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- Committer: Bazaar Package Importer
- Author(s): Johannes Ring
- Date: 2009-10-12 14:13:18 UTC
- mfrom: (1.1.1 upstream)
- Revision ID: james.westby@ubuntu.com-20091012141318-hkbxl0sq555vqv7d
Tags: 0.9.4-1
* New upstream release. This version cleans up the design of the
function class by adding a new abstraction for user-defined
functions called Expression. A number of minor bugfixes and
improvements have also been made.
* debian/watch: Update for new flat directory structure.
* Update debian/copyright.
* debian/rules: Use explicit paths to PETSc 3.0.0 and SLEPc 3.0.0.
function class by adding a new abstraction for user-defined
functions called Expression. A number of minor bugfixes and
improvements have also been made.
* debian/watch: Update for new flat directory structure.
* Update debian/copyright.
* debian/rules: Use explicit paths to PETSc 3.0.0 and SLEPc 3.0.0.
- files added:
- bench/SConscript
- bench/common
- bench/fem/speedup
- demo/function/nonmatching-interpolation
- demo/function/nonmatching-interpolation/cpp
- demo/function/nonmatching-interpolation/python
- demo/function/nonmatching-projection
- demo/function/nonmatching-projection/cpp
- demo/function/nonmatching-projection/python
- demo/ode/reaction
- demo/ode/reaction/cpp
- demo/parameters
- demo/parameters/cpp
- demo/parameters/python
- demo/pde/curl-curl
- demo/pde/curl-curl/cpp
- demo/pde/curl-curl/python
- demo/pde/dg/biharmonic
- demo/pde/dg/biharmonic/cpp
- demo/pde/dg/biharmonic/python
- demo/pde/equality
- demo/pde/equality/cpp
- demo/pde/equality/python
- demo/pde/hyperelasticity
- demo/pde/hyperelasticity/cpp
- demo/pde/hyperelasticity/python
- demo/pde/simple
- demo/pde/simple/cpp
- demo/pde/simple/python
- sandbox/passembly-0.8.0
- sandbox/passembly-bench-vec
- sandbox/passembly-bench-vec-0.8.0
- sandbox/passembly-bench-vec/result
- sandbox/passembly/result
- sandbox/pdof_map
- test/regression
- test/system/parallel-assembly-solve
- test/unit/fem
- test/unit/fem/cpp
- test/unit/fem/python
- files removed:
- bench/fem/assembly/cpp/forms/Elasticity3D.form
- bench/fem/passembly
- debian/patches
- demo/ode/tentusscher
- demo/ode/tentusscher/cpp
- sandbox/electromagnetics
- sandbox/electromagnetics/tests
- sandbox/graph
- sandbox/ilmarw
- sandbox/ilmarw/assembler_bench
- sandbox/ilmarw/assembler_bench/Elasticity_3D
- sandbox/ilmarw/assembler_bench/ICNS_3D_Momentum
- sandbox/ilmarw/assembler_bench/Laplace_2D
- sandbox/ilmarw/assembler_bench/Stokes_2D_Stab
- sandbox/ilmarw/assembler_bench/Stokes_2D_TH
- sandbox/ilmarw/test
- sandbox/jit
- sandbox/meshordering
- sandbox/nonmatching
- sandbox/partitioning
- sandbox/passembly-old
- sandbox/ufl
- sandbox/ufl/elasticity
- sandbox/ufl/poisson
- sandbox/xml
- site-packages/dolfin/ufl
- files modified:
- .hg_archival.txt
added
removed
test/unit/function/cpp/Projection.h
1
1
// This code conforms with the UFC specification version 1.0
2
// and was automatically generated by FFC version 0.6.0.
2
// and was automatically generated by FFC version 0.7.0.
3
3
//
4
4
// Warning: This code was generated with the option '-l dolfin'
5
5
// and contains DOLFIN-specific wrappers that depend on DOLFIN.
11
11
#include <stdexcept>
12
12
#include <fstream>
13
13
#include <ufc.h>
14
15
/// This class defines the interface for a finite element.
16
17
class UFC_ProjectionBilinearForm_finite_element_0: public ufc::finite_element
18
{
19
public:
20
21
/// Constructor
22
UFC_ProjectionBilinearForm_finite_element_0() : ufc::finite_element()
23
{
24
// Do nothing
25
}
26
27
/// Destructor
28
virtual ~UFC_ProjectionBilinearForm_finite_element_0()
29
{
30
// Do nothing
31
}
32
33
/// Return a string identifying the finite element
34
virtual const char* signature() const
35
{
36
return "FiniteElement('Lagrange', 'tetrahedron', 2)";
37
}
38
39
/// Return the cell shape
40
virtual ufc::shape cell_shape() const
41
{
42
return ufc::tetrahedron;
43
}
44
45
/// Return the dimension of the finite element function space
46
virtual unsigned int space_dimension() const
47
{
48
return 10;
49
}
50
51
/// Return the rank of the value space
52
virtual unsigned int value_rank() const
53
{
54
return 0;
55
}
56
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/// Return the dimension of the value space for axis i
58
virtual unsigned int value_dimension(unsigned int i) const
59
{
60
return 1;
61
}
62
63
/// Evaluate basis function i at given point in cell
64
virtual void evaluate_basis(unsigned int i,
65
double* values,
66
const double* coordinates,
67
const ufc::cell& c) const
68
{
69
// Extract vertex coordinates
70
const double * const * element_coordinates = c.coordinates;
71
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// Compute Jacobian of affine map from reference cell
73
const double J_00 = element_coordinates[1][0] - element_coordinates[0][0];
74
const double J_01 = element_coordinates[2][0] - element_coordinates[0][0];
75
const double J_02 = element_coordinates[3][0] - element_coordinates[0][0];
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const double J_10 = element_coordinates[1][1] - element_coordinates[0][1];
77
const double J_11 = element_coordinates[2][1] - element_coordinates[0][1];
78
const double J_12 = element_coordinates[3][1] - element_coordinates[0][1];
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const double J_20 = element_coordinates[1][2] - element_coordinates[0][2];
80
const double J_21 = element_coordinates[2][2] - element_coordinates[0][2];
81
const double J_22 = element_coordinates[3][2] - element_coordinates[0][2];
82
83
// Compute sub determinants
84
const double d00 = J_11*J_22 - J_12*J_21;
85
const double d01 = J_12*J_20 - J_10*J_22;
86
const double d02 = J_10*J_21 - J_11*J_20;
87
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const double d10 = J_02*J_21 - J_01*J_22;
89
const double d11 = J_00*J_22 - J_02*J_20;
90
const double d12 = J_01*J_20 - J_00*J_21;
91
92
const double d20 = J_01*J_12 - J_02*J_11;
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const double d21 = J_02*J_10 - J_00*J_12;
94
const double d22 = J_00*J_11 - J_01*J_10;
95
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// Compute determinant of Jacobian
97
double detJ = J_00*d00 + J_10*d10 + J_20*d20;
98
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// Compute inverse of Jacobian
100
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// Compute constants
102
const double C0 = d00*(element_coordinates[0][0] - element_coordinates[2][0] - element_coordinates[3][0]) \
103
+ d10*(element_coordinates[0][1] - element_coordinates[2][1] - element_coordinates[3][1]) \
104
+ d20*(element_coordinates[0][2] - element_coordinates[2][2] - element_coordinates[3][2]);
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106
const double C1 = d01*(element_coordinates[0][0] - element_coordinates[1][0] - element_coordinates[3][0]) \
107
+ d11*(element_coordinates[0][1] - element_coordinates[1][1] - element_coordinates[3][1]) \
108
+ d21*(element_coordinates[0][2] - element_coordinates[1][2] - element_coordinates[3][2]);
109
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const double C2 = d02*(element_coordinates[0][0] - element_coordinates[1][0] - element_coordinates[2][0]) \
111
+ d12*(element_coordinates[0][1] - element_coordinates[1][1] - element_coordinates[2][1]) \
112
+ d22*(element_coordinates[0][2] - element_coordinates[1][2] - element_coordinates[2][2]);
113
114
// Get coordinates and map to the UFC reference element
115
double x = (C0 + d00*coordinates[0] + d10*coordinates[1] + d20*coordinates[2]) / detJ;
116
double y = (C1 + d01*coordinates[0] + d11*coordinates[1] + d21*coordinates[2]) / detJ;
117
double z = (C2 + d02*coordinates[0] + d12*coordinates[1] + d22*coordinates[2]) / detJ;
118
119
// Map coordinates to the reference cube
120
if (std::abs(y + z - 1.0) < 1e-14)
121
x = 1.0;
122
else
123
x = -2.0 * x/(y + z - 1.0) - 1.0;
124
if (std::abs(z - 1.0) < 1e-14)
125
y = -1.0;
126
else
127
y = 2.0 * y/(1.0 - z) - 1.0;
128
z = 2.0 * z - 1.0;
129
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// Reset values
131
*values = 0;
132
133
// Map degree of freedom to element degree of freedom
134
const unsigned int dof = i;
135
136
// Generate scalings
137
const double scalings_y_0 = 1;
138
const double scalings_y_1 = scalings_y_0*(0.5 - 0.5*y);
139
const double scalings_y_2 = scalings_y_1*(0.5 - 0.5*y);
140
const double scalings_z_0 = 1;
141
const double scalings_z_1 = scalings_z_0*(0.5 - 0.5*z);
142
const double scalings_z_2 = scalings_z_1*(0.5 - 0.5*z);
143
144
// Compute psitilde_a
145
const double psitilde_a_0 = 1;
146
const double psitilde_a_1 = x;
147
const double psitilde_a_2 = 1.5*x*psitilde_a_1 - 0.5*psitilde_a_0;
148
149
// Compute psitilde_bs
150
const double psitilde_bs_0_0 = 1;
151
const double psitilde_bs_0_1 = 1.5*y + 0.5;
152
const double psitilde_bs_0_2 = 0.111111111111111*psitilde_bs_0_1 + 1.66666666666667*y*psitilde_bs_0_1 - 0.555555555555556*psitilde_bs_0_0;
153
const double psitilde_bs_1_0 = 1;
154
const double psitilde_bs_1_1 = 2.5*y + 1.5;
155
const double psitilde_bs_2_0 = 1;
156
157
// Compute psitilde_cs
158
const double psitilde_cs_00_0 = 1;
159
const double psitilde_cs_00_1 = 2*z + 1;
160
const double psitilde_cs_00_2 = 0.3125*psitilde_cs_00_1 + 1.875*z*psitilde_cs_00_1 - 0.5625*psitilde_cs_00_0;
161
const double psitilde_cs_01_0 = 1;
162
const double psitilde_cs_01_1 = 3*z + 2;
163
const double psitilde_cs_02_0 = 1;
164
const double psitilde_cs_10_0 = 1;
165
const double psitilde_cs_10_1 = 3*z + 2;
166
const double psitilde_cs_11_0 = 1;
167
const double psitilde_cs_20_0 = 1;
168
169
// Compute basisvalues
170
const double basisvalue0 = 0.866025403784439*psitilde_a_0*scalings_y_0*psitilde_bs_0_0*scalings_z_0*psitilde_cs_00_0;
171
const double basisvalue1 = 2.73861278752583*psitilde_a_1*scalings_y_1*psitilde_bs_1_0*scalings_z_1*psitilde_cs_10_0;
172
const double basisvalue2 = 1.58113883008419*psitilde_a_0*scalings_y_0*psitilde_bs_0_1*scalings_z_1*psitilde_cs_01_0;
173
const double basisvalue3 = 1.11803398874989*psitilde_a_0*scalings_y_0*psitilde_bs_0_0*scalings_z_0*psitilde_cs_00_1;
174
const double basisvalue4 = 5.1234753829798*psitilde_a_2*scalings_y_2*psitilde_bs_2_0*scalings_z_2*psitilde_cs_20_0;
175
const double basisvalue5 = 3.96862696659689*psitilde_a_1*scalings_y_1*psitilde_bs_1_1*scalings_z_2*psitilde_cs_11_0;
176
const double basisvalue6 = 2.29128784747792*psitilde_a_0*scalings_y_0*psitilde_bs_0_2*scalings_z_2*psitilde_cs_02_0;
177
const double basisvalue7 = 3.24037034920393*psitilde_a_1*scalings_y_1*psitilde_bs_1_0*scalings_z_1*psitilde_cs_10_1;
178
const double basisvalue8 = 1.87082869338697*psitilde_a_0*scalings_y_0*psitilde_bs_0_1*scalings_z_1*psitilde_cs_01_1;
179
const double basisvalue9 = 1.3228756555323*psitilde_a_0*scalings_y_0*psitilde_bs_0_0*scalings_z_0*psitilde_cs_00_2;
180
181
// Table(s) of coefficients
182
const static double coefficients0[10][10] = \
183
{{-0.0577350269189625, -0.0608580619450185, -0.0351364184463153, -0.0248451997499977, 0.0650600048632355, 0.050395263067897, 0.0290957186981323, 0.0411475599898912, 0.0237565548366599, 0.0167984210226323},
184
{-0.0577350269189625, 0.0608580619450185, -0.0351364184463153, -0.0248451997499976, 0.0650600048632355, -0.050395263067897, 0.0290957186981323, -0.0411475599898912, 0.0237565548366599, 0.0167984210226323},
185
{-0.0577350269189626, 0, 0.0702728368926306, -0.0248451997499976, 0, 0, 0.087287156094397, 0, -0.0475131096733199, 0.0167984210226323},
186
{-0.0577350269189626, 0, 0, 0.074535599249993, 0, 0, 0, 0, 0, 0.100790526135794},
187
{0.23094010767585, 0, 0.140545673785261, 0.0993807989999906, 0, 0, 0, 0, 0.1187827741833, -0.0671936840905293},
188
{0.23094010767585, 0.121716123890037, -0.0702728368926306, 0.0993807989999907, 0, 0, 0, 0.102868899974728, -0.0593913870916499, -0.0671936840905293},
189
{0.23094010767585, 0.121716123890037, 0.0702728368926307, -0.0993807989999907, 0, 0.100790526135794, -0.087287156094397, -0.0205737799949456, -0.01187827741833, 0.0167984210226323},
190
{0.23094010767585, -0.121716123890037, -0.0702728368926307, 0.0993807989999906, 0, 0, 0, -0.102868899974728, -0.0593913870916499, -0.0671936840905293},
191
{0.23094010767585, -0.121716123890037, 0.0702728368926306, -0.0993807989999907, 0, -0.100790526135794, -0.0872871560943969, 0.0205737799949456, -0.01187827741833, 0.0167984210226323},
192
{0.23094010767585, 0, -0.140545673785261, -0.0993807989999906, -0.130120009726471, 0, 0.0290957186981323, 0, 0.02375655483666, 0.0167984210226323}};
193
194
// Extract relevant coefficients
195
const double coeff0_0 = coefficients0[dof][0];
196
const double coeff0_1 = coefficients0[dof][1];
197
const double coeff0_2 = coefficients0[dof][2];
198
const double coeff0_3 = coefficients0[dof][3];
199
const double coeff0_4 = coefficients0[dof][4];
200
const double coeff0_5 = coefficients0[dof][5];
201
const double coeff0_6 = coefficients0[dof][6];
202
const double coeff0_7 = coefficients0[dof][7];
203
const double coeff0_8 = coefficients0[dof][8];
204
const double coeff0_9 = coefficients0[dof][9];
205
206
// Compute value(s)
207
*values = coeff0_0*basisvalue0 + coeff0_1*basisvalue1 + coeff0_2*basisvalue2 + coeff0_3*basisvalue3 + coeff0_4*basisvalue4 + coeff0_5*basisvalue5 + coeff0_6*basisvalue6 + coeff0_7*basisvalue7 + coeff0_8*basisvalue8 + coeff0_9*basisvalue9;
208
}
209
210
/// Evaluate all basis functions at given point in cell
211
virtual void evaluate_basis_all(double* values,
212
const double* coordinates,
213
const ufc::cell& c) const
214
{
215
throw std::runtime_error("The vectorised version of evaluate_basis() is not yet implemented.");
216
}
217
218
/// Evaluate order n derivatives of basis function i at given point in cell
219
virtual void evaluate_basis_derivatives(unsigned int i,
220
unsigned int n,
221
double* values,
222
const double* coordinates,
223
const ufc::cell& c) const
224
{
225
// Extract vertex coordinates
226
const double * const * element_coordinates = c.coordinates;
227
228
// Compute Jacobian of affine map from reference cell
229
const double J_00 = element_coordinates[1][0] - element_coordinates[0][0];
230
const double J_01 = element_coordinates[2][0] - element_coordinates[0][0];
231
const double J_02 = element_coordinates[3][0] - element_coordinates[0][0];
232
const double J_10 = element_coordinates[1][1] - element_coordinates[0][1];
233
const double J_11 = element_coordinates[2][1] - element_coordinates[0][1];
234
const double J_12 = element_coordinates[3][1] - element_coordinates[0][1];
235
const double J_20 = element_coordinates[1][2] - element_coordinates[0][2];
236
const double J_21 = element_coordinates[2][2] - element_coordinates[0][2];
237
const double J_22 = element_coordinates[3][2] - element_coordinates[0][2];
238
239
// Compute sub determinants
240
const double d00 = J_11*J_22 - J_12*J_21;
241
const double d01 = J_12*J_20 - J_10*J_22;
242
const double d02 = J_10*J_21 - J_11*J_20;
243
244
const double d10 = J_02*J_21 - J_01*J_22;
245
const double d11 = J_00*J_22 - J_02*J_20;
246
const double d12 = J_01*J_20 - J_00*J_21;
247
248
const double d20 = J_01*J_12 - J_02*J_11;
249
const double d21 = J_02*J_10 - J_00*J_12;
250
const double d22 = J_00*J_11 - J_01*J_10;
251
252
// Compute determinant of Jacobian
253
double detJ = J_00*d00 + J_10*d10 + J_20*d20;
254
255
// Compute inverse of Jacobian
256
257
// Compute constants
258
const double C0 = d00*(element_coordinates[0][0] - element_coordinates[2][0] - element_coordinates[3][0]) \
259
+ d10*(element_coordinates[0][1] - element_coordinates[2][1] - element_coordinates[3][1]) \
260
+ d20*(element_coordinates[0][2] - element_coordinates[2][2] - element_coordinates[3][2]);
261
262
const double C1 = d01*(element_coordinates[0][0] - element_coordinates[1][0] - element_coordinates[3][0]) \
263
+ d11*(element_coordinates[0][1] - element_coordinates[1][1] - element_coordinates[3][1]) \
264
+ d21*(element_coordinates[0][2] - element_coordinates[1][2] - element_coordinates[3][2]);
265
266
const double C2 = d02*(element_coordinates[0][0] - element_coordinates[1][0] - element_coordinates[2][0]) \
267
+ d12*(element_coordinates[0][1] - element_coordinates[1][1] - element_coordinates[2][1]) \
268
+ d22*(element_coordinates[0][2] - element_coordinates[1][2] - element_coordinates[2][2]);
269
270
// Get coordinates and map to the UFC reference element
271
double x = (C0 + d00*coordinates[0] + d10*coordinates[1] + d20*coordinates[2]) / detJ;
272
double y = (C1 + d01*coordinates[0] + d11*coordinates[1] + d21*coordinates[2]) / detJ;
273
double z = (C2 + d02*coordinates[0] + d12*coordinates[1] + d22*coordinates[2]) / detJ;
274
275
// Map coordinates to the reference cube
276
if (std::abs(y + z - 1.0) < 1e-14)
277
x = 1.0;
278
else
279
x = -2.0 * x/(y + z - 1.0) - 1.0;
280
if (std::abs(z - 1.0) < 1e-14)
281
y = -1.0;
282
else
283
y = 2.0 * y/(1.0 - z) - 1.0;
284
z = 2.0 * z - 1.0;
285
286
// Compute number of derivatives
287
unsigned int num_derivatives = 1;
288
289
for (unsigned int j = 0; j < n; j++)
290
num_derivatives *= 3;
291
292
293
// Declare pointer to two dimensional array that holds combinations of derivatives and initialise
294
unsigned int **combinations = new unsigned int *[num_derivatives];
295
296
for (unsigned int j = 0; j < num_derivatives; j++)
297
{
298
combinations[j] = new unsigned int [n];
299
for (unsigned int k = 0; k < n; k++)
300
combinations[j][k] = 0;
301
}
302
303
// Generate combinations of derivatives
304
for (unsigned int row = 1; row < num_derivatives; row++)
305
{
306
for (unsigned int num = 0; num < row; num++)
307
{
308
for (unsigned int col = n-1; col+1 > 0; col--)
309
{
310
if (combinations[row][col] + 1 > 2)
311
combinations[row][col] = 0;
312
else
313
{
314
combinations[row][col] += 1;
315
break;
316
}
317
}
318
}
319
}
320
321
// Compute inverse of Jacobian
322
const double Jinv[3][3] ={{d00 / detJ, d10 / detJ, d20 / detJ}, {d01 / detJ, d11 / detJ, d21 / detJ}, {d02 / detJ, d12 / detJ, d22 / detJ}};
323
324
// Declare transformation matrix
325
// Declare pointer to two dimensional array and initialise
326
double **transform = new double *[num_derivatives];
327
328
for (unsigned int j = 0; j < num_derivatives; j++)
329
{
330
transform[j] = new double [num_derivatives];
331
for (unsigned int k = 0; k < num_derivatives; k++)
332
transform[j][k] = 1;
333
}
334
335
// Construct transformation matrix
336
for (unsigned int row = 0; row < num_derivatives; row++)
337
{
338
for (unsigned int col = 0; col < num_derivatives; col++)
339
{
340
for (unsigned int k = 0; k < n; k++)
341
transform[row][col] *= Jinv[combinations[col][k]][combinations[row][k]];
342
}
343
}
344
345
// Reset values
346
for (unsigned int j = 0; j < 1*num_derivatives; j++)
347
values[j] = 0;
348
349
// Map degree of freedom to element degree of freedom
350
const unsigned int dof = i;
351
352
// Generate scalings
353
const double scalings_y_0 = 1;
354
const double scalings_y_1 = scalings_y_0*(0.5 - 0.5*y);
355
const double scalings_y_2 = scalings_y_1*(0.5 - 0.5*y);
356
const double scalings_z_0 = 1;
357
const double scalings_z_1 = scalings_z_0*(0.5 - 0.5*z);
358
const double scalings_z_2 = scalings_z_1*(0.5 - 0.5*z);
359
360
// Compute psitilde_a
361
const double psitilde_a_0 = 1;
362
const double psitilde_a_1 = x;
363
const double psitilde_a_2 = 1.5*x*psitilde_a_1 - 0.5*psitilde_a_0;
364
365
// Compute psitilde_bs
366
const double psitilde_bs_0_0 = 1;
367
const double psitilde_bs_0_1 = 1.5*y + 0.5;
368
const double psitilde_bs_0_2 = 0.111111111111111*psitilde_bs_0_1 + 1.66666666666667*y*psitilde_bs_0_1 - 0.555555555555556*psitilde_bs_0_0;
