 0.00000000, 0.00000000, 1.00000000}};
3909
3910
// Loop possible derivatives.
3911
for (unsigned int r = 0; r < num_derivatives; r++)
3912
{
3913
// Resetting dmats values to compute next derivative.
3914
for (unsigned int t = 0; t < 4; t++)
3915
{
3916
for (unsigned int u = 0; u < 4; u++)
3917
{
3918
dmats[t][u] = 0.00000000;
3919
if (t == u)
3920
{
3921
dmats[t][u] = 1.00000000;
3922
}
3923
3924
}// end loop over 'u'
3925
}// end loop over 't'
3926
3927
// Looping derivative order to generate dmats.
3928
for (unsigned int s = 0; s < n; s++)
3929
{
3930
// Updating dmats_old with new values and resetting dmats.
3931
for (unsigned int t = 0; t < 4; t++)
3932
{
3933
for (unsigned int u = 0; u < 4; u++)
3934
{
3935
dmats_old[t][u] = dmats[t][u];
3936
dmats[t][u] = 0.00000000;
3937
}// end loop over 'u'
3938
}// end loop over 't'
3939
3940
// Update dmats using an inner product.
3941
if (combinations[r][s] == 0)
3942
{
3943
for (unsigned int t = 0; t < 4; t++)
3944
{
3945
for (unsigned int u = 0; u < 4; u++)
3946
{
3947
for (unsigned int tu = 0; tu < 4; tu++)
3948
{
3949
dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
3950
}// end loop over 'tu'
3951
}// end loop over 'u'
3952
}// end loop over 't'
3953
}
3954
3955
if (combinations[r][s] == 1)
3956
{
3957
for (unsigned int t = 0; t < 4; t++)
3958
{
3959
for (unsigned int u = 0; u < 4; u++)
3960
{
3961
for (unsigned int tu = 0; tu < 4; tu++)
3962
{
3963
dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
3964
}// end loop over 'tu'
3965
}// end loop over 'u'
3966
}// end loop over 't'
3967
}
3968
3969
if (combinations[r][s] == 2)
3970
{
3971
for (unsigned int t = 0; t < 4; t++)
3972
{
3973
for (unsigned int u = 0; u < 4; u++)
3974
{
3975
for (unsigned int tu = 0; tu < 4; tu++)
3976
{
3977
dmats[t][u] += dmats2[t][tu]*dmats_old[tu][u];
3978
}// end loop over 'tu'
3979
}// end loop over 'u'
3980
}// end loop over 't'
3981
}
3982
3983
}// end loop over 's'
3984
for (unsigned int s = 0; s < 4; s++)
3985
{
3986
for (unsigned int t = 0; t < 4; t++)
3987
{
3988
derivatives[r] += coefficients0[dof][s]*dmats[s][t]*basisvalues[t];
3989
derivatives[num_derivatives + r] += coefficients1[dof][s]*dmats[s][t]*basisvalues[t];
3990
derivatives[2*num_derivatives + r] += coefficients2[dof][s]*dmats[s][t]*basisvalues[t];
3991
}// end loop over 't'
3992
}// end loop over 's'
3993
3994
// Using covariant Piola transform to map values back to the physical element
3995
const double tmp_ref0 = derivatives[r];
3996
const double tmp_ref1 = derivatives[num_derivatives + r];
3997
const double tmp_ref2 = derivatives[2*num_derivatives + r];
3998
derivatives[r] = (K_00*tmp_ref0 + K_10*tmp_ref1 + K_20*tmp_ref2);
3999
derivatives[num_derivatives + r] = (K_01*tmp_ref0 + K_11*tmp_ref1 + K_21*tmp_ref2);
4000
derivatives[2*num_derivatives + r] = (K_02*tmp_ref0 + K_12*tmp_ref1 + K_22*tmp_ref2);
4001
}// end loop over 'r'
4002
4003
// Transform derivatives back to physical element
4004
for (unsigned int r = 0; r < num_derivatives; r++)
4005
{
4006
for (unsigned int s = 0; s < num_derivatives; s++)
4007
{
4008
values[r] += transform[r][s]*derivatives[s];
4009
values[num_derivatives + r] += transform[r][s]*derivatives[num_derivatives + s];
4010
values[2*num_derivatives + r] += transform[r][s]*derivatives[2*num_derivatives + s];
4011
}// end loop over 's'
4012
}// end loop over 'r'
4013
4014
// Delete pointer to array of derivatives on FIAT element
4015
delete [] derivatives;
4016
4017
// Delete pointer to array of combinations of derivatives and transform
4018
for (unsigned int r = 0; r < num_derivatives; r++)
4019
{
4020
delete [] combinations[r];
4021
}// end loop over 'r'
4022
delete [] combinations;
4023
for (unsigned int r = 0; r < num_derivatives; r++)
4024
{
4025
delete [] transform[r];
4026
}// end loop over 'r'
4027
delete [] transform;
17915
switch (i)
17916
{
17917
case 0:
17918
{
17919
17920
// Array of basisvalues.
17921
double basisvalues[4] = {0.00000000, 0.00000000, 0.00000000, 0.00000000};
17922
17923
// Declare helper variables.
17924
unsigned int rr = 0;
17925
unsigned int ss = 0;
17926
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
17927
17928
// Compute basisvalues.
17929
basisvalues[0] = 1.00000000;
17930
basisvalues[1] = tmp0;
17931
for (unsigned int r = 0; r < 1; r++)
17932
{
17933
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
17934
ss = r*(r + 1)*(r + 2)/6;
17935
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
17936
}// end loop over 'r'
17937
for (unsigned int r = 0; r < 1; r++)
17938
{
17939
for (unsigned int s = 0; s < 1 - r; s++)
17940
{
17941
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
17942
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
17943
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
17944
}// end loop over 's'
17945
}// end loop over 'r'
17946
for (unsigned int r = 0; r < 2; r++)
17947
{
17948
for (unsigned int s = 0; s < 2 - r; s++)
17949
{
17950
for (unsigned int t = 0; t < 2 - r - s; t++)
17951
{
17952
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
17953
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
17954
}// end loop over 't'
17955
}// end loop over 's'
17956
}// end loop over 'r'
17957
17958
// Table(s) of coefficients.
17959
static const double coefficients0[4] = \
17960
{0.00000000, 0.00000000, 0.00000000, 0.00000000};
17961
17962
static const double coefficients1[4] = \
17963
{-0.28867513, 0.00000000, 0.00000000, -0.22360680};
17964
17965
static const double coefficients2[4] = \
17966
{0.28867513, 0.00000000, 0.21081851, -0.07453560};
17967
17968
// Tables of derivatives of the polynomial base (transpose).
17969
static const double dmats0[4][4] = \
17970
{{0.00000000, 0.00000000, 0.00000000, 0.00000000},
17971
{6.32455532, 0.00000000, 0.00000000, 0.00000000},
17972
{0.00000000, 0.00000000, 0.00000000, 0.00000000},
17973
{0.00000000, 0.00000000, 0.00000000, 0.00000000}};
17974
17975
static const double dmats1[4][4] = \
17976
{{0.00000000, 0.00000000, 0.00000000, 0.00000000},
17977
{3.16227766, 0.00000000, 0.00000000, 0.00000000},
17978
{5.47722558, 0.00000000, 0.00000000, 0.00000000},
17979
{0.00000000, 0.00000000, 0.00000000, 0.00000000}};
17980
17981
static const double dmats2[4][4] = \
17982
{{0.00000000, 0.00000000, 0.00000000, 0.00000000},
17983
{3.16227766, 0.00000000, 0.00000000, 0.00000000},
17984
{1.82574186, 0.00000000, 0.00000000, 0.00000000},
17985
{5.16397779, 0.00000000, 0.00000000, 0.00000000}};
17986
17987
// Compute reference derivatives.
17988
// Declare pointer to array of derivatives on FIAT element.
17989
double *derivatives = new double[3*num_derivatives];
17990
for (unsigned int r = 0; r < 3*num_derivatives; r++)
17991
{
17992
derivatives[r] = 0.00000000;
17993
}// end loop over 'r'
17994
17995
// Declare derivative matrix (of polynomial basis).
17996
double dmats[4][4] = \
17997
{{1.00000000, 0.00000000, 0.00000000, 0.00000000},
17998
{0.00000000, 1.00000000, 0.00000000, 0.00000000},
17999
{0.00000000, 0.00000000, 1.00000000, 0.00000000},
18000
{0.00000000, 0.00000000, 0.00000000, 1.00000000}};
18001
18002
// Declare (auxiliary) derivative matrix (of polynomial basis).
18003
double dmats_old[4][4] = \
18004
{{1.00000000, 0.00000000, 0.00000000, 0.00000000},
18005
{0.00000000, 1.00000000, 0.00000000, 0.00000000},
18006
{0.00000000, 0.00000000, 1.00000000, 0.00000000},
18007
{0.00000000, 0.00000000, 0.00000000, 1.00000000}};
18008
18009
// Loop possible derivatives.
18010
for (unsigned int r = 0; r < num_derivatives; r++)
18011
{
18012
// Resetting dmats values to compute next derivative.
18013
for (unsigned int t = 0; t < 4; t++)
18014
{
18015
for (unsigned int u = 0; u < 4; u++)
18016
{
18017
dmats[t][u] = 0.00000000;
18018
if (t == u)
18019
{
18020
dmats[t][u] = 1.00000000;
18021
}
18022
18023
}// end loop over 'u'
18024
}// end loop over 't'
18025
18026
// Looping derivative order to generate dmats.
18027
for (unsigned int s = 0; s < n; s++)
18028
{
18029
// Updating dmats_old with new values and resetting dmats.
18030
for (unsigned int t = 0; t < 4; t++)
18031
{
18032
for (unsigned int u = 0; u < 4; u++)
18033
{
18034
dmats_old[t][u] = dmats[t][u];
18035
dmats[t][u] = 0.00000000;
18036
}// end loop over 'u'
18037
}// end loop over 't'
18038
18039
// Update dmats using an inner product.
18040
if (combinations[r][s] == 0)
18041
{
18042
for (unsigned int t = 0; t < 4; t++)
18043
{
18044
for (unsigned int u = 0; u < 4; u++)
18045
{
18046
for (unsigned int tu = 0; tu < 4; tu++)
18047
{
18048
dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
18049
}// end loop over 'tu'
18050
}// end loop over 'u'
18051
}// end loop over 't'
18052
}
18053
18054
if (combinations[r][s] == 1)
18055
{
18056
for (unsigned int t = 0; t < 4; t++)
18057
{
18058
for (unsigned int u = 0; u < 4; u++)
18059
{
18060
for (unsigned int tu = 0; tu < 4; tu++)
18061
{
18062
dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
18063
}// end loop over 'tu'
18064
}// end loop over 'u'
18065
}// end loop over 't'
18066
}
18067
18068
if (combinations[r][s] == 2)
18069
{
18070
for (unsigned int t = 0; t < 4; t++)
18071
{
18072
for (unsigned int u = 0; u < 4; u++)
18073
{
18074
for (unsigned int tu = 0; tu < 4; tu++)
18075
{
18076
dmats[t][u] += dmats2[t][tu]*dmats_old[tu][u];
18077
}// end loop over 'tu'
18078
}// end loop over 'u'
18079
}// end loop over 't'
18080
}
18081
18082
}// end loop over 's'
18083
for (unsigned int s = 0; s < 4; s++)
18084
{
18085
for (unsigned int t = 0; t < 4; t++)
18086
{
18087
derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
18088
derivatives[num_derivatives + r] += coefficients1[s]*dmats[s][t]*basisvalues[t];
18089
derivatives[2*num_derivatives + r] += coefficients2[s]*dmats[s][t]*basisvalues[t];
18090
}// end loop over 't'
18091
}// end loop over 's'
18092
18093
// Using covariant Piola transform to map values back to the physical element
18094
const double tmp_ref0 = derivatives[r];
18095
const double tmp_ref1 = derivatives[num_derivatives + r];
18096
const double tmp_ref2 = derivatives[2*num_derivatives + r];
18097
derivatives[r] = (K_00*tmp_ref0 + K_10*tmp_ref1 + K_20*tmp_ref2);
18098
derivatives[num_derivatives + r] = (K_01*tmp_ref0 + K_11*tmp_ref1 + K_21*tmp_ref2);
18099
derivatives[2*num_derivatives + r] = (K_02*tmp_ref0 + K_12*tmp_ref1 + K_22*tmp_ref2);
18100
}// end loop over 'r'
18101
18102
// Transform derivatives back to physical element
18103
for (unsigned int r = 0; r < num_derivatives; r++)
18104
{
18105
for (unsigned int s = 0; s < num_derivatives; s++)
18106
{
18107
values[r] += transform[r][s]*derivatives[s];
18108
values[num_derivatives + r] += transform[r][s]*derivatives[num_derivatives + s];
18109
values[2*num_derivatives + r] += transform[r][s]*derivatives[2*num_derivatives + s];
18110
}// end loop over 's'
18111
}// end loop over 'r'
18112
18113
// Delete pointer to array of derivatives on FIAT element
18114
delete [] derivatives;
18115
18116
// Delete pointer to array of combinations of derivatives and transform
18117
for (unsigned int r = 0; r < num_derivatives; r++)
18118
{
18119
delete [] combinations[r];
18120
}// end loop over 'r'
18121
delete [] combinations;
18122
for (unsigned int r = 0; r < num_derivatives; r++)
18123
{
18124
delete [] transform[r];
18125
}// end loop over 'r'
18126
delete [] transform;
18127
break;
18128
}
18129
case 1:
18130
{
18131
18132
// Array of basisvalues.
18133
double basisvalues[4] = {0.00000000, 0.00000000, 0.00000000, 0.00000000};
18134
18135
// Declare helper variables.
18136
unsigned int rr = 0;
18137
unsigned int ss = 0;
18138
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
18139
18140
// Compute basisvalues.
18141
basisvalues[0] = 1.00000000;
18142
basisvalues[1] = tmp0;
18143
for (unsigned int r = 0; r < 1; r++)
18144
{
18145
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
18146
ss = r*(r + 1)*(r + 2)/6;
18147
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
18148
}// end loop over 'r'
18149
for (unsigned int r = 0; r < 1; r++)
18150
{
18151
for (unsigned int s = 0; s < 1 - r; s++)
18152
{
18153
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
18154
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
18155
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
18156
}// end loop over 's'
18157
}// end loop over 'r'
18158
for (unsigned int r = 0; r < 2; r++)
18159
{
18160
for (unsigned int s = 0; s < 2 - r; s++)
18161
{
18162
for (unsigned int t = 0; t < 2 - r - s; t++)
18163
{
18164
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
18165
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
18166
}// end loop over 't'
18167
}// end loop over 's'
18168
}// end loop over 'r'
18169
18170
// Table(s) of coefficients.
18171
static const double coefficients0[4] = \
18172
{-0.28867513, 0.00000000, 0.00000000, -0.22360680};
18173
18174
static const double coefficients1[4] = \
18175
{0.00000000, 0.00000000, 0.00000000, 0.00000000};
18176
18177
static const double coefficients2[4] = \
18178
{0.28867513, 0.18257419, -0.10540926, -0.07453560};
18179
18180
// Tables of derivatives of the polynomial base (transpose).
18181
static const double dmats0[4][4] = \
18182
{{0.00000000, 0.00000000, 0.00000000, 0.00000000},
18183
{6.32455532, 0.00000000, 0.00000000, 0.00000000},
18184
{0.00000000, 0.00000000, 0.00000000, 0.00000000},
18185
{0.00000000, 0.00000000, 0.00000000, 0.00000000}};
18186
18187
static const double dmats1[4][4] = \
18188
{{0.00000000, 0.00000000, 0.00000000, 0.00000000},
18189
{3.16227766, 0.00000000, 0.00000000, 0.00000000},
18190
{5.47722558, 0.00000000, 0.00000000, 0.00000000},
18191
{0.00000000, 0.00000000, 0.00000000, 0.00000000}};
18192
18193
static const double dmats2[4][4] = \
18194
{{0.00000000, 0.00000000, 0.00000000, 0.00000000},
18195
{3.16227766, 0.00000000, 0.00000000, 0.00000000},
18196
{1.82574186, 0.00000000, 0.00000000, 0.00000000},
18197
{5.16397779, 0.00000000, 0.00000000, 0.00000000}};
18198
18199
// Compute reference derivatives.
18200
// Declare pointer to array of derivatives on FIAT element.
18201
double *derivatives = new double[3*num_derivatives];
18202
for (unsigned int r = 0; r < 3*num_derivatives; r++)
18203
{
18204
derivatives[r] = 0.00000000;
18205
}// end loop over 'r'
18206
18207
// Declare derivative matrix (of polynomial basis).
18208
double dmats[4][4] = \
18209
{{1.00000000, 0.00000000, 0.00000000, 0.00000000},
18210
{0.00000000, 1.00000000, 0.00000000, 0.00000000},
18211
{0.00000000, 0.00000000, 1.00000000, 0.00000000},
18212
{0.00000000, 0.00000000, 0.00000000, 1.00000000}};
18213
18214
// Declare (auxiliary) derivative matrix (of polynomial basis).
18215
double dmats_old[4][4] = \
18216
{{1.00000000, 0.00000000, 0.00000000, 0.00000000},
18217
{0.00000000, 1.00000000, 0.00000000, 0.00000000},
18218
{0.00000000, 0.00000000, 1.00000000, 0.00000000},
18219
{0.00000000, 0.00000000, 0.00000000, 1.00000000}};
18220
18221
// Loop possible derivatives.
18222
for (unsigned int r = 0; r < num_derivatives; r++)
18223
{
18224
// Resetting dmats values to compute next derivative.
18225
for (unsigned int t = 0; t < 4; t++)
18226
{
18227
for (unsigned int u = 0; u < 4; u++)
18228
{
18229
dmats[t][u] = 0.00000000;
18230
if (t == u)
18231
{
18232
dmats[t][u] = 1.00000000;
18233
}
18234
18235
}// end loop over 'u'
18236
}// end loop over 't'
18237
18238
// Looping derivative order to generate dmats.
18239
for (unsigned int s = 0; s < n; s++)
18240
{
18241
// Updating dmats_old with new values and resetting dmats.
18242
for (unsigned int t = 0; t < 4; t++)
18243
{
18244
for (unsigned int u = 0; u < 4; u++)
18245
{
18246
dmats_old[t][u] = dmats[t][u];
18247
dmats[t][u] = 0.00000000;
18248
}// end loop over 'u'
18249
}// end loop over 't'
18250
18251
// Update dmats using an inner product.
18252
if (combinations[r][s] == 0)
18253
{
18254
for (unsigned int t = 0; t < 4; t++)
18255
{
18256
for (unsigned int u = 0; u < 4; u++)
18257
{
18258
for (unsigned int tu = 0; tu < 4; tu++)
18259
{
18260
dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
18261
}// end loop over 'tu'
18262
}// end loop over 'u'
18263
}// end loop over 't'
18264
}
18265
18266
if (combinations[r][s] == 1)
18267
{
18268
for (unsigned int t = 0; t < 4; t++)
18269
{
18270
for (unsigned int u = 0; u < 4; u++)
18271
{
18272
for (unsigned int tu = 0; tu < 4; tu++)
18273
{
18274
dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
18275
}// end loop over 'tu'
18276
}// end loop over 'u'
18277
}// end loop over 't'
18278
}
18279
18280
if (combinations[r][s] == 2)
18281
{
18282
for (unsigned int t = 0; t < 4; t++)
18283
{
18284
for (unsigned int u = 0; u < 4; u++)
18285
{
18286
for (unsigned int tu = 0; tu < 4; tu++)
18287
{
18288
dmats[t][u] += dmats2[t][tu]*dmats_old[tu][u];
18289
}// end loop over 'tu'
18290
}// end loop over 'u'
18291
}// end loop over 't'
18292
}
18293
18294
}// end loop over 's'
18295
for (unsigned int s = 0; s < 4; s++)
18296
{
18297
for (unsigned int t = 0; t < 4; t++)
18298
{
18299
derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
18300
derivatives[num_derivatives + r] += coefficients1[s]*dmats[s][t]*basisvalues[t];
18301
derivatives[2*num_derivatives + r] += coefficients2[s]*dmats[s][t]*basisvalues[t];
18302
}// end loop over 't'
18303
}// end loop over 's'
18304
18305
// Using covariant Piola transform to map values back to the physical element
18306
const double tmp_ref0 = derivatives[r];
18307
const double tmp_ref1 = derivatives[num_derivatives + r];
18308
const double tmp_ref2 = derivatives[2*num_derivatives + r];
18309
derivatives[r] = (K_00*tmp_ref0 + K_10*tmp_ref1 + K_20*tmp_ref2);
18310
derivatives[num_derivatives + r] = (K_01*tmp_ref0 + K_11*tmp_ref1 + K_21*tmp_ref2);
18311
derivatives[2*num_derivatives + r] = (K_02*tmp_ref0 + K_12*tmp_ref1 + K_22*tmp_ref2);
18312
}// end loop over 'r'
18313
18314
// Transform derivatives back to physical element
18315
for (unsigned int r = 0; r < num_derivatives; r++)
18316
{
18317
for (unsigned int s = 0; s < num_derivatives; s++)
18318
{
18319
values[r] += transform[r][s]*derivatives[s];
18320
values[num_derivatives + r] += transform[r][s]*derivatives[num_derivatives + s];
18321
values[2*num_derivatives + r] += transform[r][s]*derivatives[2*num_derivatives + s];
18322
}// end loop over 's'
18323
}// end loop over 'r'
18324
18325
// Delete pointer to array of derivatives on FIAT element
18326
delete [] derivatives;
18327
18328
// Delete pointer to array of combinations of derivatives and transform
18329
for (unsigned int r = 0; r < num_derivatives; r++)
18330
{
18331
delete [] combinations[r];
18332
}// end loop over 'r'
18333
delete [] combinations;
18334
for (unsigned int r = 0; r < num_derivatives; r++)
18335
{
18336
delete [] transform[r];
18337
}// end loop over 'r'
18338
delete [] transform;
18339
break;
18340
}
18341
case 2:
18342
{
18343
18344
// Array of basisvalues.
18345
double basisvalues[4] = {0.00000000, 0.00000000, 0.00000000, 0.00000000};
18346
18347
// Declare helper variables.
18348
unsigned int rr = 0;
18349
unsigned int ss = 0;
18350
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
18351
18352
// Compute basisvalues.
18353
basisvalues[0] = 1.00000000;
18354
basisvalues[1] = tmp0;
18355
for (unsigned int r = 0; r < 1; r++)
18356
{
18357
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
18358
ss = r*(r + 1)*(r + 2)/6;
18359
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
18360
}// end loop over 'r'
18361
for (unsigned int r = 0; r < 1; r++)
18362
{
18363
for (unsigned int s = 0; s < 1 - r; s++)
18364
{
18365
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
18366
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
18367
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
18368
}// end loop over 's'
18369
}// end loop over 'r'
18370
for (unsigned int r = 0; r < 2; r++)
18371
{
18372
for (unsigned int s = 0; s < 2 - r; s++)
18373
{
18374
for (unsigned int t = 0; t < 2 - r - s; t++)
18375
{
18376
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
18377
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
18378
}// end loop over 't'
18379
}// end loop over 's'
18380
}// end loop over 'r'
18381
18382
// Table(s) of coefficients.