369
const double psitilde_bs_1_0 = 1;
370
const double psitilde_bs_1_1 = 2.5*y + 1.5;
371
const double psitilde_bs_2_0 = 1;
372
373
// Compute psitilde_cs
374
const double psitilde_cs_00_0 = 1;
375
const double psitilde_cs_00_1 = 2*z + 1;
376
const double psitilde_cs_00_2 = 0.3125*psitilde_cs_00_1 + 1.875*z*psitilde_cs_00_1 - 0.5625*psitilde_cs_00_0;
377
const double psitilde_cs_01_0 = 1;
378
const double psitilde_cs_01_1 = 3*z + 2;
379
const double psitilde_cs_02_0 = 1;
380
const double psitilde_cs_10_0 = 1;
381
const double psitilde_cs_10_1 = 3*z + 2;
382
const double psitilde_cs_11_0 = 1;
383
const double psitilde_cs_20_0 = 1;
384
385
// Compute basisvalues
386
const double basisvalue0 = 0.866025403784439*psitilde_a_0*scalings_y_0*psitilde_bs_0_0*scalings_z_0*psitilde_cs_00_0;
387
const double basisvalue1 = 2.73861278752583*psitilde_a_1*scalings_y_1*psitilde_bs_1_0*scalings_z_1*psitilde_cs_10_0;
388
const double basisvalue2 = 1.58113883008419*psitilde_a_0*scalings_y_0*psitilde_bs_0_1*scalings_z_1*psitilde_cs_01_0;
389
const double basisvalue3 = 1.11803398874989*psitilde_a_0*scalings_y_0*psitilde_bs_0_0*scalings_z_0*psitilde_cs_00_1;
390
const double basisvalue4 = 5.1234753829798*psitilde_a_2*scalings_y_2*psitilde_bs_2_0*scalings_z_2*psitilde_cs_20_0;
391
const double basisvalue5 = 3.96862696659689*psitilde_a_1*scalings_y_1*psitilde_bs_1_1*scalings_z_2*psitilde_cs_11_0;
392
const double basisvalue6 = 2.29128784747792*psitilde_a_0*scalings_y_0*psitilde_bs_0_2*scalings_z_2*psitilde_cs_02_0;
393
const double basisvalue7 = 3.24037034920393*psitilde_a_1*scalings_y_1*psitilde_bs_1_0*scalings_z_1*psitilde_cs_10_1;
394
const double basisvalue8 = 1.87082869338697*psitilde_a_0*scalings_y_0*psitilde_bs_0_1*scalings_z_1*psitilde_cs_01_1;
395
const double basisvalue9 = 1.3228756555323*psitilde_a_0*scalings_y_0*psitilde_bs_0_0*scalings_z_0*psitilde_cs_00_2;
396
397
// Table(s) of coefficients
398
const static double coefficients0[10][10] = \
399
{{-0.0577350269189625, -0.0608580619450185, -0.0351364184463153, -0.0248451997499977, 0.0650600048632355, 0.050395263067897, 0.0290957186981323, 0.0411475599898912, 0.0237565548366599, 0.0167984210226323},
400
{-0.0577350269189625, 0.0608580619450185, -0.0351364184463153, -0.0248451997499976, 0.0650600048632355, -0.050395263067897, 0.0290957186981323, -0.0411475599898912, 0.0237565548366599, 0.0167984210226323},
401
{-0.0577350269189626, 0, 0.0702728368926306, -0.0248451997499976, 0, 0, 0.087287156094397, 0, -0.0475131096733199, 0.0167984210226323},
402
{-0.0577350269189626, 0, 0, 0.074535599249993, 0, 0, 0, 0, 0, 0.100790526135794},
403
{0.23094010767585, 0, 0.140545673785261, 0.0993807989999906, 0, 0, 0, 0, 0.1187827741833, -0.0671936840905293},
404
{0.23094010767585, 0.121716123890037, -0.0702728368926306, 0.0993807989999907, 0, 0, 0, 0.102868899974728, -0.0593913870916499, -0.0671936840905293},
405
{0.23094010767585, 0.121716123890037, 0.0702728368926307, -0.0993807989999907, 0, 0.100790526135794, -0.087287156094397, -0.0205737799949456, -0.01187827741833, 0.0167984210226323},
406
{0.23094010767585, -0.121716123890037, -0.0702728368926307, 0.0993807989999906, 0, 0, 0, -0.102868899974728, -0.0593913870916499, -0.0671936840905293},
407
{0.23094010767585, -0.121716123890037, 0.0702728368926306, -0.0993807989999907, 0, -0.100790526135794, -0.0872871560943969, 0.0205737799949456, -0.01187827741833, 0.0167984210226323},
408
{0.23094010767585, 0, -0.140545673785261, -0.0993807989999906, -0.130120009726471, 0, 0.0290957186981323, 0, 0.02375655483666, 0.0167984210226323}};
409
410
// Interesting (new) part
411
// Tables of derivatives of the polynomial base (transpose)
412
const static double dmats0[10][10] = \
413
{{0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
414
{6.32455532033676, 0, 0, 0, 0, 0, 0, 0, 0, 0},
415
{0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
416
{0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
417
{0, 11.2249721603218, 0, 0, 0, 0, 0, 0, 0, 0},
418
{4.58257569495584, 0, 8.36660026534076, -1.18321595661992, 0, 0, 0, 0, 0, 0},
419
{0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
420
{3.74165738677394, 0, 0, 8.69482604771366, 0, 0, 0, 0, 0, 0},
421
{0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
422
{0, 0, 0, 0, 0, 0, 0, 0, 0, 0}};
423
424
const static double dmats1[10][10] = \
425
{{0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
426
{3.16227766016838, 0, 0, 0, 0, 0, 0, 0, 0, 0},
427
{5.47722557505166, 0, 0, 0, 0, 0, 0, 0, 0, 0},
428
{0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
429
{2.95803989154981, 5.61248608016091, -1.08012344973464, -0.763762615825974, 0, 0, 0, 0, 0, 0},
430
{2.29128784747792, 7.24568837309472, 4.18330013267038, -0.591607978309962, 0, 0, 0, 0, 0, 0},
431
{-2.64575131106459, 0, 9.66091783079296, 0.683130051063974, 0, 0, 0, 0, 0, 0},
432
{1.87082869338697, 0, 0, 4.34741302385683, 0, 0, 0, 0, 0, 0},
433
{3.24037034920393, 0, 0, 7.52994023880668, 0, 0, 0, 0, 0, 0},
434
{0, 0, 0, 0, 0, 0, 0, 0, 0, 0}};
435
436
const static double dmats2[10][10] = \
437
{{0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
438
{3.16227766016838, 0, 0, 0, 0, 0, 0, 0, 0, 0},
439
{1.82574185835055, 0, 0, 0, 0, 0, 0, 0, 0, 0},
440
{5.16397779494322, 0, 0, 0, 0, 0, 0, 0, 0, 0},
441
{2.95803989154981, 5.61248608016091, -1.08012344973464, -0.763762615825973, 0, 0, 0, 0, 0, 0},
442
{2.29128784747792, 1.44913767461894, 4.18330013267038, -0.591607978309962, 0, 0, 0, 0, 0, 0},
443
{1.32287565553229, 0, 3.86436713231718, -0.341565025531986, 0, 0, 0, 0, 0, 0},
444
{1.87082869338697, 7.09929573971954, 0, 4.34741302385683, 0, 0, 0, 0, 0, 0},
445
{1.08012344973464, 0, 7.09929573971954, 2.50998007960223, 0, 0, 0, 0, 0, 0},
446
{-3.81881307912986, 0, 0, 8.87411967464942, 0, 0, 0, 0, 0, 0}};
447
448
// Compute reference derivatives
449
// Declare pointer to array of derivatives on FIAT element
450
double *derivatives = new double [num_derivatives];
451
452
// Declare coefficients
453
double coeff0_0 = 0;
454
double coeff0_1 = 0;
455
double coeff0_2 = 0;
456
double coeff0_3 = 0;
457
double coeff0_4 = 0;
458
double coeff0_5 = 0;
459
double coeff0_6 = 0;
460
double coeff0_7 = 0;
461
double coeff0_8 = 0;
462
double coeff0_9 = 0;
463
464
// Declare new coefficients
465
double new_coeff0_0 = 0;
466
double new_coeff0_1 = 0;
467
double new_coeff0_2 = 0;
468
double new_coeff0_3 = 0;
469
double new_coeff0_4 = 0;
470
double new_coeff0_5 = 0;
471
double new_coeff0_6 = 0;
472
double new_coeff0_7 = 0;
473
double new_coeff0_8 = 0;
474
double new_coeff0_9 = 0;
475
476
// Loop possible derivatives
477
for (unsigned int deriv_num = 0; deriv_num < num_derivatives; deriv_num++)
478
{
479
// Get values from coefficients array
480
new_coeff0_0 = coefficients0[dof][0];
481
new_coeff0_1 = coefficients0[dof][1];
482
new_coeff0_2 = coefficients0[dof][2];
483
new_coeff0_3 = coefficients0[dof][3];
484
new_coeff0_4 = coefficients0[dof][4];
485
new_coeff0_5 = coefficients0[dof][5];
486
new_coeff0_6 = coefficients0[dof][6];
487
new_coeff0_7 = coefficients0[dof][7];
488
new_coeff0_8 = coefficients0[dof][8];
489
new_coeff0_9 = coefficients0[dof][9];
490
491
// Loop derivative order
492
for (unsigned int j = 0; j < n; j++)
493
{
494
// Update old coefficients
495
coeff0_0 = new_coeff0_0;
496
coeff0_1 = new_coeff0_1;
497
coeff0_2 = new_coeff0_2;
498
coeff0_3 = new_coeff0_3;
499
coeff0_4 = new_coeff0_4;
500
coeff0_5 = new_coeff0_5;
501
coeff0_6 = new_coeff0_6;
502
coeff0_7 = new_coeff0_7;
503
coeff0_8 = new_coeff0_8;
504
coeff0_9 = new_coeff0_9;
505
506
if(combinations[deriv_num][j] == 0)
507
{
508
new_coeff0_0 = coeff0_0*dmats0[0][0] + coeff0_1*dmats0[1][0] + coeff0_2*dmats0[2][0] + coeff0_3*dmats0[3][0] + coeff0_4*dmats0[4][0] + coeff0_5*dmats0[5][0] + coeff0_6*dmats0[6][0] + coeff0_7*dmats0[7][0] + coeff0_8*dmats0[8][0] + coeff0_9*dmats0[9][0];
509
new_coeff0_1 = coeff0_0*dmats0[0][1] + coeff0_1*dmats0[1][1] + coeff0_2*dmats0[2][1] + coeff0_3*dmats0[3][1] + coeff0_4*dmats0[4][1] + coeff0_5*dmats0[5][1] + coeff0_6*dmats0[6][1] + coeff0_7*dmats0[7][1] + coeff0_8*dmats0[8][1] + coeff0_9*dmats0[9][1];
510
new_coeff0_2 = coeff0_0*dmats0[0][2] + coeff0_1*dmats0[1][2] + coeff0_2*dmats0[2][2] + coeff0_3*dmats0[3][2] + coeff0_4*dmats0[4][2] + coeff0_5*dmats0[5][2] + coeff0_6*dmats0[6][2] + coeff0_7*dmats0[7][2] + coeff0_8*dmats0[8][2] + coeff0_9*dmats0[9][2];
511
new_coeff0_3 = coeff0_0*dmats0[0][3] + coeff0_1*dmats0[1][3] + coeff0_2*dmats0[2][3] + coeff0_3*dmats0[3][3] + coeff0_4*dmats0[4][3] + coeff0_5*dmats0[5][3] + coeff0_6*dmats0[6][3] + coeff0_7*dmats0[7][3] + coeff0_8*dmats0[8][3] + coeff0_9*dmats0[9][3];
512
new_coeff0_4 = coeff0_0*dmats0[0][4] + coeff0_1*dmats0[1][4] + coeff0_2*dmats0[2][4] + coeff0_3*dmats0[3][4] + coeff0_4*dmats0[4][4] + coeff0_5*dmats0[5][4] + coeff0_6*dmats0[6][4] + coeff0_7*dmats0[7][4] + coeff0_8*dmats0[8][4] + coeff0_9*dmats0[9][4];
513
new_coeff0_5 = coeff0_0*dmats0[0][5] + coeff0_1*dmats0[1][5] + coeff0_2*dmats0[2][5] + coeff0_3*dmats0[3][5] + coeff0_4*dmats0[4][5] + coeff0_5*dmats0[5][5] + coeff0_6*dmats0[6][5] + coeff0_7*dmats0[7][5] + coeff0_8*dmats0[8][5] + coeff0_9*dmats0[9][5];
514
new_coeff0_6 = coeff0_0*dmats0[0][6] + coeff0_1*dmats0[1][6] + coeff0_2*dmats0[2][6] + coeff0_3*dmats0[3][6] + coeff0_4*dmats0[4][6] + coeff0_5*dmats0[5][6] + coeff0_6*dmats0[6][6] + coeff0_7*dmats0[7][6] + coeff0_8*dmats0[8][6] + coeff0_9*dmats0[9][6];
515
new_coeff0_7 = coeff0_0*dmats0[0][7] + coeff0_1*dmats0[1][7] + coeff0_2*dmats0[2][7] + coeff0_3*dmats0[3][7] + coeff0_4*dmats0[4][7] + coeff0_5*dmats0[5][7] + coeff0_6*dmats0[6][7] + coeff0_7*dmats0[7][7] + coeff0_8*dmats0[8][7] + coeff0_9*dmats0[9][7];
516
new_coeff0_8 = coeff0_0*dmats0[0][8] + coeff0_1*dmats0[1][8] + coeff0_2*dmats0[2][8] + coeff0_3*dmats0[3][8] + coeff0_4*dmats0[4][8] + coeff0_5*dmats0[5][8] + coeff0_6*dmats0[6][8] + coeff0_7*dmats0[7][8] + coeff0_8*dmats0[8][8] + coeff0_9*dmats0[9][8];
517
new_coeff0_9 = coeff0_0*dmats0[0][9] + coeff0_1*dmats0[1][9] + coeff0_2*dmats0[2][9] + coeff0_3*dmats0[3][9] + coeff0_4*dmats0[4][9] + coeff0_5*dmats0[5][9] + coeff0_6*dmats0[6][9] + coeff0_7*dmats0[7][9] + coeff0_8*dmats0[8][9] + coeff0_9*dmats0[9][9];
518
}
519
if(combinations[deriv_num][j] == 1)
520
{
521
new_coeff0_0 = coeff0_0*dmats1[0][0] + coeff0_1*dmats1[1][0] + coeff0_2*dmats1[2][0] + coeff0_3*dmats1[3][0] + coeff0_4*dmats1[4][0] + coeff0_5*dmats1[5][0] + coeff0_6*dmats1[6][0] + coeff0_7*dmats1[7][0] + coeff0_8*dmats1[8][0] + coeff0_9*dmats1[9][0];
522
new_coeff0_1 = coeff0_0*dmats1[0][1] + coeff0_1*dmats1[1][1] + coeff0_2*dmats1[2][1] + coeff0_3*dmats1[3][1] + coeff0_4*dmats1[4][1] + coeff0_5*dmats1[5][1] + coeff0_6*dmats1[6][1] + coeff0_7*dmats1[7][1] + coeff0_8*dmats1[8][1] + coeff0_9*dmats1[9][1];
523
new_coeff0_2 = coeff0_0*dmats1[0][2] + coeff0_1*dmats1[1][2] + coeff0_2*dmats1[2][2] + coeff0_3*dmats1[3][2] + coeff0_4*dmats1[4][2] + coeff0_5*dmats1[5][2] + coeff0_6*dmats1[6][2] + coeff0_7*dmats1[7][2] + coeff0_8*dmats1[8][2] + coeff0_9*dmats1[9][2];
524
new_coeff0_3 = coeff0_0*dmats1[0][3] + coeff0_1*dmats1[1][3] + coeff0_2*dmats1[2][3] + coeff0_3*dmats1[3][3] + coeff0_4*dmats1[4][3] + coeff0_5*dmats1[5][3] + coeff0_6*dmats1[6][3] + coeff0_7*dmats1[7][3] + coeff0_8*dmats1[8][3] + coeff0_9*dmats1[9][3];
525
new_coeff0_4 = coeff0_0*dmats1[0][4] + coeff0_1*dmats1[1][4] + coeff0_2*dmats1[2][4] + coeff0_3*dmats1[3][4] + coeff0_4*dmats1[4][4] + coeff0_5*dmats1[5][4] + coeff0_6*dmats1[6][4] + coeff0_7*dmats1[7][4] + coeff0_8*dmats1[8][4] + coeff0_9*dmats1[9][4];
526
new_coeff0_5 = coeff0_0*dmats1[0][5] + coeff0_1*dmats1[1][5] + coeff0_2*dmats1[2][5] + coeff0_3*dmats1[3][5] + coeff0_4*dmats1[4][5] + coeff0_5*dmats1[5][5] + coeff0_6*dmats1[6][5] + coeff0_7*dmats1[7][5] + coeff0_8*dmats1[8][5] + coeff0_9*dmats1[9][5];
527
new_coeff0_6 = coeff0_0*dmats1[0][6] + coeff0_1*dmats1[1][6] + coeff0_2*dmats1[2][6] + coeff0_3*dmats1[3][6] + coeff0_4*dmats1[4][6] + coeff0_5*dmats1[5][6] + coeff0_6*dmats1[6][6] + coeff0_7*dmats1[7][6] + coeff0_8*dmats1[8][6] + coeff0_9*dmats1[9][6];
528
new_coeff0_7 = coeff0_0*dmats1[0][7] + coeff0_1*dmats1[1][7] + coeff0_2*dmats1[2][7] + coeff0_3*dmats1[3][7] + coeff0_4*dmats1[4][7] + coeff0_5*dmats1[5][7] + coeff0_6*dmats1[6][7] + coeff0_7*dmats1[7][7] + coeff0_8*dmats1[8][7] + coeff0_9*dmats1[9][7];
529
new_coeff0_8 = coeff0_0*dmats1[0][8] + coeff0_1*dmats1[1][8] + coeff0_2*dmats1[2][8] + coeff0_3*dmats1[3][8] + coeff0_4*dmats1[4][8] + coeff0_5*dmats1[5][8] + coeff0_6*dmats1[6][8] + coeff0_7*dmats1[7][8] + coeff0_8*dmats1[8][8] + coeff0_9*dmats1[9][8];
530
new_coeff0_9 = coeff0_0*dmats1[0][9] + coeff0_1*dmats1[1][9] + coeff0_2*dmats1[2][9] + coeff0_3*dmats1[3][9] + coeff0_4*dmats1[4][9] + coeff0_5*dmats1[5][9] + coeff0_6*dmats1[6][9] + coeff0_7*dmats1[7][9] + coeff0_8*dmats1[8][9] + coeff0_9*dmats1[9][9];
531
}
532
if(combinations[deriv_num][j] == 2)
533
{
534
new_coeff0_0 = coeff0_0*dmats2[0][0] + coeff0_1*dmats2[1][0] + coeff0_2*dmats2[2][0] + coeff0_3*dmats2[3][0] + coeff0_4*dmats2[4][0] + coeff0_5*dmats2[5][0] + coeff0_6*dmats2[6][0] + coeff0_7*dmats2[7][0] + coeff0_8*dmats2[8][0] + coeff0_9*dmats2[9][0];
535
new_coeff0_1 = coeff0_0*dmats2[0][1] + coeff0_1*dmats2[1][1] + coeff0_2*dmats2[2][1] + coeff0_3*dmats2[3][1] + coeff0_4*dmats2[4][1] + coeff0_5*dmats2[5][1] + coeff0_6*dmats2[6][1] + coeff0_7*dmats2[7][1] + coeff0_8*dmats2[8][1] + coeff0_9*dmats2[9][1];
536
new_coeff0_2 = coeff0_0*dmats2[0][2] + coeff0_1*dmats2[1][2] + coeff0_2*dmats2[2][2] + coeff0_3*dmats2[3][2] + coeff0_4*dmats2[4][2] + coeff0_5*dmats2[5][2] + coeff0_6*dmats2[6][2] + coeff0_7*dmats2[7][2] + coeff0_8*dmats2[8][2] + coeff0_9*dmats2[9][2];
537
new_coeff0_3 = coeff0_0*dmats2[0][3] + coeff0_1*dmats2[1][3] + coeff0_2*dmats2[2][3] + coeff0_3*dmats2[3][3] + coeff0_4*dmats2[4][3] + coeff0_5*dmats2[5][3] + coeff0_6*dmats2[6][3] + coeff0_7*dmats2[7][3] + coeff0_8*dmats2[8][3] + coeff0_9*dmats2[9][3];
538
new_coeff0_4 = coeff0_0*dmats2[0][4] + coeff0_1*dmats2[1][4] + coeff0_2*dmats2[2][4] + coeff0_3*dmats2[3][4] + coeff0_4*dmats2[4][4] + coeff0_5*dmats2[5][4] + coeff0_6*dmats2[6][4] + coeff0_7*dmats2[7][4] + coeff0_8*dmats2[8][4] + coeff0_9*dmats2[9][4];
539
new_coeff0_5 = coeff0_0*dmats2[0][5] + coeff0_1*dmats2[1][5] + coeff0_2*dmats2[2][5] + coeff0_3*dmats2[3][5] + coeff0_4*dmats2[4][5] + coeff0_5*dmats2[5][5] + coeff0_6*dmats2[6][5] + coeff0_7*dmats2[7][5] + coeff0_8*dmats2[8][5] + coeff0_9*dmats2[9][5];
540
new_coeff0_6 = coeff0_0*dmats2[0][6] + coeff0_1*dmats2[1][6] + coeff0_2*dmats2[2][6] + coeff0_3*dmats2[3][6] + coeff0_4*dmats2[4][6] + coeff0_5*dmats2[5][6] + coeff0_6*dmats2[6][6] + coeff0_7*dmats2[7][6] + coeff0_8*dmats2[8][6] + coeff0_9*dmats2[9][6];
541
new_coeff0_7 = coeff0_0*dmats2[0][7] + coeff0_1*dmats2[1][7] + coeff0_2*dmats2[2][7] + coeff0_3*dmats2[3][7] + coeff0_4*dmats2[4][7] + coeff0_5*dmats2[5][7] + coeff0_6*dmats2[6][7] + coeff0_7*dmats2[7][7] + coeff0_8*dmats2[8][7] + coeff0_9*dmats2[9][7];
542
new_coeff0_8 = coeff0_0*dmats2[0][8] + coeff0_1*dmats2[1][8] + coeff0_2*dmats2[2][8] + coeff0_3*dmats2[3][8] + coeff0_4*dmats2[4][8] + coeff0_5*dmats2[5][8] + coeff0_6*dmats2[6][8] + coeff0_7*dmats2[7][8] + coeff0_8*dmats2[8][8] + coeff0_9*dmats2[9][8];
543
new_coeff0_9 = coeff0_0*dmats2[0][9] + coeff0_1*dmats2[1][9] + coeff0_2*dmats2[2][9] + coeff0_3*dmats2[3][9] + coeff0_4*dmats2[4][9] + coeff0_5*dmats2[5][9] + coeff0_6*dmats2[6][9] + coeff0_7*dmats2[7][9] + coeff0_8*dmats2[8][9] + coeff0_9*dmats2[9][9];
544
}
545
546
}
547
// Compute derivatives on reference element as dot product of coefficients and basisvalues
548
derivatives[deriv_num] = new_coeff0_0*basisvalue0 + new_coeff0_1*basisvalue1 + new_coeff0_2*basisvalue2 + new_coeff0_3*basisvalue3 + new_coeff0_4*basisvalue4 + new_coeff0_5*basisvalue5 + new_coeff0_6*basisvalue6 + new_coeff0_7*basisvalue7 + new_coeff0_8*basisvalue8 + new_coeff0_9*basisvalue9;
549
}
550
551
// Transform derivatives back to physical element
552
for (unsigned int row = 0; row < num_derivatives; row++)
553
{
554
for (unsigned int col = 0; col < num_derivatives; col++)
555
{
556
values[row] += transform[row][col]*derivatives[col];
557
}
558
}
559
// Delete pointer to array of derivatives on FIAT element
560
delete [] derivatives;
561
562
// Delete pointer to array of combinations of derivatives and transform
563
for (unsigned int row = 0; row < num_derivatives; row++)
564
{
565
delete [] combinations[row];
566
delete [] transform[row];
567
}
568
569
delete [] combinations;
570
delete [] transform;
571
}
572
573
/// Evaluate order n derivatives of all basis functions at given point in cell
574
virtual void evaluate_basis_derivatives_all(unsigned int n,
575
double* values,
576
const double* coordinates,
577
const ufc::cell& c) const
578
{
579
throw std::runtime_error("The vectorised version of evaluate_basis_derivatives() is not yet implemented.");
580
}
581
582
/// Evaluate linear functional for dof i on the function f
583
virtual double evaluate_dof(unsigned int i,
584
const ufc::function& f,
585
const ufc::cell& c) const
586
{
587
// The reference points, direction and weights:
588
const static double X[10][1][3] = {{{0, 0, 0}}, {{1, 0, 0}}, {{0, 1, 0}}, {{0, 0, 1}}, {{0, 0.5, 0.5}}, {{0.5, 0, 0.5}}, {{0.5, 0.5, 0}}, {{0, 0, 0.5}}, {{0, 0.5, 0}}, {{0.5, 0, 0}}};
589
const static double W[10][1] = {{1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}};
590
const static double D[10][1][1] = {{{1}}, {{1}}, {{1}}, {{1}}, {{1}}, {{1}}, {{1}}, {{1}}, {{1}}, {{1}}};
591
592
const double * const * x = c.coordinates;
593
double result = 0.0;
594
// Iterate over the points:
595
// Evaluate basis functions for affine mapping
596
const double w0 = 1.0 - X[i][0][0] - X[i][0][1] - X[i][0][2];
597
const double w1 = X[i][0][0];
598
const double w2 = X[i][0][1];
599
const double w3 = X[i][0][2];
600
601
// Compute affine mapping y = F(X)
602
double y[3];
603
y[0] = w0*x[0][0] + w1*x[1][0] + w2*x[2][0] + w3*x[3][0];
604
y[1] = w0*x[0][1] + w1*x[1][1] + w2*x[2][1] + w3*x[3][1];
605
y[2] = w0*x[0][2] + w1*x[1][2] + w2*x[2][2] + w3*x[3][2];
606
607
// Evaluate function at physical points
608
double values[1];
609
f.evaluate(values, y, c);
610
611
// Map function values using appropriate mapping
612
// Affine map: Do nothing
613
614
// Note that we do not map the weights (yet).
615
616
// Take directional components
617
for(int k = 0; k < 1; k++)
618
result += values[k]*D[i][0][k];
619
// Multiply by weights
620
result *= W[i][0];
621
622
return result;
623
}
624
625
/// Evaluate linear functionals for all dofs on the function f
626
virtual void evaluate_dofs(double* values,
627
const ufc::function& f,
628
const ufc::cell& c) const
629
{
630
throw std::runtime_error("Not implemented (introduced in UFC v1.1).");
631
}
632
633
/// Interpolate vertex values from dof values
634
virtual void interpolate_vertex_values(double* vertex_values,
635
const double* dof_values,
636
const ufc::cell& c) const
637
{
638
// Evaluate at vertices and use affine mapping
639
vertex_values[0] = dof_values[0];
640
vertex_values[1] = dof_values[1];
641
vertex_values[2] = dof_values[2];
642
vertex_values[3] = dof_values[3];
643
}
644
645
/// Return the number of sub elements (for a mixed element)
646
virtual unsigned int num_sub_elements() const
647
{
648
return 1;
649
}
650
651
/// Create a new finite element for sub element i (for a mixed element)
652
virtual ufc::finite_element* create_sub_element(unsigned int i) const
653
{
654
return new UFC_ProjectionBilinearForm_finite_element_0();
655
}
656
657
};
658
659
/// This class defines the interface for a finite element.