18383
static const double coefficients0[4] = \
18384
{-0.28867513, 0.00000000, -0.21081851, 0.07453560};
18385
18386
static const double coefficients1[4] = \
18387
{0.28867513, 0.18257419, -0.10540926, -0.07453560};
18388
18389
static const double coefficients2[4] = \
18390
{0.00000000, 0.00000000, 0.00000000, 0.00000000};
18391
18392
// Tables of derivatives of the polynomial base (transpose).
18393
static const double dmats0[4][4] = \
18394
{{0.00000000, 0.00000000, 0.00000000, 0.00000000},
18395
{6.32455532, 0.00000000, 0.00000000, 0.00000000},
18396
{0.00000000, 0.00000000, 0.00000000, 0.00000000},
18397
{0.00000000, 0.00000000, 0.00000000, 0.00000000}};
18398
18399
static const double dmats1[4][4] = \
18400
{{0.00000000, 0.00000000, 0.00000000, 0.00000000},
18401
{3.16227766, 0.00000000, 0.00000000, 0.00000000},
18402
{5.47722558, 0.00000000, 0.00000000, 0.00000000},
18403
{0.00000000, 0.00000000, 0.00000000, 0.00000000}};
18404
18405
static const double dmats2[4][4] = \
18406
{{0.00000000, 0.00000000, 0.00000000, 0.00000000},
18407
{3.16227766, 0.00000000, 0.00000000, 0.00000000},
18408
{1.82574186, 0.00000000, 0.00000000, 0.00000000},
18409
{5.16397779, 0.00000000, 0.00000000, 0.00000000}};
18410
18411
// Compute reference derivatives.
18412
// Declare pointer to array of derivatives on FIAT element.
18413
double *derivatives = new double[3*num_derivatives];
18414
for (unsigned int r = 0; r < 3*num_derivatives; r++)
18415
{
18416
derivatives[r] = 0.00000000;
18417
}// end loop over 'r'
18418
18419
// Declare derivative matrix (of polynomial basis).
18420
double dmats[4][4] = \
18421
{{1.00000000, 0.00000000, 0.00000000, 0.00000000},
18422
{0.00000000, 1.00000000, 0.00000000, 0.00000000},
18423
{0.00000000, 0.00000000, 1.00000000, 0.00000000},
18424
{0.00000000, 0.00000000, 0.00000000, 1.00000000}};
18425
18426
// Declare (auxiliary) derivative matrix (of polynomial basis).
18427
double dmats_old[4][4] = \
18428
{{1.00000000, 0.00000000, 0.00000000, 0.00000000},
18429
{0.00000000, 1.00000000, 0.00000000, 0.00000000},
18430
{0.00000000, 0.00000000, 1.00000000, 0.00000000},
18431
{0.00000000, 0.00000000, 0.00000000, 1.00000000}};
18432
18433
// Loop possible derivatives.
18434
for (unsigned int r = 0; r < num_derivatives; r++)
18435
{
18436
// Resetting dmats values to compute next derivative.
18437
for (unsigned int t = 0; t < 4; t++)
18438
{
18439
for (unsigned int u = 0; u < 4; u++)
18440
{
18441
dmats[t][u] = 0.00000000;
18442
if (t == u)
18443
{
18444
dmats[t][u] = 1.00000000;
18445
}
18446
18447
}// end loop over 'u'
18448
}// end loop over 't'
18449
18450
// Looping derivative order to generate dmats.
18451
for (unsigned int s = 0; s < n; s++)
18452
{
18453
// Updating dmats_old with new values and resetting dmats.
18454
for (unsigned int t = 0; t < 4; t++)
18455
{
18456
for (unsigned int u = 0; u < 4; u++)
18457
{
18458
dmats_old[t][u] = dmats[t][u];
18459
dmats[t][u] = 0.00000000;
18460
}// end loop over 'u'
18461
}// end loop over 't'
18462
18463
// Update dmats using an inner product.
18464
if (combinations[r][s] == 0)
18465
{
18466
for (unsigned int t = 0; t < 4; t++)
18467
{
18468
for (unsigned int u = 0; u < 4; u++)
18469
{
18470
for (unsigned int tu = 0; tu < 4; tu++)
18471
{
18472
dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
18473
}// end loop over 'tu'
18474
}// end loop over 'u'
18475
}// end loop over 't'
18476
}
18477
18478
if (combinations[r][s] == 1)
18479
{
18480
for (unsigned int t = 0; t < 4; t++)
18481
{
18482
for (unsigned int u = 0; u < 4; u++)
18483
{
18484
for (unsigned int tu = 0; tu < 4; tu++)
18485
{
18486
dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
18487
}// end loop over 'tu'
18488
}// end loop over 'u'
18489
}// end loop over 't'
18490
}
18491
18492
if (combinations[r][s] == 2)
18493
{
18494
for (unsigned int t = 0; t < 4; t++)
18495
{
18496
for (unsigned int u = 0; u < 4; u++)
18497
{
18498
for (unsigned int tu = 0; tu < 4; tu++)
18499
{
18500
dmats[t][u] += dmats2[t][tu]*dmats_old[tu][u];
18501
}// end loop over 'tu'
18502
}// end loop over 'u'
18503
}// end loop over 't'
18504
}
18505
18506
}// end loop over 's'
18507
for (unsigned int s = 0; s < 4; s++)
18508
{
18509
for (unsigned int t = 0; t < 4; t++)
18510
{
18511
derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
18512
derivatives[num_derivatives + r] += coefficients1[s]*dmats[s][t]*basisvalues[t];
18513
derivatives[2*num_derivatives + r] += coefficients2[s]*dmats[s][t]*basisvalues[t];
18514
}// end loop over 't'
18515
}// end loop over 's'
18516
18517
// Using covariant Piola transform to map values back to the physical element
18518
const double tmp_ref0 = derivatives[r];
18519
const double tmp_ref1 = derivatives[num_derivatives + r];
18520
const double tmp_ref2 = derivatives[2*num_derivatives + r];
18521
derivatives[r] = (K_00*tmp_ref0 + K_10*tmp_ref1 + K_20*tmp_ref2);
18522
derivatives[num_derivatives + r] = (K_01*tmp_ref0 + K_11*tmp_ref1 + K_21*tmp_ref2);
18523
derivatives[2*num_derivatives + r] = (K_02*tmp_ref0 + K_12*tmp_ref1 + K_22*tmp_ref2);
18524
}// end loop over 'r'
18525
18526
// Transform derivatives back to physical element
18527
for (unsigned int r = 0; r < num_derivatives; r++)
18528
{
18529
for (unsigned int s = 0; s < num_derivatives; s++)
18530
{
18531
values[r] += transform[r][s]*derivatives[s];
18532
values[num_derivatives + r] += transform[r][s]*derivatives[num_derivatives + s];
18533
values[2*num_derivatives + r] += transform[r][s]*derivatives[2*num_derivatives + s];
18534
}// end loop over 's'
18535
}// end loop over 'r'
18536
18537
// Delete pointer to array of derivatives on FIAT element
18538
delete [] derivatives;
18539
18540
// Delete pointer to array of combinations of derivatives and transform
18541
for (unsigned int r = 0; r < num_derivatives; r++)
18542
{
18543
delete [] combinations[r];
18544
}// end loop over 'r'
18545
delete [] combinations;
18546
for (unsigned int r = 0; r < num_derivatives; r++)
18547
{
18548
delete [] transform[r];
18549
}// end loop over 'r'
18550
delete [] transform;
18551
break;
18552
}
18553
case 3:
18554
{
18555
18556
// Array of basisvalues.
18557
double basisvalues[4] = {0.00000000, 0.00000000, 0.00000000, 0.00000000};
18558
18559
// Declare helper variables.
18560
unsigned int rr = 0;
18561
unsigned int ss = 0;
18562
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
18563
18564
// Compute basisvalues.
18565
basisvalues[0] = 1.00000000;
18566
basisvalues[1] = tmp0;
18567
for (unsigned int r = 0; r < 1; r++)
18568
{
18569
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
18570
ss = r*(r + 1)*(r + 2)/6;
18571
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
18572
}// end loop over 'r'
18573
for (unsigned int r = 0; r < 1; r++)
18574
{
18575
for (unsigned int s = 0; s < 1 - r; s++)
18576
{
18577
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
18578
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
18579
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
18580
}// end loop over 's'
18581
}// end loop over 'r'
18582
for (unsigned int r = 0; r < 2; r++)
18583
{
18584
for (unsigned int s = 0; s < 2 - r; s++)
18585
{
18586
for (unsigned int t = 0; t < 2 - r - s; t++)
18587
{
18588
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
18589
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
18590
}// end loop over 't'
18591
}// end loop over 's'
18592
}// end loop over 'r'
18593
18594
// Table(s) of coefficients.
18595
static const double coefficients0[4] = \
18596
{0.28867513, 0.00000000, 0.00000000, 0.22360680};
18597
18598
static const double coefficients1[4] = \
18599
{0.28867513, 0.00000000, 0.00000000, 0.22360680};
18600
18601
static const double coefficients2[4] = \
18602
{0.57735027, -0.18257419, -0.10540926, 0.14907120};
18603
18604
// Tables of derivatives of the polynomial base (transpose).
18605
static const double dmats0[4][4] = \
18606
{{0.00000000, 0.00000000, 0.00000000, 0.00000000},
18607
{6.32455532, 0.00000000, 0.00000000, 0.00000000},
18608
{0.00000000, 0.00000000, 0.00000000, 0.00000000},
18609
{0.00000000, 0.00000000, 0.00000000, 0.00000000}};
18610
18611
static const double dmats1[4][4] = \
18612
{{0.00000000, 0.00000000, 0.00000000, 0.00000000},
18613
{3.16227766, 0.00000000, 0.00000000, 0.00000000},
18614
{5.47722558, 0.00000000, 0.00000000, 0.00000000},
18615
{0.00000000, 0.00000000, 0.00000000, 0.00000000}};
18616
18617
static const double dmats2[4][4] = \
18618
{{0.00000000, 0.00000000, 0.00000000, 0.00000000},
18619
{3.16227766, 0.00000000, 0.00000000, 0.00000000},
18620
{1.82574186, 0.00000000, 0.00000000, 0.00000000},
18621
{5.16397779, 0.00000000, 0.00000000, 0.00000000}};
18622
18623
// Compute reference derivatives.
18624
// Declare pointer to array of derivatives on FIAT element.
18625
double *derivatives = new double[3*num_derivatives];
18626
for (unsigned int r = 0; r < 3*num_derivatives; r++)
18627
{
18628
derivatives[r] = 0.00000000;
18629
}// end loop over 'r'
18630
18631
// Declare derivative matrix (of polynomial basis).
18632
double dmats[4][4] = \
18633
{{1.00000000, 0.00000000, 0.00000000, 0.00000000},
18634
{0.00000000, 1.00000000, 0.00000000, 0.00000000},
18635
{0.00000000, 0.00000000, 1.00000000, 0.00000000},
18636
{0.00000000, 0.00000000, 0.00000000, 1.00000000}};
18637
18638
// Declare (auxiliary) derivative matrix (of polynomial basis).
18639
double dmats_old[4][4] = \
18640
{{1.00000000, 0.00000000, 0.00000000, 0.00000000},
18641
{0.00000000, 1.00000000, 0.00000000, 0.00000000},
18642
{0.00000000, 0.00000000, 1.00000000, 0.00000000},
18643
{0.00000000, 0.00000000, 0.00000000, 1.00000000}};
18644
18645
// Loop possible derivatives.
18646
for (unsigned int r = 0; r < num_derivatives; r++)
18647
{
18648
// Resetting dmats values to compute next derivative.
18649
for (unsigned int t = 0; t < 4; t++)
18650
{
18651
for (unsigned int u = 0; u < 4; u++)
18652
{
18653
dmats[t][u] = 0.00000000;
18654
if (t == u)
18655
{
18656
dmats[t][u] = 1.00000000;
18657
}
18658
18659
}// end loop over 'u'
18660
}// end loop over 't'
18661
18662
// Looping derivative order to generate dmats.
18663
for (unsigned int s = 0; s < n; s++)
18664
{
18665
// Updating dmats_old with new values and resetting dmats.
18666
for (unsigned int t = 0; t < 4; t++)
18667
{
18668
for (unsigned int u = 0; u < 4; u++)
18669
{
18670
dmats_old[t][u] = dmats[t][u];
18671
dmats[t][u] = 0.00000000;
18672
}// end loop over 'u'
18673
}// end loop over 't'
18674
18675
// Update dmats using an inner product.
18676
if (combinations[r][s] == 0)
18677
{
18678
for (unsigned int t = 0; t < 4; t++)
18679
{
18680
for (unsigned int u = 0; u < 4; u++)
18681
{
18682
for (unsigned int tu = 0; tu < 4; tu++)
18683
{
18684
dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
18685
}// end loop over 'tu'
18686
}// end loop over 'u'
18687
}// end loop over 't'
18688
}
18689
18690
if (combinations[r][s] == 1)
18691
{
18692
for (unsigned int t = 0; t < 4; t++)
18693
{
18694
for (unsigned int u = 0; u < 4; u++)
18695
{
18696
for (unsigned int tu = 0; tu < 4; tu++)
18697
{
18698
dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
18699
}// end loop over 'tu'
18700
}// end loop over 'u'
18701
}// end loop over 't'
18702
}
18703
18704
if (combinations[r][s] == 2)
18705
{
18706
for (unsigned int t = 0; t < 4; t++)
18707
{
18708
for (unsigned int u = 0; u < 4; u++)
18709
{
18710
for (unsigned int tu = 0; tu < 4; tu++)
18711
{
18712
dmats[t][u] += dmats2[t][tu]*dmats_old[tu][u];
18713
}// end loop over 'tu'
18714
}// end loop over 'u'
18715
}// end loop over 't'
18716
}
18717
18718
}// end loop over 's'
18719
for (unsigned int s = 0; s < 4; s++)
18720
{
18721
for (unsigned int t = 0; t < 4; t++)
18722
{
18723
derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
18724
derivatives[num_derivatives + r] += coefficients1[s]*dmats[s][t]*basisvalues[t];
18725
derivatives[2*num_derivatives + r] += coefficients2[s]*dmats[s][t]*basisvalues[t];
18726
}// end loop over 't'
18727
}// end loop over 's'
18728
18729
// Using covariant Piola transform to map values back to the physical element
18730
const double tmp_ref0 = derivatives[r];
18731
const double tmp_ref1 = derivatives[num_derivatives + r];
18732
const double tmp_ref2 = derivatives[2*num_derivatives + r];
18733
derivatives[r] = (K_00*tmp_ref0 + K_10*tmp_ref1 + K_20*tmp_ref2);
18734
derivatives[num_derivatives + r] = (K_01*tmp_ref0 + K_11*tmp_ref1 + K_21*tmp_ref2);
18735
derivatives[2*num_derivatives + r] = (K_02*tmp_ref0 + K_12*tmp_ref1 + K_22*tmp_ref2);
18736
}// end loop over 'r'
18737
18738
// Transform derivatives back to physical element
18739
for (unsigned int r = 0; r < num_derivatives; r++)
18740
{
18741
for (unsigned int s = 0; s < num_derivatives; s++)
18742
{
18743
values[r] += transform[r][s]*derivatives[s];
18744
values[num_derivatives + r] += transform[r][s]*derivatives[num_derivatives + s];
18745
values[2*num_derivatives + r] += transform[r][s]*derivatives[2*num_derivatives + s];
18746
}// end loop over 's'
18747
}// end loop over 'r'
18748
18749
// Delete pointer to array of derivatives on FIAT element
18750
delete [] derivatives;
18751
18752
// Delete pointer to array of combinations of derivatives and transform
18753
for (unsigned int r = 0; r < num_derivatives; r++)
18754
{
18755
delete [] combinations[r];
18756
}// end loop over 'r'
18757
delete [] combinations;
18758
for (unsigned int r = 0; r < num_derivatives; r++)
18759
{
18760
delete [] transform[r];
18761
}// end loop over 'r'
18762
delete [] transform;
18763
break;
18764
}
18765
case 4:
18766
{
18767
18768
// Array of basisvalues.
18769
double basisvalues[4] = {0.00000000, 0.00000000, 0.00000000, 0.00000000};
18770
18771
// Declare helper variables.
18772
unsigned int rr = 0;
18773
unsigned int ss = 0;
18774
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
18775
18776
// Compute basisvalues.
18777
basisvalues[0] = 1.00000000;
18778
basisvalues[1] = tmp0;
18779
for (unsigned int r = 0; r < 1; r++)
18780
{
18781
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
18782
ss = r*(r + 1)*(r + 2)/6;
18783
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
18784
}// end loop over 'r'
18785
for (unsigned int r = 0; r < 1; r++)
18786
{
18787
for (unsigned int s = 0; s < 1 - r; s++)
18788
{
18789
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
18790
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
18791
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
18792
}// end loop over 's'
18793
}// end loop over 'r'
18794
for (unsigned int r = 0; r < 2; r++)
18795
{
18796
for (unsigned int s = 0; s < 2 - r; s++)
18797
{
18798
for (unsigned int t = 0; t < 2 - r - s; t++)
18799
{
18800
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
18801
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
18802
}// end loop over 't'
18803
}// end loop over 's'
18804
}// end loop over 'r'
18805
18806
// Table(s) of coefficients.
18807
static const double coefficients0[4] = \
18808
{0.28867513, 0.00000000, 0.21081851, -0.07453560};
18809
18810
static const double coefficients1[4] = \
18811
{0.57735027, -0.18257419, 0.10540926, -0.14907120};
18812
18813
static const double coefficients2[4] = \
18814
{0.28867513, 0.00000000, 0.21081851, -0.07453560};
18815
18816
// Tables of derivatives of the polynomial base (transpose).
18817
static const double dmats0[4][4] = \
18818
{{0.00000000, 0.00000000, 0.00000000, 0.00000000},
18819
{6.32455532, 0.00000000, 0.00000000, 0.00000000},
18820
{0.00000000, 0.00000000, 0.00000000, 0.00000000},
18821
{0.00000000, 0.00000000, 0.00000000, 0.00000000}};
18822
18823
static const double dmats1[4][4] = \
18824
{{0.00000000, 0.00000000, 0.00000000, 0.00000000},
18825
{3.16227766, 0.00000000, 0.00000000, 0.00000000},
18826
{5.47722558, 0.00000000, 0.00000000, 0.00000000},
18827
{0.00000000, 0.00000000, 0.00000000, 0.00000000}};
18828
18829
static const double dmats2[4][4] = \
18830
{{0.00000000, 0.00000000, 0.00000000, 0.00000000},
18831
{3.16227766, 0.00000000, 0.00000000, 0.00000000},
18832
{1.82574186, 0.00000000, 0.00000000, 0.00000000},
18833
{5.16397779, 0.00000000, 0.00000000, 0.00000000}};
18834
18835
// Compute reference derivatives.
18836
// Declare pointer to array of derivatives on FIAT element.
18837
double *derivatives = new double[3*num_derivatives];
18838
for (unsigned int r = 0; r < 3*num_derivatives; r++)
18839
{
18840
derivatives[r] = 0.00000000;
18841
}// end loop over 'r'
18842
18843
// Declare derivative matrix (of polynomial basis).
18844
double dmats[4][4] = \
18845
{{1.00000000, 0.00000000, 0.00000000, 0.00000000},
18846
{0.00000000, 1.00000000, 0.00000000, 0.00000000},
18847
{0.00000000, 0.00000000, 1.00000000, 0.00000000},
18848
{0.00000000, 0.00000000, 0.00000000, 1.00000000}};
18849
18850
// Declare (auxiliary) derivative matrix (of polynomial basis).
18851
double dmats_old[4][4] = \
18852
{{1.00000000, 0.00000000, 0.00000000, 0.00000000},
18853
{0.00000000, 1.00000000, 0.00000000, 0.00000000},
18854
{0.00000000, 0.00000000, 1.00000000, 0.00000000},
18855
{0.00000000, 0.00000000, 0.00000000, 1.00000000}};
18856
18857
// Loop possible derivatives.
18858
for (unsigned int r = 0; r < num_derivatives; r++)
18859
{
18860
// Resetting dmats values to compute next derivative.
18861
for (unsigned int t = 0; t < 4; t++)
18862
{
18863
for (unsigned int u = 0; u < 4; u++)
18864
{
18865
dmats[t][u] = 0.00000000;
18866
if (t == u)
18867
{
18868
dmats[t][u] = 1.00000000;
18869
}
18870
18871
}// end loop over 'u'
18872
}// end loop over 't'
18873
18874
// Looping derivative order to generate dmats.
18875
for (unsigned int s = 0; s < n; s++)
18876
{
18877
// Updating dmats_old with new values and resetting dmats.
18878
for (unsigned int t = 0; t < 4; t++)
18879
{
18880
for (unsigned int u = 0; u < 4; u++)
18881
{
18882
dmats_old[t][u] = dmats[t][u];
18883
dmats[t][u] = 0.00000000;
18884
}// end loop over 'u'
18885
}// end loop over 't'
18886
18887
// Update dmats using an inner product.