660
661
class UFC_ProjectionBilinearForm_finite_element_1: public ufc::finite_element
662
{
663
public:
664
665
/// Constructor
666
UFC_ProjectionBilinearForm_finite_element_1() : ufc::finite_element()
667
{
668
// Do nothing
669
}
670
671
/// Destructor
672
virtual ~UFC_ProjectionBilinearForm_finite_element_1()
673
{
674
// Do nothing
675
}
676
677
/// Return a string identifying the finite element
678
virtual const char* signature() const
679
{
680
return "FiniteElement('Lagrange', 'tetrahedron', 2)";
681
}
682
683
/// Return the cell shape
684
virtual ufc::shape cell_shape() const
685
{
686
return ufc::tetrahedron;
687
}
688
689
/// Return the dimension of the finite element function space
690
virtual unsigned int space_dimension() const
691
{
692
return 10;
693
}
694
695
/// Return the rank of the value space
696
virtual unsigned int value_rank() const
697
{
698
return 0;
699
}
700
701
/// Return the dimension of the value space for axis i
702
virtual unsigned int value_dimension(unsigned int i) const
703
{
704
return 1;
705
}
706
707
/// Evaluate basis function i at given point in cell
708
virtual void evaluate_basis(unsigned int i,
709
double* values,
710
const double* coordinates,
711
const ufc::cell& c) const
712
{
713
// Extract vertex coordinates
714
const double * const * element_coordinates = c.coordinates;
715
716
// Compute Jacobian of affine map from reference cell
717
const double J_00 = element_coordinates[1][0] - element_coordinates[0][0];
718
const double J_01 = element_coordinates[2][0] - element_coordinates[0][0];
719
const double J_02 = element_coordinates[3][0] - element_coordinates[0][0];
720
const double J_10 = element_coordinates[1][1] - element_coordinates[0][1];
721
const double J_11 = element_coordinates[2][1] - element_coordinates[0][1];
722
const double J_12 = element_coordinates[3][1] - element_coordinates[0][1];
723
const double J_20 = element_coordinates[1][2] - element_coordinates[0][2];
724
const double J_21 = element_coordinates[2][2] - element_coordinates[0][2];
725
const double J_22 = element_coordinates[3][2] - element_coordinates[0][2];
726
727
// Compute sub determinants
728
const double d00 = J_11*J_22 - J_12*J_21;
729
const double d01 = J_12*J_20 - J_10*J_22;
730
const double d02 = J_10*J_21 - J_11*J_20;
731
732
const double d10 = J_02*J_21 - J_01*J_22;
733
const double d11 = J_00*J_22 - J_02*J_20;
734
const double d12 = J_01*J_20 - J_00*J_21;
735
736
const double d20 = J_01*J_12 - J_02*J_11;
737
const double d21 = J_02*J_10 - J_00*J_12;
738
const double d22 = J_00*J_11 - J_01*J_10;
739
740
// Compute determinant of Jacobian
741
double detJ = J_00*d00 + J_10*d10 + J_20*d20;
742
743
// Compute inverse of Jacobian
744
745
// Compute constants
746
const double C0 = d00*(element_coordinates[0][0] - element_coordinates[2][0] - element_coordinates[3][0]) \
747
+ d10*(element_coordinates[0][1] - element_coordinates[2][1] - element_coordinates[3][1]) \
748
+ d20*(element_coordinates[0][2] - element_coordinates[2][2] - element_coordinates[3][2]);
749
750
const double C1 = d01*(element_coordinates[0][0] - element_coordinates[1][0] - element_coordinates[3][0]) \
751
+ d11*(element_coordinates[0][1] - element_coordinates[1][1] - element_coordinates[3][1]) \
752
+ d21*(element_coordinates[0][2] - element_coordinates[1][2] - element_coordinates[3][2]);
753
754
const double C2 = d02*(element_coordinates[0][0] - element_coordinates[1][0] - element_coordinates[2][0]) \
755
+ d12*(element_coordinates[0][1] - element_coordinates[1][1] - element_coordinates[2][1]) \
756
+ d22*(element_coordinates[0][2] - element_coordinates[1][2] - element_coordinates[2][2]);
757
758
// Get coordinates and map to the UFC reference element
759
double x = (C0 + d00*coordinates[0] + d10*coordinates[1] + d20*coordinates[2]) / detJ;
760
double y = (C1 + d01*coordinates[0] + d11*coordinates[1] + d21*coordinates[2]) / detJ;
761
double z = (C2 + d02*coordinates[0] + d12*coordinates[1] + d22*coordinates[2]) / detJ;
762
763
// Map coordinates to the reference cube
764
if (std::abs(y + z - 1.0) < 1e-14)
765
x = 1.0;
766
else
767
x = -2.0 * x/(y + z - 1.0) - 1.0;
768
if (std::abs(z - 1.0) < 1e-14)
769
y = -1.0;
770
else
771
y = 2.0 * y/(1.0 - z) - 1.0;
772
z = 2.0 * z - 1.0;
773
774
// Reset values
775
*values = 0;
776
777
// Map degree of freedom to element degree of freedom
778
const unsigned int dof = i;
779
780
// Generate scalings
781
const double scalings_y_0 = 1;
782
const double scalings_y_1 = scalings_y_0*(0.5 - 0.5*y);
783
const double scalings_y_2 = scalings_y_1*(0.5 - 0.5*y);
784
const double scalings_z_0 = 1;
785
const double scalings_z_1 = scalings_z_0*(0.5 - 0.5*z);
786
const double scalings_z_2 = scalings_z_1*(0.5 - 0.5*z);
787
788
// Compute psitilde_a
789
const double psitilde_a_0 = 1;
790
const double psitilde_a_1 = x;
791
const double psitilde_a_2 = 1.5*x*psitilde_a_1 - 0.5*psitilde_a_0;
792
793
// Compute psitilde_bs
794
const double psitilde_bs_0_0 = 1;
795
const double psitilde_bs_0_1 = 1.5*y + 0.5;
796
const double psitilde_bs_0_2 = 0.111111111111111*psitilde_bs_0_1 + 1.66666666666667*y*psitilde_bs_0_1 - 0.555555555555556*psitilde_bs_0_0;
797
const double psitilde_bs_1_0 = 1;
798
const double psitilde_bs_1_1 = 2.5*y + 1.5;
799
const double psitilde_bs_2_0 = 1;
800
801
// Compute psitilde_cs
802
const double psitilde_cs_00_0 = 1;
803
const double psitilde_cs_00_1 = 2*z + 1;
804
const double psitilde_cs_00_2 = 0.3125*psitilde_cs_00_1 + 1.875*z*psitilde_cs_00_1 - 0.5625*psitilde_cs_00_0;
805
const double psitilde_cs_01_0 = 1;
806
const double psitilde_cs_01_1 = 3*z + 2;
807
const double psitilde_cs_02_0 = 1;
808
const double psitilde_cs_10_0 = 1;
809
const double psitilde_cs_10_1 = 3*z + 2;
810
const double psitilde_cs_11_0 = 1;
811
const double psitilde_cs_20_0 = 1;
812
813
// Compute basisvalues
814
const double basisvalue0 = 0.866025403784439*psitilde_a_0*scalings_y_0*psitilde_bs_0_0*scalings_z_0*psitilde_cs_00_0;
815
const double basisvalue1 = 2.73861278752583*psitilde_a_1*scalings_y_1*psitilde_bs_1_0*scalings_z_1*psitilde_cs_10_0;
816
const double basisvalue2 = 1.58113883008419*psitilde_a_0*scalings_y_0*psitilde_bs_0_1*scalings_z_1*psitilde_cs_01_0;
817
const double basisvalue3 = 1.11803398874989*psitilde_a_0*scalings_y_0*psitilde_bs_0_0*scalings_z_0*psitilde_cs_00_1;
818
const double basisvalue4 = 5.1234753829798*psitilde_a_2*scalings_y_2*psitilde_bs_2_0*scalings_z_2*psitilde_cs_20_0;
819
const double basisvalue5 = 3.96862696659689*psitilde_a_1*scalings_y_1*psitilde_bs_1_1*scalings_z_2*psitilde_cs_11_0;
820
const double basisvalue6 = 2.29128784747792*psitilde_a_0*scalings_y_0*psitilde_bs_0_2*scalings_z_2*psitilde_cs_02_0;
821
const double basisvalue7 = 3.24037034920393*psitilde_a_1*scalings_y_1*psitilde_bs_1_0*scalings_z_1*psitilde_cs_10_1;
822
const double basisvalue8 = 1.87082869338697*psitilde_a_0*scalings_y_0*psitilde_bs_0_1*scalings_z_1*psitilde_cs_01_1;
823
const double basisvalue9 = 1.3228756555323*psitilde_a_0*scalings_y_0*psitilde_bs_0_0*scalings_z_0*psitilde_cs_00_2;
824
825
// Table(s) of coefficients
826
const static double coefficients0[10][10] = \
827
{{-0.0577350269189625, -0.0608580619450185, -0.0351364184463153, -0.0248451997499977, 0.0650600048632355, 0.050395263067897, 0.0290957186981323, 0.0411475599898912, 0.0237565548366599, 0.0167984210226323},
828
{-0.0577350269189625, 0.0608580619450185, -0.0351364184463153, -0.0248451997499976, 0.0650600048632355, -0.050395263067897, 0.0290957186981323, -0.0411475599898912, 0.0237565548366599, 0.0167984210226323},
829
{-0.0577350269189626, 0, 0.0702728368926306, -0.0248451997499976, 0, 0, 0.087287156094397, 0, -0.0475131096733199, 0.0167984210226323},
830
{-0.0577350269189626, 0, 0, 0.074535599249993, 0, 0, 0, 0, 0, 0.100790526135794},
831
{0.23094010767585, 0, 0.140545673785261, 0.0993807989999906, 0, 0, 0, 0, 0.1187827741833, -0.0671936840905293},
832
{0.23094010767585, 0.121716123890037, -0.0702728368926306, 0.0993807989999907, 0, 0, 0, 0.102868899974728, -0.0593913870916499, -0.0671936840905293},
833
{0.23094010767585, 0.121716123890037, 0.0702728368926307, -0.0993807989999907, 0, 0.100790526135794, -0.087287156094397, -0.0205737799949456, -0.01187827741833, 0.0167984210226323},
834
{0.23094010767585, -0.121716123890037, -0.0702728368926307, 0.0993807989999906, 0, 0, 0, -0.102868899974728, -0.0593913870916499, -0.0671936840905293},
835
{0.23094010767585, -0.121716123890037, 0.0702728368926306, -0.0993807989999907, 0, -0.100790526135794, -0.0872871560943969, 0.0205737799949456, -0.01187827741833, 0.0167984210226323},
836
{0.23094010767585, 0, -0.140545673785261, -0.0993807989999906, -0.130120009726471, 0, 0.0290957186981323, 0, 0.02375655483666, 0.0167984210226323}};
837
838
// Extract relevant coefficients
839
const double coeff0_0 = coefficients0[dof][0];
840
const double coeff0_1 = coefficients0[dof][1];
841
const double coeff0_2 = coefficients0[dof][2];
842
const double coeff0_3 = coefficients0[dof][3];
843
const double coeff0_4 = coefficients0[dof][4];
844
const double coeff0_5 = coefficients0[dof][5];
845
const double coeff0_6 = coefficients0[dof][6];
846
const double coeff0_7 = coefficients0[dof][7];
847
const double coeff0_8 = coefficients0[dof][8];
848
const double coeff0_9 = coefficients0[dof][9];
849
850
// Compute value(s)
851
*values = coeff0_0*basisvalue0 + coeff0_1*basisvalue1 + coeff0_2*basisvalue2 + coeff0_3*basisvalue3 + coeff0_4*basisvalue4 + coeff0_5*basisvalue5 + coeff0_6*basisvalue6 + coeff0_7*basisvalue7 + coeff0_8*basisvalue8 + coeff0_9*basisvalue9;
852
}
853
854
/// Evaluate all basis functions at given point in cell
855
virtual void evaluate_basis_all(double* values,
856
const double* coordinates,
857
const ufc::cell& c) const
858
{
859
throw std::runtime_error("The vectorised version of evaluate_basis() is not yet implemented.");
860
}
861
862
/// Evaluate order n derivatives of basis function i at given point in cell
863
virtual void evaluate_basis_derivatives(unsigned int i,
864
unsigned int n,
865
double* values,
866
const double* coordinates,
867
const ufc::cell& c) const
868
{
869
// Extract vertex coordinates
870
const double * const * element_coordinates = c.coordinates;
871
872
// Compute Jacobian of affine map from reference cell
873
const double J_00 = element_coordinates[1][0] - element_coordinates[0][0];
874
const double J_01 = element_coordinates[2][0] - element_coordinates[0][0];
875
const double J_02 = element_coordinates[3][0] - element_coordinates[0][0];
876
const double J_10 = element_coordinates[1][1] - element_coordinates[0][1];
877
const double J_11 = element_coordinates[2][1] - element_coordinates[0][1];
878
const double J_12 = element_coordinates[3][1] - element_coordinates[0][1];
879
const double J_20 = element_coordinates[1][2] - element_coordinates[0][2];
880
const double J_21 = element_coordinates[2][2] - element_coordinates[0][2];
881
const double J_22 = element_coordinates[3][2] - element_coordinates[0][2];
882
883
// Compute sub determinants
884
const double d00 = J_11*J_22 - J_12*J_21;
885
const double d01 = J_12*J_20 - J_10*J_22;
886
const double d02 = J_10*J_21 - J_11*J_20;
887
888
const double d10 = J_02*J_21 - J_01*J_22;
889
const double d11 = J_00*J_22 - J_02*J_20;
890
const double d12 = J_01*J_20 - J_00*J_21;
891
892
const double d20 = J_01*J_12 - J_02*J_11;
893
const double d21 = J_02*J_10 - J_00*J_12;
894
const double d22 = J_00*J_11 - J_01*J_10;
895
896
// Compute determinant of Jacobian
897
double detJ = J_00*d00 + J_10*d10 + J_20*d20;
898
899
// Compute inverse of Jacobian
900
901
// Compute constants
902
const double C0 = d00*(element_coordinates[0][0] - element_coordinates[2][0] - element_coordinates[3][0]) \
903
+ d10*(element_coordinates[0][1] - element_coordinates[2][1] - element_coordinates[3][1]) \
904
+ d20*(element_coordinates[0][2] - element_coordinates[2][2] - element_coordinates[3][2]);
905
906
const double C1 = d01*(element_coordinates[0][0] - element_coordinates[1][0] - element_coordinates[3][0]) \
907
+ d11*(element_coordinates[0][1] - element_coordinates[1][1] - element_coordinates[3][1]) \
908
+ d21*(element_coordinates[0][2] - element_coordinates[1][2] - element_coordinates[3][2]);
909
910
const double C2 = d02*(element_coordinates[0][0] - element_coordinates[1][0] - element_coordinates[2][0]) \
911
+ d12*(element_coordinates[0][1] - element_coordinates[1][1] - element_coordinates[2][1]) \
912
+ d22*(element_coordinates[0][2] - element_coordinates[1][2] - element_coordinates[2][2]);
913
914
// Get coordinates and map to the UFC reference element
915
double x = (C0 + d00*coordinates[0] + d10*coordinates[1] + d20*coordinates[2]) / detJ;
916
double y = (C1 + d01*coordinates[0] + d11*coordinates[1] + d21*coordinates[2]) / detJ;
917
double z = (C2 + d02*coordinates[0] + d12*coordinates[1] + d22*coordinates[2]) / detJ;
918
919
// Map coordinates to the reference cube
920
if (std::abs(y + z - 1.0) < 1e-14)
921
x = 1.0;
922
else
923
x = -2.0 * x/(y + z - 1.0) - 1.0;
924
if (std::abs(z - 1.0) < 1e-14)
925
y = -1.0;
926
else
927
y = 2.0 * y/(1.0 - z) - 1.0;
928
z = 2.0 * z - 1.0;
929
930
// Compute number of derivatives
931
unsigned int num_derivatives = 1;
932
933
for (unsigned int j = 0; j < n; j++)
934
num_derivatives *= 3;
935
936
937
// Declare pointer to two dimensional array that holds combinations of derivatives and initialise
938
unsigned int **combinations = new unsigned int *[num_derivatives];
939
940
for (unsigned int j = 0; j < num_derivatives; j++)
941
{
942
combinations[j] = new unsigned int [n];
943
for (unsigned int k = 0; k < n; k++)
944
combinations[j][k] = 0;
945
}
946
947
// Generate combinations of derivatives
948
for (unsigned int row = 1; row < num_derivatives; row++)
949
{
950
for (unsigned int num = 0; num < row; num++)
951
{
952
for (unsigned int col = n-1; col+1 > 0; col--)
953
{
954
if (combinations[row][col] + 1 > 2)
955
combinations[row][col] = 0;
956
else
957
{
958
combinations[row][col] += 1;
959
break;
960
}
961
}
962
}
963
}
964
965
// Compute inverse of Jacobian
966
const double Jinv[3][3] ={{d00 / detJ, d10 / detJ, d20 / detJ}, {d01 / detJ, d11 / detJ, d21 / detJ}, {d02 / detJ, d12 / detJ, d22 / detJ}};
967
968
// Declare transformation matrix
969
// Declare pointer to two dimensional array and initialise
970
double **transform = new double *[num_derivatives];
971
972
for (unsigned int j = 0; j < num_derivatives; j++)
973
{
974
transform[j] = new double [num_derivatives];
975
for (unsigned int k = 0; k < num_derivatives; k++)
976
transform[j][k] = 1;
977
}
978
979
// Construct transformation matrix
980
for (unsigned int row = 0; row < num_derivatives; row++)
981
{
982
for (unsigned int col = 0; col < num_derivatives; col++)
983
{
984
for (unsigned int k = 0; k < n; k++)
985
transform[row][col] *= Jinv[combinations[col][k]][combinations[row][k]];
986
}
987
}
988
989
// Reset values
990
for (unsigned int j = 0; j < 1*num_derivatives; j++)
991
values[j] = 0;
992
993
// Map degree of freedom to element degree of freedom
994
const unsigned int dof = i;
995
996
// Generate scalings
997
const double scalings_y_0 = 1;
998
const double scalings_y_1 = scalings_y_0*(0.5 - 0.5*y);
999
const double scalings_y_2 = scalings_y_1*(0.5 - 0.5*y);
1000
const double scalings_z_0 = 1;
1001
const double scalings_z_1 = scalings_z_0*(0.5 - 0.5*z);
1002
const double scalings_z_2 = scalings_z_1*(0.5 - 0.5*z);
1003
1004
// Compute psitilde_a
1005
const double psitilde_a_0 = 1;
1006
const double psitilde_a_1 = x;
1007
const double psitilde_a_2 = 1.5*x*psitilde_a_1 - 0.5*psitilde_a_0;
1008
1009
// Compute psitilde_bs
1010
const double psitilde_bs_0_0 = 1;
1011
const double psitilde_bs_0_1 = 1.5*y + 0.5;
1012
const double psitilde_bs_0_2 = 0.111111111111111*psitilde_bs_0_1 + 1.66666666666667*y*psitilde_bs_0_1 - 0.555555555555556*psitilde_bs_0_0;
1013
const double psitilde_bs_1_0 = 1;
1014
const double psitilde_bs_1_1 = 2.5*y + 1.5;
1015
const double psitilde_bs_2_0 = 1;
1016
1017
// Compute psitilde_cs
1018
const double psitilde_cs_00_0 = 1;
1019
const double psitilde_cs_00_1 = 2*z + 1;
1020
const double psitilde_cs_00_2 = 0.3125*psitilde_cs_00_1 + 1.875*z*psitilde_cs_00_1 - 0.5625*psitilde_cs_00_0;
1021
const double psitilde_cs_01_0 = 1;
1022
const double psitilde_cs_01_1 = 3*z + 2;
1023
const double psitilde_cs_02_0 = 1;
1024
const double psitilde_cs_10_0 = 1;
1025
const double psitilde_cs_10_1 = 3*z + 2;
1026
const double psitilde_cs_11_0 = 1;
1027
const double psitilde_cs_20_0 = 1;
1028
1029
// Compute basisvalues
1030
const double basisvalue0 = 0.866025403784439*psitilde_a_0*scalings_y_0*psitilde_bs_0_0*scalings_z_0*psitilde_cs_00_0;
1031
const double basisvalue1 = 2.73861278752583*psitilde_a_1*scalings_y_1*psitilde_bs_1_0*scalings_z_1*psitilde_cs_10_0;
1032
const double basisvalue2 = 1.58113883008419*psitilde_a_0*scalings_y_0*psitilde_bs_0_1*scalings_z_1*psitilde_cs_01_0;
1033
const double basisvalue3 = 1.11803398874989*psitilde_a_0*scalings_y_0*psitilde_bs_0_0*scalings_z_0*psitilde_cs_00_1;
1034
const double basisvalue4 = 5.1234753829798*psitilde_a_2*scalings_y_2*psitilde_bs_2_0*scalings_z_2*psitilde_cs_20_0;
1035
const double basisvalue5 = 3.96862696659689*psitilde_a_1*scalings_y_1*psitilde_bs_1_1*scalings_z_2*psitilde_cs_11_0;
1036
const double basisvalue6 = 2.29128784747792*psitilde_a_0*scalings_y_0*psitilde_bs_0_2*scalings_z_2*psitilde_cs_02_0;
1037
const double basisvalue7 = 3.24037034920393*psitilde_a_1*scalings_y_1*psitilde_bs_1_0*scalings_z_1*psitilde_cs_10_1;
1038
const double basisvalue8 = 1.87082869338697*psitilde_a_0*scalings_y_0*psitilde_bs_0_1*scalings_z_1*psitilde_cs_01_1;
1039
const double basisvalue9 = 1.3228756555323*psitilde_a_0*scalings_y_0*psitilde_bs_0_0*scalings_z_0*psitilde_cs_00_2;
1040
1041
// Table(s) of coefficients
1042
const static double coefficients0[10][10] = \
1043
{{-0.0577350269189625, -0.0608580619450185, -0.0351364184463153, -0.0248451997499977, 0.0650600048632355, 0.050395263067897, 0.0290957186981323, 0.0411475599898912, 0.0237565548366599, 0.0167984210226323},
1044
{-0.0577350269189625, 0.0608580619450185, -0.0351364184463153, -0.0248451997499976, 0.0650600048632355, -0.050395263067897, 0.0290957186981323, -0.0411475599898912, 0.0237565548366599, 0.0167984210226323},
1045
{-0.0577350269189626, 0, 0.0702728368926306, -0.0248451997499976, 0, 0, 0.087287156094397, 0, -0.0475131096733199, 0.0167984210226323},
1046
{-0.0577350269189626, 0, 0, 0.074535599249993, 0, 0, 0, 0, 0, 0.100790526135794},
1047
{0.23094010767585, 0, 0.140545673785261, 0.0993807989999906, 0, 0, 0, 0, 0.1187827741833, -0.0671936840905293},
1048
{0.23094010767585, 0.121716123890037, -0.0702728368926306, 0.0993807989999907, 0, 0, 0, 0.102868899974728, -0.0593913870916499, -0.0671936840905293},
1049
{0.23094010767585, 0.121716123890037, 0.0702728368926307, -0.0993807989999907, 0, 0.100790526135794, -0.087287156094397, -0.0205737799949456, -0.01187827741833, 0.0167984210226323},
1050
{0.23094010767585, -0.121716123890037, -0.0702728368926307, 0.0993807989999906, 0, 0, 0, -0.102868899974728, -0.0593913870916499, -0.0671936840905293},
1051
{0.23094010767585, -0.121716123890037, 0.0702728368926306, -0.0993807989999907, 0, -0.100790526135794, -0.0872871560943969, 0.0205737799949456, -0.01187827741833, 0.0167984210226323},
1052
{0.23094010767585, 0, -0.140545673785261, -0.0993807989999906, -0.130120009726471, 0, 0.0290957186981323, 0, 0.02375655483666, 0.0167984210226323}};
1053
1054
// Interesting (new) part
1055
// Tables of derivatives of the polynomial base (transpose)
1056
const static double dmats0[10][10] = \
1057
{{0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
1058
{6.32455532033676, 0, 0, 0, 0, 0, 0, 0, 0, 0},
1059
{0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
1060
{0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
1061
{0, 11.2249721603218, 0, 0, 0, 0, 0, 0, 0, 0},
1062
{4.58257569495584, 0, 8.36660026534076, -1.18321595661992, 0, 0, 0, 0, 0, 0},
1063
{0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
1064
{3.74165738677394, 0, 0, 8.69482604771366, 0, 0, 0, 0, 0, 0},
1065
{0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
1066
{0, 0, 0, 0, 0, 0, 0, 0, 0, 0}};
1067
1068
const static double dmats1[10][10] = \
1069
{{0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
1070
{3.16227766016838, 0, 0, 0, 0, 0, 0, 0, 0, 0},
1071
{5.47722557505166, 0, 0, 0, 0, 0, 0, 0, 0, 0},
1072
{0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
1073
{2.95803989154981, 5.61248608016091, -1.08012344973464, -0.763762615825974, 0, 0, 0, 0, 0, 0},
1074
{2.29128784747792, 7.24568837309472, 4.18330013267038, -0.591607978309962, 0, 0, 0, 0, 0, 0},
1075
{-2.64575131106459, 0, 9.66091783079296, 0.683130051063974, 0, 0, 0, 0, 0, 0},
1076
{1.87082869338697, 0, 0, 4.34741302385683, 0, 0, 0, 0, 0, 0},
1077
{3.24037034920393, 0, 0, 7.52994023880668, 0, 0, 0, 0, 0, 0},
1078
{0, 0, 0, 0, 0, 0, 0, 0, 0, 0}};
1079
1080