18888
if (combinations[r][s] == 0)
18889
{
18890
for (unsigned int t = 0; t < 4; t++)
18891
{
18892
for (unsigned int u = 0; u < 4; u++)
18893
{
18894
for (unsigned int tu = 0; tu < 4; tu++)
18895
{
18896
dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
18897
}// end loop over 'tu'
18898
}// end loop over 'u'
18899
}// end loop over 't'
18900
}
18901
18902
if (combinations[r][s] == 1)
18903
{
18904
for (unsigned int t = 0; t < 4; t++)
18905
{
18906
for (unsigned int u = 0; u < 4; u++)
18907
{
18908
for (unsigned int tu = 0; tu < 4; tu++)
18909
{
18910
dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
18911
}// end loop over 'tu'
18912
}// end loop over 'u'
18913
}// end loop over 't'
18914
}
18915
18916
if (combinations[r][s] == 2)
18917
{
18918
for (unsigned int t = 0; t < 4; t++)
18919
{
18920
for (unsigned int u = 0; u < 4; u++)
18921
{
18922
for (unsigned int tu = 0; tu < 4; tu++)
18923
{
18924
dmats[t][u] += dmats2[t][tu]*dmats_old[tu][u];
18925
}// end loop over 'tu'
18926
}// end loop over 'u'
18927
}// end loop over 't'
18928
}
18929
18930
}// end loop over 's'
18931
for (unsigned int s = 0; s < 4; s++)
18932
{
18933
for (unsigned int t = 0; t < 4; t++)
18934
{
18935
derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
18936
derivatives[num_derivatives + r] += coefficients1[s]*dmats[s][t]*basisvalues[t];
18937
derivatives[2*num_derivatives + r] += coefficients2[s]*dmats[s][t]*basisvalues[t];
18938
}// end loop over 't'
18939
}// end loop over 's'
18940
18941
// Using covariant Piola transform to map values back to the physical element
18942
const double tmp_ref0 = derivatives[r];
18943
const double tmp_ref1 = derivatives[num_derivatives + r];
18944
const double tmp_ref2 = derivatives[2*num_derivatives + r];
18945
derivatives[r] = (K_00*tmp_ref0 + K_10*tmp_ref1 + K_20*tmp_ref2);
18946
derivatives[num_derivatives + r] = (K_01*tmp_ref0 + K_11*tmp_ref1 + K_21*tmp_ref2);
18947
derivatives[2*num_derivatives + r] = (K_02*tmp_ref0 + K_12*tmp_ref1 + K_22*tmp_ref2);
18948
}// end loop over 'r'
18949
18950
// Transform derivatives back to physical element
18951
for (unsigned int r = 0; r < num_derivatives; r++)
18952
{
18953
for (unsigned int s = 0; s < num_derivatives; s++)
18954
{
18955
values[r] += transform[r][s]*derivatives[s];
18956
values[num_derivatives + r] += transform[r][s]*derivatives[num_derivatives + s];
18957
values[2*num_derivatives + r] += transform[r][s]*derivatives[2*num_derivatives + s];
18958
}// end loop over 's'
18959
}// end loop over 'r'
18960
18961
// Delete pointer to array of derivatives on FIAT element
18962
delete [] derivatives;
18963
18964
// Delete pointer to array of combinations of derivatives and transform
18965
for (unsigned int r = 0; r < num_derivatives; r++)
18966
{
18967
delete [] combinations[r];
18968
}// end loop over 'r'
18969
delete [] combinations;
18970
for (unsigned int r = 0; r < num_derivatives; r++)
18971
{
18972
delete [] transform[r];
18973
}// end loop over 'r'
18974
delete [] transform;
18975
break;
18976
}
18977
case 5:
18978
{
18979
18980
// Array of basisvalues.
18981
double basisvalues[4] = {0.00000000, 0.00000000, 0.00000000, 0.00000000};
18982
18983
// Declare helper variables.
18984
unsigned int rr = 0;
18985
unsigned int ss = 0;
18986
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
18987
18988
// Compute basisvalues.
18989
basisvalues[0] = 1.00000000;
18990
basisvalues[1] = tmp0;
18991
for (unsigned int r = 0; r < 1; r++)
18992
{
18993
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
18994
ss = r*(r + 1)*(r + 2)/6;
18995
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
18996
}// end loop over 'r'
18997
for (unsigned int r = 0; r < 1; r++)
18998
{
18999
for (unsigned int s = 0; s < 1 - r; s++)
19000
{
19001
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
19002
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
19003
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
19004
}// end loop over 's'
19005
}// end loop over 'r'
19006
for (unsigned int r = 0; r < 2; r++)
19007
{
19008
for (unsigned int s = 0; s < 2 - r; s++)
19009
{
19010
for (unsigned int t = 0; t < 2 - r - s; t++)
19011
{
19012
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
19013
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
19014
}// end loop over 't'
19015
}// end loop over 's'
19016
}// end loop over 'r'
19017
19018
// Table(s) of coefficients.
19019
static const double coefficients0[4] = \
19020
{0.57735027, 0.00000000, -0.21081851, -0.14907120};
19021
19022
static const double coefficients1[4] = \
19023
{0.28867513, 0.18257419, -0.10540926, -0.07453560};
19024
19025
static const double coefficients2[4] = \
19026
{0.28867513, 0.18257419, -0.10540926, -0.07453560};
19027
19028
// Tables of derivatives of the polynomial base (transpose).
19029
static const double dmats0[4][4] = \
19030
{{0.00000000, 0.00000000, 0.00000000, 0.00000000},
19031
{6.32455532, 0.00000000, 0.00000000, 0.00000000},
19032
{0.00000000, 0.00000000, 0.00000000, 0.00000000},
19033
{0.00000000, 0.00000000, 0.00000000, 0.00000000}};
19034
19035
static const double dmats1[4][4] = \
19036
{{0.00000000, 0.00000000, 0.00000000, 0.00000000},
19037
{3.16227766, 0.00000000, 0.00000000, 0.00000000},
19038
{5.47722558, 0.00000000, 0.00000000, 0.00000000},
19039
{0.00000000, 0.00000000, 0.00000000, 0.00000000}};
19040
19041
static const double dmats2[4][4] = \
19042
{{0.00000000, 0.00000000, 0.00000000, 0.00000000},
19043
{3.16227766, 0.00000000, 0.00000000, 0.00000000},
19044
{1.82574186, 0.00000000, 0.00000000, 0.00000000},
19045
{5.16397779, 0.00000000, 0.00000000, 0.00000000}};
19046
19047
// Compute reference derivatives.
19048
// Declare pointer to array of derivatives on FIAT element.
19049
double *derivatives = new double[3*num_derivatives];
19050
for (unsigned int r = 0; r < 3*num_derivatives; r++)
19051
{
19052
derivatives[r] = 0.00000000;
19053
}// end loop over 'r'
19054
19055
// Declare derivative matrix (of polynomial basis).
19056
double dmats[4][4] = \
19057
{{1.00000000, 0.00000000, 0.00000000, 0.00000000},
19058
{0.00000000, 1.00000000, 0.00000000, 0.00000000},
19059
{0.00000000, 0.00000000, 1.00000000, 0.00000000},
19060
{0.00000000, 0.00000000, 0.00000000, 1.00000000}};
19061
19062
// Declare (auxiliary) derivative matrix (of polynomial basis).
19063
double dmats_old[4][4] = \
19064
{{1.00000000, 0.00000000, 0.00000000, 0.00000000},
19065
{0.00000000, 1.00000000, 0.00000000, 0.00000000},
19066
{0.00000000, 0.00000000, 1.00000000, 0.00000000},
19067
{0.00000000, 0.00000000, 0.00000000, 1.00000000}};
19068
19069
// Loop possible derivatives.
19070
for (unsigned int r = 0; r < num_derivatives; r++)
19071
{
19072
// Resetting dmats values to compute next derivative.
19073
for (unsigned int t = 0; t < 4; t++)
19074
{
19075
for (unsigned int u = 0; u < 4; u++)
19076
{
19077
dmats[t][u] = 0.00000000;
19078
if (t == u)
19079
{
19080
dmats[t][u] = 1.00000000;
19081
}
19082
19083
}// end loop over 'u'
19084
}// end loop over 't'
19085
19086
// Looping derivative order to generate dmats.
19087
for (unsigned int s = 0; s < n; s++)
19088
{
19089
// Updating dmats_old with new values and resetting dmats.
19090
for (unsigned int t = 0; t < 4; t++)
19091
{
19092
for (unsigned int u = 0; u < 4; u++)
19093
{
19094
dmats_old[t][u] = dmats[t][u];
19095
dmats[t][u] = 0.00000000;
19096
}// end loop over 'u'
19097
}// end loop over 't'
19098
19099
// Update dmats using an inner product.
19100
if (combinations[r][s] == 0)
19101
{
19102
for (unsigned int t = 0; t < 4; t++)
19103
{
19104
for (unsigned int u = 0; u < 4; u++)
19105
{
19106
for (unsigned int tu = 0; tu < 4; tu++)
19107
{
19108
dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
19109
}// end loop over 'tu'
19110
}// end loop over 'u'
19111
}// end loop over 't'
19112
}
19113
19114
if (combinations[r][s] == 1)
19115
{
19116
for (unsigned int t = 0; t < 4; t++)
19117
{
19118
for (unsigned int u = 0; u < 4; u++)
19119
{
19120
for (unsigned int tu = 0; tu < 4; tu++)
19121
{
19122
dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
19123
}// end loop over 'tu'
19124
}// end loop over 'u'
19125
}// end loop over 't'
19126
}
19127
19128
if (combinations[r][s] == 2)
19129
{
19130
for (unsigned int t = 0; t < 4; t++)
19131
{
19132
for (unsigned int u = 0; u < 4; u++)
19133
{
19134
for (unsigned int tu = 0; tu < 4; tu++)
19135
{
19136
dmats[t][u] += dmats2[t][tu]*dmats_old[tu][u];
19137
}// end loop over 'tu'
19138
}// end loop over 'u'
19139
}// end loop over 't'
19140
}
19141
19142
}// end loop over 's'
19143
for (unsigned int s = 0; s < 4; s++)
19144
{
19145
for (unsigned int t = 0; t < 4; t++)
19146
{
19147
derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
19148
derivatives[num_derivatives + r] += coefficients1[s]*dmats[s][t]*basisvalues[t];
19149
derivatives[2*num_derivatives + r] += coefficients2[s]*dmats[s][t]*basisvalues[t];
19150
}// end loop over 't'
19151
}// end loop over 's'
19152
19153
// Using covariant Piola transform to map values back to the physical element
19154
const double tmp_ref0 = derivatives[r];
19155
const double tmp_ref1 = derivatives[num_derivatives + r];
19156
const double tmp_ref2 = derivatives[2*num_derivatives + r];
19157
derivatives[r] = (K_00*tmp_ref0 + K_10*tmp_ref1 + K_20*tmp_ref2);
19158
derivatives[num_derivatives + r] = (K_01*tmp_ref0 + K_11*tmp_ref1 + K_21*tmp_ref2);
19159
derivatives[2*num_derivatives + r] = (K_02*tmp_ref0 + K_12*tmp_ref1 + K_22*tmp_ref2);
19160
}// end loop over 'r'
19161
19162
// Transform derivatives back to physical element
19163
for (unsigned int r = 0; r < num_derivatives; r++)
19164
{
19165
for (unsigned int s = 0; s < num_derivatives; s++)
19166
{
19167
values[r] += transform[r][s]*derivatives[s];
19168
values[num_derivatives + r] += transform[r][s]*derivatives[num_derivatives + s];
19169
values[2*num_derivatives + r] += transform[r][s]*derivatives[2*num_derivatives + s];
19170
}// end loop over 's'
19171
}// end loop over 'r'
19172
19173
// Delete pointer to array of derivatives on FIAT element
19174
delete [] derivatives;
19175
19176
// Delete pointer to array of combinations of derivatives and transform
19177
for (unsigned int r = 0; r < num_derivatives; r++)
19178
{
19179
delete [] combinations[r];
19180
}// end loop over 'r'
19181
delete [] combinations;
19182
for (unsigned int r = 0; r < num_derivatives; r++)
19183
{
19184
delete [] transform[r];
19185
}// end loop over 'r'
19186
delete [] transform;
19187
break;
19188
}
19189
}
19190
4028
19191
}
4029
19192
4030
19193
/// Evaluate order n derivatives of all basis functions at given point in cell
4402
19565
values[1] = 0.00000000;
4403
19566
values[2] = 0.00000000;
4404
19567
values[3] = 0.00000000;
4405
if (0 <= i && i <= 3)
4406
{
4407
// Map degree of freedom to element degree of freedom
4408
const unsigned int dof = i;
4409
4410
// Array of basisvalues.
4411
double basisvalues[4] = {0.00000000, 0.00000000, 0.00000000, 0.00000000};
4412
4413
// Declare helper variables.
4414
unsigned int rr = 0;
4415
unsigned int ss = 0;
4416
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
4417
4418
// Compute basisvalues.
4419
basisvalues[0] = 1.00000000;
4420
basisvalues[1] = tmp0;
4421
for (unsigned int r = 0; r < 1; r++)
4422
{
4423
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
4424
ss = r*(r + 1)*(r + 2)/6;
4425
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
4426
}// end loop over 'r'
4427
for (unsigned int r = 0; r < 1; r++)
4428
{
4429
for (unsigned int s = 0; s < 1 - r; s++)
4430
{
4431
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
4432
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
4433
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
4434
}// end loop over 's'
4435
}// end loop over 'r'
4436
for (unsigned int r = 0; r < 2; r++)
4437
{
4438
for (unsigned int s = 0; s < 2 - r; s++)
4439
{
4440
for (unsigned int t = 0; t < 2 - r - s; t++)
4441
{
4442
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
4443
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
4444
}// end loop over 't'
4445
}// end loop over 's'
4446
}// end loop over 'r'
4447
4448
// Table(s) of coefficients.
4449
static const double coefficients0[4][4] = \
4450
{{0.28867513, -0.18257419, -0.10540926, -0.07453560},
4451
{0.28867513, 0.18257419, -0.10540926, -0.07453560},
4452
{0.28867513, 0.00000000, 0.21081851, -0.07453560},
4453
{0.28867513, 0.00000000, 0.00000000, 0.22360680}};
4454
4455
// Compute value(s).
4456
for (unsigned int r = 0; r < 4; r++)
4457
{
4458
values[0] += coefficients0[dof][r]*basisvalues[r];
4459
}// end loop over 'r'
4460
}
4461
4462
if (4 <= i && i <= 9)
4463
{
4464
// Map degree of freedom to element degree of freedom
4465
const unsigned int dof = i - 4;
4466
4467
// Array of basisvalues.
4468
double basisvalues[4] = {0.00000000, 0.00000000, 0.00000000, 0.00000000};
4469
4470
// Declare helper variables.
4471
unsigned int rr = 0;
4472
unsigned int ss = 0;
4473
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
4474
4475
// Compute basisvalues.
4476
basisvalues[0] = 1.00000000;
4477
basisvalues[1] = tmp0;
4478
for (unsigned int r = 0; r < 1; r++)
4479
{
4480
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
4481
ss = r*(r + 1)*(r + 2)/6;
4482
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
4483
}// end loop over 'r'
4484
for (unsigned int r = 0; r < 1; r++)
4485
{
4486
for (unsigned int s = 0; s < 1 - r; s++)
4487
{
4488
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
4489
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
4490
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
4491
}// end loop over 's'
4492
}// end loop over 'r'
4493
for (unsigned int r = 0; r < 2; r++)
4494
{
4495
for (unsigned int s = 0; s < 2 - r; s++)
4496
{
4497
for (unsigned int t = 0; t < 2 - r - s; t++)
4498
{
4499
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
4500
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
4501
}// end loop over 't'
4502
}// end loop over 's'
4503
}// end loop over 'r'
4504
4505
// Table(s) of coefficients.
4506
static const double coefficients0[6][4] = \
4507
{{0.00000000, 0.00000000, 0.00000000, 0.00000000},
4508
{-0.28867513, 0.00000000, 0.00000000, -0.22360680},
4509
{-0.28867513, 0.00000000, -0.21081851, 0.07453560},
4510
{0.28867513, 0.00000000, 0.00000000, 0.22360680},
4511
{0.28867513, 0.00000000, 0.21081851, -0.07453560},
4512
{0.57735027, 0.00000000, -0.21081851, -0.14907120}};
4513
4514
static const double coefficients1[6][4] = \
4515
{{-0.28867513, 0.00000000, 0.00000000, -0.22360680},
4516
{0.00000000, 0.00000000, 0.00000000, 0.00000000},
4517
{0.28867513, 0.18257419, -0.10540926, -0.07453560},
4518
{0.28867513, 0.00000000, 0.00000000, 0.22360680},
4519
{0.57735027, -0.18257419, 0.10540926, -0.14907120},
4520
{0.28867513, 0.18257419, -0.10540926, -0.07453560}};
4521
4522
static const double coefficients2[6][4] = \
4523
{{0.28867513, 0.00000000, 0.21081851, -0.07453560},
4524
{0.28867513, 0.18257419, -0.10540926, -0.07453560},
4525
{0.00000000, 0.00000000, 0.00000000, 0.00000000},
4526
{0.57735027, -0.18257419, -0.10540926, 0.14907120},
4527
{0.28867513, 0.00000000, 0.21081851, -0.07453560},
4528
{0.28867513, 0.18257419, -0.10540926, -0.07453560}};
4529
4530
// Compute value(s).
4531
for (unsigned int r = 0; r < 4; r++)
4532
{
4533
values[1] += coefficients0[dof][r]*basisvalues[r];
4534
values[2] += coefficients1[dof][r]*basisvalues[r];
4535
values[3] += coefficients2[dof][r]*basisvalues[r];
4536
}// end loop over 'r'
4537
4538
// Using covariant Piola transform to map values back to the physical element.
4539
const double tmp_ref0 = values[1];
4540
const double tmp_ref1 = values[2];
4541
const double tmp_ref2 = values[3];
4542
values[1] = (K_00*tmp_ref0 + K_10*tmp_ref1 + K_20*tmp_ref2);
4543
values[2] = (K_01*tmp_ref0 + K_11*tmp_ref1 + K_21*tmp_ref2);
4544
values[3] = (K_02*tmp_ref0 + K_12*tmp_ref1 + K_22*tmp_ref2);
19568
switch (i)
19569
{
19570
case 0:
19571
{
19572
19573
// Array of basisvalues.
19574
double basisvalues[4] = {0.00000000, 0.00000000, 0.00000000, 0.00000000};
19575
19576
// Declare helper variables.
19577
unsigned int rr = 0;
19578
unsigned int ss = 0;
19579
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
19580
19581
// Compute basisvalues.
19582
basisvalues[0] = 1.00000000;
19583
basisvalues[1] = tmp0;
19584
for (unsigned int r = 0; r < 1; r++)
19585
{
19586
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
19587
ss = r*(r + 1)*(r + 2)/6;
19588
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
19589
}// end loop over 'r'
19590
for (unsigned int r = 0; r < 1; r++)
19591
{
19592
for (unsigned int s = 0; s < 1 - r; s++)
19593
{
19594
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
19595
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
19596
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
19597
}// end loop over 's'
19598
}// end loop over 'r'
19599
for (unsigned int r = 0; r < 2; r++)
19600
{
19601
for (unsigned int s = 0; s < 2 - r; s++)
19602
{
19603
for (unsigned int t = 0; t < 2 - r - s; t++)
19604
{
19605
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
19606
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
19607
}// end loop over 't'
19608
}// end loop over 's'
19609
}// end loop over 'r'
19610
19611
// Table(s) of coefficients.
19612
static const double coefficients0[4] = \
19613
{0.28867513, -0.18257419, -0.10540926, -0.07453560};
19614
19615
// Compute value(s).
19616
for (unsigned int r = 0; r < 4; r++)
19617
{
19618
values[0] += coefficients0[r]*basisvalues[r];
19619
}// end loop over 'r'
19620
break;
19621
}
19622
case 1:
19623
{
19624
19625
// Array of basisvalues.
19626
double basisvalues[4] = {0.00000000, 0.00000000, 0.00000000, 0.00000000};
19627
19628
// Declare helper variables.
19629
unsigned int rr = 0;
19630
unsigned int ss = 0;
19631
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
19632
19633
// Compute basisvalues.
19634
basisvalues[0] = 1.00000000;
19635
basisvalues[1] = tmp0;
19636
for (unsigned int r = 0; r < 1; r++)
19637
{
19638
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
19639
ss = r*(r + 1)*(r + 2)/6;
19640
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
19641
}// end loop over 'r'
19642
for (unsigned int r = 0; r < 1; r++)
19643
{
19644
for (unsigned int s = 0; s < 1 - r; s++)
19645
{
19646
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
19647
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
19648
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
19649
}// end loop over 's'
19650
}// end loop over 'r'
19651
for (unsigned int r = 0; r < 2; r++)
19652
{
19653
for (unsigned int s = 0; s < 2 - r; s++)
19654
{
19655
for (unsigned int t = 0; t < 2 - r - s; t++)
19656
{
19657
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
19658
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
19659
}// end loop over 't'
19660
}// end loop over 's'
19661
}// end loop over 'r'
19662
19663
// Table(s) of coefficients.
19664
static const double coefficients0[4] = \
19665
{0.28867513, 0.18257419, -0.10540926, -0.07453560};
19666
19667
// Compute value(s).
19668
for (unsigned int r = 0; r < 4; r++)
19669
{
19670
values[0] += coefficients0[r]*basisvalues[r];
19671
}// end loop over 'r'
19672
break;
19673
}
19674
case 2:
19675
{
19676
19677
// Array of basisvalues.
19678
double basisvalues[4] = {0.00000000, 0.00000000, 0.00000000, 0.00000000};
19679
19680
// Declare helper variables.
19681
unsigned int rr = 0;
19682
unsigned int ss = 0;
19683
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
19684
19685
// Compute basisvalues.
19686
basisvalues[0] = 1.00000000;
19687
basisvalues[1] = tmp0;
19688
for (unsigned int r = 0; r < 1; r++)
19689
{
19690
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
19691
ss = r*(r + 1)*(r + 2)/6;
19692
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
19693
}// end loop over 'r'
19694
for (unsigned int r = 0; r < 1; r++)
19695
{
19696
for (unsigned int s = 0; s < 1 - r; s++)
19697
{
19698
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
19699
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
19700
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
19701
}// end loop over 's'
19702
}// end loop over 'r'
19703
for (unsigned int r = 0; r < 2; r++)
19704
{
19705
for (unsigned int s = 0; s < 2 - r; s++)
19706
{
19707
for (unsigned int t = 0; t < 2 - r - s; t++)
19708
{
19709
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
19710
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
19711
}// end loop over 't'
19712
}// end loop over 's'
19713
}// end loop over 'r'
19714
19715
// Table(s) of coefficients.
19716
static const double coefficients0[4] = \
19717
{0.28867513, 0.00000000, 0.21081851, -0.07453560};
19718
19719
// Compute value(s).
19720
for (unsigned int r = 0; r < 4; r++)
19721
{
19722
values[0] += coefficients0[r]*basisvalues[r];
19723
}// end loop over 'r'
19724
break;
19725
}
19726
case 3:
19727
{
19728
19729
// Array of basisvalues.
19730
double basisvalues[4] = {0.00000000, 0.00000000, 0.00000000, 0.00000000};
19731
19732
// Declare helper variables.
19733
unsigned int rr = 0;
19734
unsigned int ss = 0;
19735
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
19736
19737
// Compute basisvalues.
19738
basisvalues[0] = 1.00000000;
19739
basisvalues[1] = tmp0;
19740
for (unsigned int r = 0; r < 1; r++)
19741
{
19742
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
19743
ss = r*(r + 1)*(r + 2)/6;
19744
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
19745
}// end loop over 'r'
19746
for (unsigned int r = 0; r < 1; r++)
19747
{
19748
for (unsigned int s = 0; s < 1 - r; s++)
19749
{
19750
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
19751
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
19752
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
19753
}// end loop over 's'
19754
}// end loop over 'r'
19755
for (unsigned int r = 0; r < 2; r++)
19756
{
19757
for (unsigned int s = 0; s < 2 - r; s++)
19758
{
19759
for (unsigned int t = 0; t < 2 - r - s; t++)
19760
{
19761
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
19762
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
19763
}// end loop over 't'
19764
}// end loop over 's'
19765
}// end loop over 'r'
19766
19767
// Table(s) of coefficients.
19768
static const double coefficients0[4] = \
19769
{0.28867513, 0.00000000, 0.00000000, 0.22360680};
19770
19771
// Compute value(s).
19772
for (unsigned int r = 0; r < 4; r++)
19773
{
19774
values[0] += coefficients0[r]*basisvalues[r];
19775
}// end loop over 'r'
19776
break;
19777
}
19778
case 4:
19779
{
19780
19781
// Array of basisvalues.
19782
double basisvalues[4] = {0.00000000, 0.00000000, 0.00000000, 0.00000000};
19783
19784
// Declare helper variables.
19785
unsigned int rr = 0;
19786
unsigned int ss = 0;
19787
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
19788
19789
// Compute basisvalues.
19790
basisvalues[0] = 1.00000000;
19791
basisvalues[1] = tmp0;
19792
for (unsigned int r = 0; r < 1; r++)
19793
{
19794
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
19795
ss = r*(r + 1)*(r + 2)/6;
19796
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
19797
}// end loop over 'r'
19798
for (unsigned int r = 0; r < 1; r++)
19799
{
19800
for (unsigned int s = 0; s < 1 - r; s++)
19801
{
19802
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
19803
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
19804
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
19805
}// end loop over 's'
19806
}// end loop over 'r'
19807
for (unsigned int r = 0; r < 2; r++)
19808
{
19809
for (unsigned int s = 0; s < 2 - r; s++)
19810
{
19811
for (unsigned int t = 0; t < 2 - r - s; t++)
19812
{
19813
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
19814
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
19815
}// end loop over 't'
19816
}// end loop over 's'
19817
}// end loop over 'r'
19818
19819
// Table(s) of coefficients.
19820
static const double coefficients0[4] = \
19821
{0.00000000, 0.00000000, 0.00000000, 0.00000000};
19822
19823
static const double coefficients1[4] = \
19824
{-0.28867513, 0.00000000, 0.00000000, -0.22360680};
19825
19826
static const double coefficients2[4] = \
19827
{0.28867513, 0.00000000, 0.21081851, -0.07453560};
19828
19829
// Compute value(s).
19830
for (unsigned int r = 0; r < 4; r++)
19831
{
19832
values[1] += coefficients0[r]*basisvalues[r];
19833
values[2] += coefficients1[r]*basisvalues[r];
19834
values[3] += coefficients2[r]*basisvalues[r];
19835
}// end loop over 'r'
19836
19837
// Using covariant Piola transform to map values back to the physical element.
19838
const double tmp_ref0 = values[1];
19839
const double tmp_ref1 = values[2];
19840
const double tmp_ref2 = values[3];
19841
values[1] = (K_00*tmp_ref0 + K_10*tmp_ref1 + K_20*tmp_ref2);
19842
values[2] = (K_01*tmp_ref0 + K_11*tmp_ref1 + K_21*tmp_ref2);
19843
values[3] = (K_02*tmp_ref0 + K_12*tmp_ref1 + K_22*tmp_ref2);
19844
break;
19845
}
19846
case 5:
19847
{
19848
19849
// Array of basisvalues.
19850
double basisvalues[4] = {0.00000000, 0.00000000, 0.00000000, 0.00000000};
19851
19852
// Declare helper variables.
19853
unsigned int rr = 0;
19854
unsigned int ss = 0;
19855
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
19856
19857
// Compute basisvalues.
19858
basisvalues[0] = 1.00000000;
19859
basisvalues[1] = tmp0;
19860
for (unsigned int r = 0; r < 1; r++)
19861
{
19862
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
19863
ss = r*(r + 1)*(r + 2)/6;
19864
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
19865
}// end loop over 'r'
19866
for (unsigned int r = 0; r < 1; r++)
19867
{
19868
for (unsigned int s = 0; s < 1 - r; s++)
19869
{
19870
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
19871
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
19872
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
19873
}// end loop over 's'
19874
}// end loop over 'r'
19875
for (unsigned int r = 0; r < 2; r++)
19876
{
19877
for (unsigned int s = 0; s < 2 - r; s++)
19878
{
19879
for (unsigned int t = 0; t < 2 - r - s; t++)
19880
{
19881
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
19882
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
19883
}// end loop over 't'
19884
}// end loop over 's'
19885
}// end loop over 'r'
19886
19887
// Table(s) of coefficients.
19888
static const double coefficients0[4] = \
19889
{-0.28867513, 0.00000000, 0.00000000, -0.22360680};
19890
19891
static const double coefficients1[4] = \
19892
{0.00000000, 0.00000000, 0.00000000, 0.00000000};
19893
19894
static const double coefficients2[4] = \
19895
{0.28867513, 0.18257419, -0.10540926, -0.07453560};
19896
19897
// Compute value(s).
19898
for (unsigned int r = 0; r < 4; r++)
19899
{
19900
values[1] += coefficients0[r]*basisvalues[r];
19901
values[2] += coefficients1[r]*basisvalues[r];
19902
values[3] += coefficients2[r]*basisvalues[r];
19903
}// end loop over 'r'
19904
19905
// Using covariant Piola transform to map values back to the physical element.
19906
const double tmp_ref0 = values[1];
19907
const double tmp_ref1 = values[2];
19908
const double tmp_ref2 = values[3];
19909
values[1] = (K_00*tmp_ref0 + K_10*tmp_ref1 + K_20*tmp_ref2);
19910
values[2] = (K_01*tmp_ref0 + K_11*tmp_ref1 + K_21*tmp_ref2);
19911
values[3] = (K_02*tmp_ref0 + K_12*tmp_ref1 + K_22*tmp_ref2);
19912
break;
19913
}
19914
case 6:
19915
{
19916
19917
// Array of basisvalues.
19918
double basisvalues[4] = {0.00000000, 0.00000000, 0.00000000, 0.00000000};
19919
19920
// Declare helper variables.
19921
unsigned int rr = 0;
19922
unsigned int ss = 0;
19923
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
19924
19925
// Compute basisvalues.
19926
basisvalues[0] = 1.00000000;
19927
basisvalues[1] = tmp0;
19928
for (unsigned int r = 0; r < 1; r++)
19929
{
19930
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
19931
ss = r*(r + 1)*(r + 2)/6;
19932
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
19933
}// end loop over 'r'
19934
for (unsigned int r = 0; r < 1; r++)
19935
{
19936
for (unsigned int s = 0; s < 1 - r; s++)
19937
{
19938
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
19939
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
19940
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
19941
}// end loop over 's'
19942
}// end loop over 'r'
19943
for (unsigned int r = 0; r < 2; r++)
19944
{
19945
for (unsigned int s = 0; s < 2 - r; s++)
19946
{
19947
for (unsigned int t = 0; t < 2 - r - s; t++)
19948
{
19949
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
19950
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
19951
}// end loop over 't'
19952
}// end loop over 's'
19953
}// end loop over 'r'
19954
19955
// Table(s) of coefficients.
19956
static const double coefficients0[4] = \
19957
{-0.28867513, 0.00000000, -0.21081851, 0.07453560};
19958
19959
static const double coefficients1[4] = \
19960
{0.28867513, 0.18257419, -0.10540926, -0.07453560};
19961
19962
static const double coefficients2[4] = \
19963
{0.00000000, 0.00000000, 0.00000000, 0.00000000};
19964
19965
// Compute value(s).
19966
for (unsigned int r = 0; r < 4; r++)
19967
{
19968
values[1] += coefficients0[r]*basisvalues[r];
19969
values[2] += coefficients1[r]*basisvalues[r];
19970
values[3] += coefficients2[r]*basisvalues[r];
19971
}// end loop over 'r'
19972
19973
// Using covariant Piola transform to map values back to the physical element.
19974
const double tmp_ref0 = values[1];
19975
const double tmp_ref1 = values[2];
19976
const double tmp_ref2 = values[3];
19977
values[1] = (K_00*tmp_ref0 + K_10*tmp_ref1 + K_20*tmp_ref2);
19978
values[2] = (K_01*tmp_ref0 + K_11*tmp_ref1 + K_21*tmp_ref2);
19979
values[3] = (K_02*tmp_ref0 + K_12*tmp_ref1 + K_22*tmp_ref2);
19980
break;
19981
}
19982
case 7:
19983
{
19984
19985
// Array of basisvalues.
19986
double basisvalues[4] = {0.00000000, 0.00000000, 0.00000000, 0.00000000};
19987
19988
// Declare helper variables.
19989
unsigned int rr = 0;
19990
unsigned int ss = 0;
19991
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
19992
19993
// Compute basisvalues.
19994
basisvalues[0] = 1.00000000;
19995
basisvalues[1] = tmp0;
19996
for (unsigned int r = 0; r < 1; r++)
19997
{
19998
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
19999
ss = r*(r + 1)*(r + 2)/6;
20000
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
20001
}// end loop over 'r'
20002
for (unsigned int r = 0; r < 1; r++)
20003
{
20004
for (unsigned int s = 0; s < 1 - r; s++)
20005
{
20006
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
20007
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
20008
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
20009
}// end loop over 's'
20010
}// end loop over 'r'
20011
for (unsigned int r = 0; r < 2; r++)
20012
{
20013
for (unsigned int s = 0; s < 2 - r; s++)
20014
{
20015
for (unsigned int t = 0; t < 2 - r - s; t++)
20016
{
20017
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
20018
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
20019
}// end loop over 't'
20020
}// end loop over 's'
20021
}// end loop over 'r'
20022
20023
// Table(s) of coefficients.
20024
static const double coefficients0[4] = \
20025
{0.28867513, 0.00000000, 0.00000000, 0.22360680};
20026
20027
static const double coefficients1[4] = \
20028
{0.28867513, 0.00000000, 0.00000000, 0.22360680};
20029
20030
static const double coefficients2[4] = \
20031
{0.57735027, -0.18257419, -0.10540926, 0.14907120};
20032
20033
// Compute value(s).
20034
for (unsigned int r = 0; r < 4; r++)
20035
{
20036
values[1] += coefficients0[r]*basisvalues[r];
20037
values[2] += coefficients1[r]*basisvalues[r];
20038
values[3] += coefficients2[r]*basisvalues[r];
20039
}// end loop over 'r'
20040
20041
// Using covariant Piola transform to map values back to the physical element.
20042
const double tmp_ref0 = values[1];
20043
const double tmp_ref1 = values[2];
20044
const double tmp_ref2 = values[3];
20045
values[1] = (K_00*tmp_ref0 + K_10*tmp_ref1 + K_20*tmp_ref2);
20046
values[2] = (K_01*tmp_ref0 + K_11*tmp_ref1 + K_21*tmp_ref2);
20047
values[3] = (K_02*tmp_ref0 + K_12*tmp_ref1 + K_22*tmp_ref2);
20048
break;
20049
}
20050
case 8:
20051
{
20052
20053
// Array of basisvalues.
20054
double basisvalues[4] = {0.00000000, 0.00000000, 0.00000000, 0.00000000};
20055
20056
// Declare helper variables.
20057
unsigned int rr = 0;
20058
unsigned int ss = 0;
20059
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
20060
20061
// Compute basisvalues.
20062
basisvalues[0] = 1.00000000;
20063
basisvalues[1] = tmp0;
20064
for (unsigned int r = 0; r < 1; r++)
20065
{
20066
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
20067
ss = r*(r + 1)*(r + 2)/6;
20068
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
20069
}// end loop over 'r'
20070
for (unsigned int r = 0; r < 1; r++)
20071
{
20072
for (unsigned int s = 0; s < 1 - r; s++)
20073
{
20074
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
20075
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
20076
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
20077
}// end loop over 's'
20078
}// end loop over 'r'
20079
for (unsigned int r = 0; r < 2; r++)
20080
{
20081
for (unsigned int s = 0; s < 2 - r; s++)
20082
{
20083
for (unsigned int t = 0; t < 2 - r - s; t++)
20084
{
20085
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
20086
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
20087
}// end loop over 't'
20088
}// end loop over 's'
20089
}// end loop over 'r'
20090
20091
// Table(s) of coefficients.
20092
static const double coefficients0[4] = \
20093
{0.28867513, 0.00000000, 0.21081851, -0.07453560};
20094
20095
static const double coefficients1[4] = \
20096
{0.57735027, -0.18257419, 0.10540926, -0.14907120};
20097
20098
static const double coefficients2[4] = \
20099
{0.28867513, 0.00000000, 0.21081851, -0.07453560};
20100
20101
// Compute value(s).
20102
for (unsigned int r = 0; r < 4; r++)
20103
{
20104
values[1] += coefficients0[r]*basisvalues[r];
20105
values[2] += coefficients1[r]*basisvalues[r];
20106
values[3] += coefficients2[r]*basisvalues[r];
20107
}// end loop over 'r'
20108
20109
// Using covariant Piola transform to map values back to the physical element.
20110
const double tmp_ref0 = values[1];
20111
const double tmp_ref1 = values[2];
20112
const double tmp_ref2 = values[3];
20113
values[1] = (K_00*tmp_ref0 + K_10*tmp_ref1 + K_20*tmp_ref2);
20114
values[2] = (K_01*tmp_ref0 + K_11*tmp_ref1 + K_21*tmp_ref2);
20115
values[3] = (K_02*tmp_ref0 + K_12*tmp_ref1 + K_22*tmp_ref2);
20116
break;
20117
}
20118
case 9:
20119
{
20120
20121
// Array of basisvalues.
20122
double basisvalues[4] = {0.00000000, 0.00000000, 0.00000000, 0.00000000};
20123
20124
// Declare helper variables.
20125
unsigned int rr = 0;
20126
unsigned int ss = 0;
20127
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
20128
20129
// Compute basisvalues.
20130
basisvalues[0] = 1.00000000;
20131
basisvalues[1] = tmp0;
20132
for (unsigned int r = 0; r < 1; r++)
20133
{
20134
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
20135
ss = r*(r + 1)*(r + 2)/6;
20136
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
20137
}// end loop over 'r'
20138
for (unsigned int r = 0; r < 1; r++)
20139
{
20140
for (unsigned int s = 0; s < 1 - r; s++)
20141
{
20142
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
20143
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
20144
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
20145
}// end loop over 's'
20146
}// end loop over 'r'
20147
for (unsigned int r = 0; r < 2; r++)
20148
{
20149
for (unsigned int s = 0; s < 2 - r; s++)
20150
{
20151
for (unsigned int t = 0; t < 2 - r - s; t++)
20152
{
20153
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
20154
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
20155
}// end loop over 't'
20156
}// end loop over 's'
20157
}// end loop over 'r'
20158
20159
// Table(s) of coefficients.
20160
static const double coefficients0[4] = \
20161
{0.57735027, 0.00000000, -0.21081851, -0.14907120};
20162
20163
static const double coefficients1[4] = \
20164
{0.28867513, 0.18257419, -0.10540926, -0.07453560};
20165
20166
static const double coefficients2[4] = \
20167
{0.28867513, 0.18257419, -0.10540926, -0.07453560};
20168
20169
// Compute value(s).
20170
for (unsigned int r = 0; r < 4; r++)
20171
{
20172
values[1] += coefficients0[r]*basisvalues[r];
20173
values[2] += coefficients1[r]*basisvalues[r];
20174
values[3] += coefficients2[r]*basisvalues[r];
20175
}// end loop over 'r'
20176
20177
// Using covariant Piola transform to map values back to the physical element.
20178
const double tmp_ref0 = values[1];
20179
const double tmp_ref1 = values[2];
20180
const double tmp_ref2 = values[3];
20181
values[1] = (K_00*tmp_ref0 + K_10*tmp_ref1 + K_20*tmp_ref2);
20182
values[2] = (K_01*tmp_ref0 + K_11*tmp_ref1 + K_21*tmp_ref2);
20183
values[3] = (K_02*tmp_ref0 + K_12*tmp_ref1 + K_22*tmp_ref2);
20184
break;
20185
}
4545
20186
}
4546
20187
4547
20188
}
4686
20327
values[r] = 0.00000000;
4687
20328
}// end loop over 'r'
4688
20329
4689
if (0 <= i && i <= 3)
4690
{
4691
// Map degree of freedom to element degree of freedom
4692
const unsigned int dof = i;
4693
4694
// Array of basisvalues.
4695
double basisvalues[4] = {0.00000000, 0.00000000, 0.00000000, 0.00000000};
4696
4697
// Declare helper variables.
4698
unsigned int rr = 0;
4699
unsigned int ss = 0;
4700
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
4701
4702
// Compute basisvalues.
4703
basisvalues[0] = 1.00000000;
4704
basisvalues[1] = tmp0;
4705
for (unsigned int r = 0; r < 1; r++)
4706
{
4707
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
4708
ss = r*(r + 1)*(r + 2)/6;
4709
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
4710
}// end loop over 'r'
4711
for (unsigned int r = 0; r < 1; r++)
4712
{
4713
for (unsigned int s = 0; s < 1 - r; s++)
4714
{
4715
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
4716
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
4717
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
4718
}// end loop over 's'
4719
}// end loop over 'r'
4720
for (unsigned int r = 0; r < 2; r++)
4721
{
4722
for (unsigned int s = 0; s < 2 - r; s++)
4723
{
4724
for (unsigned int t = 0; t < 2 - r - s; t++)
4725
{
4726
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
4727
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
4728
}// end loop over 't'
4729
}// end loop over 's'
4730
}// end loop over 'r'
4731
4732
// Table(s) of coefficients.
4733
static const double coefficients0[4][4] = \
4734
{{0.28867513, -0.18257419, -0.10540926, -0.07453560},
4735
{0.28867513, 0.18257419, -0.10540926, -0.07453560},
4736
{0.28867513, 0.00000000, 0.21081851, -0.07453560},
4737
{0.28867513, 0.00000000, 0.00000000, 0.22360680}};
4738
4739
// Tables of derivatives of the polynomial base (transpose).
4740
static const double dmats0[4][4] = \
4741
{{0.00000000, 0.00000000, 0.00000000, 0.00000000},
4742
{6.32455532, 0.00000000, 0.00000000, 0.00000000},
4743
{0.00000000, 0.00000000, 0.00000000, 0.00000000},
4744
{0.00000000, 0.00000000, 0.00000000, 0.00000000}};
4745
4746
static const double dmats1[4][4] = \
4747
{{0.00000000, 0.00000000, 0.00000000, 0.00000000},
4748
{3.16227766, 0.00000000, 0.00000000, 0.00000000},
4749
{5.47722558, 0.00000000, 0.00000000, 0.00000000},
4750
{0.00000000, 0.00000000, 0.00000000, 0.00000000}};
4751
4752
static const double dmats2[4][4] = \
4753
{{0.00000000, 0.00000000, 0.00000000, 0.00000000},
4754
{3.16227766, 0.00000000, 0.00000000, 0.00000000},
4755
{1.82574186, 0.00000000, 0.00000000, 0.00000000},
4756
{5.16397779, 0.00000000, 0.00000000, 0.00000000}};
4757
4758
// Compute reference derivatives.
4759
// Declare pointer to array of derivatives on FIAT element.
4760
double *derivatives = new double[num_derivatives];
4761
for (unsigned int r = 0; r < num_derivatives; r++)
4762
{
4763
derivatives[r] = 0.00000000;
4764
}// end loop over 'r'
4765
4766
// Declare derivative matrix (of polynomial basis).
4767
double dmats[4][4] = \
4768
{{1.00000000, 0.00000000, 0.00000000, 0.00000000},
4769
{0.00000000, 1.00000000, 0.00000000, 0.00000000},
4770
{0.00000000, 0.00000000, 1.00000000, 0.00000000},
4771
{0.00000000, 0.00000000, 0.00000000, 1.00000000}};
4772
4773
// Declare (auxiliary) derivative matrix (of polynomial basis).
4774
double dmats_old[4][4] = \
4775
{{1.00000000, 0.00000000, 0.00000000, 0.00000000},
4776
{0.00000000, 1.00000000, 0.00000000, 0.00000000},
4777
{0.00000000, 0.00000000, 1.00000000, 0.00000000},
4778
{0.00000000, 0.00000000, 0.00000000, 1.00000000}};
4779
4780
// Loop possible derivatives.
4781
for (unsigned int r = 0; r < num_derivatives; r++)
4782
{
4783
// Resetting dmats values to compute next derivative.
4784
for (unsigned int t = 0; t < 4; t++)
4785
{
4786
for (unsigned int u = 0; u < 4; u++)
4787
{
4788
dmats[t][u] = 0.00000000;
4789
if (t == u)
4790
{
4791
dmats[t][u] = 1.00000000;
4792
}
4793
4794
}// end loop over 'u'
4795
}// end loop over 't'
4796
4797
// Looping derivative order to generate dmats.
4798
for (unsigned int s = 0; s < n; s++)
4799
{
4800
// Updating dmats_old with new values and resetting dmats.
4801
for (unsigned int t = 0; t < 4; t++)
4802
{
4803
for (unsigned int u = 0; u < 4; u++)
4804
{
4805
dmats_old[t][u] = dmats[t][u];
4806
dmats[t][u] = 0.00000000;
4807
}// end loop over 'u'
4808
}// end loop over 't'
4809
4810
// Update dmats using an inner product.
4811
if (combinations[r][s] == 0)
4812
{
4813
for (unsigned int t = 0; t < 4; t++)
4814
{
4815
for (unsigned int u = 0; u < 4; u++)
4816
{
4817
for (unsigned int tu = 0; tu < 4; tu++)
4818
{
4819
dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
4820
}// end loop over 'tu'
4821
}// end loop over 'u'
4822
}// end loop over 't'
4823
}
4824
4825
if (combinations[r][s] == 1)
4826
{
4827
for (unsigned int t = 0; t < 4; t++)
4828
{
4829
for (unsigned int u = 0; u < 4; u++)
4830
{
4831
for (unsigned int tu = 0; tu < 4; tu++)
4832
{
4833
dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
4834
}// end loop over 'tu'
4835
}// end loop over 'u'
4836
}// end loop over 't'
4837
}
4838
4839
if (combinations[r][s] == 2)
4840
{
4841
for (unsigned int t = 0; t < 4; t++)
4842
{
4843
for (unsigned int u = 0; u < 4; u++)
4844
{
4845
for (unsigned int tu = 0; tu < 4; tu++)
4846
{
4847
dmats[t][u] += dmats2[t][tu]*dmats_old[tu][u];
4848
}// end loop over 'tu'
4849
}// end loop over 'u'
4850
}// end loop over 't'
4851
}
4852
4853
}// end loop over 's'
4854
for (unsigned int s = 0; s < 4; s++)
4855
{
4856
for (unsigned int t = 0; t < 4; t++)
4857
{
4858
derivatives[r] += coefficients0[dof][s]*dmats[s][t]*basisvalues[t];
4859
}// end loop over 't'
4860
}// end loop over 's'
4861
}// end loop over 'r'
4862
4863
// Transform derivatives back to physical element
4864
for (unsigned int r = 0; r < num_derivatives; r++)
4865
{
4866
for (unsigned int s = 0; s < num_derivatives; s++)
4867
{
4868
values[r] += transform[r][s]*derivatives[s];
4869
}// end loop over 's'
4870
}// end loop over 'r'
4871
4872
// Delete pointer to array of derivatives on FIAT element
4873
delete [] derivatives;
4874
4875
// Delete pointer to array of combinations of derivatives and transform
4876
for (unsigned int r = 0; r < num_derivatives; r++)
4877
{
4878
delete [] combinations[r];
4879
}// end loop over 'r'
4880
delete [] combinations;
4881
for (unsigned int r = 0; r < num_derivatives; r++)
4882
{
4883
delete [] transform[r];
4884
}// end loop over 'r'
4885
delete [] transform;
4886
}
4887
4888
if (4 <= i && i <= 9)
4889
{
4890
// Map degree of freedom to element degree of freedom
4891
const unsigned int dof = i - 4;
4892
4893
// Array of basisvalues.