const static double dmats2[10][10] = \
1081
{{0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
1082
{3.16227766016838, 0, 0, 0, 0, 0, 0, 0, 0, 0},
1083
{1.82574185835055, 0, 0, 0, 0, 0, 0, 0, 0, 0},
1084
{5.16397779494322, 0, 0, 0, 0, 0, 0, 0, 0, 0},
1085
{2.95803989154981, 5.61248608016091, -1.08012344973464, -0.763762615825973, 0, 0, 0, 0, 0, 0},
1086
{2.29128784747792, 1.44913767461894, 4.18330013267038, -0.591607978309962, 0, 0, 0, 0, 0, 0},
1087
{1.32287565553229, 0, 3.86436713231718, -0.341565025531986, 0, 0, 0, 0, 0, 0},
1088
{1.87082869338697, 7.09929573971954, 0, 4.34741302385683, 0, 0, 0, 0, 0, 0},
1089
{1.08012344973464, 0, 7.09929573971954, 2.50998007960223, 0, 0, 0, 0, 0, 0},
1090
{-3.81881307912986, 0, 0, 8.87411967464942, 0, 0, 0, 0, 0, 0}};
1091
1092
// Compute reference derivatives
1093
// Declare pointer to array of derivatives on FIAT element
1094
double *derivatives = new double [num_derivatives];
1095
1096
// Declare coefficients
1097
double coeff0_0 = 0;
1098
double coeff0_1 = 0;
1099
double coeff0_2 = 0;
1100
double coeff0_3 = 0;
1101
double coeff0_4 = 0;
1102
double coeff0_5 = 0;
1103
double coeff0_6 = 0;
1104
double coeff0_7 = 0;
1105
double coeff0_8 = 0;
1106
double coeff0_9 = 0;
1107
1108
// Declare new coefficients
1109
double new_coeff0_0 = 0;
1110
double new_coeff0_1 = 0;
1111
double new_coeff0_2 = 0;
1112
double new_coeff0_3 = 0;
1113
double new_coeff0_4 = 0;
1114
double new_coeff0_5 = 0;
1115
double new_coeff0_6 = 0;
1116
double new_coeff0_7 = 0;
1117
double new_coeff0_8 = 0;
1118
double new_coeff0_9 = 0;
1119
1120
// Loop possible derivatives
1121
for (unsigned int deriv_num = 0; deriv_num < num_derivatives; deriv_num++)
1122
{
1123
// Get values from coefficients array
1124
new_coeff0_0 = coefficients0[dof][0];
1125
new_coeff0_1 = coefficients0[dof][1];
1126
new_coeff0_2 = coefficients0[dof][2];
1127
new_coeff0_3 = coefficients0[dof][3];
1128
new_coeff0_4 = coefficients0[dof][4];
1129
new_coeff0_5 = coefficients0[dof][5];
1130
new_coeff0_6 = coefficients0[dof][6];
1131
new_coeff0_7 = coefficients0[dof][7];
1132
new_coeff0_8 = coefficients0[dof][8];
1133
new_coeff0_9 = coefficients0[dof][9];
1134
1135
// Loop derivative order
1136
for (unsigned int j = 0; j < n; j++)
1137
{
1138
// Update old coefficients
1139
coeff0_0 = new_coeff0_0;
1140
coeff0_1 = new_coeff0_1;
1141
coeff0_2 = new_coeff0_2;
1142
coeff0_3 = new_coeff0_3;
1143
coeff0_4 = new_coeff0_4;
1144
coeff0_5 = new_coeff0_5;
1145
coeff0_6 = new_coeff0_6;
1146
coeff0_7 = new_coeff0_7;
1147
coeff0_8 = new_coeff0_8;
1148
coeff0_9 = new_coeff0_9;
1149
1150
if(combinations[deriv_num][j] == 0)
1151
{
1152
new_coeff0_0 = coeff0_0*dmats0[0][0] + coeff0_1*dmats0[1][0] + coeff0_2*dmats0[2][0] + coeff0_3*dmats0[3][0] + coeff0_4*dmats0[4][0] + coeff0_5*dmats0[5][0] + coeff0_6*dmats0[6][0] + coeff0_7*dmats0[7][0] + coeff0_8*dmats0[8][0] + coeff0_9*dmats0[9][0];
1153
new_coeff0_1 = coeff0_0*dmats0[0][1] + coeff0_1*dmats0[1][1] + coeff0_2*dmats0[2][1] + coeff0_3*dmats0[3][1] + coeff0_4*dmats0[4][1] + coeff0_5*dmats0[5][1] + coeff0_6*dmats0[6][1] + coeff0_7*dmats0[7][1] + coeff0_8*dmats0[8][1] + coeff0_9*dmats0[9][1];
1154
new_coeff0_2 = coeff0_0*dmats0[0][2] + coeff0_1*dmats0[1][2] + coeff0_2*dmats0[2][2] + coeff0_3*dmats0[3][2] + coeff0_4*dmats0[4][2] + coeff0_5*dmats0[5][2] + coeff0_6*dmats0[6][2] + coeff0_7*dmats0[7][2] + coeff0_8*dmats0[8][2] + coeff0_9*dmats0[9][2];
1155
new_coeff0_3 = coeff0_0*dmats0[0][3] + coeff0_1*dmats0[1][3] + coeff0_2*dmats0[2][3] + coeff0_3*dmats0[3][3] + coeff0_4*dmats0[4][3] + coeff0_5*dmats0[5][3] + coeff0_6*dmats0[6][3] + coeff0_7*dmats0[7][3] + coeff0_8*dmats0[8][3] + coeff0_9*dmats0[9][3];
1156
new_coeff0_4 = coeff0_0*dmats0[0][4] + coeff0_1*dmats0[1][4] + coeff0_2*dmats0[2][4] + coeff0_3*dmats0[3][4] + coeff0_4*dmats0[4][4] + coeff0_5*dmats0[5][4] + coeff0_6*dmats0[6][4] + coeff0_7*dmats0[7][4] + coeff0_8*dmats0[8][4] + coeff0_9*dmats0[9][4];
1157
new_coeff0_5 = coeff0_0*dmats0[0][5] + coeff0_1*dmats0[1][5] + coeff0_2*dmats0[2][5] + coeff0_3*dmats0[3][5] + coeff0_4*dmats0[4][5] + coeff0_5*dmats0[5][5] + coeff0_6*dmats0[6][5] + coeff0_7*dmats0[7][5] + coeff0_8*dmats0[8][5] + coeff0_9*dmats0[9][5];
1158
new_coeff0_6 = coeff0_0*dmats0[0][6] + coeff0_1*dmats0[1][6] + coeff0_2*dmats0[2][6] + coeff0_3*dmats0[3][6] + coeff0_4*dmats0[4][6] + coeff0_5*dmats0[5][6] + coeff0_6*dmats0[6][6] + coeff0_7*dmats0[7][6] + coeff0_8*dmats0[8][6] + coeff0_9*dmats0[9][6];
1159
new_coeff0_7 = coeff0_0*dmats0[0][7] + coeff0_1*dmats0[1][7] + coeff0_2*dmats0[2][7] + coeff0_3*dmats0[3][7] + coeff0_4*dmats0[4][7] + coeff0_5*dmats0[5][7] + coeff0_6*dmats0[6][7] + coeff0_7*dmats0[7][7] + coeff0_8*dmats0[8][7] + coeff0_9*dmats0[9][7];
1160
new_coeff0_8 = coeff0_0*dmats0[0][8] + coeff0_1*dmats0[1][8] + coeff0_2*dmats0[2][8] + coeff0_3*dmats0[3][8] + coeff0_4*dmats0[4][8] + coeff0_5*dmats0[5][8] + coeff0_6*dmats0[6][8] + coeff0_7*dmats0[7][8] + coeff0_8*dmats0[8][8] + coeff0_9*dmats0[9][8];
1161
new_coeff0_9 = coeff0_0*dmats0[0][9] + coeff0_1*dmats0[1][9] + coeff0_2*dmats0[2][9] + coeff0_3*dmats0[3][9] + coeff0_4*dmats0[4][9] + coeff0_5*dmats0[5][9] + coeff0_6*dmats0[6][9] + coeff0_7*dmats0[7][9] + coeff0_8*dmats0[8][9] + coeff0_9*dmats0[9][9];
1162
}
1163
if(combinations[deriv_num][j] == 1)
1164
{
1165
new_coeff0_0 = coeff0_0*dmats1[0][0] + coeff0_1*dmats1[1][0] + coeff0_2*dmats1[2][0] + coeff0_3*dmats1[3][0] + coeff0_4*dmats1[4][0] + coeff0_5*dmats1[5][0] + coeff0_6*dmats1[6][0] + coeff0_7*dmats1[7][0] + coeff0_8*dmats1[8][0] + coeff0_9*dmats1[9][0];
1166
new_coeff0_1 = coeff0_0*dmats1[0][1] + coeff0_1*dmats1[1][1] + coeff0_2*dmats1[2][1] + coeff0_3*dmats1[3][1] + coeff0_4*dmats1[4][1] + coeff0_5*dmats1[5][1] + coeff0_6*dmats1[6][1] + coeff0_7*dmats1[7][1] + coeff0_8*dmats1[8][1] + coeff0_9*dmats1[9][1];
1167
new_coeff0_2 = coeff0_0*dmats1[0][2] + coeff0_1*dmats1[1][2] + coeff0_2*dmats1[2][2] + coeff0_3*dmats1[3][2] + coeff0_4*dmats1[4][2] + coeff0_5*dmats1[5][2] + coeff0_6*dmats1[6][2] + coeff0_7*dmats1[7][2] + coeff0_8*dmats1[8][2] + coeff0_9*dmats1[9][2];
1168
new_coeff0_3 = coeff0_0*dmats1[0][3] + coeff0_1*dmats1[1][3] + coeff0_2*dmats1[2][3] + coeff0_3*dmats1[3][3] + coeff0_4*dmats1[4][3] + coeff0_5*dmats1[5][3] + coeff0_6*dmats1[6][3] + coeff0_7*dmats1[7][3] + coeff0_8*dmats1[8][3] + coeff0_9*dmats1[9][3];
1169
new_coeff0_4 = coeff0_0*dmats1[0][4] + coeff0_1*dmats1[1][4] + coeff0_2*dmats1[2][4] + coeff0_3*dmats1[3][4] + coeff0_4*dmats1[4][4] + coeff0_5*dmats1[5][4] + coeff0_6*dmats1[6][4] + coeff0_7*dmats1[7][4] + coeff0_8*dmats1[8][4] + coeff0_9*dmats1[9][4];
1170
new_coeff0_5 = coeff0_0*dmats1[0][5] + coeff0_1*dmats1[1][5] + coeff0_2*dmats1[2][5] + coeff0_3*dmats1[3][5] + coeff0_4*dmats1[4][5] + coeff0_5*dmats1[5][5] + coeff0_6*dmats1[6][5] + coeff0_7*dmats1[7][5] + coeff0_8*dmats1[8][5] + coeff0_9*dmats1[9][5];
1171
new_coeff0_6 = coeff0_0*dmats1[0][6] + coeff0_1*dmats1[1][6] + coeff0_2*dmats1[2][6] + coeff0_3*dmats1[3][6] + coeff0_4*dmats1[4][6] + coeff0_5*dmats1[5][6] + coeff0_6*dmats1[6][6] + coeff0_7*dmats1[7][6] + coeff0_8*dmats1[8][6] + coeff0_9*dmats1[9][6];
1172
new_coeff0_7 = coeff0_0*dmats1[0][7] + coeff0_1*dmats1[1][7] + coeff0_2*dmats1[2][7] + coeff0_3*dmats1[3][7] + coeff0_4*dmats1[4][7] + coeff0_5*dmats1[5][7] + coeff0_6*dmats1[6][7] + coeff0_7*dmats1[7][7] + coeff0_8*dmats1[8][7] + coeff0_9*dmats1[9][7];
1173
new_coeff0_8 = coeff0_0*dmats1[0][8] + coeff0_1*dmats1[1][8] + coeff0_2*dmats1[2][8] + coeff0_3*dmats1[3][8] + coeff0_4*dmats1[4][8] + coeff0_5*dmats1[5][8] + coeff0_6*dmats1[6][8] + coeff0_7*dmats1[7][8] + coeff0_8*dmats1[8][8] + coeff0_9*dmats1[9][8];
1174
new_coeff0_9 = coeff0_0*dmats1[0][9] + coeff0_1*dmats1[1][9] + coeff0_2*dmats1[2][9] + coeff0_3*dmats1[3][9] + coeff0_4*dmats1[4][9] + coeff0_5*dmats1[5][9] + coeff0_6*dmats1[6][9] + coeff0_7*dmats1[7][9] + coeff0_8*dmats1[8][9] + coeff0_9*dmats1[9][9];
1175
}
1176
if(combinations[deriv_num][j] == 2)
1177
{
1178
new_coeff0_0 = coeff0_0*dmats2[0][0] + coeff0_1*dmats2[1][0] + coeff0_2*dmats2[2][0] + coeff0_3*dmats2[3][0] + coeff0_4*dmats2[4][0] + coeff0_5*dmats2[5][0] + coeff0_6*dmats2[6][0] + coeff0_7*dmats2[7][0] + coeff0_8*dmats2[8][0] + coeff0_9*dmats2[9][0];
1179
new_coeff0_1 = coeff0_0*dmats2[0][1] + coeff0_1*dmats2[1][1] + coeff0_2*dmats2[2][1] + coeff0_3*dmats2[3][1] + coeff0_4*dmats2[4][1] + coeff0_5*dmats2[5][1] + coeff0_6*dmats2[6][1] + coeff0_7*dmats2[7][1] + coeff0_8*dmats2[8][1] + coeff0_9*dmats2[9][1];
1180
new_coeff0_2 = coeff0_0*dmats2[0][2] + coeff0_1*dmats2[1][2] + coeff0_2*dmats2[2][2] + coeff0_3*dmats2[3][2] + coeff0_4*dmats2[4][2] + coeff0_5*dmats2[5][2] + coeff0_6*dmats2[6][2] + coeff0_7*dmats2[7][2] + coeff0_8*dmats2[8][2] + coeff0_9*dmats2[9][2];
1181
new_coeff0_3 = coeff0_0*dmats2[0][3] + coeff0_1*dmats2[1][3] + coeff0_2*dmats2[2][3] + coeff0_3*dmats2[3][3] + coeff0_4*dmats2[4][3] + coeff0_5*dmats2[5][3] + coeff0_6*dmats2[6][3] + coeff0_7*dmats2[7][3] + coeff0_8*dmats2[8][3] + coeff0_9*dmats2[9][3];
1182
new_coeff0_4 = coeff0_0*dmats2[0][4] + coeff0_1*dmats2[1][4] + coeff0_2*dmats2[2][4] + coeff0_3*dmats2[3][4] + coeff0_4*dmats2[4][4] + coeff0_5*dmats2[5][4] + coeff0_6*dmats2[6][4] + coeff0_7*dmats2[7][4] + coeff0_8*dmats2[8][4] + coeff0_9*dmats2[9][4];
1183
new_coeff0_5 = coeff0_0*dmats2[0][5] + coeff0_1*dmats2[1][5] + coeff0_2*dmats2[2][5] + coeff0_3*dmats2[3][5] + coeff0_4*dmats2[4][5] + coeff0_5*dmats2[5][5] + coeff0_6*dmats2[6][5] + coeff0_7*dmats2[7][5] + coeff0_8*dmats2[8][5] + coeff0_9*dmats2[9][5];
1184
new_coeff0_6 = coeff0_0*dmats2[0][6] + coeff0_1*dmats2[1][6] + coeff0_2*dmats2[2][6] + coeff0_3*dmats2[3][6] + coeff0_4*dmats2[4][6] + coeff0_5*dmats2[5][6] + coeff0_6*dmats2[6][6] + coeff0_7*dmats2[7][6] + coeff0_8*dmats2[8][6] + coeff0_9*dmats2[9][6];
1185
new_coeff0_7 = coeff0_0*dmats2[0][7] + coeff0_1*dmats2[1][7] + coeff0_2*dmats2[2][7] + coeff0_3*dmats2[3][7] + coeff0_4*dmats2[4][7] + coeff0_5*dmats2[5][7] + coeff0_6*dmats2[6][7] + coeff0_7*dmats2[7][7] + coeff0_8*dmats2[8][7] + coeff0_9*dmats2[9][7];
1186
new_coeff0_8 = coeff0_0*dmats2[0][8] + coeff0_1*dmats2[1][8] + coeff0_2*dmats2[2][8] + coeff0_3*dmats2[3][8] + coeff0_4*dmats2[4][8] + coeff0_5*dmats2[5][8] + coeff0_6*dmats2[6][8] + coeff0_7*dmats2[7][8] + coeff0_8*dmats2[8][8] + coeff0_9*dmats2[9][8];
1187
new_coeff0_9 = coeff0_0*dmats2[0][9] + coeff0_1*dmats2[1][9] + coeff0_2*dmats2[2][9] + coeff0_3*dmats2[3][9] + coeff0_4*dmats2[4][9] + coeff0_5*dmats2[5][9] + coeff0_6*dmats2[6][9] + coeff0_7*dmats2[7][9] + coeff0_8*dmats2[8][9] + coeff0_9*dmats2[9][9];
1188
}
1189
1190
}
1191
// Compute derivatives on reference element as dot product of coefficients and basisvalues
1192
derivatives[deriv_num] = new_coeff0_0*basisvalue0 + new_coeff0_1*basisvalue1 + new_coeff0_2*basisvalue2 + new_coeff0_3*basisvalue3 + new_coeff0_4*basisvalue4 + new_coeff0_5*basisvalue5 + new_coeff0_6*basisvalue6 + new_coeff0_7*basisvalue7 + new_coeff0_8*basisvalue8 + new_coeff0_9*basisvalue9;
1193
}
1194
1195
// Transform derivatives back to physical element
1196
for (unsigned int row = 0; row < num_derivatives; row++)
1197
{
1198
for (unsigned int col = 0; col < num_derivatives; col++)
1199
{
1200
values[row] += transform[row][col]*derivatives[col];
1201
}
1202
}
1203
// Delete pointer to array of derivatives on FIAT element
1204
delete [] derivatives;
1205
1206
// Delete pointer to array of combinations of derivatives and transform
1207
for (unsigned int row = 0; row < num_derivatives; row++)
1208
{
1209
delete [] combinations[row];
1210
delete [] transform[row];
1211
}
1212
1213
delete [] combinations;
1214
delete [] transform;
1215
}
1216
1217
/// Evaluate order n derivatives of all basis functions at given point in cell
1218
virtual void evaluate_basis_derivatives_all(unsigned int n,
1219
double* values,
1220
const double* coordinates,
1221
const ufc::cell& c) const
1222
{
1223
throw std::runtime_error("The vectorised version of evaluate_basis_derivatives() is not yet implemented.");
1224
}
1225
1226
/// Evaluate linear functional for dof i on the function f
1227
virtual double evaluate_dof(unsigned int i,
1228
const ufc::function& f,
1229
const ufc::cell& c) const
1230
{
1231
// The reference points, direction and weights:
1232
const static double X[10][1][3] = {{{0, 0, 0}}, {{1, 0, 0}}, {{0, 1, 0}}, {{0, 0, 1}}, {{0, 0.5, 0.5}}, {{0.5, 0, 0.5}}, {{0.5, 0.5, 0}}, {{0, 0, 0.5}}, {{0, 0.5, 0}}, {{0.5, 0, 0}}};
1233
const static double W[10][1] = {{1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}};
1234
const static double D[10][1][1] = {{{1}}, {{1}}, {{1}}, {{1}}, {{1}}, {{1}}, {{1}}, {{1}}, {{1}}, {{1}}};
1235
1236
const double * const * x = c.coordinates;
1237
double result = 0.0;
1238
// Iterate over the points:
1239
// Evaluate basis functions for affine mapping
1240
const double w0 = 1.0 - X[i][0][0] - X[i][0][1] - X[i][0][2];
1241
const double w1 = X[i][0][0];
1242
const double w2 = X[i][0][1];
1243
const double w3 = X[i][0][2];
1244
1245
// Compute affine mapping y = F(X)
1246
double y[3];
1247
y[0] = w0*x[0][0] + w1*x[1][0] + w2*x[2][0] + w3*x[3][0];
1248
y[1] = w0*x[0][1] + w1*x[1][1] + w2*x[2][1] + w3*x[3][1];
1249
y[2] = w0*x[0][2] + w1*x[1][2] + w2*x[2][2] + w3*x[3][2];
1250
1251
// Evaluate function at physical points
1252
double values[1];
1253
f.evaluate(values, y, c);
1254
1255
// Map function values using appropriate mapping
1256
// Affine map: Do nothing
1257
1258
// Note that we do not map the weights (yet).
1259
1260
// Take directional components
1261
for(int k = 0; k < 1; k++)
1262
result += values[k]*D[i][0][k];
1263
// Multiply by weights
1264
result *= W[i][0];
1265
1266
return result;
1267
}
1268
1269
/// Evaluate linear functionals for all dofs on the function f
1270
virtual void evaluate_dofs(double* values,
1271
const ufc::function& f,
1272
const ufc::cell& c) const
1273
{
1274
throw std::runtime_error("Not implemented (introduced in UFC v1.1).");
1275
}
1276
1277
/// Interpolate vertex values from dof values
1278
virtual void interpolate_vertex_values(double* vertex_values,
1279
const double* dof_values,
1280
const ufc::cell& c) const
1281
{
1282
// Evaluate at vertices and use affine mapping
1283
vertex_values[0] = dof_values[0];
1284
vertex_values[1] = dof_values[1];
1285
vertex_values[2] = dof_values[2];
1286
vertex_values[3] = dof_values[3];
1287
}
1288
1289
/// Return the number of sub elements (for a mixed element)
1290
virtual unsigned int num_sub_elements() const
1291
{
1292
return 1;
1293
}
1294
1295
/// Create a new finite element for sub element i (for a mixed element)
1296
virtual ufc::finite_element* create_sub_element(unsigned int i) const
1297
{
1298
return new UFC_ProjectionBilinearForm_finite_element_1();
1299
}
1300
1301
};
1302
1303
/// This class defines the interface for a local-to-global mapping of
1304
/// degrees of freedom (dofs).
1305
1306
class UFC_ProjectionBilinearForm_dof_map_0: public ufc::dof_map
1307
{
1308
private:
1309
1310
unsigned int __global_dimension;
1311
1312
public:
1313
1314
/// Constructor
1315
UFC_ProjectionBilinearForm_dof_map_0() : ufc::dof_map()
1316
{
1317
__global_dimension = 0;
1318
}
1319
1320
/// Destructor
1321
virtual ~UFC_ProjectionBilinearForm_dof_map_0()
1322
{
1323
// Do nothing
1324
}
1325
1326
/// Return a string identifying the dof map
1327
virtual const char* signature() const
1328
{
1329
return "FFC dof map for FiniteElement('Lagrange', 'tetrahedron', 2)";
1330
}
1331
1332
/// Return true iff mesh entities of topological dimension d are needed
1333
virtual bool needs_mesh_entities(unsigned int d) const
1334
{
1335
switch ( d )
1336
{
1337
case 0:
1338
return true;
1339
break;
1340
case 1:
1341
return true;
1342
break;
1343
case 2:
1344
return false;
1345
break;
1346
case 3:
1347
return false;
1348
break;
1349
}
1350
return false;
1351
}
1352
1353
/// Initialize dof map for mesh (return true iff init_cell() is needed)
1354
virtual bool init_mesh(const ufc::mesh& m)
1355
{
1356
__global_dimension = m.num_entities[0] + m.num_entities[1];
1357
return false;
1358
}
1359
1360
/// Initialize dof map for given cell
1361
virtual void init_cell(const ufc::mesh& m,
1362
const ufc::cell& c)
1363
{
1364
// Do nothing
1365
}
1366
1367
/// Finish initialization of dof map for cells
1368
virtual void init_cell_finalize()
1369
{
1370
// Do nothing
1371
}
1372
1373
/// Return the dimension of the global finite element function space
1374
virtual unsigned int global_dimension() const
1375
{
1376
return __global_dimension;
1377
}
1378
1379
/// Return the dimension of the local finite element function space
1380
virtual unsigned int local_dimension() const
1381
{
1382
return 10;
1383
}
1384
1385
// Return the geometric dimension of the coordinates this dof map provides
1386
virtual unsigned int geometric_dimension() const
1387
{
1388
return 3;
1389
}
1390
1391
/// Return the number of dofs on each cell facet
1392
virtual unsigned int num_facet_dofs() const
1393
{
1394
return 6;
1395
}
1396
1397
/// Return the number of dofs associated with each cell entity of dimension d
1398
virtual unsigned int num_entity_dofs(unsigned int d) const
1399
{
1400
throw std::runtime_error("Not implemented (introduced in UFC v1.1).");
1401
}
1402
1403
/// Tabulate the local-to-global mapping of dofs on a cell
1404
virtual void tabulate_dofs(unsigned int* dofs,
1405
const ufc::mesh& m,
1406
const ufc::cell& c) const
1407
{
1408
dofs[0] = c.entity_indices[0][0];
1409
dofs[1] = c.entity_indices[0][1];
1410
dofs[2] = c.entity_indices[0][2];
1411
dofs[3] = c.entity_indices[0][3];
1412
unsigned int offset = m.num_entities[0];
1413
dofs[4] = offset + c.entity_indices[1][0];
1414
dofs[5] = offset + c.entity_indices[1][1];
1415
dofs[6] = offset + c.entity_indices[1][2];
1416
dofs[7] = offset + c.entity_indices[1][3];
1417
dofs[8] = offset + c.entity_indices[1][4];
1418
dofs[9] = offset + c.entity_indices[1][5];
1419
}
1420
1421
/// Tabulate the local-to-local mapping from facet dofs to cell dofs
1422
virtual void tabulate_facet_dofs(unsigned int* dofs,
1423
unsigned int facet) const
1424
{
1425
switch ( facet )
1426
{
1427
case 0:
1428
dofs[0] = 1;
1429
dofs[1] = 2;
1430
dofs[2] = 3;
1431
dofs[3] = 4;
1432
dofs[4] = 5;
1433
dofs[5] = 6;
1434
break;
1435
case 1:
1436
dofs[0] = 0;
1437
dofs[1] = 2;
1438
dofs[2] = 3;
1439
dofs[3] = 4;
1440
dofs[4] = 7;
1441
dofs[5] = 8;
1442
break;
1443
case 2:
1444
dofs[0] = 0;
1445
dofs[1] = 1;
1446
dofs[2] = 3;
1447
dofs[3] = 5;
1448
dofs[4] = 7;
1449
dofs[5] = 9;
1450
break;
1451
case 3:
1452
dofs[0] = 0;
1453
dofs[1] = 1;
1454
dofs[2] = 2;
1455
dofs[3] = 6;
1456
dofs[4] = 8;
1457
dofs[5] = 9;
1458
break;
1459
}
1460
}
1461
1462
/// Tabulate the local-to-local mapping of dofs on entity (d, i)
1463
virtual void tabulate_entity_dofs(unsigned int* dofs,
1464
unsigned int d, unsigned int i) const
1465
{
1466
throw std::runtime_error("Not implemented (introduced in UFC v1.1).");
1467
}
1468
1469
/// Tabulate the coordinates of all dofs on a cell
1470
virtual void tabulate_coordinates(double** coordinates,
1471
const ufc::cell& c) const
1472
{
1473
const double * const * x = c.coordinates;
1474
coordinates[0][0] = x[0][0];
1475
coordinates[0][1] = x[0][1];
1476
coordinates[0][2] = x[0][2];
1477
coordinates[1][0] = x[1][0];
1478
coordinates[1][1] = x[1][1];
1479
coordinates[1][2] = x[1][2];
1480
coordinates[2][0] = x[2][0];
1481
coordinates[2][1] = x[2][1];
1482
coordinates[2][2] = x[2][2];
1483
coordinates[3][0] = x[3][0];
1484
coordinates[3][1] = x[3][1];
1485
coordinates[3][2] = x[3][2];
1486
coordinates[4][0] = 0.5*x[2][0] + 0.5*x[3][0];
1487
coordinates[4][1] = 0.5*x[2][1] + 0.5*x[3][1];
1488
coordinates[4][2] = 0.5*x[2][2] + 0.5*x[3][2];
1489
coordinates[5][0] = 0.5*x[1][0] + 0.5*x[3][0];
1490
coordinates[5][1] = 0.5*x[1][1] + 0.5*x[3][1];
1491
coordinates[5][2] = 0.5*x[1][2] + 0.5*x[3][2];
1492
coordinates[6][0] = 0.5*x[1][0] + 0.5*x[2][0];
1493
coordinates[6][1] = 0.5*x[1][1] + 0.5*x[2][1];
1494
coordinates[6][2] = 0.5*x[1][2] + 0.5*x[2][2];
1495
coordinates[7][0] = 0.5*x[0][0] + 0.5*x[3][0];
1496
coordinates[7][1] = 0.5*x[0][1] + 0.5*x[3][1];
1497
coordinates[7][2] = 0.5*x[0][2] + 0.5*x[3][2];
1498
coordinates[8][0] = 0.5*x[0][0] + 0.5*x[2][0];
1499
coordinates[8][1] = 0.5*x[0][1] + 0.5*x[2][1];
1500
coordinates[8][2] = 0.5*x[0][2] + 0.5*x[2][2];
1501
coordinates[9][0] = 0.5*x[0][0] + 0.5*x[1][0];
1502
coordinates[9][1] = 0.5*x[0][1] + 0.5*x[1][1];
1503
coordinates[9][2] = 0.5*x[0][2] + 0.5*x[1][2];
1504
}
1505
1506
/// Return the number of sub dof maps (for a mixed element)
1507
virtual unsigned int num_sub_dof_maps() const
1508
{
1509
return 1;
1510
}
1511
1512
/// Create a new dof_map for sub dof map i (for a mixed element)
1513
virtual ufc::dof_map* create_sub_dof_map(unsigned int i) const
1514
{
1515
return new UFC_ProjectionBilinearForm_dof_map_0();
1516
}
1517
1518
};
1519
1520
/// This class defines the interface for a local-to-global mapping of
1521
/// degrees of freedom (dofs).