4894
double basisvalues[4] = {0.00000000, 0.00000000, 0.00000000, 0.00000000};
4895
4896
// Declare helper variables.
4897
unsigned int rr = 0;
4898
unsigned int ss = 0;
4899
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
4900
4901
// Compute basisvalues.
4902
basisvalues[0] = 1.00000000;
4903
basisvalues[1] = tmp0;
4904
for (unsigned int r = 0; r < 1; r++)
4905
{
4906
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
4907
ss = r*(r + 1)*(r + 2)/6;
4908
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
4909
}// end loop over 'r'
4910
for (unsigned int r = 0; r < 1; r++)
4911
{
4912
for (unsigned int s = 0; s < 1 - r; s++)
4913
{
4914
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
4915
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
4916
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
4917
}// end loop over 's'
4918
}// end loop over 'r'
4919
for (unsigned int r = 0; r < 2; r++)
4920
{
4921
for (unsigned int s = 0; s < 2 - r; s++)
4922
{
4923
for (unsigned int t = 0; t < 2 - r - s; t++)
4924
{
4925
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
4926
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
4927
}// end loop over 't'
4928
}// end loop over 's'
4929
}// end loop over 'r'
4930
4931
// Table(s) of coefficients.
4932
static const double coefficients0[6][4] = \
4933
{{0.00000000, 0.00000000, 0.00000000, 0.00000000},
4934
{-0.28867513, 0.00000000, 0.00000000, -0.22360680},
4935
{-0.28867513, 0.00000000, -0.21081851, 0.07453560},
4936
{0.28867513, 0.00000000, 0.00000000, 0.22360680},
4937
{0.28867513, 0.00000000, 0.21081851, -0.07453560},
4938
{0.57735027, 0.00000000, -0.21081851, -0.14907120}};
4939
4940
static const double coefficients1[6][4] = \
4941
{{-0.28867513, 0.00000000, 0.00000000, -0.22360680},
4942
{0.00000000, 0.00000000, 0.00000000, 0.00000000},
4943
{0.28867513, 0.18257419, -0.10540926, -0.07453560},
4944
{0.28867513, 0.00000000, 0.00000000, 0.22360680},
4945
{0.57735027, -0.18257419, 0.10540926, -0.14907120},
4946
{0.28867513, 0.18257419, -0.10540926, -0.07453560}};
4947
4948
static const double coefficients2[6][4] = \
4949
{{0.28867513, 0.00000000, 0.21081851, -0.07453560},
4950
{0.28867513, 0.18257419, -0.10540926, -0.07453560},
4951
{0.00000000, 0.00000000, 0.00000000, 0.00000000},
4952
{0.57735027, -0.18257419, -0.10540926, 0.14907120},
4953
{0.28867513, 0.00000000, 0.21081851, -0.07453560},
4954
{0.28867513, 0.18257419, -0.10540926, -0.07453560}};
4955
4956
// Tables of derivatives of the polynomial base (transpose).
4957
static const double dmats0[4][4] = \
4958
{{0.00000000, 0.00000000, 0.00000000, 0.00000000},
4959
{6.32455532, 0.00000000, 0.00000000, 0.00000000},
4960
{0.00000000, 0.00000000, 0.00000000, 0.00000000},
4961
{0.00000000, 0.00000000, 0.00000000, 0.00000000}};
4962
4963
static const double dmats1[4][4] = \
4964
{{0.00000000, 0.00000000, 0.00000000, 0.00000000},
4965
{3.16227766, 0.00000000, 0.00000000, 0.00000000},
4966
{5.47722558, 0.00000000, 0.00000000, 0.00000000},
4967
{0.00000000, 0.00000000, 0.00000000, 0.00000000}};
4968
4969
static const double dmats2[4][4] = \
4970
{{0.00000000, 0.00000000, 0.00000000, 0.00000000},
4971
{3.16227766, 0.00000000, 0.00000000, 0.00000000},
4972
{1.82574186, 0.00000000, 0.00000000, 0.00000000},
4973
{5.16397779, 0.00000000, 0.00000000, 0.00000000}};
4974
4975
// Compute reference derivatives.
4976
// Declare pointer to array of derivatives on FIAT element.
4977
double *derivatives = new double[3*num_derivatives];
4978
for (unsigned int r = 0; r < 3*num_derivatives; r++)
4979
{
4980
derivatives[r] = 0.00000000;
4981
}// end loop over 'r'
4982
4983
// Declare derivative matrix (of polynomial basis).
4984
double dmats[4][4] = \
4985
{{1.00000000, 0.00000000, 0.00000000, 0.00000000},
4986
{0.00000000, 1.00000000, 0.00000000, 0.00000000},
4987
{0.00000000, 0.00000000, 1.00000000, 0.00000000},
4988
{0.00000000, 0.00000000, 0.00000000, 1.00000000}};
4989
4990
// Declare (auxiliary) derivative matrix (of polynomial basis).
4991
double dmats_old[4][4] = \
4992
{{1.00000000, 0.00000000, 0.00000000, 0.00000000},
4993
{0.00000000, 1.00000000, 0.00000000, 0.00000000},
4994
{0.00000000, 0.00000000, 1.00000000, 0.00000000},
4995
{0.00000000, 0.00000000, 0.00000000, 1.00000000}};
4996
4997
// Loop possible derivatives.
4998
for (unsigned int r = 0; r < num_derivatives; r++)
4999
{
5000
// Resetting dmats values to compute next derivative.
5001
for (unsigned int t = 0; t < 4; t++)
5002
{
5003
for (unsigned int u = 0; u < 4; u++)
5004
{
5005
dmats[t][u] = 0.00000000;
5006
if (t == u)
5007
{
5008
dmats[t][u] = 1.00000000;
5009
}
5010
5011
}// end loop over 'u'
5012
}// end loop over 't'
5013
5014
// Looping derivative order to generate dmats.
5015
for (unsigned int s = 0; s < n; s++)
5016
{
5017
// Updating dmats_old with new values and resetting dmats.
5018
for (unsigned int t = 0; t < 4; t++)
5019
{
5020
for (unsigned int u = 0; u < 4; u++)
5021
{
5022
dmats_old[t][u] = dmats[t][u];
5023
dmats[t][u] = 0.00000000;
5024
}// end loop over 'u'
5025
}// end loop over 't'
5026
5027
// Update dmats using an inner product.
5028
if (combinations[r][s] == 0)
5029
{
5030
for (unsigned int t = 0; t < 4; t++)
5031
{
5032
for (unsigned int u = 0; u < 4; u++)
5033
{
5034
for (unsigned int tu = 0; tu < 4; tu++)
5035
{
5036
dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
5037
}// end loop over 'tu'
5038
}// end loop over 'u'
5039
}// end loop over 't'
5040
}
5041
5042
if (combinations[r][s] == 1)
5043
{
5044
for (unsigned int t = 0; t < 4; t++)
5045
{
5046
for (unsigned int u = 0; u < 4; u++)
5047
{
5048
for (unsigned int tu = 0; tu < 4; tu++)
5049
{
5050
dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
5051
}// end loop over 'tu'
5052
}// end loop over 'u'
5053
}// end loop over 't'
5054
}
5055
5056
if (combinations[r][s] == 2)
5057
{
5058
for (unsigned int t = 0; t < 4; t++)
5059
{
5060
for (unsigned int u = 0; u < 4; u++)
5061
{
5062
for (unsigned int tu = 0; tu < 4; tu++)
5063
{
5064
dmats[t][u] += dmats2[t][tu]*dmats_old[tu][u];
5065
}// end loop over 'tu'
5066
}// end loop over 'u'
5067
}// end loop over 't'
5068
}
5069
5070
}// end loop over 's'
5071
for (unsigned int s = 0; s < 4; s++)
5072
{
5073
for (unsigned int t = 0; t < 4; t++)
5074
{
5075
derivatives[r] += coefficients0[dof][s]*dmats[s][t]*basisvalues[t];
5076
derivatives[num_derivatives + r] += coefficients1[dof][s]*dmats[s][t]*basisvalues[t];
5077
derivatives[2*num_derivatives + r] += coefficients2[dof][s]*dmats[s][t]*basisvalues[t];
5078
}// end loop over 't'
5079
}// end loop over 's'
5080
5081
// Using covariant Piola transform to map values back to the physical element
5082
const double tmp_ref0 = derivatives[r];
5083
const double tmp_ref1 = derivatives[num_derivatives + r];
5084
const double tmp_ref2 = derivatives[2*num_derivatives + r];
5085
derivatives[r] = (K_00*tmp_ref0 + K_10*tmp_ref1 + K_20*tmp_ref2);
5086
derivatives[num_derivatives + r] = (K_01*tmp_ref0 + K_11*tmp_ref1 + K_21*tmp_ref2);
5087
derivatives[2*num_derivatives + r] = (K_02*tmp_ref0 + K_12*tmp_ref1 + K_22*tmp_ref2);
5088
}// end loop over 'r'
5089
5090
// Transform derivatives back to physical element
5091
for (unsigned int r = 0; r < num_derivatives; r++)
5092
{
5093
for (unsigned int s = 0; s < num_derivatives; s++)
5094
{
5095
values[num_derivatives + r] += transform[r][s]*derivatives[s];
5096
values[2*num_derivatives + r] += transform[r][s]*derivatives[num_derivatives + s];
5097
values[3*num_derivatives + r] += transform[r][s]*derivatives[2*num_derivatives + s];
5098
}// end loop over 's'
5099
}// end loop over 'r'
5100
5101
// Delete pointer to array of derivatives on FIAT element
5102
delete [] derivatives;
5103
5104
// Delete pointer to array of combinations of derivatives and transform
5105
for (unsigned int r = 0; r < num_derivatives; r++)
5106
{
5107
delete [] combinations[r];
5108
}// end loop over 'r'
5109
delete [] combinations;
5110
for (unsigned int r = 0; r < num_derivatives; r++)
5111
{
5112
delete [] transform[r];
5113
}// end loop over 'r'
5114
delete [] transform;
20330
switch (i)
20331
{
20332
case 0:
20333
{
20334
20335
// Array of basisvalues.
20336
double basisvalues[4] = {0.00000000, 0.00000000, 0.00000000, 0.00000000};
20337
20338
// Declare helper variables.
20339
unsigned int rr = 0;
20340
unsigned int ss = 0;
20341
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
20342
20343
// Compute basisvalues.
20344
basisvalues[0] = 1.00000000;
20345
basisvalues[1] = tmp0;
20346
for (unsigned int r = 0; r < 1; r++)
20347
{
20348
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
20349
ss = r*(r + 1)*(r + 2)/6;
20350
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
20351
}// end loop over 'r'
20352
for (unsigned int r = 0; r < 1; r++)
20353
{
20354
for (unsigned int s = 0; s < 1 - r; s++)
20355
{
20356
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
20357
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
20358
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
20359
}// end loop over 's'
20360
}// end loop over 'r'
20361
for (unsigned int r = 0; r < 2; r++)
20362
{
20363
for (unsigned int s = 0; s < 2 - r; s++)
20364
{
20365
for (unsigned int t = 0; t < 2 - r - s; t++)
20366
{
20367
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
20368
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
20369
}// end loop over 't'
20370
}// end loop over 's'
20371
}// end loop over 'r'
20372
20373
// Table(s) of coefficients.
20374
static const double coefficients0[4] = \
20375
{0.28867513, -0.18257419, -0.10540926, -0.07453560};
20376
20377
// Tables of derivatives of the polynomial base (transpose).
20378
static const double dmats0[4][4] = \
20379
{{0.00000000, 0.00000000, 0.00000000, 0.00000000},
20380
{6.32455532, 0.00000000, 0.00000000, 0.00000000},
20381
{0.00000000, 0.00000000, 0.00000000, 0.00000000},
20382
{0.00000000, 0.00000000, 0.00000000, 0.00000000}};
20383
20384
static const double dmats1[4][4] = \
20385
{{0.00000000, 0.00000000, 0.00000000, 0.00000000},
20386
{3.16227766, 0.00000000, 0.00000000, 0.00000000},
20387
{5.47722558, 0.00000000, 0.00000000, 0.00000000},
20388
{0.00000000, 0.00000000, 0.00000000, 0.00000000}};
20389
20390
static const double dmats2[4][4] = \
20391
{{0.00000000, 0.00000000, 0.00000000, 0.00000000},
20392
{3.16227766, 0.00000000, 0.00000000, 0.00000000},
20393
{1.82574186, 0.00000000, 0.00000000, 0.00000000},
20394
{5.16397779, 0.00000000, 0.00000000, 0.00000000}};
20395
20396
// Compute reference derivatives.
20397
// Declare pointer to array of derivatives on FIAT element.
20398
double *derivatives = new double[num_derivatives];
20399
for (unsigned int r = 0; r < num_derivatives; r++)
20400
{
20401
derivatives[r] = 0.00000000;
20402
}// end loop over 'r'
20403
20404
// Declare derivative matrix (of polynomial basis).
20405
double dmats[4][4] = \
20406
{{1.00000000, 0.00000000, 0.00000000, 0.00000000},
20407
{0.00000000, 1.00000000, 0.00000000, 0.00000000},
20408
{0.00000000, 0.00000000, 1.00000000, 0.00000000},
20409
{0.00000000, 0.00000000, 0.00000000, 1.00000000}};
20410
20411
// Declare (auxiliary) derivative matrix (of polynomial basis).
20412
double dmats_old[4][4] = \
20413
{{1.00000000, 0.00000000, 0.00000000, 0.00000000},
20414
{0.00000000, 1.00000000, 0.00000000, 0.00000000},
20415
{0.00000000, 0.00000000, 1.00000000, 0.00000000},
20416
{0.00000000, 0.00000000, 0.00000000, 1.00000000}};
20417
20418
// Loop possible derivatives.
20419
for (unsigned int r = 0; r < num_derivatives; r++)
20420
{
20421
// Resetting dmats values to compute next derivative.
20422
for (unsigned int t = 0; t < 4; t++)
20423
{
20424
for (unsigned int u = 0; u < 4; u++)
20425
{
20426
dmats[t][u] = 0.00000000;
20427
if (t == u)
20428
{
20429
dmats[t][u] = 1.00000000;
20430
}
20431
20432
}// end loop over 'u'
20433
}// end loop over 't'
20434
20435
// Looping derivative order to generate dmats.
20436
for (unsigned int s = 0; s < n; s++)
20437
{
20438
// Updating dmats_old with new values and resetting dmats.
20439
for (unsigned int t = 0; t < 4; t++)
20440
{
20441
for (unsigned int u = 0; u < 4; u++)
20442
{
20443
dmats_old[t][u] = dmats[t][u];
20444
dmats[t][u] = 0.00000000;
20445
}// end loop over 'u'
20446
}// end loop over 't'
20447
20448
// Update dmats using an inner product.
20449
if (combinations[r][s] == 0)
20450
{
20451
for (unsigned int t = 0; t < 4; t++)
20452
{
20453
for (unsigned int u = 0; u < 4; u++)
20454
{
20455
for (unsigned int tu = 0; tu < 4; tu++)
20456
{
20457
dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
20458
}// end loop over 'tu'
20459
}// end loop over 'u'
20460
}// end loop over 't'
20461
}
20462
20463
if (combinations[r][s] == 1)
20464
{
20465
for (unsigned int t = 0; t < 4; t++)
20466
{
20467
for (unsigned int u = 0; u < 4; u++)
20468
{
20469
for (unsigned int tu = 0; tu < 4; tu++)
20470
{
20471
dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
20472
}// end loop over 'tu'
20473
}// end loop over 'u'
20474
}// end loop over 't'
20475
}
20476
20477
if (combinations[r][s] == 2)
20478
{
20479
for (unsigned int t = 0; t < 4; t++)
20480
{
20481
for (unsigned int u = 0; u < 4; u++)
20482
{
20483
for (unsigned int tu = 0; tu < 4; tu++)
20484
{
20485
dmats[t][u] += dmats2[t][tu]*dmats_old[tu][u];
20486
}// end loop over 'tu'
20487
}// end loop over 'u'
20488
}// end loop over 't'
20489
}
20490
20491
}// end loop over 's'
20492
for (unsigned int s = 0; s < 4; s++)
20493
{
20494
for (unsigned int t = 0; t < 4; t++)
20495
{
20496
derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
20497
}// end loop over 't'
20498
}// end loop over 's'
20499
}// end loop over 'r'
20500
20501
// Transform derivatives back to physical element
20502
for (unsigned int r = 0; r < num_derivatives; r++)
20503
{
20504
for (unsigned int s = 0; s < num_derivatives; s++)
20505
{
20506
values[r] += transform[r][s]*derivatives[s];
20507
}// end loop over 's'
20508
}// end loop over 'r'
20509
20510
// Delete pointer to array of derivatives on FIAT element
20511
delete [] derivatives;
20512
20513
// Delete pointer to array of combinations of derivatives and transform
20514
for (unsigned int r = 0; r < num_derivatives; r++)
20515
{
20516
delete [] combinations[r];
20517
}// end loop over 'r'
20518
delete [] combinations;
20519
for (unsigned int r = 0; r < num_derivatives; r++)
20520
{
20521
delete [] transform[r];
20522
}// end loop over 'r'
20523
delete [] transform;
20524
break;
20525
}
20526
case 1:
20527
{
20528
20529
// Array of basisvalues.
20530
double basisvalues[4] = {0.00000000, 0.00000000, 0.00000000, 0.00000000};
20531
20532
// Declare helper variables.
20533
unsigned int rr = 0;
20534
unsigned int ss = 0;
20535
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
20536
20537
// Compute basisvalues.
20538
basisvalues[0] = 1.00000000;
20539
basisvalues[1] = tmp0;
20540
for (unsigned int r = 0; r < 1; r++)
20541
{
20542
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
20543
ss = r*(r + 1)*(r + 2)/6;
20544
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
20545
}// end loop over 'r'
20546
for (unsigned int r = 0; r < 1; r++)
20547
{
20548
for (unsigned int s = 0; s < 1 - r; s++)
20549
{
20550
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
20551
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
20552
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
20553
}// end loop over 's'
20554
}// end loop over 'r'
20555
for (unsigned int r = 0; r < 2; r++)
20556
{
20557
for (unsigned int s = 0; s < 2 - r; s++)
20558
{
20559
for (unsigned int t = 0; t < 2 - r - s; t++)
20560
{
20561
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
20562
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
20563
}// end loop over 't'
20564
}// end loop over 's'
20565
}// end loop over 'r'
20566
20567
// Table(s) of coefficients.
20568
static const double coefficients0[4] = \
20569
{0.28867513, 0.18257419, -0.10540926, -0.07453560};
20570
20571
// Tables of derivatives of the polynomial base (transpose).
20572
static const double dmats0[4][4] = \
20573
{{0.00000000, 0.00000000, 0.00000000, 0.00000000},
20574
{6.32455532, 0.00000000, 0.00000000, 0.00000000},
20575
{0.00000000, 0.00000000, 0.00000000, 0.00000000},
20576
{0.00000000, 0.00000000, 0.00000000, 0.00000000}};
20577
20578
static const double dmats1[4][4] = \
20579
{{0.00000000, 0.00000000, 0.00000000, 0.00000000},
20580
{3.16227766, 0.00000000, 0.00000000, 0.00000000},
20581
{5.47722558, 0.00000000, 0.00000000, 0.00000000},
20582
{0.00000000, 0.00000000, 0.00000000, 0.00000000}};
20583
20584
static const double dmats2[4][4] = \
20585
{{0.00000000, 0.00000000, 0.00000000, 0.00000000},
20586
{3.16227766, 0.00000000, 0.00000000, 0.00000000},
20587
{1.82574186, 0.00000000, 0.00000000, 0.00000000},
20588
{5.16397779, 0.00000000, 0.00000000, 0.00000000}};
20589
20590
// Compute reference derivatives.
20591
// Declare pointer to array of derivatives on FIAT element.
20592
double *derivatives = new double[num_derivatives];
20593
for (unsigned int r = 0; r < num_derivatives; r++)
20594
{
20595
derivatives[r] = 0.00000000;
20596
}// end loop over 'r'
20597
20598
// Declare derivative matrix (of polynomial basis).
20599
double dmats[4][4] = \
20600
{{1.00000000, 0.00000000, 0.00000000, 0.00000000},
20601
{0.00000000, 1.00000000, 0.00000000, 0.00000000},
20602
{0.00000000, 0.00000000, 1.00000000, 0.00000000},
20603
{0.00000000, 0.00000000, 0.00000000, 1.00000000}};
20604
20605
// Declare (auxiliary) derivative matrix (of polynomial basis).
20606
double dmats_old[4][4] = \
20607
{{1.00000000, 0.00000000, 0.00000000, 0.00000000},
20608
{0.00000000, 1.00000000, 0.00000000, 0.00000000},
20609
{0.00000000, 0.00000000, 1.00000000, 0.00000000},
20610
{0.00000000, 0.00000000, 0.00000000, 1.00000000}};
20611
20612
// Loop possible derivatives.
20613
for (unsigned int r = 0; r < num_derivatives; r++)
20614
{
20615
// Resetting dmats values to compute next derivative.
20616
for (unsigned int t = 0; t < 4; t++)
20617
{
20618
for (unsigned int u = 0; u < 4; u++)
20619
{
20620
dmats[t][u] = 0.00000000;
20621
if (t == u)
20622
{
20623
dmats[t][u] = 1.00000000;
20624
}
20625
20626
}// end loop over 'u'
20627
}// end loop over 't'
20628
20629
// Looping derivative order to generate dmats.
20630
for (unsigned int s = 0; s < n; s++)
20631
{
20632
// Updating dmats_old with new values and resetting dmats.
20633
for (unsigned int t = 0; t < 4; t++)
20634
{
20635
for (unsigned int u = 0; u < 4; u++)
20636
{
20637
dmats_old[t][u] = dmats[t][u];
20638
dmats[t][u] = 0.00000000;
20639
}// end loop over 'u'
20640
}// end loop over 't'
20641
20642
// Update dmats using an inner product.