1522
1523
class UFC_ProjectionBilinearForm_dof_map_1: public ufc::dof_map
1524
{
1525
private:
1526
1527
unsigned int __global_dimension;
1528
1529
public:
1530
1531
/// Constructor
1532
UFC_ProjectionBilinearForm_dof_map_1() : ufc::dof_map()
1533
{
1534
__global_dimension = 0;
1535
}
1536
1537
/// Destructor
1538
virtual ~UFC_ProjectionBilinearForm_dof_map_1()
1539
{
1540
// Do nothing
1541
}
1542
1543
/// Return a string identifying the dof map
1544
virtual const char* signature() const
1545
{
1546
return "FFC dof map for FiniteElement('Lagrange', 'tetrahedron', 2)";
1547
}
1548
1549
/// Return true iff mesh entities of topological dimension d are needed
1550
virtual bool needs_mesh_entities(unsigned int d) const
1551
{
1552
switch ( d )
1553
{
1554
case 0:
1555
return true;
1556
break;
1557
case 1:
1558
return true;
1559
break;
1560
case 2:
1561
return false;
1562
break;
1563
case 3:
1564
return false;
1565
break;
1566
}
1567
return false;
1568
}
1569
1570
/// Initialize dof map for mesh (return true iff init_cell() is needed)
1571
virtual bool init_mesh(const ufc::mesh& m)
1572
{
1573
__global_dimension = m.num_entities[0] + m.num_entities[1];
1574
return false;
1575
}
1576
1577
/// Initialize dof map for given cell
1578
virtual void init_cell(const ufc::mesh& m,
1579
const ufc::cell& c)
1580
{
1581
// Do nothing
1582
}
1583
1584
/// Finish initialization of dof map for cells
1585
virtual void init_cell_finalize()
1586
{
1587
// Do nothing
1588
}
1589
1590
/// Return the dimension of the global finite element function space
1591
virtual unsigned int global_dimension() const
1592
{
1593
return __global_dimension;
1594
}
1595
1596
/// Return the dimension of the local finite element function space
1597
virtual unsigned int local_dimension() const
1598
{
1599
return 10;
1600
}
1601
1602
// Return the geometric dimension of the coordinates this dof map provides
1603
virtual unsigned int geometric_dimension() const
1604
{
1605
return 3;
1606
}
1607
1608
/// Return the number of dofs on each cell facet
1609
virtual unsigned int num_facet_dofs() const
1610
{
1611
return 6;
1612
}
1613
1614
/// Return the number of dofs associated with each cell entity of dimension d
1615
virtual unsigned int num_entity_dofs(unsigned int d) const
1616
{
1617
throw std::runtime_error("Not implemented (introduced in UFC v1.1).");
1618
}
1619
1620
/// Tabulate the local-to-global mapping of dofs on a cell
1621
virtual void tabulate_dofs(unsigned int* dofs,
1622
const ufc::mesh& m,
1623
const ufc::cell& c) const
1624
{
1625
dofs[0] = c.entity_indices[0][0];
1626
dofs[1] = c.entity_indices[0][1];
1627
dofs[2] = c.entity_indices[0][2];
1628
dofs[3] = c.entity_indices[0][3];
1629
unsigned int offset = m.num_entities[0];
1630
dofs[4] = offset + c.entity_indices[1][0];
1631
dofs[5] = offset + c.entity_indices[1][1];
1632
dofs[6] = offset + c.entity_indices[1][2];
1633
dofs[7] = offset + c.entity_indices[1][3];
1634
dofs[8] = offset + c.entity_indices[1][4];
1635
dofs[9] = offset + c.entity_indices[1][5];
1636
}
1637
1638
/// Tabulate the local-to-local mapping from facet dofs to cell dofs
1639
virtual void tabulate_facet_dofs(unsigned int* dofs,
1640
unsigned int facet) const
1641
{
1642
switch ( facet )
1643
{
1644
case 0:
1645
dofs[0] = 1;
1646
dofs[1] = 2;
1647
dofs[2] = 3;
1648
dofs[3] = 4;
1649
dofs[4] = 5;
1650
dofs[5] = 6;
1651
break;
1652
case 1:
1653
dofs[0] = 0;
1654
dofs[1] = 2;
1655
dofs[2] = 3;
1656
dofs[3] = 4;
1657
dofs[4] = 7;
1658
dofs[5] = 8;
1659
break;
1660
case 2:
1661
dofs[0] = 0;
1662
dofs[1] = 1;
1663
dofs[2] = 3;
1664
dofs[3] = 5;
1665
dofs[4] = 7;
1666
dofs[5] = 9;
1667
break;
1668
case 3:
1669
dofs[0] = 0;
1670
dofs[1] = 1;
1671
dofs[2] = 2;
1672
dofs[3] = 6;
1673
dofs[4] = 8;
1674
dofs[5] = 9;
1675
break;
1676
}
1677
}
1678
1679
/// Tabulate the local-to-local mapping of dofs on entity (d, i)
1680
virtual void tabulate_entity_dofs(unsigned int* dofs,
1681
unsigned int d, unsigned int i) const
1682
{
1683
throw std::runtime_error("Not implemented (introduced in UFC v1.1).");
1684
}
1685
1686
/// Tabulate the coordinates of all dofs on a cell
1687
virtual void tabulate_coordinates(double** coordinates,
1688
const ufc::cell& c) const
1689
{
1690
const double * const * x = c.coordinates;
1691
coordinates[0][0] = x[0][0];
1692
coordinates[0][1] = x[0][1];
1693
coordinates[0][2] = x[0][2];
1694
coordinates[1][0] = x[1][0];
1695
coordinates[1][1] = x[1][1];
1696
coordinates[1][2] = x[1][2];
1697
coordinates[2][0] = x[2][0];
1698
coordinates[2][1] = x[2][1];
1699
coordinates[2][2] = x[2][2];
1700
coordinates[3][0] = x[3][0];
1701
coordinates[3][1] = x[3][1];
1702
coordinates[3][2] = x[3][2];
1703
coordinates[4][0] = 0.5*x[2][0] + 0.5*x[3][0];
1704
coordinates[4][1] = 0.5*x[2][1] + 0.5*x[3][1];
1705
coordinates[4][2] = 0.5*x[2][2] + 0.5*x[3][2];
1706
coordinates[5][0] = 0.5*x[1][0] + 0.5*x[3][0];
1707
coordinates[5][1] = 0.5*x[1][1] + 0.5*x[3][1];
1708
coordinates[5][2] = 0.5*x[1][2] + 0.5*x[3][2];
1709
coordinates[6][0] = 0.5*x[1][0] + 0.5*x[2][0];
1710
coordinates[6][1] = 0.5*x[1][1] + 0.5*x[2][1];
1711
coordinates[6][2] = 0.5*x[1][2] + 0.5*x[2][2];
1712
coordinates[7][0] = 0.5*x[0][0] + 0.5*x[3][0];
1713
coordinates[7][1] = 0.5*x[0][1] + 0.5*x[3][1];
1714
coordinates[7][2] = 0.5*x[0][2] + 0.5*x[3][2];
1715
coordinates[8][0] = 0.5*x[0][0] + 0.5*x[2][0];
1716
coordinates[8][1] = 0.5*x[0][1] + 0.5*x[2][1];
1717
coordinates[8][2] = 0.5*x[0][2] + 0.5*x[2][2];
1718
coordinates[9][0] = 0.5*x[0][0] + 0.5*x[1][0];
1719
coordinates[9][1] = 0.5*x[0][1] + 0.5*x[1][1];
1720
coordinates[9][2] = 0.5*x[0][2] + 0.5*x[1][2];
1721
}
1722
1723
/// Return the number of sub dof maps (for a mixed element)
1724
virtual unsigned int num_sub_dof_maps() const
1725
{
1726
return 1;
1727
}
1728
1729
/// Create a new dof_map for sub dof map i (for a mixed element)
1730
virtual ufc::dof_map* create_sub_dof_map(unsigned int i) const
1731
{
1732
return new UFC_ProjectionBilinearForm_dof_map_1();
14
15
/// This class defines the interface for a finite element.
16
17
class projection_0_finite_element_0: public ufc::finite_element
18
{
19
public:
20
21
/// Constructor
22
projection_0_finite_element_0() : ufc::finite_element()
23
{
24
// Do nothing
25
}
26
27
/// Destructor
28
virtual ~projection_0_finite_element_0()
29
{
30
// Do nothing
31
}
32
33
/// Return a string identifying the finite element
34
virtual const char* signature() const
35
{
36
return "FiniteElement('Lagrange', 'tetrahedron', 2)";
37
}
38
39
/// Return the cell shape
40
virtual ufc::shape cell_shape() const
41
{
42
return ufc::tetrahedron;
43
}
44
45
/// Return the dimension of the finite element function space
46
virtual unsigned int space_dimension() const
47
{
48
return 10;
49
}
50
51
/// Return the rank of the value space
52
virtual unsigned int value_rank() const
53
{
54
return 0;
55
}
56
57
/// Return the dimension of the value space for axis i
58
virtual unsigned int value_dimension(unsigned int i) const
59
{
60
return 1;
61
}
62
63
/// Evaluate basis function i at given point in cell
64
virtual void evaluate_basis(unsigned int i,
65
double* values,
66
const double* coordinates,
67
const ufc::cell& c) const
68
{
69
// Extract vertex coordinates
70
const double * const * element_coordinates = c.coordinates;
71
72
// Compute Jacobian of affine map from reference cell
73
const double J_00 = element_coordinates[1][0] - element_coordinates[0][0];
74
const double J_01 = element_coordinates[2][0] - element_coordinates[0][0];
75
const double J_02 = element_coordinates[3][0] - element_coordinates[0][0];
76
const double J_10 = element_coordinates[1][1] - element_coordinates[0][1];
77
const double J_11 = element_coordinates[2][1] - element_coordinates[0][1];
78
const double J_12 = element_coordinates[3][1] - element_coordinates[0][1];
79
const double J_20 = element_coordinates[1][2] - element_coordinates[0][2];
80
const double J_21 = element_coordinates[2][2] - element_coordinates[0][2];
81
const double J_22 = element_coordinates[3][2] - element_coordinates[0][2];
82
83
// Compute sub determinants
84
const double d00 = J_11*J_22 - J_12*J_21;
85
const double d01 = J_12*J_20 - J_10*J_22;
86
const double d02 = J_10*J_21 - J_11*J_20;
87
88
const double d10 = J_02*J_21 - J_01*J_22;
89
const double d11 = J_00*J_22 - J_02*J_20;
90
const double d12 = J_01*J_20 - J_00*J_21;
91
92
const double d20 = J_01*J_12 - J_02*J_11;
93
const double d21 = J_02*J_10 - J_00*J_12;
94
const double d22 = J_00*J_11 - J_01*J_10;
95
96
// Compute determinant of Jacobian
97
double detJ = J_00*d00 + J_10*d10 + J_20*d20;
98
99
// Compute inverse of Jacobian
100
101
// Compute constants
102
const double C0 = d00*(element_coordinates[0][0] - element_coordinates[2][0] - element_coordinates[3][0]) \
103
+ d10*(element_coordinates[0][1] - element_coordinates[2][1] - element_coordinates[3][1]) \
104
+ d20*(element_coordinates[0][2] - element_coordinates[2][2] - element_coordinates[3][2]);
105
106
const double C1 = d01*(element_coordinates[0][0] - element_coordinates[1][0] - element_coordinates[3][0]) \
107
+ d11*(element_coordinates[0][1] - element_coordinates[1][1] - element_coordinates[3][1]) \
108
+ d21*(element_coordinates[0][2] - element_coordinates[1][2] - element_coordinates[3][2]);
109
110
const double C2 = d02*(element_coordinates[0][0] - element_coordinates[1][0] - element_coordinates[2][0]) \
111
+ d12*(element_coordinates[0][1] - element_coordinates[1][1] - element_coordinates[2][1]) \
112
+ d22*(element_coordinates[0][2] - element_coordinates[1][2] - element_coordinates[2][2]);
113
114
// Get coordinates and map to the UFC reference element
115
double x = (C0 + d00*coordinates[0] + d10*coordinates[1] + d20*coordinates[2]) / detJ;
116
double y = (C1 + d01*coordinates[0] + d11*coordinates[1] + d21*coordinates[2]) / detJ;
117
double z = (C2 + d02*coordinates[0] + d12*coordinates[1] + d22*coordinates[2]) / detJ;
118
119
// Map coordinates to the reference cube
120
if (std::abs(y + z - 1.0) < 1e-14)
121
x = 1.0;
122
else
123
x = -2.0 * x/(y + z - 1.0) - 1.0;
124
if (std::abs(z - 1.0) < 1e-14)
125
y = -1.0;
126
else
127
y = 2.0 * y/(1.0 - z) - 1.0;
128
z = 2.0 * z - 1.0;
129
130
// Reset values
131
*values = 0;
132
133
// Map degree of freedom to element degree of freedom
134
const unsigned int dof = i;
135
136
// Generate scalings
137
const double scalings_y_0 = 1;
138
const double scalings_y_1 = scalings_y_0*(0.5 - 0.5*y);
139
const double scalings_y_2 = scalings_y_1*(0.5 - 0.5*y);
140
const double scalings_z_0 = 1;
141
const double scalings_z_1 = scalings_z_0*(0.5 - 0.5*z);
142
const double scalings_z_2 = scalings_z_1*(0.5 - 0.5*z);
143
144
// Compute psitilde_a
145
const double psitilde_a_0 = 1;
146
const double psitilde_a_1 = x;
147
const double psitilde_a_2 = 1.5*x*psitilde_a_1 - 0.5*psitilde_a_0;
148
149
// Compute psitilde_bs
150
const double psitilde_bs_0_0 = 1;
151
const double psitilde_bs_0_1 = 1.5*y + 0.5;
152
const double psitilde_bs_0_2 = 0.111111111111111*psitilde_bs_0_1 + 1.66666666666667*y*psitilde_bs_0_1 - 0.555555555555556*psitilde_bs_0_0;
153
const double psitilde_bs_1_0 = 1;
154
const double psitilde_bs_1_1 = 2.5*y + 1.5;
155
const double psitilde_bs_2_0 = 1;
156
157
// Compute psitilde_cs
158
const double psitilde_cs_00_0 = 1;
159
const double psitilde_cs_00_1 = 2*z + 1;
160
const double psitilde_cs_00_2 = 0.3125*psitilde_cs_00_1 + 1.875*z*psitilde_cs_00_1 - 0.5625*psitilde_cs_00_0;
161
const double psitilde_cs_01_0 = 1;
162
const double psitilde_cs_01_1 = 3*z + 2;
163
const double psitilde_cs_02_0 = 1;
164
const double psitilde_cs_10_0 = 1;
165
const double psitilde_cs_10_1 = 3*z + 2;
166
const double psitilde_cs_11_0 = 1;
167
const double psitilde_cs_20_0 = 1;
168
169
// Compute basisvalues
170
const double basisvalue0 = 0.866025403784439*psitilde_a_0*scalings_y_0*psitilde_bs_0_0*scalings_z_0*psitilde_cs_00_0;
171
const double basisvalue1 = 2.73861278752583*psitilde_a_1*scalings_y_1*psitilde_bs_1_0*scalings_z_1*psitilde_cs_10_0;
172
const double basisvalue2 = 1.58113883008419*psitilde_a_0*scalings_y_0*psitilde_bs_0_1*scalings_z_1*psitilde_cs_01_0;
173
const double basisvalue3 = 1.11803398874989*psitilde_a_0*scalings_y_0*psitilde_bs_0_0*scalings_z_0*psitilde_cs_00_1;
174
const double basisvalue4 = 5.1234753829798*psitilde_a_2*scalings_y_2*psitilde_bs_2_0*scalings_z_2*psitilde_cs_20_0;
175
const double basisvalue5 = 3.96862696659689*psitilde_a_1*scalings_y_1*psitilde_bs_1_1*scalings_z_2*psitilde_cs_11_0;
176
const double basisvalue6 = 2.29128784747792*psitilde_a_0*scalings_y_0*psitilde_bs_0_2*scalings_z_2*psitilde_cs_02_0;
177
const double basisvalue7 = 3.24037034920393*psitilde_a_1*scalings_y_1*psitilde_bs_1_0*scalings_z_1*psitilde_cs_10_1;
178
const double basisvalue8 = 1.87082869338697*psitilde_a_0*scalings_y_0*psitilde_bs_0_1*scalings_z_1*psitilde_cs_01_1;
179
const double basisvalue9 = 1.3228756555323*psitilde_a_0*scalings_y_0*psitilde_bs_0_0*scalings_z_0*psitilde_cs_00_2;
180
181
// Table(s) of coefficients
182
static const double coefficients0[10][10] = \
183
{{-0.0577350269189626, -0.0608580619450185, -0.0351364184463153, -0.0248451997499977, 0.0650600048632355, 0.0503952630678969, 0.0290957186981323, 0.0411475599898912, 0.0237565548366599, 0.0167984210226323},
184
{-0.0577350269189625, 0.0608580619450185, -0.0351364184463153, -0.0248451997499977, 0.0650600048632355, -0.050395263067897, 0.0290957186981323, -0.0411475599898912, 0.0237565548366599, 0.0167984210226323},
185
{-0.0577350269189626, 0, 0.0702728368926307, -0.0248451997499977, 0, 0, 0.0872871560943969, 0, -0.0475131096733199, 0.0167984210226323},
186
{-0.0577350269189626, 0, 0, 0.074535599249993, 0, 0, 0, 0, 0, 0.100790526135794},
187
{0.23094010767585, 0, 0.140545673785261, 0.0993807989999906, 0, 0, 0, 0, 0.1187827741833, -0.0671936840905293},
188
{0.23094010767585, 0.121716123890037, -0.0702728368926307, 0.0993807989999907, 0, 0, 0, 0.102868899974728, -0.0593913870916499, -0.0671936840905293},
189
{0.23094010767585, 0.121716123890037, 0.0702728368926306, -0.0993807989999906, 0, 0.100790526135794, -0.0872871560943969, -0.0205737799949456, -0.01187827741833, 0.0167984210226323},
190
{0.23094010767585, -0.121716123890037, -0.0702728368926307, 0.0993807989999907, 0, 0, 0, -0.102868899974728, -0.0593913870916499, -0.0671936840905293},
191
{0.23094010767585, -0.121716123890037, 0.0702728368926306, -0.0993807989999907, 0, -0.100790526135794, -0.0872871560943969, 0.0205737799949456, -0.01187827741833, 0.0167984210226323},
192
{0.23094010767585, 0, -0.140545673785261, -0.0993807989999906, -0.130120009726471, 0, 0.0290957186981323, 0, 0.02375655483666, 0.0167984210226323}};
193
194
// Extract relevant coefficients
195
const double coeff0_0 = coefficients0[dof][0];
196
const double coeff0_1 = coefficients0[dof][1];
197
const double coeff0_2 = coefficients0[dof][2];
198
const double coeff0_3 = coefficients0[dof][3];
199
const double coeff0_4 = coefficients0[dof][4];
200
const double coeff0_5 = coefficients0[dof][5];
201
const double coeff0_6 = coefficients0[dof][6];
202
const double coeff0_7 = coefficients0[dof][7];
203
const double coeff0_8 = coefficients0[dof][8];
204
const double coeff0_9 = coefficients0[dof][9];
205
206
// Compute value(s)
207
*values = coeff0_0*basisvalue0 + coeff0_1*basisvalue1 + coeff0_2*basisvalue2 + coeff0_3*basisvalue3 + coeff0_4*basisvalue4 + coeff0_5*basisvalue5 + coeff0_6*basisvalue6 + coeff0_7*basisvalue7 + coeff0_8*basisvalue8 + coeff0_9*basisvalue9;
208
}
209
210
/// Evaluate all basis functions at given point in cell
211
virtual void evaluate_basis_all(double* values,
212
const double* coordinates,
213
const ufc::cell& c) const
214
{
215
throw std::runtime_error("The vectorised version of evaluate_basis() is not yet implemented.");
216
}
217
218
/// Evaluate order n derivatives of basis function i at given point in cell
219
virtual void evaluate_basis_derivatives(unsigned int i,
220
unsigned int n,
221
double* values,
222
const double* coordinates,
223
const ufc::cell& c) const
224
{
225
// Extract vertex coordinates
226
const double * const * element_coordinates = c.coordinates;
227
228
// Compute Jacobian of affine map from reference cell
229
const double J_00 = element_coordinates[1][0] - element_coordinates[0][0];
230
const double J_01 = element_coordinates[2][0] - element_coordinates[0][0];
231
const double J_02 = element_coordinates[3][0] - element_coordinates[0][0];
232
const double J_10 = element_coordinates[1][1] - element_coordinates[0][1];
233
const double J_11 = element_coordinates[2][1] - element_coordinates[0][1];
234
const double J_12 = element_coordinates[3][1] - element_coordinates[0][1];
235
const double J_20 = element_coordinates[1][2] - element_coordinates[0][2];
236
const double J_21 = element_coordinates[2][2] - element_coordinates[0][2];
237
const double J_22 = element_coordinates[3][2] - element_coordinates[0][2];
238
239
// Compute sub determinants
240
const double d00 = J_11*J_22 - J_12*J_21;
241
const double d01 = J_12*J_20 - J_10*J_22;
242
const double d02 = J_10*J_21 - J_11*J_20;
243
244
const double d10 = J_02*J_21 - J_01*J_22;
245
const double d11 = J_00*J_22 - J_02*J_20;
246
const double d12 = J_01*J_20 - J_00*J_21;
247
248
const double d20 = J_01*J_12 - J_02*J_11;
249
const double d21 = J_02*J_10 - J_00*J_12;
250
const double d22 = J_00*J_11 - J_01*J_10;
251
252
// Compute determinant of Jacobian
253
double detJ = J_00*d00 + J_10*d10 + J_20*d20;
254
255
// Compute inverse of Jacobian
256
257
// Compute constants
258
const double C0 = d00*(element_coordinates[0][0] - element_coordinates[2][0] - element_coordinates[3][0]) \
259
+ d10*(element_coordinates[0][1] - element_coordinates[2][1] - element_coordinates[3][1]) \
260
+ d20*(element_coordinates[0][2] - element_coordinates[2][2] - element_coordinates[3][2]);
261
262
const double C1 = d01*(element_coordinates[0][0] - element_coordinates[1][0] - element_coordinates[3][0]) \
263
+ d11*(element_coordinates[0][1] - element_coordinates[1][1] - element_coordinates[3][1]) \
264
+ d21*(element_coordinates[0][2] - element_coordinates[1][2] - element_coordinates[3][2]);
265
266
const double C2 = d02*(element_coordinates[0][0] - element_coordinates[1][0] - element_coordinates[2][0]) \
267
+ d12*(element_coordinates[0][1] - element_coordinates[1][1] - element_coordinates[2][1]) \
268
+ d22*(element_coordinates[0][2] - element_coordinates[1][2] - element_coordinates[2][2]);
269
270
// Get coordinates and map to the UFC reference element
271
double x = (C0 + d00*coordinates[0] + d10*coordinates[1] + d20*coordinates[2]) / detJ;
272
double y = (C1 + d01*coordinates[0] + d11*coordinates[1] + d21*coordinates[2]) / detJ;
273
double z = (C2 + d02*coordinates[0] + d12*coordinates[1] + d22*coordinates[2]) / detJ;
274
275
// Map coordinates to the reference cube
276
if (std::abs(y + z - 1.0) < 1e-14)
277
x = 1.0;
278
else
279
x = -2.0 * x/(y + z - 1.0) - 1.0;
280
if (std::abs(z - 1.0) < 1e-14)
281
y = -1.0;
282
else
283
y = 2.0 * y/(1.0 - z) - 1.0;
284
z = 2.0 * z - 1.0;
285
286
// Compute number of derivatives
287
unsigned int num_derivatives = 1;
288
289
for (unsigned int j = 0; j < n; j++)
290
num_derivatives *= 3;
291
292
293
// Declare pointer to two dimensional array that holds combinations of derivatives and initialise
294
unsigned int **combinations = new unsigned int *[num_derivatives];
295
296
for (unsigned int j = 0; j < num_derivatives; j++)
297
{
298
combinations[j] = new unsigned int [n];
299
for (unsigned int k = 0; k < n; k++)
300
combinations[j][k] = 0;
301
}
302
303
// Generate combinations of derivatives
304
for (unsigned int row = 1; row < num_derivatives; row++)
305
{
306
for (unsigned int num = 0; num < row; num++)
307
{
308
for (unsigned int col = n-1; col+1 > 0; col--)
309
{
310
if (combinations[row][col] + 1 > 2)
311
combinations[row][col] = 0;
312
else
313
{
314
combinations[row][col] += 1;
315
break;
316
}
317
}
318
}
319
}
320
321
// Compute inverse of Jacobian
322
const double Jinv[3][3] ={{d00 / detJ, d10 / detJ, d20 / detJ}, {d01 / detJ, d11 / detJ, d21 / detJ}, {d02 / detJ, d12 / detJ, d22 / detJ}};
323
324
// Declare transformation matrix
325
// Declare pointer to two dimensional array and initialise
326
double **transform = new double *[num_derivatives];
327
328
for (unsigned int j = 0; j < num_derivatives; j++)
329
{
330
transform[j] = new double [num_derivatives];
331
for (unsigned int k = 0; k < num_derivatives; k++)
332
transform[j][k] = 1;
333
}
334
335
// Construct transformation matrix
336
for (unsigned int row = 0; row < num_derivatives; row++)
337
{
338
for (unsigned int col = 0; col < num_derivatives; col++)
339
{
340
for (unsigned int k = 0; k < n; k++)
341
transform[row][col] *= Jinv[combinations[col][k]][combinations[row][k]];
342
}
343
}
344
345
// Reset values
346
for (unsigned int j = 0; j < 1*num_derivatives; j++)
347
values[j] = 0;
348
349
// Map degree of freedom to element degree of freedom
350
const unsigned int dof = i;
351
352
// Generate scalings
353
const double scalings_y_0 = 1;
354
const double scalings_y_1 = scalings_y_0*(0.5 - 0.5*y);
355
const double scalings_y_2 = scalings_y_1*(0.5 - 0.5*y);
356
const double scalings_z_0 = 1;
357
const double scalings_z_1 = scalings_z_0*(0.5 - 0.5*z);
358
const double scalings_z_2 = scalings_z_1*(0.5 - 0.5*z);
359
360
// Compute psitilde_a
361
const double psitilde_a_0 = 1;
362
const double psitilde_a_1 = x;
363
const double psitilde_a_2 = 1.5*x*psitilde_a_1 - 0.5*psitilde_a_0;
364
365
// Compute psitilde_bs
366
const double psitilde_bs_0_0 = 1;
367
const double psitilde_bs_0_1 = 1.5*y + 0.5;
368
const double psitilde_bs_0_2 = 0.111111111111111*psitilde_bs_0_1 + 1.66666666666667*y*psitilde_bs_0_1 - 0.555555555555556*psitilde_bs_0_0;
369
const double psitilde_bs_1_0 = 1;
370
const double psitilde_bs_1_1 = 2.5*y + 1.5;
371
const double psitilde_bs_2_0 = 1;
372
373
// Compute psitilde_cs
374
const double psitilde_cs_00_0 = 1;
375
const double psitilde_cs_00_1 = 2*z + 1;
376
const double psitilde_cs_00_2 = 0.3125*psitilde_cs_00_1 + 1.875*z*psitilde_cs_00_1 - 0.5625*psitilde_cs_00_0;
377
const double psitilde_cs_01_0 = 1;
378
const double psitilde_cs_01_1 = 3*z + 2;
379
const double psitilde_cs_02_0 = 1;
380
const double psitilde_cs_10_0 = 1;
381
const double psitilde_cs_10_1 = 3*z + 2;
382
const double psitilde_cs_11_0 = 1;
383
const double psitilde_cs_20_0 = 1;
384
385
// Compute basisvalues
386
const double basisvalue0 = 0.866025403784439*psitilde_a_0*scalings_y_0*psitilde_bs_0_0*scalings_z_0*psitilde_cs_00_0;
387
const double basisvalue1 = 2.73861278752583*psitilde_a_1*scalings_y_1*psitilde_bs_1_0*scalings_z_1*psitilde_cs_10_0;
388
const double basisvalue2 = 1.58113883008419*psitilde_a_0*scalings_y_0*psitilde_bs_0_1*scalings_z_1*psitilde_cs_01_0;
389
const double basisvalue3 = 1.11803398874989*psitilde_a_0*scalings_y_0*psitilde_bs_0_0*scalings_z_0*psitilde_cs_00_1;
390
const double basisvalue4 = 5.1234753829798*psitilde_a_2*scalings_y_2*psitilde_bs_2_0*scalings_z_2*psitilde_cs_20_0;
391
const double basisvalue5 = 3.96862696659689*psitilde_a_1*scalings_y_1*psitilde_bs_1_1*scalings_z_2*psitilde_cs_11_0;
392
const double basisvalue6 = 2.29128784747792*psitilde_a_0*scalings_y_0*psitilde_bs_0_2*scalings_z_2*psitilde_cs_02_0;
393
const double basisvalue7 = 3.24037034920393*psitilde_a_1*scalings_y_1*psitilde_bs_1_0*scalings_z_1*psitilde_cs_10_1;
394
const double basisvalue8 = 1.87082869338697*psitilde_a_0*scalings_y_0*psitilde_bs_0_1*scalings_z_1*psitilde_cs_01_1;
395
const double basisvalue9 = 1.3228756555323*psitilde_a_0*scalings_y_0*psitilde_bs_0_0*scalings_z_0*psitilde_cs_00_2;
396
397
// Table(s) of coefficients
398
static const double coefficients0[10][10] = \
399
{{-0.0577350269189626, -0.0608580619450185, -0.0351364184463153, -0.0248451997499977, 0.0650600048632355, 0.0503952630678969, 0.0290957186981323, 0.0411475599898912, 0.0237565548366599, 0.0167984210226323},
400
{-0.0577350269189625, 0.0608580619450185, -0.0351364184463153, -0.0248451997499977, 0.0650600048632355, -0.050395263067897, 0.0290957186981323, -0.0411475599898912, 0.0237565548366599, 0.0167984210226323},
401
{-0.0577350269189626, 0, 0.0702728368926307, -0.0248451997499977, 0, 0, 0.0872871560943969, 0, -0.0475131096733199, 0.0167984210226323},
402
{-0.0577350269189626, 0, 0, 0.074535599249993, 0, 0, 0, 0, 0, 0.100790526135794},
403
{0.23094010767585, 0, 0.140545673785261, 0.0993807989999906, 0, 0, 0, 0, 0.1187827741833, -0.0671936840905293},
404
{0.23094010767585, 0.121716123890037, -0.0702728368926307, 0.0993807989999907, 0, 0, 0, 0.102868899974728, -0.0593913870916499, -0.0671936840905293},
405
{0.23094010767585, 0.121716123890037, 0.0702728368926306, -0.0993807989999906, 0, 0.100790526135794, -0.0872871560943969, -0.0205737799949456, -0.01187827741833, 0.0167984210226323},
406
{0.23094010767585, -0.121716123890037, -0.0702728368926307, 0.0993807989999907, 0, 0, 0, -0.102868899974728, -0.0593913870916499, -0.0671936840905293},
407
{0.23094010767585, -0.121716123890037, 0.0702728368926306, -0.0993807989999907, 0, -0.100790526135794, -0.0872871560943969, 0.0205737799949456, -0.01187827741833, 0.0167984210226323},
408
{0.23094010767585, 0, -0.140545673785261, -0.0993807989999906, -0.130120009726471, 0, 0.0290957186981323, 0, 0.02375655483666, 0.0167984210226323}};
409
410
// Interesting (new) part
411
// Tables of derivatives of the polynomial base (transpose)
412
static const double dmats0[10][10] = \
413
{{0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
414
{6.32455532033676, 0, 0, 0, 0, 0, 0, 0, 0, 0},
415
{0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
416
{0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
417
{0, 11.2249721603218, 0, 0, 0, 0, 0, 0, 0, 0},
418
{4.58257569495584, 0, 8.36660026534076, -1.18321595661992, 0, 0, 0, 0, 0, 0},
419
{0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
420
{3.74165738677394, 0, 0, 8.69482604771366, 0, 0, 0, 0, 0, 0},
421
{0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
422
{0, 0, 0, 0, 0, 0, 0, 0, 0, 0}};
423
424
static const double dmats1[10][10] = \
425
{{0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
426
{3.16227766016838, 0, 0, 0, 0, 0, 0, 0, 0, 0},
427
{5.47722557505166, 0, 0, 0, 0, 0, 0, 0, 0, 0},
428
{0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
429
{2.95803989154981, 5.61248608016091, -1.08012344973464, -0.763762615825973, 0, 0, 0, 0, 0, 0},
430
{2.29128784747792, 7.24568837309472, 4.18330013267038, -0.591607978309962, 0, 0, 0, 0, 0, 0},
431
{-2.64575131106459, 0, 9.66091783079296, 0.683130051063973, 0, 0, 0, 0, 0, 0},
432
{1.87082869338697, 0, 0, 4.34741302385683, 0, 0, 0, 0, 0, 0},
433
{3.24037034920393, 0, 0, 7.52994023880668, 0, 0, 0, 0, 0, 0},
434
{0, 0, 0, 0, 0, 0, 0, 0, 0, 0}};
435
436
static const double dmats2[10][10] = \
437
{{0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
438
{3.16227766016838, 0, 0, 0, 0, 0, 0, 0, 0, 0},
439
{1.82574185835055, 0, 0, 0, 0, 0, 0, 0, 0, 0},
440
{5.16397779494322, 0, 0, 0, 0, 0, 0, 0, 0, 0},
441
{2.95803989154981, 5.61248608016091, -1.08012344973464, -0.763762615825973, 0, 0, 0, 0, 0, 0},
442
{2.29128784747792, 1.44913767461894, 4.18330013267038, -0.591607978309962, 0, 0, 0, 0, 0, 0},
443
{1.3228756555323, 0, 3.86436713231718, -0.341565025531986, 0, 0, 0, 0, 0, 0},
444
{1.87082869338697, 7.09929573971954, 0, 4.34741302385683, 0, 0, 0, 0, 0, 0},
445
{1.08012344973464, 0, 7.09929573971954, 2.50998007960223, 0, 0, 0, 0, 0, 0},
446
{-3.81881307912987, 0, 0, 8.87411967464942, 0, 0, 0, 0, 0, 0}};
447
448
// Compute reference derivatives
449
// Declare pointer to array of derivatives on FIAT element
450
double *derivatives = new double [num_derivatives];
451
452
// Declare coefficients
453
double coeff0_0 = 0;
454
double coeff0_1 = 0;
455
double coeff0_2 = 0;
456
double coeff0_3 = 0;
457
double coeff0_4 = 0;
458
double coeff0_5 = 0;
459
double coeff0_6 = 0;
460
double coeff0_7 = 0;
461
double coeff0_8 = 0;
462
double coeff0_9 = 0;
463
464
// Declare new coefficients
465
double new_coeff0_0 = 0;
466
double new_coeff0_1 = 0;
467
double new_coeff0_2 = 0;
468
double new_coeff0_3 = 0;
469
double new_coeff0_4 = 0;
470
double new_coeff0_5 = 0;
471
double new_coeff0_6 = 0;
472
double new_coeff0_7 = 0;
473
double new_coeff0_8 = 0;
474
double new_coeff0_9 = 0;
475
476
// Loop possible derivatives
477
for (unsigned int deriv_num = 0; deriv_num < num_derivatives; deriv_num++)
478
{
479
// Get values from coefficients array
480
new_coeff0_0 = coefficients0[dof][0];
481
new_coeff0_1 = coefficients0[dof][1];
482
new_coeff0_2 = coefficients0[dof][2];
483
new_coeff0_3 = coefficients0[dof][3];
484
new_coeff0_4 = coefficients0[dof][4];
485
new_coeff0_5 = coefficients0[dof][5];
486
new_coeff0_6 = coefficients0[dof][6];
487
new_coeff0_7 = coefficients0[dof][7];
488
new_coeff0_8 = coefficients0[dof][8];
489
new_coeff0_9 = coefficients0[dof][9];
490
491
// Loop derivative order
492
for (unsigned int j = 0; j < n; j++)
493
{
494
// Update old coefficients
495
coeff0_0 = new_coeff0_0;
496
coeff0_1 = new_coeff0_1;
497
coeff0_2 = new_coeff0_2;
498
coeff0_3 = new_coeff0_3;
499
coeff0_4 = new_coeff0_4;
500
coeff0_5 = new_coeff0_5;
501
coeff0_6 = new_coeff0_6;
502
coeff0_7 = new_coeff0_7;
503
coeff0_8 = new_coeff0_8;
504
coeff0_9 = new_coeff0_9;
505
506
if(combinations[deriv_num][j] == 0)
507
{
508
new_coeff0_0 = coeff0_0*dmats0[0][0] + coeff0_1*dmats0[1][0] + coeff0_2*dmats0[2][0] + coeff0_3*dmats0[3][0] + coeff0_4*dmats0[4][0] + coeff0_5*dmats0[5][0] + coeff0_6*dmats0[6][0] + coeff0_7*dmats0[7][0] + coeff0_8*dmats0[8][0] + coeff0_9*dmats0[9][0];
509
new_coeff0_1 = coeff0_0*dmats0[0][1] + coeff0_1*dmats0[1][1] + coeff0_2*dmats0[2][1] + coeff0_3*dmats0[3][1] + coeff0_4*dmats0[4][1] + coeff0_5*dmats0[5][1] + coeff0_6*dmats0[6][1] + coeff0_7*dmats0[7][1] + coeff0_8*dmats0[8][1] + coeff0_9*dmats0[9][1];
510
new_coeff0_2 = coeff0_0*dmats0[0][2] + coeff0_1*dmats0[1][2] + coeff0_2*dmats0[2][2] + coeff0_3*dmats0[3][2] + coeff0_4*dmats0[4][2] + coeff0_5*dmats0[5][2] + coeff0_6*dmats0[6][2] + coeff0_7*dmats0[7][2] + coeff0_8*dmats0[8][2] + coeff0_9*dmats0[9][2];
511
new_coeff0_3 = coeff0_0*dmats0[0][3] + coeff0_1*dmats0[1][3] + coeff0_2*dmats0[2][3] + coeff0_3*dmats0[3][3] + coeff0_4*dmats0[4][3] + coeff0_5*dmats0[5][3] + coeff0_6*dmats0[6][3] + coeff0_7*dmats0[7][3] + coeff0_8*dmats0[8][3] + coeff0_9*dmats0[9][3];
512
new_coeff0_4 = coeff0_0*dmats0[0][4] + coeff0_1*dmats0[1][4] + coeff0_2*dmats0[2][4] + coeff0_3*dmats0[3][4] + coeff0_4*dmats0[4][4] + coeff0_5*dmats0[5][4] + coeff0_6*dmats0[6][4] + coeff0_7*dmats0[7][4] + coeff0_8*dmats0[8][4] + coeff0_9*dmats0[9][4];
513
new_coeff0_5 = coeff0_0*dmats0[0][5] + coeff0_1*dmats0[1][5] + coeff0_2*dmats0[2][5] + coeff0_3*dmats0[3][5] + coeff0_4*dmats0[4][5] + coeff0_5*dmats0[5][5] + coeff0_6*dmats0[6][5] + coeff0_7*dmats0[7][5] + coeff0_8*dmats0[8][5] + coeff0_9*dmats0[9][5];
514
new_coeff0_6 = coeff0_0*dmats0[0][6] + coeff0_1*dmats0[1][6] + coeff0_2*dmats0[2][6] + coeff0_3*dmats0[3][6] + coeff0_4*dmats0[4][6] + coeff0_5*dmats0[5][6] + coeff0_6*dmats0[6][6] + coeff0_7*dmats0[7][6] + coeff0_8*dmats0[8][6] + coeff0_9*dmats0[9][6];
515
new_coeff0_7 = coeff0_0*dmats0[0][7] + coeff0_1*dmats0[1][7] + coeff0_2*dmats0[2][7] + coeff0_3*dmats0[3][7] + coeff0_4*dmats0[4][7] + coeff0_5*dmats0[5][7] + coeff0_6*dmats0[6][7] + coeff0_7*dmats0[7][7] + coeff0_8*dmats0[8][7] + coeff0_9*dmats0[9][7];
516
new_coeff0_8 = coeff0_0*dmats0[0][8] + coeff0_1*dmats0[1][8] + coeff0_2*dmats0[2][8] + coeff0_3*dmats0[3][8] + coeff0_4*dmats0[4][8] + coeff0_5*dmats0[5][8] + coeff0_6*dmats0[6][8] + coeff0_7*dmats0[7][8] + coeff0_8*dmats0[8][8] + coeff0_9*dmats0[9][8];
517
new_coeff0_9 = coeff0_0*dmats0[0][9] + coeff0_1*dmats0[1][9] + coeff0_2*dmats0[2][9] + coeff0_3*dmats0[3][9] + coeff0_4*dmats0[4][9] + coeff0_5*dmats0[5][9] + coeff0_6*dmats0[6][9] + coeff0_7*dmats0[7][9] + coeff0_8*dmats0[8][9] + coeff0_9*dmats0[9][9];
518
}
519
if(combinations[deriv_num][j] == 1)
520
{
521
new_coeff0_0 = coeff0_0*dmats1[0][0] + coeff0_1*dmats1[1][0] + coeff0_2*dmats1[2][0] + coeff0_3*dmats1[3][0] + coeff0_4*dmats1[4][0] + coeff0_5*dmats1[5][0] + coeff0_6*dmats1[6][0] + coeff0_7*dmats1[7][0] + coeff0_8*dmats1[8][0] + coeff0_9*dmats1[9][0];
522
new_coeff0_1 = coeff0_0*dmats1[0][1] + coeff0_1*dmats1[1][1] + coeff0_2*dmats1[2][1] + coeff0_3*dmats1[3][1] + coeff0_4*dmats1[4][1] + coeff0_5*dmats1[5][1] + coeff0_6*dmats1[6][1] + coeff0_7*dmats1[7][1] + coeff0_8*dmats1[8][1] + coeff0_9*dmats1[9][1];
523
new_coeff0_2 = coeff0_0*dmats1[0][2] + coeff0_1*dmats1[1][2] + coeff0_2*dmats1[2][2] + coeff0_3*dmats1[3][2] + coeff0_4*dmats1[4][2] + coeff0_5*dmats1[5][2] + coeff0_6*dmats1[6][2] + coeff0_7*dmats1[7][2] + coeff0_8*dmats1[8][2] + coeff0_9*dmats1[9][2];
524
new_coeff0_3 = coeff0_0*dmats1[0][3] + coeff0_1*dmats1[1][3] + coeff0_2*dmats1[2][3] + coeff0_3*dmats1[3][3] + coeff0_4*dmats1[4][3] + coeff0_5*dmats1[5][3] + coeff0_6*dmats1[6][3] + coeff0_7*dmats1[7][3] + coeff0_8*dmats1[8][3] + coeff0_9*dmats1[9][3];
525
new_coeff0_4 = coeff0_0*dmats1[0][4] + coeff0_1*dmats1[1][4] + coeff0_2*dmats1[2][4] + coeff0_3*dmats1[3][4] + coeff0_4*dmats1[4][4] + coeff0_5*dmats1[5][4] + coeff0_6*dmats1[6][4] + coeff0_7*dmats1[7][4] + coeff0_8*dmats1[8][4] + coeff0_9*dmats1[9][4];
526
new_coeff0_5 = coeff0_0*dmats1[0][5] + coeff0_1*dmats1[1][5] + coeff0_2*dmats1[2][5] + coeff0_3*dmats1[3][5] + coeff0_4*dmats1[4][5] + coeff0_5*dmats1[5][5] + coeff0_6*dmats1[6][5] + coeff0_7*dmats1[7][5] + coeff0_8*dmats1[8][5] + coeff0_9*dmats1[9][5];
527
new_coeff0_6 = coeff0_0*dmats1[0][6] + coeff0_1*dmats1[1][6] + coeff0_2*dmats1[2][6] + coeff0_3*dmats1[3][6] + coeff0_4*dmats1[4][6] + coeff0_5*dmats1[5][6] + coeff0_6*dmats1[6][6] + coeff0_7*dmats1[7][6] + coeff0_8*dmats1[8][6] + coeff0_9*dmats1[9][6];
528
new_coeff0_7 = coeff0_0*dmats1[0][7] + coeff0_1*dmats1[1][7] + coeff0_2*dmats1[2][7] + coeff0_3*dmats1[3][7] + coeff0_4*dmats1[4][7] + coeff0_5*dmats1[5][7] + coeff0_6*dmats1[6][7] + coeff0_7*dmats1[7][7] + coeff0_8*dmats1[8][7] + coeff0_9*dmats1[9][7];
529
new_coeff0_8 = coeff0_0*dmats1[0][8] + coeff0_1*dmats1[1][8] + coeff0_2*dmats1[2][8] + coeff0_3*dmats1[3][8] + coeff0_4*dmats1[4][8] + coeff0_5*dmats1[5][8] + coeff0_6*dmats1[6][8] + coeff0_7*dmats1[7][8] + coeff0_8*dmats1[8][8] + coeff0_9*dmats1[9][8];
530
new_coeff0_9 = coeff0_0*dmats1[0][9] + coeff0_1*dmats1[1][9] + coeff0_2*dmats1[2][9] + coeff0_3*dmats1[3][9] + coeff0_4*dmats1[4][9] + coeff0_5*dmats1[5][9] + coeff0_6*dmats1[6][9] + coeff0_7*dmats1[7][9] + coeff0_8*dmats1[8][9] + coeff0_9*dmats1[9][9];
531
}
532
if(combinations[deriv_num][j] == 2)
533
{
534
new_coeff0_0 = coeff0_0*dmats2[0][0] + coeff0_1*dmats2[1][0] + coeff0_2*dmats2[2][0] + coeff0_3*dmats2[3][0] + coeff0_4*dmats2[4][0] + coeff0_5*dmats2[5][0] + coeff0_6*dmats2[6][0] + coeff0_7*dmats2[7][0] + coeff0_8*dmats2[8][0] + coeff0_9*dmats2[9][0];
535
new_coeff0_1 = coeff0_0*dmats2[0][1] + coeff0_1*dmats2[1][1] + coeff0_2*dmats2[2][1] + coeff0_3*dmats2[3][1] + coeff0_4*dmats2[4][1] + coeff0_5*dmats2[5][1] + coeff0_6*dmats2[6][1] + coeff0_7*dmats2[7][1] + coeff0_8*dmats2[8][1] + coeff0_9*dmats2[9][1];
536
new_coeff0_2 = coeff0_0*dmats2[0][2] + coeff0_1*dmats2[1][2] + coeff0_2*dmats2[2][2] + coeff0_3*dmats2[3][2] + coeff0_4*dmats2[4][2] + coeff0_5*dmats2[5][2] + coeff0_6*dmats2[6][2] + coeff0_7*dmats2[7][2] + coeff0_8*dmats2[8][2] + coeff0_9*dmats2[9][2];
537
new_coeff0_3 = coeff0_0*dmats2[0][3] + coeff0_1*dmats2[1][3] + coeff0_2*dmats2[2][3] + coeff0_3*dmats2[3][3] + coeff0_4*dmats2[4][3] + coeff0_5*dmats2[5][3] + coeff0_6*dmats2[6][3] + coeff0_7*dmats2[7][3] + coeff0_8*dmats2[8][3] + coeff0_9*dmats2[9][3];
538
new_coeff0_4 = coeff0_0*dmats2[0][4] + coeff0_1*dmats2[1][4] + coeff0_2*dmats2[2][4] + coeff0_3*dmats2[3][4] + coeff0_4*dmats2[4][4] + coeff0_5*dmats2[5][4] + coeff0_6*dmats2[6][4] + coeff0_7*dmats2[7][4] + coeff0_8*dmats2[8][4] + coeff0_9*dmats2[9][4];
539
new_coeff0_5 = coeff0_0*dmats2[0][5] + coeff0_1*dmats2[1][5] + coeff0_2*dmats2[2][5] + coeff0_3*dmats2[3][5] + coeff0_4*dmats2[4][5] + coeff0_5*dmats2[5][5] + coeff0_6*dmats2[6][5] + coeff0_7*dmats2[7][5] + coeff0_8*dmats2[8][5] + coeff0_9*dmats2[9][5];
540
new_coeff0_6 = coeff0_0*dmats2[0][6] + coeff0_1*dmats2[1][6] + coeff0_2*dmats2[2][6] + coeff0_3*dmats2[3][6] + coeff0_4*dmats2[4][6] + coeff0_5*dmats2[5][6] + coeff0_6*dmats2[6][6] + coeff0_7*dmats2[7][6] + coeff0_8*dmats2[8][6] + coeff0_9*dmats2[9][6];
541
new_coeff0_7 = coeff0_0*dmats2[0][7] + coeff0_1*dmats2[1][7] + coeff0_2*dmats2[2][7] + coeff0_3*dmats2[3][7] + coeff0_4*dmats2[4][7] + coeff0_5*dmats2[5][7] + coeff0_6*dmats2[6][7] + coeff0_7*dmats2[7][7] + coeff0_8*dmats2[8][7] + coeff0_9*dmats2[9][7];
542
new_coeff0_8 = coeff0_0*dmats2[0][8] + coeff0_1*dmats2[1][8] + coeff0_2*dmats2[2][8] + coeff0_3*dmats2[3][8] + coeff0_4*dmats2[4][8] + coeff0_5*dmats2[5][8] + coeff0_6*dmats2[6][8] + coeff0_7*dmats2[7][8] + coeff0_8*dmats2[8][8] + coeff0_9*dmats2[9][8];
543
new_coeff0_9 = coeff0_0*dmats2[0][9] + coeff0_1*dmats2[1][9] + coeff0_2*dmats2[2][9] + coeff0_3*dmats2[3][9] + coeff0_4*dmats2[4][9] + coeff0_5*dmats2[5][9] + coeff0_6*dmats2[6][9] + coeff0_7*dmats2[7][9] + coeff0_8*dmats2[8][9] + coeff0_9*dmats2[9][9];
544
}
545
546
}
547
// Compute derivatives on reference element as dot product of coefficients and basisvalues
548
derivatives[deriv_num] = new_coeff0_0*basisvalue0 + new_coeff0_1*basisvalue1 + new_coeff0_2*basisvalue2 + new_coeff0_3*basisvalue3 + new_coeff0_4*basisvalue4 + new_coeff0_5*basisvalue5 + new_coeff0_6*basisvalue6 + new_coeff0_7*basisvalue7 + new_coeff0_8*basisvalue8 + new_coeff0_9*basisvalue9;
549
}
550
551
// Transform derivatives back to physical element
552
for (unsigned int row = 0; row < num_derivatives; row++)
553
{
554
for (unsigned int col = 0; col < num_derivatives; col++)
555
{
556
values[row] += transform[row][col]*derivatives[col];
557
}
558
}
559
// Delete pointer to array of derivatives on FIAT element
560
delete [] derivatives;
561
562
// Delete pointer to array of combinations of derivatives and transform
563
for (unsigned int row = 0; row < num_derivatives; row++)
564
{
565
delete [] combinations[row];
566
delete [] transform[row];
567
}
568
569
delete [] combinations;
570
delete [] transform;
571
}
572
573
/// Evaluate order n derivatives of all basis functions at given point in cell
574
virtual void evaluate_basis_derivatives_all(unsigned int n,
575
double* values,
576
const double* coordinates,
577
const ufc::cell& c) const
578
{
579
throw std::runtime_error("The vectorised version of evaluate_basis_derivatives() is not yet implemented.");
580
}
581
582
/// Evaluate linear functional for dof i on the function f
583
virtual double evaluate_dof(unsigned int i,
584
const ufc::function& f,
585
const ufc::cell& c) const
586
{
587
// The reference points, direction and weights:
588
static const double X[10][1][3] = {{{0, 0, 0}}, {{1, 0, 0}}, {{0, 1, 0}}, {{0, 0, 1}}, {{0, 0.5, 0.5}}, {{0.5, 0, 0.5}}, {{0.5, 0.5, 0}}, {{0, 0, 0.5}}, {{0, 0.5, 0}}, {{0.5, 0, 0}}};
589
static const double W[10][1] = {{1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}};
590
static const double D[10][1][1] = {{{1}}, {{1}}, {{1}}, {{1}}, {{1}}, {{1}}, {{1}}, {{1}}, {{1}}, {{1}}};
591
592
const double * const * x = c.coordinates;
593
double result = 0.0;
594
// Iterate over the points:
595
// Evaluate basis functions for affine mapping
596
const double w0 = 1.0 - X[i][0][0] - X[i][0][1] - X[i][0][2];
597
const double w1 = X[i][0][0];
598
const double w2 = X[i][0][1];
599
const double w3 = X[i][0][2];
600
601
// Compute affine mapping y = F(X)
602
double y[3];
603
y[0] = w0*x[0][0] + w1*x[1][0] + w2*x[2][0] + w3*x[3][0];
604
y[1] = w0*x[0][1] + w1*x[1][1] + w2*x[2][1] + w3*x[3][1];
605
y[2] = w0*x[0][2] + w1*x[1][2] + w2*x[2][2] + w3*x[3][2];
606
607
// Evaluate function at physical points
608
double values[1];
609
f.evaluate(values, y, c);
610
611
// Map function values using appropriate mapping
612
// Affine map: Do nothing
613
614
// Note that we do not map the weights (yet).