20643
if (combinations[r][s] == 0)
20644
{
20645
for (unsigned int t = 0; t < 4; t++)
20646
{
20647
for (unsigned int u = 0; u < 4; u++)
20648
{
20649
for (unsigned int tu = 0; tu < 4; tu++)
20650
{
20651
dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
20652
}// end loop over 'tu'
20653
}// end loop over 'u'
20654
}// end loop over 't'
20655
}
20656
20657
if (combinations[r][s] == 1)
20658
{
20659
for (unsigned int t = 0; t < 4; t++)
20660
{
20661
for (unsigned int u = 0; u < 4; u++)
20662
{
20663
for (unsigned int tu = 0; tu < 4; tu++)
20664
{
20665
dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
20666
}// end loop over 'tu'
20667
}// end loop over 'u'
20668
}// end loop over 't'
20669
}
20670
20671
if (combinations[r][s] == 2)
20672
{
20673
for (unsigned int t = 0; t < 4; t++)
20674
{
20675
for (unsigned int u = 0; u < 4; u++)
20676
{
20677
for (unsigned int tu = 0; tu < 4; tu++)
20678
{
20679
dmats[t][u] += dmats2[t][tu]*dmats_old[tu][u];
20680
}// end loop over 'tu'
20681
}// end loop over 'u'
20682
}// end loop over 't'
20683
}
20684
20685
}// end loop over 's'
20686
for (unsigned int s = 0; s < 4; s++)
20687
{
20688
for (unsigned int t = 0; t < 4; t++)
20689
{
20690
derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
20691
}// end loop over 't'
20692
}// end loop over 's'
20693
}// end loop over 'r'
20694
20695
// Transform derivatives back to physical element
20696
for (unsigned int r = 0; r < num_derivatives; r++)
20697
{
20698
for (unsigned int s = 0; s < num_derivatives; s++)
20699
{
20700
values[r] += transform[r][s]*derivatives[s];
20701
}// end loop over 's'
20702
}// end loop over 'r'
20703
20704
// Delete pointer to array of derivatives on FIAT element
20705
delete [] derivatives;
20706
20707
// Delete pointer to array of combinations of derivatives and transform
20708
for (unsigned int r = 0; r < num_derivatives; r++)
20709
{
20710
delete [] combinations[r];
20711
}// end loop over 'r'
20712
delete [] combinations;
20713
for (unsigned int r = 0; r < num_derivatives; r++)
20714
{
20715
delete [] transform[r];
20716
}// end loop over 'r'
20717
delete [] transform;
20718
break;
20719
}
20720
case 2:
20721
{
20722
20723
// Array of basisvalues.
20724
double basisvalues[4] = {0.00000000, 0.00000000, 0.00000000, 0.00000000};
20725
20726
// Declare helper variables.
20727
unsigned int rr = 0;
20728
unsigned int ss = 0;
20729
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
20730
20731
// Compute basisvalues.
20732
basisvalues[0] = 1.00000000;
20733
basisvalues[1] = tmp0;
20734
for (unsigned int r = 0; r < 1; r++)
20735
{
20736
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
20737
ss = r*(r + 1)*(r + 2)/6;
20738
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
20739
}// end loop over 'r'
20740
for (unsigned int r = 0; r < 1; r++)
20741
{
20742
for (unsigned int s = 0; s < 1 - r; s++)
20743
{
20744
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
20745
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
20746
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
20747
}// end loop over 's'
20748
}// end loop over 'r'
20749
for (unsigned int r = 0; r < 2; r++)
20750
{
20751
for (unsigned int s = 0; s < 2 - r; s++)
20752
{
20753
for (unsigned int t = 0; t < 2 - r - s; t++)
20754
{
20755
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
20756
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
20757
}// end loop over 't'
20758
}// end loop over 's'
20759
}// end loop over 'r'
20760
20761
// Table(s) of coefficients.
20762
static const double coefficients0[4] = \
20763
{0.28867513, 0.00000000, 0.21081851, -0.07453560};
20764
20765
// Tables of derivatives of the polynomial base (transpose).
20766
static const double dmats0[4][4] = \
20767
{{0.00000000, 0.00000000, 0.00000000, 0.00000000},
20768
{6.32455532, 0.00000000, 0.00000000, 0.00000000},
20769
{0.00000000, 0.00000000, 0.00000000, 0.00000000},
20770
{0.00000000, 0.00000000, 0.00000000, 0.00000000}};
20771
20772
static const double dmats1[4][4] = \
20773
{{0.00000000, 0.00000000, 0.00000000, 0.00000000},
20774
{3.16227766, 0.00000000, 0.00000000, 0.00000000},
20775
{5.47722558, 0.00000000, 0.00000000, 0.00000000},
20776
{0.00000000, 0.00000000, 0.00000000, 0.00000000}};
20777
20778
static const double dmats2[4][4] = \
20779
{{0.00000000, 0.00000000, 0.00000000, 0.00000000},
20780
{3.16227766, 0.00000000, 0.00000000, 0.00000000},
20781
{1.82574186, 0.00000000, 0.00000000, 0.00000000},
20782
{5.16397779, 0.00000000, 0.00000000, 0.00000000}};
20783
20784
// Compute reference derivatives.
20785
// Declare pointer to array of derivatives on FIAT element.
20786
double *derivatives = new double[num_derivatives];
20787
for (unsigned int r = 0; r < num_derivatives; r++)
20788
{
20789
derivatives[r] = 0.00000000;
20790
}// end loop over 'r'
20791
20792
// Declare derivative matrix (of polynomial basis).
20793
double dmats[4][4] = \
20794
{{1.00000000, 0.00000000, 0.00000000, 0.00000000},
20795
{0.00000000, 1.00000000, 0.00000000, 0.00000000},
20796
{0.00000000, 0.00000000, 1.00000000, 0.00000000},
20797
{0.00000000, 0.00000000, 0.00000000, 1.00000000}};
20798
20799
// Declare (auxiliary) derivative matrix (of polynomial basis).
20800
double dmats_old[4][4] = \
20801
{{1.00000000, 0.00000000, 0.00000000, 0.00000000},
20802
{0.00000000, 1.00000000, 0.00000000, 0.00000000},
20803
{0.00000000, 0.00000000, 1.00000000, 0.00000000},
20804
{0.00000000, 0.00000000, 0.00000000, 1.00000000}};
20805
20806
// Loop possible derivatives.
20807
for (unsigned int r = 0; r < num_derivatives; r++)
20808
{
20809
// Resetting dmats values to compute next derivative.
20810
for (unsigned int t = 0; t < 4; t++)
20811
{
20812
for (unsigned int u = 0; u < 4; u++)
20813
{
20814
dmats[t][u] = 0.00000000;
20815
if (t == u)
20816
{
20817
dmats[t][u] = 1.00000000;
20818
}
20819
20820
}// end loop over 'u'
20821
}// end loop over 't'
20822
20823
// Looping derivative order to generate dmats.
20824
for (unsigned int s = 0; s < n; s++)
20825
{
20826
// Updating dmats_old with new values and resetting dmats.
20827
for (unsigned int t = 0; t < 4; t++)
20828
{
20829
for (unsigned int u = 0; u < 4; u++)
20830
{
20831
dmats_old[t][u] = dmats[t][u];
20832
dmats[t][u] = 0.00000000;
20833
}// end loop over 'u'
20834
}// end loop over 't'
20835
20836
// Update dmats using an inner product.
20837
if (combinations[r][s] == 0)
20838
{
20839
for (unsigned int t = 0; t < 4; t++)
20840
{
20841
for (unsigned int u = 0; u < 4; u++)
20842
{
20843
for (unsigned int tu = 0; tu < 4; tu++)
20844
{
20845
dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
20846
}// end loop over 'tu'
20847
}// end loop over 'u'
20848
}// end loop over 't'
20849
}
20850
20851
if (combinations[r][s] == 1)
20852
{
20853
for (unsigned int t = 0; t < 4; t++)
20854
{
20855
for (unsigned int u = 0; u < 4; u++)
20856
{
20857
for (unsigned int tu = 0; tu < 4; tu++)
20858
{
20859
dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
20860
}// end loop over 'tu'
20861
}// end loop over 'u'
20862
}// end loop over 't'
20863
}
20864
20865
if (combinations[r][s] == 2)
20866
{
20867
for (unsigned int t = 0; t < 4; t++)
20868
{
20869
for (unsigned int u = 0; u < 4; u++)
20870
{
20871
for (unsigned int tu = 0; tu < 4; tu++)
20872
{
20873
dmats[t][u] += dmats2[t][tu]*dmats_old[tu][u];
20874
}// end loop over 'tu'
20875
}// end loop over 'u'
20876
}// end loop over 't'
20877
}
20878
20879
}// end loop over 's'
20880
for (unsigned int s = 0; s < 4; s++)
20881
{
20882
for (unsigned int t = 0; t < 4; t++)
20883
{
20884
derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
20885
}// end loop over 't'
20886
}// end loop over 's'
20887
}// end loop over 'r'
20888
20889
// Transform derivatives back to physical element
20890
for (unsigned int r = 0; r < num_derivatives; r++)
20891
{
20892
for (unsigned int s = 0; s < num_derivatives; s++)
20893
{
20894
values[r] += transform[r][s]*derivatives[s];
20895
}// end loop over 's'
20896
}// end loop over 'r'
20897
20898
// Delete pointer to array of derivatives on FIAT element
20899
delete [] derivatives;
20900
20901
// Delete pointer to array of combinations of derivatives and transform
20902
for (unsigned int r = 0; r < num_derivatives; r++)
20903
{
20904
delete [] combinations[r];
20905
}// end loop over 'r'
20906
delete [] combinations;
20907
for (unsigned int r = 0; r < num_derivatives; r++)
20908
{
20909
delete [] transform[r];
20910
}// end loop over 'r'
20911
delete [] transform;
20912
break;
20913
}
20914
case 3:
20915
{
20916
20917
// Array of basisvalues.
20918
double basisvalues[4] = {0.00000000, 0.00000000, 0.00000000, 0.00000000};
20919
20920
// Declare helper variables.
20921
unsigned int rr = 0;
20922
unsigned int ss = 0;
20923
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
20924
20925
// Compute basisvalues.
20926
basisvalues[0] = 1.00000000;
20927
basisvalues[1] = tmp0;
20928
for (unsigned int r = 0; r < 1; r++)
20929
{
20930
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
20931
ss = r*(r + 1)*(r + 2)/6;
20932
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
20933
}// end loop over 'r'
20934
for (unsigned int r = 0; r < 1; r++)
20935
{
20936
for (unsigned int s = 0; s < 1 - r; s++)
20937
{
20938
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
20939
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
20940
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
20941
}// end loop over 's'
20942
}// end loop over 'r'
20943
for (unsigned int r = 0; r < 2; r++)
20944
{
20945
for (unsigned int s = 0; s < 2 - r; s++)
20946
{
20947
for (unsigned int t = 0; t < 2 - r - s; t++)
20948
{
20949
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
20950
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
20951
}// end loop over 't'
20952
}// end loop over 's'
20953
}// end loop over 'r'
20954
20955
// Table(s) of coefficients.
20956
static const double coefficients0[4] = \
20957
{0.28867513, 0.00000000, 0.00000000, 0.22360680};
20958
20959
// Tables of derivatives of the polynomial base (transpose).
20960
static const double dmats0[4][4] = \
20961
{{0.00000000, 0.00000000, 0.00000000, 0.00000000},
20962
{6.32455532, 0.00000000, 0.00000000, 0.00000000},
20963
{0.00000000, 0.00000000, 0.00000000, 0.00000000},
20964
{0.00000000, 0.00000000, 0.00000000, 0.00000000}};
20965
20966
static const double dmats1[4][4] = \
20967
{{0.00000000, 0.00000000, 0.00000000, 0.00000000},
20968
{3.16227766, 0.00000000, 0.00000000, 0.00000000},
20969
{5.47722558, 0.00000000, 0.00000000, 0.00000000},
20970
{0.00000000, 0.00000000, 0.00000000, 0.00000000}};
20971
20972
static const double dmats2[4][4] = \
20973
{{0.00000000, 0.00000000, 0.00000000, 0.00000000},
20974
{3.16227766, 0.00000000, 0.00000000, 0.00000000},
20975
{1.82574186, 0.00000000, 0.00000000, 0.00000000},
20976
{5.16397779, 0.00000000, 0.00000000, 0.00000000}};
20977
20978
// Compute reference derivatives.
20979
// Declare pointer to array of derivatives on FIAT element.
20980
double *derivatives = new double[num_derivatives];
20981
for (unsigned int r = 0; r < num_derivatives; r++)
20982
{
20983
derivatives[r] = 0.00000000;
20984
}// end loop over 'r'
20985
20986
// Declare derivative matrix (of polynomial basis).
20987
double dmats[4][4] = \
20988
{{1.00000000, 0.00000000, 0.00000000, 0.00000000},
20989
{0.00000000, 1.00000000, 0.00000000, 0.00000000},
20990
{0.00000000, 0.00000000, 1.00000000, 0.00000000},
20991
{0.00000000, 0.00000000, 0.00000000, 1.00000000}};
20992
20993
// Declare (auxiliary) derivative matrix (of polynomial basis).
20994
double dmats_old[4][4] = \
20995
{{1.00000000, 0.00000000, 0.00000000, 0.00000000},
20996
{0.00000000, 1.00000000, 0.00000000, 0.00000000},
20997
{0.00000000, 0.00000000, 1.00000000, 0.00000000},
20998
{0.00000000, 0.00000000, 0.00000000, 1.00000000}};
20999
21000
// Loop possible derivatives.
21001
for (unsigned int r = 0; r < num_derivatives; r++)
21002
{
21003
// Resetting dmats values to compute next derivative.
21004
for (unsigned int t = 0; t < 4; t++)
21005
{
21006
for (unsigned int u = 0; u < 4; u++)
21007
{
21008
dmats[t][u] = 0.00000000;
21009
if (t == u)
21010
{
21011
dmats[t][u] = 1.00000000;
21012
}
21013
21014
}// end loop over 'u'
21015
}// end loop over 't'
21016
21017
// Looping derivative order to generate dmats.
21018
for (unsigned int s = 0; s < n; s++)
21019
{
21020
// Updating dmats_old with new values and resetting dmats.
21021
for (unsigned int t = 0; t < 4; t++)
21022
{
21023
for (unsigned int u = 0; u < 4; u++)
21024
{
21025
dmats_old[t][u] = dmats[t][u];
21026
dmats[t][u] = 0.00000000;
21027
}// end loop over 'u'
21028
}// end loop over 't'
21029
21030
// Update dmats using an inner product.
21031
if (combinations[r][s] == 0)
21032
{
21033
for (unsigned int t = 0; t < 4; t++)
21034
{
21035
for (unsigned int u = 0; u < 4; u++)
21036
{
21037
for (unsigned int tu = 0; tu < 4; tu++)
21038
{
21039
dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
21040
}// end loop over 'tu'
21041
}// end loop over 'u'
21042
}// end loop over 't'
21043
}
21044
21045
if (combinations[r][s] == 1)
21046
{
21047
for (unsigned int t = 0; t < 4; t++)
21048
{
21049
for (unsigned int u = 0; u < 4; u++)
21050
{
21051
for (unsigned int tu = 0; tu < 4; tu++)
21052
{
21053
dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
21054
}// end loop over 'tu'
21055
}// end loop over 'u'
21056
}// end loop over 't'
21057
}
21058
21059
if (combinations[r][s] == 2)
21060
{
21061
for (unsigned int t = 0; t < 4; t++)
21062
{
21063
for (unsigned int u = 0; u < 4; u++)
21064
{
21065
for (unsigned int tu = 0; tu < 4; tu++)
21066
{
21067
dmats[t][u] += dmats2[t][tu]*dmats_old[tu][u];
21068
}// end loop over 'tu'
21069
}// end loop over 'u'
21070
}// end loop over 't'
21071
}
21072
21073
}// end loop over 's'
21074
for (unsigned int s = 0; s < 4; s++)
21075
{
21076
for (unsigned int t = 0; t < 4; t++)
21077
{
21078
derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
21079
}// end loop over 't'
21080
}// end loop over 's'
21081
}// end loop over 'r'
21082
21083
// Transform derivatives back to physical element
21084
for (unsigned int r = 0; r < num_derivatives; r++)
21085
{
21086
for (unsigned int s = 0; s < num_derivatives; s++)
21087
{
21088
values[r] += transform[r][s]*derivatives[s];
21089
}// end loop over 's'
21090
}// end loop over 'r'
21091
21092
// Delete pointer to array of derivatives on FIAT element
21093
delete [] derivatives;
21094
21095
// Delete pointer to array of combinations of derivatives and transform
21096
for (unsigned int r = 0; r < num_derivatives; r++)
21097
{
21098
delete [] combinations[r];
21099
}// end loop over 'r'
21100
delete [] combinations;
21101
for (unsigned int r = 0; r < num_derivatives; r++)
21102
{
21103
delete [] transform[r];
21104
}// end loop over 'r'
21105
delete [] transform;
21106
break;
21107
}
21108
case 4:
21109
{
21110
21111
// Array of basisvalues.
21112
double basisvalues[4] = {0.00000000, 0.00000000, 0.00000000, 0.00000000};
21113
21114
// Declare helper variables.
21115
unsigned int rr = 0;
21116
unsigned int ss = 0;
21117
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
21118
21119
// Compute basisvalues.
21120
basisvalues[0] = 1.00000000;
21121
basisvalues[1] = tmp0;
21122
for (unsigned int r = 0; r < 1; r++)
21123
{
21124
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
21125
ss = r*(r + 1)*(r + 2)/6;
21126
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
21127
}// end loop over 'r'
21128
for (unsigned int r = 0; r < 1; r++)
21129
{
21130
for (unsigned int s = 0; s < 1 - r; s++)
21131
{
21132
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
21133
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
21134
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
21135
}// end loop over 's'
21136
}// end loop over 'r'
21137
for (unsigned int r = 0; r < 2; r++)
21138
{
21139
for (unsigned int s = 0; s < 2 - r; s++)
21140
{
21141
for (unsigned int t = 0; t < 2 - r - s; t++)
21142
{
21143
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
21144
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
21145
}// end loop over 't'
21146
}// end loop over 's'
21147
}// end loop over 'r'
21148
21149
// Table(s) of coefficients.
21150
static const double coefficients0[4] = \
21151
{0.00000000, 0.00000000, 0.00000000, 0.00000000};
21152
21153
static const double coefficients1[4] = \
21154
{-0.28867513, 0.00000000, 0.00000000, -0.22360680};
21155
21156
static const double coefficients2[4] = \
21157
{0.28867513, 0.00000000, 0.21081851, -0.07453560};
21158
21159
// Tables of derivatives of the polynomial base (transpose).
21160
static const double dmats0[4][4] = \
21161
{{0.00000000, 0.00000000, 0.00000000, 0.00000000},
21162
{6.32455532, 0.00000000, 0.00000000, 0.00000000},
21163
{0.00000000, 0.00000000, 0.00000000, 0.00000000},
21164
{0.00000000, 0.00000000, 0.00000000, 0.00000000}};
21165
21166
static const double dmats1[4][4] = \
21167
{{0.00000000, 0.00000000, 0.00000000, 0.00000000},
21168
{3.16227766, 0.00000000, 0.00000000, 0.00000000},
21169
{5.47722558, 0.00000000, 0.00000000, 0.00000000},
21170
{0.00000000, 0.00000000, 0.00000000, 0.00000000}};
21171
21172
static const double dmats2[4][4] = \
21173
{{0.00000000, 0.00000000, 0.00000000, 0.00000000},
21174
{3.16227766, 0.00000000, 0.00000000, 0.00000000},
21175
{1.82574186, 0.00000000, 0.00000000, 0.00000000},
21176
{5.16397779, 0.00000000, 0.00000000, 0.00000000}};
21177
21178
// Compute reference derivatives.
21179
// Declare pointer to array of derivatives on FIAT element.
21180
double *derivatives = new double[3*num_derivatives];
21181
for (unsigned int r = 0; r < 3*num_derivatives; r++)
21182
{
21183
derivatives[r] = 0.00000000;
21184
}// end loop over 'r'
21185
21186
// Declare derivative matrix (of polynomial basis).
21187
double dmats[4][4] = \
21188
{{1.00000000, 0.00000000, 0.00000000, 0.00000000},
21189
{0.00000000, 1.00000000, 0.00000000, 0.00000000},
21190
{0.00000000, 0.00000000, 1.00000000, 0.00000000},
21191
{0.00000000, 0.00000000, 0.00000000, 1.00000000}};
21192
21193
// Declare (auxiliary) derivative matrix (of polynomial basis).
21194
double dmats_old[4][4] = \
21195
{{1.00000000, 0.00000000, 0.00000000, 0.00000000},
21196
{0.00000000, 1.00000000, 0.00000000, 0.00000000},
21197
{0.00000000, 0.00000000, 1.00000000, 0.00000000},
21198
{0.00000000, 0.00000000, 0.00000000, 1.00000000}};
21199
21200
// Loop possible derivatives.
21201
for (unsigned int r = 0; r < num_derivatives; r++)
21202
{
21203
// Resetting dmats values to compute next derivative.
21204
for (unsigned int t = 0; t < 4; t++)
21205
{
21206
for (unsigned int u = 0; u < 4; u++)
21207
{
21208
dmats[t][u] = 0.00000000;
21209
if (t == u)
21210
{
21211
dmats[t][u] = 1.00000000;
21212
}
21213
21214
}// end loop over 'u'
21215
}// end loop over 't'
21216
21217
// Looping derivative order to generate dmats.
21218
for (unsigned int s = 0; s < n; s++)
21219
{
21220
// Updating dmats_old with new values and resetting dmats.
21221
for (unsigned int t = 0; t < 4; t++)
21222
{
21223
for (unsigned int u = 0; u < 4; u++)
21224
{
21225
dmats_old[t][u] = dmats[t][u];
21226
dmats[t][u] = 0.00000000;
21227
}// end loop over 'u'
21228
}// end loop over 't'
21229
21230
// Update dmats using an inner product.
21231
if (combinations[r][s] == 0)
21232
{
21233
for (unsigned int t = 0; t < 4; t++)
21234
{
21235
for (unsigned int u = 0; u < 4; u++)
21236
{
21237
for (unsigned int tu = 0; tu < 4; tu++)
21238
{
21239
dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
21240
}// end loop over 'tu'
21241
}// end loop over 'u'
21242
}// end loop over 't'
21243
}
21244
21245
if (combinations[r][s] == 1)
21246
{
21247
for (unsigned int t = 0; t < 4; t++)
21248
{
21249
for (unsigned int u = 0; u < 4; u++)
21250
{
21251
for (unsigned int tu = 0; tu < 4; tu++)
21252
{
21253
dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
21254
}// end loop over 'tu'
21255
}// end loop over 'u'
21256
}// end loop over 't'
21257
}
21258
21259
if (combinations[r][s] == 2)
21260
{
21261
for (unsigned int t = 0; t < 4; t++)
21262
{
21263
for (unsigned int u = 0; u < 4; u++)
21264
{
21265
for (unsigned int tu = 0; tu < 4; tu++)
21266
{
21267
dmats[t][u] += dmats2[t][tu]*dmats_old[tu][u];
21268
}// end loop over 'tu'
21269
}// end loop over 'u'
21270
}// end loop over 't'
21271
}
21272
21273
}// end loop over 's'
21274
for (unsigned int s = 0; s < 4; s++)
21275
{
21276
for (unsigned int t = 0; t < 4; t++)
21277
{
21278
derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
21279
derivatives[num_derivatives + r] += coefficients1[s]*dmats[s][t]*basisvalues[t];
21280
derivatives[2*num_derivatives + r] += coefficients2[s]*dmats[s][t]*basisvalues[t];
21281
}// end loop over 't'
21282
}// end loop over 's'
21283
21284
// Using covariant Piola transform to map values back to the physical element
21285
const double tmp_ref0 = derivatives[r];
21286
const double tmp_ref1 = derivatives[num_derivatives + r];
21287
const double tmp_ref2 = derivatives[2*num_derivatives + r];
21288
derivatives[r] = (K_00*tmp_ref0 + K_10*tmp_ref1 + K_20*tmp_ref2);
21289
derivatives[num_derivatives + r] = (K_01*tmp_ref0 + K_11*tmp_ref1 + K_21*tmp_ref2);
21290
derivatives[2*num_derivatives + r] = (K_02*tmp_ref0 + K_12*tmp_ref1 + K_22*tmp_ref2);
21291
}// end loop over 'r'
21292
21293
// Transform derivatives back to physical element
21294
for (unsigned int r = 0; r < num_derivatives; r++)
21295
{
21296
for (unsigned int s = 0; s < num_derivatives; s++)
21297
{
21298
values[num_derivatives + r] += transform[r][s]*derivatives[s];
21299
values[2*num_derivatives + r] += transform[r][s]*derivatives[num_derivatives + s];
21300
values[3*num_derivatives + r] += transform[r][s]*derivatives[2*num_derivatives + s];
21301
}// end loop over 's'
21302
}// end loop over 'r'
21303
21304
// Delete pointer to array of derivatives on FIAT element
21305
delete [] derivatives;
21306
21307
// Delete pointer to array of combinations of derivatives and transform
21308
for (unsigned int r = 0; r < num_derivatives; r++)
21309
{
21310
delete [] combinations[r];
21311
}// end loop over 'r'
21312
delete [] combinations;
21313
for (unsigned int r = 0; r < num_derivatives; r++)
21314
{
21315
delete [] transform[r];
21316
}// end loop over 'r'
21317
delete [] transform;
21318
break;
21319
}
21320
case 5:
21321
{
21322
21323
// Array of basisvalues.
21324
double basisvalues[4] = {0.00000000, 0.00000000, 0.00000000, 0.00000000};
21325
21326
// Declare helper variables.
21327
unsigned int rr = 0;
21328
unsigned int ss = 0;
21329
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
21330
21331
// Compute basisvalues.
21332
basisvalues[0] = 1.00000000;
21333
basisvalues[1] = tmp0;
21334
for (unsigned int r = 0; r < 1; r++)
21335
{
21336
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
21337
ss = r*(r + 1)*(r + 2)/6;
21338
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
21339
}// end loop over 'r'
21340
for (unsigned int r = 0; r < 1; r++)
21341
{
21342
for (unsigned int s = 0; s < 1 - r; s++)
21343
{
21344
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
21345
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
21346
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
21347
}// end loop over 's'
21348
}// end loop over 'r'
21349
for (unsigned int r = 0; r < 2; r++)
21350
{
21351
for (unsigned int s = 0; s < 2 - r; s++)
21352
{
21353
for (unsigned int t = 0; t < 2 - r - s; t++)
21354
{
21355
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
21356
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
21357
}// end loop over 't'
21358
}// end loop over 's'
21359
}// end loop over 'r'
21360
21361
// Table(s) of coefficients.
21362
static const double coefficients0[4] = \
21363
{-0.28867513, 0.00000000, 0.00000000, -0.22360680};
21364
21365
static const double coefficients1[4] = \
21366
{0.00000000, 0.00000000, 0.00000000, 0.00000000};
21367
21368
static const double coefficients2[4] = \
21369
{0.28867513, 0.18257419, -0.10540926, -0.07453560};
21370
21371
// Tables of derivatives of the polynomial base (transpose).
21372
static const double dmats0[4][4] = \
21373
{{0.00000000, 0.00000000, 0.00000000, 0.00000000},
21374
{6.32455532, 0.00000000, 0.00000000, 0.00000000},
21375
{0.00000000, 0.00000000, 0.00000000, 0.00000000},
21376
{0.00000000, 0.00000000, 0.00000000, 0.00000000}};
21377
21378
static const double dmats1[4][4] = \
21379
{{0.00000000, 0.00000000, 0.00000000, 0.00000000},
21380
{3.16227766, 0.00000000, 0.00000000, 0.00000000},
21381
{5.47722558, 0.00000000, 0.00000000, 0.00000000},
21382
{0.00000000, 0.00000000, 0.00000000, 0.00000000}};
21383
21384
static const double dmats2[4][4] = \
21385
{{0.00000000, 0.00000000, 0.00000000, 0.00000000},
21386
{3.16227766, 0.00000000, 0.00000000, 0.00000000},
21387
{1.82574186, 0.00000000, 0.00000000, 0.00000000},
21388
{5.16397779, 0.00000000, 0.00000000, 0.00000000}};
21389
21390
// Compute reference derivatives.
21391
// Declare pointer to array of derivatives on FIAT element.
21392
double *derivatives = new double[3*num_derivatives];
21393
for (unsigned int r = 0; r < 3*num_derivatives; r++)
21394
{
21395
derivatives[r] = 0.00000000;
21396
}// end loop over 'r'
21397
21398
// Declare derivative matrix (of polynomial basis).
21399
double dmats[4][4] = \
21400
{{1.00000000, 0.00000000, 0.00000000, 0.00000000},
21401
{0.00000000, 1.00000000, 0.00000000, 0.00000000},
21402
{0.00000000, 0.00000000, 1.00000000, 0.00000000},
21403
{0.00000000, 0.00000000, 0.00000000, 1.00000000}};
21404
21405
// Declare (auxiliary) derivative matrix (of polynomial basis).
21406
double dmats_old[4][4] = \
21407
{{1.00000000, 0.00000000, 0.00000000, 0.00000000},
21408
{0.00000000, 1.00000000, 0.00000000, 0.00000000},
21409
{0.00000000, 0.00000000, 1.00000000, 0.00000000},
21410
{0.00000000, 0.00000000, 0.00000000, 1.00000000}};
21411
21412
// Loop possible derivatives.
21413
for (unsigned int r = 0; r < num_derivatives; r++)
21414
{
21415
// Resetting dmats values to compute next derivative.
21416
for (unsigned int t = 0; t < 4; t++)
21417
{
21418
for (unsigned int u = 0; u < 4; u++)
21419
{
21420
dmats[t][u] = 0.00000000;
21421
if (t == u)
21422
{
21423
dmats[t][u] = 1.00000000;
21424
}
21425
21426
}// end loop over 'u'
21427
}// end loop over 't'
21428
21429
// Looping derivative order to generate dmats.
21430
for (unsigned int s = 0; s < n; s++)
21431
{
21432
// Updating dmats_old with new values and resetting dmats.
21433
for (unsigned int t = 0; t < 4; t++)
21434
{
21435
for (unsigned int u = 0; u < 4; u++)
21436
{
21437
dmats_old[t][u] = dmats[t][u];
21438
dmats[t][u] = 0.00000000;
21439
}// end loop over 'u'
21440
}// end loop over 't'
21441
21442
// Update dmats using an inner product.
21443
if (combinations[r][s] == 0)
21444
{
21445
for (unsigned int t = 0; t < 4; t++)
21446
{
21447
for (unsigned int u = 0; u < 4; u++)
21448
{
21449
for (unsigned int tu = 0; tu < 4; tu++)
21450
{
21451
dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
21452
}// end loop over 'tu'
21453
}// end loop over 'u'
21454
}// end loop over 't'
21455
}
21456
21457
if (combinations[r][s] == 1)
21458
{
21459
for (unsigned int t = 0; t < 4; t++)
21460
{
21461
for (unsigned int u = 0; u < 4; u++)
21462
{
21463
for (unsigned int tu = 0; tu < 4; tu++)
21464
{
21465
dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
21466
}// end loop over 'tu'
21467
}// end loop over 'u'
21468
}// end loop over 't'
21469
}
21470
21471
if (combinations[r][s] == 2)
21472
{
21473
for (unsigned int t = 0; t < 4; t++)
21474
{
21475
for (unsigned int u = 0; u < 4; u++)
21476
{
21477
for (unsigned int tu = 0; tu < 4; tu++)
21478
{
21479
dmats[t][u] += dmats2[t][tu]*dmats_old[tu][u];
21480
}// end loop over 'tu'
21481
}// end loop over 'u'
21482
}// end loop over 't'
21483
}
21484
21485
}// end loop over 's'
21486
for (unsigned int s = 0; s < 4; s++)
21487
{
21488
for (unsigned int t = 0; t < 4; t++)
21489
{
21490
derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
21491
derivatives[num_derivatives + r] += coefficients1[s]*dmats[s][t]*basisvalues[t];
21492
derivatives[2*num_derivatives + r] += coefficients2[s]*dmats[s][t]*basisvalues[t];
21493
}// end loop over 't'
21494
}// end loop over 's'
21495
21496
// Using covariant Piola transform to map values back to the physical element
21497
const double tmp_ref0 = derivatives[r];
21498
const double tmp_ref1 = derivatives[num_derivatives + r];
21499
const double tmp_ref2 = derivatives[2*num_derivatives + r];
21500
derivatives[r] = (K_00*tmp_ref0 + K_10*tmp_ref1 + K_20*tmp_ref2);
21501
derivatives[num_derivatives + r] = (K_01*tmp_ref0 + K_11*tmp_ref1 + K_21*tmp_ref2);
21502
derivatives[2*num_derivatives + r] = (K_02*tmp_ref0 + K_12*tmp_ref1 + K_22*tmp_ref2);
21503
}// end loop over 'r'
21504
21505
// Transform derivatives back to physical element
21506
for (unsigned int r = 0; r < num_derivatives; r++)
21507
{
21508
for (unsigned int s = 0; s < num_derivatives; s++)
21509
{
21510
values[num_derivatives + r] += transform[r][s]*derivatives[s];
21511
values[2*num_derivatives + r] += transform[r][s]*derivatives[num_derivatives + s];
21512
values[3*num_derivatives + r] += transform[r][s]*derivatives[2*num_derivatives + s];
21513
}// end loop over 's'
21514
}// end loop over 'r'
21515
21516
// Delete pointer to array of derivatives on FIAT element
21517
delete [] derivatives;
21518
21519
// Delete pointer to array of combinations of derivatives and transform
21520
for (unsigned int r = 0; r < num_derivatives; r++)
21521
{
21522
delete [] combinations[r];
21523
}// end loop over 'r'
21524
delete [] combinations;
21525
for (unsigned int r = 0; r < num_derivatives; r++)
21526
{
21527
delete [] transform[r];
21528
}// end loop over 'r'
21529
delete [] transform;
21530
break;
21531
}
21532
case 6:
21533
{
21534
21535
// Array of basisvalues.
21536
double basisvalues[4] = {0.00000000, 0.00000000, 0.00000000, 0.00000000};
21537
21538
// Declare helper variables.
21539
unsigned int rr = 0;
21540
unsigned int ss = 0;
21541
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
21542
21543
// Compute basisvalues.
21544
basisvalues[0] = 1.00000000;
21545
basisvalues[1] = tmp0;
21546
for (unsigned int r = 0; r < 1; r++)
21547
{
21548
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
21549
ss = r*(r + 1)*(r + 2)/6;
21550
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
21551
}// end loop over 'r'
21552
for (unsigned int r = 0; r < 1; r++)
21553
{
21554
for (unsigned int s = 0; s < 1 - r; s++)
21555
{
21556
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
21557
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
21558
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
21559
}// end loop over 's'
21560
}// end loop over 'r'
21561
for (unsigned int r = 0; r < 2; r++)
21562
{
21563
for (unsigned int s = 0; s < 2 - r; s++)
21564
{
21565
for (unsigned int t = 0; t < 2 - r - s; t++)
21566
{
21567
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
21568
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
21569
}// end loop over 't'
21570
}// end loop over 's'
21571
}// end loop over 'r'
21572
21573
// Table(s) of coefficients.
21574
static const double coefficients0[4] = \
21575
{-0.28867513, 0.00000000, -0.21081851, 0.07453560};
21576
21577
static const double coefficients1[4] = \
21578
{0.28867513, 0.18257419, -0.10540926, -0.07453560};
21579
21580
static const double coefficients2[4] = \
21581
{0.00000000, 0.00000000, 0.00000000, 0.00000000};
21582
21583
// Tables of derivatives of the polynomial base (transpose).
21584
static const double dmats0[4][4] = \
21585
{{0.00000000, 0.00000000, 0.00000000, 0.00000000},
21586
{6.32455532, 0.00000000, 0.00000000, 0.00000000},
21587
{0.00000000, 0.00000000, 0.00000000, 0.00000000},
21588
{0.00000000, 0.00000000, 0.00000000, 0.00000000}};
21589
21590
static const double dmats1[4][4] = \
21591
{{0.00000000, 0.00000000, 0.00000000, 0.00000000},
21592
{3.16227766, 0.00000000, 0.00000000, 0.00000000},
21593
{5.47722558, 0.00000000, 0.00000000, 0.00000000},
21594
{0.00000000, 0.00000000, 0.00000000, 0.00000000}};
21595
21596
static const double dmats2[4][4] = \
21597
{{0.00000000, 0.00000000, 0.00000000, 0.00000000},
21598
{3.16227766, 0.00000000, 0.00000000, 0.00000000},
21599
{1.82574186, 0.00000000, 0.00000000, 0.00000000},
21600
{5.16397779, 0.00000000, 0.00000000, 0.00000000}};
21601
21602
// Compute reference derivatives.
21603
// Declare pointer to array of derivatives on FIAT element.
21604
double *derivatives = new double[3*num_derivatives];
21605
for (unsigned int r = 0; r < 3*num_derivatives; r++)
21606
{
21607
derivatives[r] = 0.00000000;
21608
}// end loop over 'r'
21609
21610
// Declare derivative matrix (of polynomial basis).
21611
double dmats[4][4] = \
21612
{{1.00000000, 0.00000000, 0.00000000, 0.00000000},
21613
{0.00000000, 1.00000000, 0.00000000, 0.00000000},
21614
{0.00000000, 0.00000000, 1.00000000, 0.00000000},
21615
{0.00000000, 0.00000000, 0.00000000, 1.00000000}};
21616
21617
// Declare (auxiliary) derivative matrix (of polynomial basis).
21618
double dmats_old[4][4] = \
21619
{{1.00000000, 0.00000000, 0.00000000, 0.00000000},
21620
{0.00000000, 1.00000000, 0.00000000, 0.00000000},
21621
{0.00000000, 0.00000000, 1.00000000, 0.00000000},
21622
{0.00000000, 0.00000000, 0.00000000, 1.00000000}};
21623
21624
// Loop possible derivatives.
21625
for (unsigned int r = 0; r < num_derivatives; r++)
21626
{
21627
// Resetting dmats values to compute next derivative.
21628
for (unsigned int t = 0; t < 4; t++)
21629
{
21630
for (unsigned int u = 0; u < 4; u++)
21631
{
21632
dmats[t][u] = 0.00000000;
21633
if (t == u)
21634
{
21635
dmats[t][u] = 1.00000000;
21636
}
21637
21638
}// end loop over 'u'
21639
}// end loop over 't'
21640
21641
// Looping derivative order to generate dmats.
21642
for (unsigned int s = 0; s < n; s++)
21643
{
21644
// Updating dmats_old with new values and resetting dmats.
21645
for (unsigned int t = 0; t < 4; t++)
21646
{
21647
for (unsigned int u = 0; u < 4; u++)
21648
{
21649
dmats_old[t][u] = dmats[t][u];
21650
dmats[t][u] = 0.00000000;
21651
}// end loop over 'u'
21652
}// end loop over 't'
21653
21654
// Update dmats using an inner product.
21655
if (combinations[r][s] == 0)
21656
{
21657
for (unsigned int t = 0; t < 4; t++)
21658
{
21659
for (unsigned int u = 0; u < 4; u++)
21660
{
21661
for (unsigned int tu = 0; tu < 4; tu++)
21662
{
21663
dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
21664
}// end loop over 'tu'
21665
}// end loop over 'u'
21666
}// end loop over 't'
21667
}
21668
21669
if (combinations[r][s] == 1)
21670
{
21671
for (unsigned int t = 0; t < 4; t++)
21672
{
21673
for (unsigned int u = 0; u < 4; u++)
21674
{
21675
for (unsigned int tu = 0; tu < 4; tu++)
21676
{
21677
dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
21678
}// end loop over 'tu'
21679
}// end loop over 'u'
21680
}// end loop over 't'
21681
}
21682
21683
if (combinations[r][s] == 2)
21684
{
21685
for (unsigned int t = 0; t < 4; t++)
21686
{
21687
for (unsigned int u = 0; u < 4; u++)
21688
{
21689
for (unsigned int tu = 0; tu < 4; tu++)
21690
{
21691
dmats[t][u] += dmats2[t][tu]*dmats_old[tu][u];
21692
}// end loop over 'tu'
21693
}// end loop over 'u'
21694
}// end loop over 't'
21695
}
21696
21697
}// end loop over 's'
21698
for (unsigned int s = 0; s < 4; s++)
21699
{
21700
for (unsigned int t = 0; t < 4; t++)
21701
{
21702
derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
21703
derivatives[num_derivatives + r] += coefficients1[s]*dmats[s][t]*basisvalues[t];
21704
derivatives[2*num_derivatives + r] += coefficients2[s]*dmats[s][t]*basisvalues[t];
21705
}// end loop over 't'
21706
}// end loop over 's'
21707
21708
// Using covariant Piola transform to map values back to the physical element
21709
const double tmp_ref0 = derivatives[r];
21710
const double tmp_ref1 = derivatives[num_derivatives + r];
21711
const double tmp_ref2 = derivatives[2*num_derivatives + r];
21712
derivatives[r] = (K_00*tmp_ref0 + K_10*tmp_ref1 + K_20*tmp_ref2);
21713
derivatives[num_derivatives + r] = (K_01*tmp_ref0 + K_11*tmp_ref1 + K_21*tmp_ref2);
21714
derivatives[2*num_derivatives + r] = (K_02*tmp_ref0 + K_12*tmp_ref1 + K_22*tmp_ref2);
21715
}// end loop over 'r'
21716
21717
// Transform derivatives back to physical element
21718
for (unsigned int r = 0; r < num_derivatives; r++)
21719
{
21720
for (unsigned int s = 0; s < num_derivatives; s++)
21721
{
21722
values[num_derivatives + r] += transform[r][s]*derivatives[s];
21723
values[2*num_derivatives + r] += transform[r][s]*derivatives[num_derivatives + s];
21724
values[3*num_derivatives + r] += transform[r][s]*derivatives[2*num_derivatives + s];
21725
}// end loop over 's'
21726
}// end loop over 'r'
21727
21728
// Delete pointer to array of derivatives on FIAT element
21729
delete [] derivatives;
21730
21731
// Delete pointer to array of combinations of derivatives and transform
21732
for (unsigned int r = 0; r < num_derivatives; r++)
21733
{
21734
delete [] combinations[r];
21735
}// end loop over 'r'
21736
delete [] combinations;
21737
for (unsigned int r = 0; r < num_derivatives; r++)
21738
{
21739
delete [] transform[r];
21740
}// end loop over 'r'
21741
delete [] transform;
21742
break;
21743
}
21744
case 7:
21745
{
21746
21747
// Array of basisvalues.
21748
double basisvalues[4] = {0.00000000, 0.00000000, 0.00000000, 0.00000000};
21749
21750
// Declare helper variables.
21751
unsigned int rr = 0;
21752
unsigned int ss = 0;
21753
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
21754
21755
// Compute basisvalues.
21756
basisvalues[0] = 1.00000000;
21757
basisvalues[1] = tmp0;
21758
for (unsigned int r = 0; r < 1; r++)
21759
{
21760
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
21761
ss = r*(r + 1)*(r + 2)/6;
21762
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
21763
}// end loop over 'r'
21764
for (unsigned int r = 0; r < 1; r++)
21765
{
21766
for (unsigned int s = 0; s < 1 - r; s++)
21767
{
21768
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
21769
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
21770
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
21771
}// end loop over 's'
21772
}// end loop over 'r'
21773
for (unsigned int r = 0; r < 2; r++)
21774
{
21775
for (unsigned int s = 0; s < 2 - r; s++)
21776
{
21777
for (unsigned int t = 0; t < 2 - r - s; t++)
21778
{
21779
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
21780
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
21781
}// end loop over 't'
21782
}// end loop over 's'
21783
}// end loop over 'r'
21784
21785
// Table(s) of coefficients.
21786
static const double coefficients0[4] = \
21787
{0.28867513, 0.00000000, 0.00000000, 0.22360680};
21788
21789
static const double coefficients1[4] = \
21790
{0.28867513, 0.00000000, 0.00000000, 0.22360680};
21791
21792
static const double coefficients2[4] = \
21793
{0.57735027, -0.18257419, -0.10540926, 0.14907120};
21794
21795
// Tables of derivatives of the polynomial base (transpose).
21796
static const double dmats0[4][4] = \
21797
{{0.00000000, 0.00000000, 0.00000000, 0.00000000},
21798
{6.32455532, 0.00000000, 0.00000000, 0.00000000},
21799
{0.00000000, 0.00000000, 0.00000000, 0.00000000},
21800
{0.00000000, 0.00000000, 0.00000000, 0.00000000}};
21801
21802
static const double dmats1[4][4] = \
21803
{{0.00000000, 0.00000000, 0.00000000, 0.00000000},
21804
{3.16227766, 0.00000000, 0.00000000, 0.00000000},
21805
{5.47722558, 0.00000000, 0.00000000, 0.00000000},
21806
{0.00000000, 0.00000000, 0.00000000, 0.00000000}};
21807
21808
static const double dmats2[4][4] = \
21809
{{0.00000000, 0.00000000, 0.00000000, 0.00000000},
21810
{3.16227766, 0.00000000, 0.00000000, 0.00000000},
21811
{1.82574186, 0.00000000, 0.00000000, 0.00000000},
21812
{5.16397779, 0.00000000, 0.00000000, 0.00000000}};
21813
21814
// Compute reference derivatives.
21815
// Declare pointer to array of derivatives on FIAT element.
21816
double *derivatives = new double[3*num_derivatives];
21817
for (unsigned int r = 0; r < 3*num_derivatives; r++)
21818
{
21819
derivatives[r] = 0.00000000;
21820
}// end loop over 'r'
21821
21822
// Declare derivative matrix (of polynomial basis).
21823
double dmats[4][4] = \
21824
{{1.00000000, 0.00000000, 0.00000000, 0.00000000},
21825
{0.00000000, 1.00000000, 0.00000000, 0.00000000},
21826
{0.00000000, 0.00000000, 1.00000000, 0.00000000},
21827
{0.00000000, 0.00000000, 0.00000000, 1.00000000}};
21828
21829
// Declare (auxiliary) derivative matrix (of polynomial basis).