615
616
// Take directional components
617
for(int k = 0; k < 1; k++)
618
result += values[k]*D[i][0][k];
619
// Multiply by weights
620
result *= W[i][0];
621
622
return result;
623
}
624
625
/// Evaluate linear functionals for all dofs on the function f
626
virtual void evaluate_dofs(double* values,
627
const ufc::function& f,
628
const ufc::cell& c) const
629
{
630
throw std::runtime_error("Not implemented (introduced in UFC v1.1).");
631
}
632
633
/// Interpolate vertex values from dof values
634
virtual void interpolate_vertex_values(double* vertex_values,
635
const double* dof_values,
636
const ufc::cell& c) const
637
{
638
// Evaluate at vertices and use affine mapping
639
vertex_values[0] = dof_values[0];
640
vertex_values[1] = dof_values[1];
641
vertex_values[2] = dof_values[2];
642
vertex_values[3] = dof_values[3];
643
}
644
645
/// Return the number of sub elements (for a mixed element)
646
virtual unsigned int num_sub_elements() const
647
{
648
return 1;
649
}
650
651
/// Create a new finite element for sub element i (for a mixed element)
652
virtual ufc::finite_element* create_sub_element(unsigned int i) const
653
{
654
return new projection_0_finite_element_0();
655
}
656
657
};
658
659
/// This class defines the interface for a finite element.
660
661
class projection_0_finite_element_1: public ufc::finite_element
662
{
663
public:
664
665
/// Constructor
666
projection_0_finite_element_1() : ufc::finite_element()
667
{
668
// Do nothing
669
}
670
671
/// Destructor
672
virtual ~projection_0_finite_element_1()
673
{
674
// Do nothing
675
}
676
677
/// Return a string identifying the finite element
678
virtual const char* signature() const
679
{
680
return "FiniteElement('Lagrange', 'tetrahedron', 2)";
681
}
682
683
/// Return the cell shape
684
virtual ufc::shape cell_shape() const
685
{
686
return ufc::tetrahedron;
687
}
688
689
/// Return the dimension of the finite element function space
690
virtual unsigned int space_dimension() const
691
{
692
return 10;
693
}
694
695
/// Return the rank of the value space
696
virtual unsigned int value_rank() const
697
{
698
return 0;
699
}
700
701
/// Return the dimension of the value space for axis i
702
virtual unsigned int value_dimension(unsigned int i) const
703
{
704
return 1;
705
}
706
707
/// Evaluate basis function i at given point in cell
708
virtual void evaluate_basis(unsigned int i,
709
double* values,
710
const double* coordinates,
711
const ufc::cell& c) const
712
{
713
// Extract vertex coordinates
714
const double * const * element_coordinates = c.coordinates;
715
716
// Compute Jacobian of affine map from reference cell
717
const double J_00 = element_coordinates[1][0] - element_coordinates[0][0];
718
const double J_01 = element_coordinates[2][0] - element_coordinates[0][0];
719
const double J_02 = element_coordinates[3][0] - element_coordinates[0][0];
720
const double J_10 = element_coordinates[1][1] - element_coordinates[0][1];
721
const double J_11 = element_coordinates[2][1] - element_coordinates[0][1];
722
const double J_12 = element_coordinates[3][1] - element_coordinates[0][1];
723
const double J_20 = element_coordinates[1][2] - element_coordinates[0][2];
724
const double J_21 = element_coordinates[2][2] - element_coordinates[0][2];
725
const double J_22 = element_coordinates[3][2] - element_coordinates[0][2];
726
727
// Compute sub determinants
728
const double d00 = J_11*J_22 - J_12*J_21;
729
const double d01 = J_12*J_20 - J_10*J_22;
730
const double d02 = J_10*J_21 - J_11*J_20;
731
732
const double d10 = J_02*J_21 - J_01*J_22;
733
const double d11 = J_00*J_22 - J_02*J_20;
734
const double d12 = J_01*J_20 - J_00*J_21;
735
736
const double d20 = J_01*J_12 - J_02*J_11;
737
const double d21 = J_02*J_10 - J_00*J_12;
738
const double d22 = J_00*J_11 - J_01*J_10;
739
740
// Compute determinant of Jacobian
741
double detJ = J_00*d00 + J_10*d10 + J_20*d20;
742
743
// Compute inverse of Jacobian
744
745
// Compute constants
746
const double C0 = d00*(element_coordinates[0][0] - element_coordinates[2][0] - element_coordinates[3][0]) \
747
+ d10*(element_coordinates[0][1] - element_coordinates[2][1] - element_coordinates[3][1]) \
748
+ d20*(element_coordinates[0][2] - element_coordinates[2][2] - element_coordinates[3][2]);
749
750
const double C1 = d01*(element_coordinates[0][0] - element_coordinates[1][0] - element_coordinates[3][0]) \
751
+ d11*(element_coordinates[0][1] - element_coordinates[1][1] - element_coordinates[3][1]) \
752
+ d21*(element_coordinates[0][2] - element_coordinates[1][2] - element_coordinates[3][2]);
753
754
const double C2 = d02*(element_coordinates[0][0] - element_coordinates[1][0] - element_coordinates[2][0]) \
755
+ d12*(element_coordinates[0][1] - element_coordinates[1][1] - element_coordinates[2][1]) \
756
+ d22*(element_coordinates[0][2] - element_coordinates[1][2] - element_coordinates[2][2]);
757
758
// Get coordinates and map to the UFC reference element
759
double x = (C0 + d00*coordinates[0] + d10*coordinates[1] + d20*coordinates[2]) / detJ;
760
double y = (C1 + d01*coordinates[0] + d11*coordinates[1] + d21*coordinates[2]) / detJ;
761
double z = (C2 + d02*coordinates[0] + d12*coordinates[1] + d22*coordinates[2]) / detJ;
762
763
// Map coordinates to the reference cube
764
if (std::abs(y + z - 1.0) < 1e-14)
765
x = 1.0;
766
else
767
x = -2.0 * x/(y + z - 1.0) - 1.0;
768
if (std::abs(z - 1.0) < 1e-14)
769
y = -1.0;
770
else
771
y = 2.0 * y/(1.0 - z) - 1.0;
772
z = 2.0 * z - 1.0;
773
774
// Reset values
775
*values = 0;
776
777
// Map degree of freedom to element degree of freedom
778
const unsigned int dof = i;
779
780
// Generate scalings
781
const double scalings_y_0 = 1;
782
const double scalings_y_1 = scalings_y_0*(0.5 - 0.5*y);
783
const double scalings_y_2 = scalings_y_1*(0.5 - 0.5*y);
784
const double scalings_z_0 = 1;
785
const double scalings_z_1 = scalings_z_0*(0.5 - 0.5*z);
786
const double scalings_z_2 = scalings_z_1*(0.5 - 0.5*z);
787
788
// Compute psitilde_a
789
const double psitilde_a_0 = 1;
790
const double psitilde_a_1 = x;
791
const double psitilde_a_2 = 1.5*x*psitilde_a_1 - 0.5*psitilde_a_0;
792
793
// Compute psitilde_bs
794
const double psitilde_bs_0_0 = 1;
795
const double psitilde_bs_0_1 = 1.5*y + 0.5;
796
const double psitilde_bs_0_2 = 0.111111111111111*psitilde_bs_0_1 + 1.66666666666667*y*psitilde_bs_0_1 - 0.555555555555556*psitilde_bs_0_0;
797
const double psitilde_bs_1_0 = 1;
798
const double psitilde_bs_1_1 = 2.5*y + 1.5;
799
const double psitilde_bs_2_0 = 1;
800
801
// Compute psitilde_cs
802
const double psitilde_cs_00_0 = 1;
803
const double psitilde_cs_00_1 = 2*z + 1;
804
const double psitilde_cs_00_2 = 0.3125*psitilde_cs_00_1 + 1.875*z*psitilde_cs_00_1 - 0.5625*psitilde_cs_00_0;
805
const double psitilde_cs_01_0 = 1;
806
const double psitilde_cs_01_1 = 3*z + 2;
807
const double psitilde_cs_02_0 = 1;
808
const double psitilde_cs_10_0 = 1;
809
const double psitilde_cs_10_1 = 3*z + 2;
810
const double psitilde_cs_11_0 = 1;
811
const double psitilde_cs_20_0 = 1;
812
813
// Compute basisvalues
814
const double basisvalue0 = 0.866025403784439*psitilde_a_0*scalings_y_0*psitilde_bs_0_0*scalings_z_0*psitilde_cs_00_0;
815
const double basisvalue1 = 2.73861278752583*psitilde_a_1*scalings_y_1*psitilde_bs_1_0*scalings_z_1*psitilde_cs_10_0;
816
const double basisvalue2 = 1.58113883008419*psitilde_a_0*scalings_y_0*psitilde_bs_0_1*scalings_z_1*psitilde_cs_01_0;
817
const double basisvalue3 = 1.11803398874989*psitilde_a_0*scalings_y_0*psitilde_bs_0_0*scalings_z_0*psitilde_cs_00_1;
818
const double basisvalue4 = 5.1234753829798*psitilde_a_2*scalings_y_2*psitilde_bs_2_0*scalings_z_2*psitilde_cs_20_0;
819
const double basisvalue5 = 3.96862696659689*psitilde_a_1*scalings_y_1*psitilde_bs_1_1*scalings_z_2*psitilde_cs_11_0;
820
const double basisvalue6 = 2.29128784747792*psitilde_a_0*scalings_y_0*psitilde_bs_0_2*scalings_z_2*psitilde_cs_02_0;
821
const double basisvalue7 = 3.24037034920393*psitilde_a_1*scalings_y_1*psitilde_bs_1_0*scalings_z_1*psitilde_cs_10_1;
822
const double basisvalue8 = 1.87082869338697*psitilde_a_0*scalings_y_0*psitilde_bs_0_1*scalings_z_1*psitilde_cs_01_1;
823
const double basisvalue9 = 1.3228756555323*psitilde_a_0*scalings_y_0*psitilde_bs_0_0*scalings_z_0*psitilde_cs_00_2;
824
825
// Table(s) of coefficients
826
static const double coefficients0[10][10] = \
827
{{-0.0577350269189626, -0.0608580619450185, -0.0351364184463153, -0.0248451997499977, 0.0650600048632355, 0.0503952630678969, 0.0290957186981323, 0.0411475599898912, 0.0237565548366599, 0.0167984210226323},
828
{-0.0577350269189625, 0.0608580619450185, -0.0351364184463153, -0.0248451997499977, 0.0650600048632355, -0.050395263067897, 0.0290957186981323, -0.0411475599898912, 0.0237565548366599, 0.0167984210226323},
829
{-0.0577350269189626, 0, 0.0702728368926307, -0.0248451997499977, 0, 0, 0.0872871560943969, 0, -0.0475131096733199, 0.0167984210226323},
830
{-0.0577350269189626, 0, 0, 0.074535599249993, 0, 0, 0, 0, 0, 0.100790526135794},
831
{0.23094010767585, 0, 0.140545673785261, 0.0993807989999906, 0, 0, 0, 0, 0.1187827741833, -0.0671936840905293},
832
{0.23094010767585, 0.121716123890037, -0.0702728368926307, 0.0993807989999907, 0, 0, 0, 0.102868899974728, -0.0593913870916499, -0.0671936840905293},
833
{0.23094010767585, 0.121716123890037, 0.0702728368926306, -0.0993807989999906, 0, 0.100790526135794, -0.0872871560943969, -0.0205737799949456, -0.01187827741833, 0.0167984210226323},
834
{0.23094010767585, -0.121716123890037, -0.0702728368926307, 0.0993807989999907, 0, 0, 0, -0.102868899974728, -0.0593913870916499, -0.0671936840905293},
835
{0.23094010767585, -0.121716123890037, 0.0702728368926306, -0.0993807989999907, 0, -0.100790526135794, -0.0872871560943969, 0.0205737799949456, -0.01187827741833, 0.0167984210226323},
836
{0.23094010767585, 0, -0.140545673785261, -0.0993807989999906, -0.130120009726471, 0, 0.0290957186981323, 0, 0.02375655483666, 0.0167984210226323}};
837
838
// Extract relevant coefficients
839
const double coeff0_0 = coefficients0[dof][0];
840
const double coeff0_1 = coefficients0[dof][1];
841
const double coeff0_2 = coefficients0[dof][2];
842
const double coeff0_3 = coefficients0[dof][3];
843
const double coeff0_4 = coefficients0[dof][4];
844
const double coeff0_5 = coefficients0[dof][5];
845
const double coeff0_6 = coefficients0[dof][6];
846
const double coeff0_7 = coefficients0[dof][7];
847
const double coeff0_8 = coefficients0[dof][8];
848
const double coeff0_9 = coefficients0[dof][9];
849
850
// Compute value(s)
851
*values = coeff0_0*basisvalue0 + coeff0_1*basisvalue1 + coeff0_2*basisvalue2 + coeff0_3*basisvalue3 + coeff0_4*basisvalue4 + coeff0_5*basisvalue5 + coeff0_6*basisvalue6 + coeff0_7*basisvalue7 + coeff0_8*basisvalue8 + coeff0_9*basisvalue9;
852
}
853
854
/// Evaluate all basis functions at given point in cell
855
virtual void evaluate_basis_all(double* values,
856
const double* coordinates,
857
const ufc::cell& c) const
858
{
859
throw std::runtime_error("The vectorised version of evaluate_basis() is not yet implemented.");
860
}
861
862
/// Evaluate order n derivatives of basis function i at given point in cell
863
virtual void evaluate_basis_derivatives(unsigned int i,
864
unsigned int n,
865
double* values,
866
const double* coordinates,
867
const ufc::cell& c) const
868
{
869
// Extract vertex coordinates
870
const double * const * element_coordinates = c.coordinates;
871
872
// Compute Jacobian of affine map from reference cell
873
const double J_00 = element_coordinates[1][0] - element_coordinates[0][0];
874
const double J_01 = element_coordinates[2][0] - element_coordinates[0][0];
875
const double J_02 = element_coordinates[3][0] - element_coordinates[0][0];
876
const double J_10 = element_coordinates[1][1] - element_coordinates[0][1];
877
const double J_11 = element_coordinates[2][1] - element_coordinates[0][1];
878
const double J_12 = element_coordinates[3][1] - element_coordinates[0][1];
879
const double J_20 = element_coordinates[1][2] - element_coordinates[0][2];
880
const double J_21 = element_coordinates[2][2] - element_coordinates[0][2];
881
const double J_22 = element_coordinates[3][2] - element_coordinates[0][2];
882
883
// Compute sub determinants
884
const double d00 = J_11*J_22 - J_12*J_21;
885
const double d01 = J_12*J_20 - J_10*J_22;
886
const double d02 = J_10*J_21 - J_11*J_20;
887
888
const double d10 = J_02*J_21 - J_01*J_22;
889
const double d11 = J_00*J_22 - J_02*J_20;
890
const double d12 = J_01*J_20 - J_00*J_21;
891
892
const double d20 = J_01*J_12 - J_02*J_11;
893
const double d21 = J_02*J_10 - J_00*J_12;
894
const double d22 = J_00*J_11 - J_01*J_10;
895
896
// Compute determinant of Jacobian
897
double detJ = J_00*d00 + J_10*d10 + J_20*d20;
898
899
// Compute inverse of Jacobian
900
901
// Compute constants
902
const double C0 = d00*(element_coordinates[0][0] - element_coordinates[2][0] - element_coordinates[3][0]) \
903
+ d10*(element_coordinates[0][1] - element_coordinates[2][1] - element_coordinates[3][1]) \
904
+ d20*(element_coordinates[0][2] - element_coordinates[2][2] - element_coordinates[3][2]);
905
906
const double C1 = d01*(element_coordinates[0][0] - element_coordinates[1][0] - element_coordinates[3][0]) \
907
+ d11*(element_coordinates[0][1] - element_coordinates[1][1] - element_coordinates[3][1]) \
908
+ d21*(element_coordinates[0][2] - element_coordinates[1][2] - element_coordinates[3][2]);
909
910
const double C2 = d02*(element_coordinates[0][0] - element_coordinates[1][0] - element_coordinates[2][0]) \
911
+ d12*(element_coordinates[0][1] - element_coordinates[1][1] - element_coordinates[2][1]) \
912
+ d22*(element_coordinates[0][2] - element_coordinates[1][2] - element_coordinates[2][2]);
913
914
// Get coordinates and map to the UFC reference element
915
double x = (C0 + d00*coordinates[0] + d10*coordinates[1] + d20*coordinates[2]) / detJ;
916
double y = (C1 + d01*coordinates[0] + d11*coordinates[1] + d21*coordinates[2]) / detJ;
917
double z = (C2 + d02*coordinates[0] + d12*coordinates[1] + d22*coordinates[2]) / detJ;
918
919
// Map coordinates to the reference cube
920
if (std::abs(y + z - 1.0) < 1e-14)
921
x = 1.0;
922
else
923
x = -2.0 * x/(y + z - 1.0) - 1.0;
924
if (std::abs(z - 1.0) < 1e-14)
925
y = -1.0;
926
else
927
y = 2.0 * y/(1.0 - z) - 1.0;
928
z = 2.0 * z - 1.0;
929
930
// Compute number of derivatives
931
unsigned int num_derivatives = 1;
932
933
for (unsigned int j = 0; j < n; j++)
934
num_derivatives *= 3;
935
936
937
// Declare pointer to two dimensional array that holds combinations of derivatives and initialise
938
unsigned int **combinations = new unsigned int *[num_derivatives];
939
940
for (unsigned int j = 0; j < num_derivatives; j++)
941
{
942
combinations[j] = new unsigned int [n];
943
for (unsigned int k = 0; k < n; k++)
944
combinations[j][k] = 0;
945
}
946
947
// Generate combinations of derivatives
948
for (unsigned int row = 1; row < num_derivatives; row++)
949
{
950
for (unsigned int num = 0; num < row; num++)
951
{
952
for (unsigned int col = n-1; col+1 > 0; col--)
953
{
954
if (combinations[row][col] + 1 > 2)
955
combinations[row][col] = 0;
956
else
957
{
958
combinations[row][col] += 1;
959
break;
960
}
961
}
962
}
963
}
964
965
// Compute inverse of Jacobian
966
const double Jinv[3][3] ={{d00 / detJ, d10 / detJ, d20 / detJ}, {d01 / detJ, d11 / detJ, d21 / detJ}, {d02 / detJ, d12 / detJ, d22 / detJ}};
967
968
// Declare transformation matrix
969
// Declare pointer to two dimensional array and initialise
970
double **transform = new double *[num_derivatives];
971
972
for (unsigned int j = 0; j < num_derivatives; j++)
973
{
974
transform[j] = new double [num_derivatives];
975
for (unsigned int k = 0; k < num_derivatives; k++)
976
transform[j][k] = 1;
977
}
978
979
// Construct transformation matrix
980
for (unsigned int row = 0; row < num_derivatives; row++)
981
{
982
for (unsigned int col = 0; col < num_derivatives; col++)
983
{
984
for (unsigned int k = 0; k < n; k++)
985
transform[row][col] *= Jinv[combinations[col][k]][combinations[row][k]];
986
}
987
}
988
989
// Reset values
990
for (unsigned int j = 0; j < 1*num_derivatives; j++)
991
values[j] = 0;
992
993
// Map degree of freedom to element degree of freedom
994
const unsigned int dof = i;
995
996
// Generate scalings
997
const double scalings_y_0 = 1;
998
const double scalings_y_1 = scalings_y_0*(0.5 - 0.5*y);
999
const double scalings_y_2 = scalings_y_1*(0.5 - 0.5*y);
1000
const double scalings_z_0 = 1;
1001
const double scalings_z_1 = scalings_z_0*(0.5 - 0.5*z);
1002
const double scalings_z_2 = scalings_z_1*(0.5 - 0.5*z);
1003
1004
// Compute psitilde_a
1005
const double psitilde_a_0 = 1;
1006
const double psitilde_a_1 = x;
1007
const double psitilde_a_2 = 1.5*x*psitilde_a_1 - 0.5*psitilde_a_0;
1008
1009
// Compute psitilde_bs
1010
const double psitilde_bs_0_0 = 1;
1011
const double psitilde_bs_0_1 = 1.5*y + 0.5;
1012
const double psitilde_bs_0_2 = 0.111111111111111*psitilde_bs_0_1 + 1.66666666666667*y*psitilde_bs_0_1 - 0.555555555555556*psitilde_bs_0_0;
1013
const double psitilde_bs_1_0 = 1;
1014
const double psitilde_bs_1_1 = 2.5*y + 1.5;
1015
const double psitilde_bs_2_0 = 1;
1016
1017
// Compute psitilde_cs
1018
const double psitilde_cs_00_0 = 1;
1019
const double psitilde_cs_00_1 = 2*z + 1;
1020
const double psitilde_cs_00_2 = 0.3125*psitilde_cs_00_1 + 1.875*z*psitilde_cs_00_1 - 0.5625*psitilde_cs_00_0;