21830
double dmats_old[4][4] = \
21831
{{1.00000000, 0.00000000, 0.00000000, 0.00000000},
21832
{0.00000000, 1.00000000, 0.00000000, 0.00000000},
21833
{0.00000000, 0.00000000, 1.00000000, 0.00000000},
21834
{0.00000000, 0.00000000, 0.00000000, 1.00000000}};
21835
21836
// Loop possible derivatives.
21837
for (unsigned int r = 0; r < num_derivatives; r++)
21838
{
21839
// Resetting dmats values to compute next derivative.
21840
for (unsigned int t = 0; t < 4; t++)
21841
{
21842
for (unsigned int u = 0; u < 4; u++)
21843
{
21844
dmats[t][u] = 0.00000000;
21845
if (t == u)
21846
{
21847
dmats[t][u] = 1.00000000;
21848
}
21849
21850
}// end loop over 'u'
21851
}// end loop over 't'
21852
21853
// Looping derivative order to generate dmats.
21854
for (unsigned int s = 0; s < n; s++)
21855
{
21856
// Updating dmats_old with new values and resetting dmats.
21857
for (unsigned int t = 0; t < 4; t++)
21858
{
21859
for (unsigned int u = 0; u < 4; u++)
21860
{
21861
dmats_old[t][u] = dmats[t][u];
21862
dmats[t][u] = 0.00000000;
21863
}// end loop over 'u'
21864
}// end loop over 't'
21865
21866
// Update dmats using an inner product.
21867
if (combinations[r][s] == 0)
21868
{
21869
for (unsigned int t = 0; t < 4; t++)
21870
{
21871
for (unsigned int u = 0; u < 4; u++)
21872
{
21873
for (unsigned int tu = 0; tu < 4; tu++)
21874
{
21875
dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
21876
}// end loop over 'tu'
21877
}// end loop over 'u'
21878
}// end loop over 't'
21879
}
21880
21881
if (combinations[r][s] == 1)
21882
{
21883
for (unsigned int t = 0; t < 4; t++)
21884
{
21885
for (unsigned int u = 0; u < 4; u++)
21886
{
21887
for (unsigned int tu = 0; tu < 4; tu++)
21888
{
21889
dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
21890
}// end loop over 'tu'
21891
}// end loop over 'u'
21892
}// end loop over 't'
21893
}
21894
21895
if (combinations[r][s] == 2)
21896
{
21897
for (unsigned int t = 0; t < 4; t++)
21898
{
21899
for (unsigned int u = 0; u < 4; u++)
21900
{
21901
for (unsigned int tu = 0; tu < 4; tu++)
21902
{
21903
dmats[t][u] += dmats2[t][tu]*dmats_old[tu][u];
21904
}// end loop over 'tu'
21905
}// end loop over 'u'
21906
}// end loop over 't'
21907
}
21908
21909
}// end loop over 's'
21910
for (unsigned int s = 0; s < 4; s++)
21911
{
21912
for (unsigned int t = 0; t < 4; t++)
21913
{
21914
derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
21915
derivatives[num_derivatives + r] += coefficients1[s]*dmats[s][t]*basisvalues[t];
21916
derivatives[2*num_derivatives + r] += coefficients2[s]*dmats[s][t]*basisvalues[t];
21917
}// end loop over 't'
21918
}// end loop over 's'
21919
21920
// Using covariant Piola transform to map values back to the physical element
21921
const double tmp_ref0 = derivatives[r];
21922
const double tmp_ref1 = derivatives[num_derivatives + r];
21923
const double tmp_ref2 = derivatives[2*num_derivatives + r];
21924
derivatives[r] = (K_00*tmp_ref0 + K_10*tmp_ref1 + K_20*tmp_ref2);
21925
derivatives[num_derivatives + r] = (K_01*tmp_ref0 + K_11*tmp_ref1 + K_21*tmp_ref2);
21926
derivatives[2*num_derivatives + r] = (K_02*tmp_ref0 + K_12*tmp_ref1 + K_22*tmp_ref2);
21927
}// end loop over 'r'
21928
21929
// Transform derivatives back to physical element
21930
for (unsigned int r = 0; r < num_derivatives; r++)
21931
{
21932
for (unsigned int s = 0; s < num_derivatives; s++)
21933
{
21934
values[num_derivatives + r] += transform[r][s]*derivatives[s];
21935
values[2*num_derivatives + r] += transform[r][s]*derivatives[num_derivatives + s];
21936
values[3*num_derivatives + r] += transform[r][s]*derivatives[2*num_derivatives + s];
21937
}// end loop over 's'
21938
}// end loop over 'r'
21939
21940
// Delete pointer to array of derivatives on FIAT element
21941
delete [] derivatives;
21942
21943
// Delete pointer to array of combinations of derivatives and transform
21944
for (unsigned int r = 0; r < num_derivatives; r++)
21945
{
21946
delete [] combinations[r];
21947
}// end loop over 'r'
21948
delete [] combinations;
21949
for (unsigned int r = 0; r < num_derivatives; r++)
21950
{
21951
delete [] transform[r];
21952
}// end loop over 'r'
21953
delete [] transform;
21954
break;
21955
}
21956
case 8:
21957
{
21958
21959
// Array of basisvalues.
21960
double basisvalues[4] = {0.00000000, 0.00000000, 0.00000000, 0.00000000};
21961
21962
// Declare helper variables.
21963
unsigned int rr = 0;
21964
unsigned int ss = 0;
21965
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
21966
21967
// Compute basisvalues.
21968
basisvalues[0] = 1.00000000;
21969
basisvalues[1] = tmp0;
21970
for (unsigned int r = 0; r < 1; r++)
21971
{
21972
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
21973
ss = r*(r + 1)*(r + 2)/6;
21974
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
21975
}// end loop over 'r'
21976
for (unsigned int r = 0; r < 1; r++)
21977
{
21978
for (unsigned int s = 0; s < 1 - r; s++)
21979
{
21980
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
21981
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
21982
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
21983
}// end loop over 's'
21984
}// end loop over 'r'
21985
for (unsigned int r = 0; r < 2; r++)
21986
{
21987
for (unsigned int s = 0; s < 2 - r; s++)
21988
{
21989
for (unsigned int t = 0; t < 2 - r - s; t++)
21990
{
21991
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
21992
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
21993
}// end loop over 't'
21994
}// end loop over 's'
21995
}// end loop over 'r'
21996
21997
// Table(s) of coefficients.
21998
static const double coefficients0[4] = \
21999
{0.28867513, 0.00000000, 0.21081851, -0.07453560};
22000
22001
static const double coefficients1[4] = \
22002
{0.57735027, -0.18257419, 0.10540926, -0.14907120};
22003
22004
static const double coefficients2[4] = \
22005
{0.28867513, 0.00000000, 0.21081851, -0.07453560};
22006
22007
// Tables of derivatives of the polynomial base (transpose).
22008
static const double dmats0[4][4] = \
22009
{{0.00000000, 0.00000000, 0.00000000, 0.00000000},
22010
{6.32455532, 0.00000000, 0.00000000, 0.00000000},
22011
{0.00000000, 0.00000000, 0.00000000, 0.00000000},
22012
{0.00000000, 0.00000000, 0.00000000, 0.00000000}};
22013
22014
static const double dmats1[4][4] = \
22015
{{0.00000000, 0.00000000, 0.00000000, 0.00000000},
22016
{3.16227766, 0.00000000, 0.00000000, 0.00000000},
22017
{5.47722558, 0.00000000, 0.00000000, 0.00000000},
22018
{0.00000000, 0.00000000, 0.00000000, 0.00000000}};
22019
22020
static const double dmats2[4][4] = \
22021
{{0.00000000, 0.00000000, 0.00000000, 0.00000000},
22022
{3.16227766, 0.00000000, 0.00000000, 0.00000000},
22023
{1.82574186, 0.00000000, 0.00000000, 0.00000000},
22024
{5.16397779, 0.00000000, 0.00000000, 0.00000000}};
22025
22026
// Compute reference derivatives.
22027
// Declare pointer to array of derivatives on FIAT element.
22028
double *derivatives = new double[3*num_derivatives];
22029
for (unsigned int r = 0; r < 3*num_derivatives; r++)
22030
{
22031
derivatives[r] = 0.00000000;
22032
}// end loop over 'r'
22033
22034
// Declare derivative matrix (of polynomial basis).
22035
double dmats[4][4] = \
22036
{{1.00000000, 0.00000000, 0.00000000, 0.00000000},
22037
{0.00000000, 1.00000000, 0.00000000, 0.00000000},
22038
{0.00000000, 0.00000000, 1.00000000, 0.00000000},
22039
{0.00000000, 0.00000000, 0.00000000, 1.00000000}};
22040
22041
// Declare (auxiliary) derivative matrix (of polynomial basis).
22042
double dmats_old[4][4] = \
22043
{{1.00000000, 0.00000000, 0.00000000, 0.00000000},
22044
{0.00000000, 1.00000000, 0.00000000, 0.00000000},
22045
{0.00000000, 0.00000000, 1.00000000, 0.00000000},
22046
{0.00000000, 0.00000000, 0.00000000, 1.00000000}};
22047
22048
// Loop possible derivatives.
22049
for (unsigned int r = 0; r < num_derivatives; r++)
22050
{
22051
// Resetting dmats values to compute next derivative.
22052
for (unsigned int t = 0; t < 4; t++)
22053
{
22054
for (unsigned int u = 0; u < 4; u++)
22055
{
22056
dmats[t][u] = 0.00000000;
22057
if (t == u)
22058
{
22059
dmats[t][u] = 1.00000000;
22060
}
22061
22062
}// end loop over 'u'
22063
}// end loop over 't'
22064
22065
// Looping derivative order to generate dmats.
22066
for (unsigned int s = 0; s < n; s++)
22067
{
22068
// Updating dmats_old with new values and resetting dmats.
22069
for (unsigned int t = 0; t < 4; t++)
22070
{
22071
for (unsigned int u = 0; u < 4; u++)
22072
{
22073
dmats_old[t][u] = dmats[t][u];
22074
dmats[t][u] = 0.00000000;
22075
}// end loop over 'u'
22076
}// end loop over 't'
22077
22078
// Update dmats using an inner product.
22079
if (combinations[r][s] == 0)
22080
{
22081
for (unsigned int t = 0; t < 4; t++)
22082
{
22083
for (unsigned int u = 0; u < 4; u++)
22084
{
22085
for (unsigned int tu = 0; tu < 4; tu++)
22086
{
22087
dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
22088
}// end loop over 'tu'
22089
}// end loop over 'u'
22090
}// end loop over 't'
22091
}
22092
22093
if (combinations[r][s] == 1)
22094
{
22095
for (unsigned int t = 0; t < 4; t++)
22096
{
22097
for (unsigned int u = 0; u < 4; u++)
22098
{
22099
for (unsigned int tu = 0; tu < 4; tu++)
22100
{
22101
dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
22102
}// end loop over 'tu'
22103
}// end loop over 'u'
22104
}// end loop over 't'
22105
}
22106
22107
if (combinations[r][s] == 2)
22108
{
22109
for (unsigned int t = 0; t < 4; t++)
22110
{
22111
for (unsigned int u = 0; u < 4; u++)
22112
{
22113
for (unsigned int tu = 0; tu < 4; tu++)
22114
{
22115
dmats[t][u] += dmats2[t][tu]*dmats_old[tu][u];
22116
}// end loop over 'tu'
22117
}// end loop over 'u'
22118
}// end loop over 't'
22119
}
22120
22121
}// end loop over 's'
22122
for (unsigned int s = 0; s < 4; s++)
22123
{
22124
for (unsigned int t = 0; t < 4; t++)
22125
{
22126
derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
22127
derivatives[num_derivatives + r] += coefficients1[s]*dmats[s][t]*basisvalues[t];
22128
derivatives[2*num_derivatives + r] += coefficients2[s]*dmats[s][t]*basisvalues[t];
22129
}// end loop over 't'
22130
}// end loop over 's'
22131
22132
// Using covariant Piola transform to map values back to the physical element
22133
const double tmp_ref0 = derivatives[r];
22134
const double tmp_ref1 = derivatives[num_derivatives + r];
22135
const double tmp_ref2 = derivatives[2*num_derivatives + r];
22136
derivatives[r] = (K_00*tmp_ref0 + K_10*tmp_ref1 + K_20*tmp_ref2);
22137
derivatives[num_derivatives + r] = (K_01*tmp_ref0 + K_11*tmp_ref1 + K_21*tmp_ref2);
22138
derivatives[2*num_derivatives + r] = (K_02*tmp_ref0 + K_12*tmp_ref1 + K_22*tmp_ref2);
22139
}// end loop over 'r'
22140
22141
// Transform derivatives back to physical element
22142
for (unsigned int r = 0; r < num_derivatives; r++)
22143
{
22144
for (unsigned int s = 0; s < num_derivatives; s++)
22145
{
22146
values[num_derivatives + r] += transform[r][s]*derivatives[s];
22147
values[2*num_derivatives + r] += transform[r][s]*derivatives[num_derivatives + s];
22148
values[3*num_derivatives + r] += transform[r][s]*derivatives[2*num_derivatives + s];
22149
}// end loop over 's'
22150
}// end loop over 'r'
22151
22152
// Delete pointer to array of derivatives on FIAT element
22153
delete [] derivatives;
22154
22155
// Delete pointer to array of combinations of derivatives and transform
22156
for (unsigned int r = 0; r < num_derivatives; r++)
22157
{
22158
delete [] combinations[r];
22159
}// end loop over 'r'
22160
delete [] combinations;
22161
for (unsigned int r = 0; r < num_derivatives; r++)
22162
{
22163
delete [] transform[r];
22164
}// end loop over 'r'
22165
delete [] transform;
22166
break;
22167
}
22168
case 9:
22169
{
22170
22171
// Array of basisvalues.
22172
double basisvalues[4] = {0.00000000, 0.00000000, 0.00000000, 0.00000000};
22173
22174
// Declare helper variables.
22175
unsigned int rr = 0;
22176
unsigned int ss = 0;
22177
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
22178
22179
// Compute basisvalues.
22180
basisvalues[0] = 1.00000000;
22181
basisvalues[1] = tmp0;
22182
for (unsigned int r = 0; r < 1; r++)
22183
{
22184
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
22185
ss = r*(r + 1)*(r + 2)/6;
22186
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
22187
}// end loop over 'r'
22188
for (unsigned int r = 0; r < 1; r++)
22189
{
22190
for (unsigned int s = 0; s < 1 - r; s++)
22191
{
22192
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
22193
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
22194
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
22195
}// end loop over 's'
22196
}// end loop over 'r'
22197
for (unsigned int r = 0; r < 2; r++)
22198
{
22199
for (unsigned int s = 0; s < 2 - r; s++)
22200
{
22201
for (unsigned int t = 0; t < 2 - r - s; t++)
22202
{
22203
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
22204
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
22205
}// end loop over 't'
22206
}// end loop over 's'
22207
}// end loop over 'r'
22208
22209
// Table(s) of coefficients.
22210
static const double coefficients0[4] = \
22211
{0.57735027, 0.00000000, -0.21081851, -0.14907120};
22212
22213
static const double coefficients1[4] = \
22214
{0.28867513, 0.18257419, -0.10540926, -0.07453560};
22215
22216
static const double coefficients2[4] = \
22217
{0.28867513, 0.18257419, -0.10540926, -0.07453560};
22218
22219
// Tables of derivatives of the polynomial base (transpose).
22220
static const double dmats0[4][4] = \
22221
{{0.00000000, 0.00000000, 0.00000000, 0.00000000},
22222
{6.32455532, 0.00000000, 0.00000000, 0.00000000},
22223
{0.00000000, 0.00000000, 0.00000000, 0.00000000},
22224
{0.00000000, 0.00000000, 0.00000000, 0.00000000}};
22225
22226
static const double dmats1[4][4] = \
22227
{{0.00000000, 0.00000000, 0.00000000, 0.00000000},
22228
{3.16227766, 0.00000000, 0.00000000, 0.00000000},
22229
{5.47722558, 0.00000000, 0.00000000, 0.00000000},
22230
{0.00000000, 0.00000000, 0.00000000, 0.00000000}};
22231
22232
static const double dmats2[4][4] = \
22233
{{0.00000000, 0.00000000, 0.00000000, 0.00000000},
22234
{3.16227766, 0.00000000, 0.00000000, 0.00000000},
22235
{1.82574186, 0.00000000, 0.00000000, 0.00000000},
22236
{5.16397779, 0.00000000, 0.00000000, 0.00000000}};
22237
22238
// Compute reference derivatives.
22239
// Declare pointer to array of derivatives on FIAT element.
22240
double *derivatives = new double[3*num_derivatives];
22241
for (unsigned int r = 0; r < 3*num_derivatives; r++)
22242
{
22243
derivatives[r] = 0.00000000;
22244
}// end loop over 'r'
22245
22246
// Declare derivative matrix (of polynomial basis).
22247
double dmats[4][4] = \
22248
{{1.00000000, 0.00000000, 0.00000000, 0.00000000},
22249
{0.00000000, 1.00000000, 0.00000000, 0.00000000},
22250
{0.00000000, 0.00000000, 1.00000000, 0.00000000},
22251
{0.00000000, 0.00000000, 0.00000000, 1.00000000}};
22252
22253
// Declare (auxiliary) derivative matrix (of polynomial basis).
22254
double dmats_old[4][4] = \
22255
{{1.00000000, 0.00000000, 0.00000000, 0.00000000},
22256
{0.00000000, 1.00000000, 0.00000000, 0.00000000},
22257
{0.00000000, 0.00000000, 1.00000000, 0.00000000},
22258
{0.00000000, 0.00000000, 0.00000000, 1.00000000}};
22259
22260
// Loop possible derivatives.
22261
for (unsigned int r = 0; r < num_derivatives; r++)
22262
{
22263
// Resetting dmats values to compute next derivative.
22264
for (unsigned int t = 0; t < 4; t++)
22265
{
22266
for (unsigned int u = 0; u < 4; u++)
22267
{
22268
dmats[t][u] = 0.00000000;
22269
if (t == u)
22270
{
22271
dmats[t][u] = 1.00000000;
22272
}
22273
22274
}// end loop over 'u'
22275
}// end loop over 't'
22276
22277
// Looping derivative order to generate dmats.
22278
for (unsigned int s = 0; s < n; s++)
22279
{
22280
// Updating dmats_old with new values and resetting dmats.
22281
for (unsigned int t = 0; t < 4; t++)
22282
{
22283
for (unsigned int u = 0; u < 4; u++)
22284
{
22285
dmats_old[t][u] = dmats[t][u];
22286
dmats[t][u] = 0.00000000;
22287
}// end loop over 'u'
22288
}// end loop over 't'
22289
22290
// Update dmats using an inner product.
22291
if (combinations[r][s] == 0)
22292
{
22293
for (unsigned int t = 0; t < 4; t++)
22294
{
22295
for (unsigned int u = 0; u < 4; u++)
22296
{
22297
for (unsigned int tu = 0; tu < 4; tu++)
22298
{
22299
dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
22300
}// end loop over 'tu'
22301
}// end loop over 'u'
22302
}// end loop over 't'
22303
}
22304
22305
if (combinations[r][s] == 1)
22306
{
22307
for (unsigned int t = 0; t < 4; t++)
22308
{
22309
for (unsigned int u = 0; u < 4; u++)
22310
{
22311
for (unsigned int tu = 0; tu < 4; tu++)
22312
{
22313
dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
22314
}// end loop over 'tu'
22315
}// end loop over 'u'
22316
}// end loop over 't'
22317
}
22318
22319
if (combinations[r][s] == 2)
22320
{
22321
for (unsigned int t = 0; t < 4; t++)
22322
{
22323
for (unsigned int u = 0; u < 4; u++)
22324
{
22325
for (unsigned int tu = 0; tu < 4; tu++)
22326
{
22327
dmats[t][u] += dmats2[t][tu]*dmats_old[tu][u];
22328
}// end loop over 'tu'
22329
}// end loop over 'u'
22330
}// end loop over 't'
22331
}
22332
22333
}// end loop over 's'
22334
for (unsigned int s = 0; s < 4; s++)
22335
{
22336
for (unsigned int t = 0; t < 4; t++)
22337
{
22338
derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
22339
derivatives[num_derivatives + r] += coefficients1[s]*dmats[s][t]*basisvalues[t];
22340
derivatives[2*num_derivatives + r] += coefficients2[s]*dmats[s][t]*basisvalues[t];
22341
}// end loop over 't'
22342
}// end loop over 's'
22343
22344
// Using covariant Piola transform to map values back to the physical element
22345
const double tmp_ref0 = derivatives[r];
22346
const double tmp_ref1 = derivatives[num_derivatives + r];
22347
const double tmp_ref2 = derivatives[2*num_derivatives + r];
22348
derivatives[r] = (K_00*tmp_ref0 + K_10*tmp_ref1 + K_20*tmp_ref2);
22349
derivatives[num_derivatives + r] = (K_01*tmp_ref0 + K_11*tmp_ref1 + K_21*tmp_ref2);
22350
derivatives[2*num_derivatives + r] = (K_02*tmp_ref0 + K_12*tmp_ref1 + K_22*tmp_ref2);
22351
}// end loop over 'r'
22352
22353
// Transform derivatives back to physical element
22354
for (unsigned int r = 0; r < num_derivatives; r++)
22355
{
22356
for (unsigned int s = 0; s < num_derivatives; s++)
22357
{
22358
values[num_derivatives + r] += transform[r][s]*derivatives[s];
22359
values[2*num_derivatives + r] += transform[r][s]*derivatives[num_derivatives + s];
22360
values[3*num_derivatives + r] += transform[r][s]*derivatives[2*num_derivatives + s];
22361
}// end loop over 's'
22362
}// end loop over 'r'
22363
22364
// Delete pointer to array of derivatives on FIAT element
22365
delete [] derivatives;
22366
22367
// Delete pointer to array of combinations of derivatives and transform
22368
for (unsigned int r = 0; r < num_derivatives; r++)
22369
{
22370
delete [] combinations[r];
22371
}// end loop over 'r'
22372
delete [] combinations;
22373
for (unsigned int r = 0; r < num_derivatives; r++)
22374
{
22375
delete [] transform[r];
22376
}// end loop over 'r'
22377
delete [] transform;
22378
break;
22379
}
5115
22380
}
5116
22381
5117
22382
}
7521
24786
}// end loop over 'r'
7522
24787
7523
24788
// Compute element tensor using UFL quadrature representation
7524
// Optimisations: ('simplify expressions', False), ('ignore zero tables', False), ('non zero columns', False), ('remove zero terms', False), ('ignore ones', False)
24789
// Optimisations: ('eliminate zeros', False), ('ignore ones', False), ('ignore zero tables', False), ('optimisation', False), ('remove zero terms', False)
7525
24790
7526
24791
// Loop quadrature points for integral.
7527
24792
// Number of operations to compute element tensor for following IP loop = 325600
Loggerhead is a web-based interface for Breezy
Version: 2.0.1