1021
const double psitilde_cs_01_0 = 1;
1022
const double psitilde_cs_01_1 = 3*z + 2;
1023
const double psitilde_cs_02_0 = 1;
1024
const double psitilde_cs_10_0 = 1;
1025
const double psitilde_cs_10_1 = 3*z + 2;
1026
const double psitilde_cs_11_0 = 1;
1027
const double psitilde_cs_20_0 = 1;
1028
1029
// Compute basisvalues
1030
const double basisvalue0 = 0.866025403784439*psitilde_a_0*scalings_y_0*psitilde_bs_0_0*scalings_z_0*psitilde_cs_00_0;
1031
const double basisvalue1 = 2.73861278752583*psitilde_a_1*scalings_y_1*psitilde_bs_1_0*scalings_z_1*psitilde_cs_10_0;
1032
const double basisvalue2 = 1.58113883008419*psitilde_a_0*scalings_y_0*psitilde_bs_0_1*scalings_z_1*psitilde_cs_01_0;
1033
const double basisvalue3 = 1.11803398874989*psitilde_a_0*scalings_y_0*psitilde_bs_0_0*scalings_z_0*psitilde_cs_00_1;
1034
const double basisvalue4 = 5.1234753829798*psitilde_a_2*scalings_y_2*psitilde_bs_2_0*scalings_z_2*psitilde_cs_20_0;
1035
const double basisvalue5 = 3.96862696659689*psitilde_a_1*scalings_y_1*psitilde_bs_1_1*scalings_z_2*psitilde_cs_11_0;
1036
const double basisvalue6 = 2.29128784747792*psitilde_a_0*scalings_y_0*psitilde_bs_0_2*scalings_z_2*psitilde_cs_02_0;
1037
const double basisvalue7 = 3.24037034920393*psitilde_a_1*scalings_y_1*psitilde_bs_1_0*scalings_z_1*psitilde_cs_10_1;
1038
const double basisvalue8 = 1.87082869338697*psitilde_a_0*scalings_y_0*psitilde_bs_0_1*scalings_z_1*psitilde_cs_01_1;
1039
const double basisvalue9 = 1.3228756555323*psitilde_a_0*scalings_y_0*psitilde_bs_0_0*scalings_z_0*psitilde_cs_00_2;
1040
1041
// Table(s) of coefficients
1042
static const double coefficients0[10][10] = \
1043
{{-0.0577350269189626, -0.0608580619450185, -0.0351364184463153, -0.0248451997499977, 0.0650600048632355, 0.0503952630678969, 0.0290957186981323, 0.0411475599898912, 0.0237565548366599, 0.0167984210226323},
1044
{-0.0577350269189625, 0.0608580619450185, -0.0351364184463153, -0.0248451997499977, 0.0650600048632355, -0.050395263067897, 0.0290957186981323, -0.0411475599898912, 0.0237565548366599, 0.0167984210226323},
1045
{-0.0577350269189626, 0, 0.0702728368926307, -0.0248451997499977, 0, 0, 0.0872871560943969, 0, -0.0475131096733199, 0.0167984210226323},
1046
{-0.0577350269189626, 0, 0, 0.074535599249993, 0, 0, 0, 0, 0, 0.100790526135794},
1047
{0.23094010767585, 0, 0.140545673785261, 0.0993807989999906, 0, 0, 0, 0, 0.1187827741833, -0.0671936840905293},
1048
{0.23094010767585, 0.121716123890037, -0.0702728368926307, 0.0993807989999907, 0, 0, 0, 0.102868899974728, -0.0593913870916499, -0.0671936840905293},
1049
{0.23094010767585, 0.121716123890037, 0.0702728368926306, -0.0993807989999906, 0, 0.100790526135794, -0.0872871560943969, -0.0205737799949456, -0.01187827741833, 0.0167984210226323},
1050
{0.23094010767585, -0.121716123890037, -0.0702728368926307, 0.0993807989999907, 0, 0, 0, -0.102868899974728, -0.0593913870916499, -0.0671936840905293},
1051
{0.23094010767585, -0.121716123890037, 0.0702728368926306, -0.0993807989999907, 0, -0.100790526135794, -0.0872871560943969, 0.0205737799949456, -0.01187827741833, 0.0167984210226323},
1052
{0.23094010767585, 0, -0.140545673785261, -0.0993807989999906, -0.130120009726471, 0, 0.0290957186981323, 0, 0.02375655483666, 0.0167984210226323}};
1053
1054
// Interesting (new) part
1055
// Tables of derivatives of the polynomial base (transpose)
1056
static const double dmats0[10][10] = \
1057
{{0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
1058
{6.32455532033676, 0, 0, 0, 0, 0, 0, 0, 0, 0},
1059
{0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
1060
{0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
1061
{0, 11.2249721603218, 0, 0, 0, 0, 0, 0, 0, 0},
1062
{4.58257569495584, 0, 8.36660026534076, -1.18321595661992, 0, 0, 0, 0, 0, 0},
1063
{0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
1064
{3.74165738677394, 0, 0, 8.69482604771366, 0, 0, 0, 0, 0, 0},
1065
{0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
1066
{0, 0, 0, 0, 0, 0, 0, 0, 0, 0}};
1067
1068
static const double dmats1[10][10] = \
1069
{{0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
1070
{3.16227766016838, 0, 0, 0, 0, 0, 0, 0, 0, 0},
1071
{5.47722557505166, 0, 0, 0, 0, 0, 0, 0, 0, 0},
1072
{0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
1073
{2.95803989154981, 5.61248608016091, -1.08012344973464, -0.763762615825973, 0, 0, 0, 0, 0, 0},
1074
{2.29128784747792, 7.24568837309472, 4.18330013267038, -0.591607978309962, 0, 0, 0, 0, 0, 0},
1075
{-2.64575131106459, 0, 9.66091783079296, 0.683130051063973, 0, 0, 0, 0, 0, 0},
1076
{1.87082869338697, 0, 0, 4.34741302385683, 0, 0, 0, 0, 0, 0},
1077
{3.24037034920393, 0, 0, 7.52994023880668, 0, 0, 0, 0, 0, 0},
1078
{0, 0, 0, 0, 0, 0, 0, 0, 0, 0}};
1079
1080
static const double dmats2[10][10] = \
1081
{{0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
1082
{3.16227766016838, 0, 0, 0, 0, 0, 0, 0, 0, 0},
1083
{1.82574185835055, 0, 0, 0, 0, 0, 0, 0, 0, 0},
1084
{5.16397779494322, 0, 0, 0, 0, 0, 0, 0, 0, 0},
1085
{2.95803989154981, 5.61248608016091, -1.08012344973464, -0.763762615825973, 0, 0, 0, 0, 0, 0},
1086
{2.29128784747792, 1.44913767461894, 4.18330013267038, -0.591607978309962, 0, 0, 0, 0, 0, 0},
1087
{1.3228756555323, 0, 3.86436713231718, -0.341565025531986, 0, 0, 0, 0, 0, 0},
1088
{1.87082869338697, 7.09929573971954, 0, 4.34741302385683, 0, 0, 0, 0, 0, 0},
1089
{1.08012344973464, 0, 7.09929573971954, 2.50998007960223, 0, 0, 0, 0, 0, 0},
1090
{-3.81881307912987, 0, 0, 8.87411967464942, 0, 0, 0, 0, 0, 0}};
1091
1092
// Compute reference derivatives
1093
// Declare pointer to array of derivatives on FIAT element
1094
double *derivatives = new double [num_derivatives];
1095
1096
// Declare coefficients
1097
double coeff0_0 = 0;
1098
double coeff0_1 = 0;
1099
double coeff0_2 = 0;
1100
double coeff0_3 = 0;
1101
double coeff0_4 = 0;
1102
double coeff0_5 = 0;
1103
double coeff0_6 = 0;
1104
double coeff0_7 = 0;
1105
double coeff0_8 = 0;
1106
double coeff0_9 = 0;
1107
1108
// Declare new coefficients
1109
double new_coeff0_0 = 0;
1110
double new_coeff0_1 = 0;
1111
double new_coeff0_2 = 0;
1112
double new_coeff0_3 = 0;
1113
double new_coeff0_4 = 0;
1114
double new_coeff0_5 = 0;
1115
double new_coeff0_6 = 0;
1116
double new_coeff0_7 = 0;
1117
double new_coeff0_8 = 0;
1118
double new_coeff0_9 = 0;
1119
1120
// Loop possible derivatives
1121
for (unsigned int deriv_num = 0; deriv_num < num_derivatives; deriv_num++)
1122
{
1123
// Get values from coefficients array
1124
new_coeff0_0 = coefficients0[dof][0];
1125
new_coeff0_1 = coefficients0[dof][1];
1126
new_coeff0_2 = coefficients0[dof][2];
1127
new_coeff0_3 = coefficients0[dof][3];
1128
new_coeff0_4 = coefficients0[dof][4];
1129
new_coeff0_5 = coefficients0[dof][5];
1130
new_coeff0_6 = coefficients0[dof][6];
1131
new_coeff0_7 = coefficients0[dof][7];
1132
new_coeff0_8 = coefficients0[dof][8];
1133
new_coeff0_9 = coefficients0[dof][9];
1134
1135
// Loop derivative order
1136
for (unsigned int j = 0; j < n; j++)
1137
{
1138
// Update old coefficients
1139
coeff0_0 = new_coeff0_0;
1140
coeff0_1 = new_coeff0_1;
1141
coeff0_2 = new_coeff0_2;
1142
coeff0_3 = new_coeff0_3;
1143
coeff0_4 = new_coeff0_4;
1144
coeff0_5 = new_coeff0_5;
1145
coeff0_6 = new_coeff0_6;
1146
coeff0_7 = new_coeff0_7;
1147
coeff0_8 = new_coeff0_8;
1148
coeff0_9 = new_coeff0_9;
1149
1150
if(combinations[deriv_num][j] == 0)
1151
{
1152
new_coeff0_0 = coeff0_0*dmats0[0][0] + coeff0_1*dmats0[1][0] + coeff0_2*dmats0[2][0] + coeff0_3*dmats0[3][0] + coeff0_4*dmats0[4][0] + coeff0_5*dmats0[5][0] + coeff0_6*dmats0[6][0] + coeff0_7*dmats0[7][0] + coeff0_8*dmats0[8][0] + coeff0_9*dmats0[9][0];
1153
new_coeff0_1 = coeff0_0*dmats0[0][1] + coeff0_1*dmats0[1][1] + coeff0_2*dmats0[2][1] + coeff0_3*dmats0[3][1] + coeff0_4*dmats0[4][1] + coeff0_5*dmats0[5][1] + coeff0_6*dmats0[6][1] + coeff0_7*dmats0[7][1] + coeff0_8*dmats0[8][1] + coeff0_9*dmats0[9][1];
1154
new_coeff0_2 = coeff0_0*dmats0[0][2] + coeff0_1*dmats0[1][2] + coeff0_2*dmats0[2][2] + coeff0_3*dmats0[3][2] + coeff0_4*dmats0[4][2] + coeff0_5*dmats0[5][2] + coeff0_6*dmats0[6][2] + coeff0_7*dmats0[7][2] + coeff0_8*dmats0[8][2] + coeff0_9*dmats0[9][2];
1155
new_coeff0_3 = coeff0_0*dmats0[0][3] + coeff0_1*dmats0[1][3] + coeff0_2*dmats0[2][3] + coeff0_3*dmats0[3][3] + coeff0_4*dmats0[4][3] + coeff0_5*dmats0[5][3] + coeff0_6*dmats0[6][3] + coeff0_7*dmats0[7][3] + coeff0_8*dmats0[8][3] + coeff0_9*dmats0[9][3];
1156
new_coeff0_4 = coeff0_0*dmats0[0][4] + coeff0_1*dmats0[1][4] + coeff0_2*dmats0[2][4] + coeff0_3*dmats0[3][4] + coeff0_4*dmats0[4][4] + coeff0_5*dmats0[5][4] + coeff0_6*dmats0[6][4] + coeff0_7*dmats0[7][4] + coeff0_8*dmats0[8][4] + coeff0_9*dmats0[9][4];
1157
new_coeff0_5 = coeff0_0*dmats0[0][5] + coeff0_1*dmats0[1][5] + coeff0_2*dmats0[2][5] + coeff0_3*dmats0[3][5] + coeff0_4*dmats0[4][5] + coeff0_5*dmats0[5][5] + coeff0_6*dmats0[6][5] + coeff0_7*dmats0[7][5] + coeff0_8*dmats0[8][5] + coeff0_9*dmats0[9][5];
1158
new_coeff0_6 = coeff0_0*dmats0[0][6] + coeff0_1*dmats0[1][6] + coeff0_2*dmats0[2][6] + coeff0_3*dmats0[3][6] + coeff0_4*dmats0[4][6] + coeff0_5*dmats0[5][6] + coeff0_6*dmats0[6][6] + coeff0_7*dmats0[7][6] + coeff0_8*dmats0[8][6] + coeff0_9*dmats0[9][6];
1159
new_coeff0_7 = coeff0_0*dmats0[0][7] + coeff0_1*dmats0[1][7] + coeff0_2*dmats0[2][7] + coeff0_3*dmats0[3][7] + coeff0_4*dmats0[4][7] + coeff0_5*dmats0[5][7] + coeff0_6*dmats0[6][7] + coeff0_7*dmats0[7][7] + coeff0_8*dmats0[8][7] + coeff0_9*dmats0[9][7];
1160
new_coeff0_8 = coeff0_0*dmats0[0][8] + coeff0_1*dmats0[1][8] + coeff0_2*dmats0[2][8] + coeff0_3*dmats0[3][8] + coeff0_4*dmats0[4][8] + coeff0_5*dmats0[5][8] + coeff0_6*dmats0[6][8] + coeff0_7*dmats0[7][8] + coeff0_8*dmats0[8][8] + coeff0_9*dmats0[9][8];
1161
new_coeff0_9 = coeff0_0*dmats0[0][9] + coeff0_1*dmats0[1][9] + coeff0_2*dmats0[2][9] + coeff0_3*dmats0[3][9] + coeff0_4*dmats0[4][9] + coeff0_5*dmats0[5][9] + coeff0_6*dmats0[6][9] + coeff0_7*dmats0[7][9] + coeff0_8*dmats0[8][9] + coeff0_9*dmats0[9][9];
1162
}
1163
if(combinations[deriv_num][j] == 1)
1164
{
1165
new_coeff0_0 = coeff0_0*dmats1[0][0] + coeff0_1*dmats1[1][0] + coeff0_2*dmats1[2][0] + coeff0_3*dmats1[3][0] + coeff0_4*dmats1[4][0] + coeff0_5*dmats1[5][0] + coeff0_6*dmats1[6][0] + coeff0_7*dmats1[7][0] + coeff0_8*dmats1[8][0] + coeff0_9*dmats1[9][0];
1166
new_coeff0_1 = coeff0_0*dmats1[0][1] + coeff0_1*dmats1[1][1] + coeff0_2*dmats1[2][1] + coeff0_3*dmats1[3][1] + coeff0_4*dmats1[4][1] + coeff0_5*dmats1[5][1] + coeff0_6*dmats1[6][1] + coeff0_7*dmats1[7][1] + coeff0_8*dmats1[8][1] + coeff0_9*dmats1[9][1];
1167
new_coeff0_2 = coeff0_0*dmats1[0][2] + coeff0_1*dmats1[1][2] + coeff0_2*dmats1[2][2] + coeff0_3*dmats1[3][2] + coeff0_4*dmats1[4][2] + coeff0_5*dmats1[5][2] + coeff0_6*dmats1[6][2] + coeff0_7*dmats1[7][2] + coeff0_8*dmats1[8][2] + coeff0_9*dmats1[9][2];
1168
new_coeff0_3 = coeff0_0*dmats1[0][3] + coeff0_1*dmats1[1][3] + coeff0_2*dmats1[2][3] + coeff0_3*dmats1[3][3] + coeff0_4*dmats1[4][3] + coeff0_5*dmats1[5][3] + coeff0_6*dmats1[6][3] + coeff0_7*dmats1[7][3] + coeff0_8*dmats1[8][3] + coeff0_9*dmats1[9][3];
1169
new_coeff0_4 = coeff0_0*dmats1[0][4] + coeff0_1*dmats1[1][4] + coeff0_2*dmats1[2][4] + coeff0_3*dmats1[3][4] + coeff0_4*dmats1[4][4] + coeff0_5*dmats1[5][4] + coeff0_6*dmats1[6][4] + coeff0_7*dmats1[7][4] + coeff0_8*dmats1[8][4] + coeff0_9*dmats1[9][4];
1170
new_coeff0_5 = coeff0_0*dmats1[0][5] + coeff0_1*dmats1[1][5] + coeff0_2*dmats1[2][5] + coeff0_3*dmats1[3][5] + coeff0_4*dmats1[4][5] + coeff0_5*dmats1[5][5] + coeff0_6*dmats1[6][5] + coeff0_7*dmats1[7][5] + coeff0_8*dmats1[8][5] + coeff0_9*dmats1[9][5];
1171
new_coeff0_6 = coeff0_0*dmats1[0][6] + coeff0_1*dmats1[1][6] + coeff0_2*dmats1[2][6] + coeff0_3*dmats1[3][6] + coeff0_4*dmats1[4][6] + coeff0_5*dmats1[5][6] + coeff0_6*dmats1[6][6] + coeff0_7*dmats1[7][6] + coeff0_8*dmats1[8][6] + coeff0_9*dmats1[9][6];
1172
new_coeff0_7 = coeff0_0*dmats1[0][7] + coeff0_1*dmats1[1][7] + coeff0_2*dmats1[2][7] + coeff0_3*dmats1[3][7] + coeff0_4*dmats1[4][7] + coeff0_5*dmats1[5][7] + coeff0_6*dmats1[6][7] + coeff0_7*dmats1[7][7] + coeff0_8*dmats1[8][7] + coeff0_9*dmats1[9][7];
1173
new_coeff0_8 = coeff0_0*dmats1[0][8] + coeff0_1*dmats1[1][8] + coeff0_2*dmats1[2][8] + coeff0_3*dmats1[3][8] + coeff0_4*dmats1[4][8] + coeff0_5*dmats1[5][8] + coeff0_6*dmats1[6][8] + coeff0_7*dmats1[7][8] + coeff0_8*dmats1[8][8] + coeff0_9*dmats1[9][8];
1174
new_coeff0_9 = coeff0_0*dmats1[0][9] + coeff0_1*dmats1[1][9] + coeff0_2*dmats1[2][9] + coeff0_3*dmats1[3][9] + coeff0_4*dmats1[4][9] + coeff0_5*dmats1[5][9] + coeff0_6*dmats1[6][9] + coeff0_7*dmats1[7][9] + coeff0_8*dmats1[8][9] + coeff0_9*dmats1[9][9];
1175
}
1176
if(combinations[deriv_num][j] == 2)
1177
{
1178
new_coeff0_0 = coeff0_0*dmats2[0][0] + coeff0_1*dmats2[1][0] + coeff0_2*dmats2[2][0] + coeff0_3*dmats2[3][0] + coeff0_4*dmats2[4][0] + coeff0_5*dmats2[5][0] + coeff0_6*dmats2[6][0] + coeff0_7*dmats2[7][0] + coeff0_8*dmats2[8][0] + coeff0_9*dmats2[9][0];
1179
new_coeff0_1 = coeff0_0*dmats2[0][1] + coeff0_1*dmats2[1][1] + coeff0_2*dmats2[2][1] + coeff0_3*dmats2[3][1] + coeff0_4*dmats2[4][1] + coeff0_5*dmats2[5][1] + coeff0_6*dmats2[6][1] + coeff0_7*dmats2[7][1] + coeff0_8*dmats2[8][1] + coeff0_9*dmats2[9][1];
1180
new_coeff0_2 = coeff0_0*dmats2[0][2] + coeff0_1*dmats2[1][2] + coeff0_2*dmats2[2][2] + coeff0_3*dmats2[3][2] + coeff0_4*dmats2[4][2] + coeff0_5*dmats2[5][2] + coeff0_6*dmats2[6][2] + coeff0_7*dmats2[7][2] + coeff0_8*dmats2[8][2] + coeff0_9*dmats2[9][2];
1181
new_coeff0_3 = coeff0_0*dmats2[0][3] + coeff0_1*dmats2[1][3] + coeff0_2*dmats2[2][3] + coeff0_3*dmats2[3][3] + coeff0_4*dmats2[4][3] + coeff0_5*dmats2[5][3] + coeff0_6*dmats2[6][3] + coeff0_7*dmats2[7][3] + coeff0_8*dmats2[8][3] + coeff0_9*dmats2[9][3];
1182
new_coeff0_4 = coeff0_0*dmats2[0][4] + coeff0_1*dmats2[1][4] + coeff0_2*dmats2[2][4] + coeff0_3*dmats2[3][4] + coeff0_4*dmats2[4][4] + coeff0_5*dmats2[5][4] + coeff0_6*dmats2[6][4] + coeff0_7*dmats2[7][4] + coeff0_8*dmats2[8][4] + coeff0_9*dmats2[9][4];
1183
new_coeff0_5 = coeff0_0*dmats2[0][5] + coeff0_1*dmats2[1][5] + coeff0_2*dmats2[2][5] + coeff0_3*dmats2[3][5] + coeff0_4*dmats2[4][5] + coeff0_5*dmats2[5][5] + coeff0_6*dmats2[6][5] + coeff0_7*dmats2[7][5] + coeff0_8*dmats2[8][5] + coeff0_9*dmats2[9][5];
1184
new_coeff0_6 = coeff0_0*dmats2[0][6] + coeff0_1*dmats2[1][6] + coeff0_2*dmats2[2][6] + coeff0_3*dmats2[3][6] + coeff0_4*dmats2[4][6] + coeff0_5*dmats2[5][6] + coeff0_6*dmats2[6][6] + coeff0_7*dmats2[7][6] + coeff0_8*dmats2[8][6] + coeff0_9*dmats2[9][6];
1185
new_coeff0_7 = coeff0_0*dmats2[0][7] + coeff0_1*dmats2[1][7] + coeff0_2*dmats2[2][7] + coeff0_3*dmats2[3][7] + coeff0_4*dmats2[4][7] + coeff0_5*dmats2[5][7] + coeff0_6*dmats2[6][7] + coeff0_7*dmats2[7][7] + coeff0_8*dmats2[8][7] + coeff0_9*dmats2[9][7];
1186
new_coeff0_8 = coeff0_0*dmats2[0][8] + coeff0_1*dmats2[1][8] + coeff0_2*dmats2[2][8] + coeff0_3*dmats2[3][8] + coeff0_4*dmats2[4][8] + coeff0_5*dmats2[5][8] + coeff0_6*dmats2[6][8] + coeff0_7*dmats2[7][8] + coeff0_8*dmats2[8][8] + coeff0_9*dmats2[9][8];
1187
new_coeff0_9 = coeff0_0*dmats2[0][9] + coeff0_1*dmats2[1][9] + coeff0_2*dmats2[2][9] + coeff0_3*dmats2[3][9] + coeff0_4*dmats2[4][9] + coeff0_5*dmats2[5][9] + coeff0_6*dmats2[6][9] + coeff0_7*dmats2[7][9] + coeff0_8*dmats2[8][9] + coeff0_9*dmats2[9][9];
1188
}
1189
1190
}
1191
// Compute derivatives on reference element as dot product of coefficients and basisvalues
1192
derivatives[deriv_num] = new_coeff0_0*basisvalue0 + new_coeff0_1*basisvalue1 + new_coeff0_2*basisvalue2 + new_coeff0_3*basisvalue3 + new_coeff0_4*basisvalue4 + new_coeff0_5*basisvalue5 + new_coeff0_6*basisvalue6 + new_coeff0_7*basisvalue7 + new_coeff0_8*basisvalue8 + new_coeff0_9*basisvalue9;
1193
}
1194
1195
// Transform derivatives back to physical element
1196
for (unsigned int row = 0; row < num_derivatives; row++)
1197
{
1198
for (unsigned int col = 0; col < num_derivatives; col++)
1199
{
1200
values[row] += transform[row][col]*derivatives[col];
1201
}
1202
}
1203
// Delete pointer to array of derivatives on FIAT element
1204
delete [] derivatives;
1205
1206
// Delete pointer to array of combinations of derivatives and transform
1207
for (unsigned int row = 0; row < num_derivatives; row++)
1208
{
1209
delete [] combinations[row];
1210
delete [] transform[row];
1211
}
1212
1213
delete [] combinations;
1214
delete [] transform;
1215
}
1216
1217
/// Evaluate order n derivatives of all basis functions at given point in cell
1218
virtual void evaluate_basis_derivatives_all(unsigned int n,
1219
double* values,
1220
const double* coordinates,
1221
const ufc::cell& c) const
1222
{
1223
throw std::runtime_error("The vectorised version of evaluate_basis_derivatives() is not yet implemented.");
1224
}
1225
1226
/// Evaluate linear functional for dof i on the function f
1227
virtual double evaluate_dof(unsigned int i,
1228
const ufc::function& f,
1229
const ufc::cell& c) const
1230
{
1231
// The reference points, direction and weights:
1232
static const double X[10][1][3] = {{{0, 0, 0}}, {{1, 0, 0}}, {{0, 1, 0}}, {{0, 0, 1}}, {{0, 0.5, 0.5}}, {{0.5, 0, 0.5}}, {{0.5, 0.5, 0}}, {{0, 0, 0.5}}, {{0, 0.5, 0}}, {{0.5, 0, 0}}};
1233
static const double W[10][1] = {{1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}};
1234
static const double D[10][1][1] = {{{1}}, {{1}}, {{1}}, {{1}}, {{1}}, {{1}}, {{1}}, {{1}}, {{1}}, {{1}}};
1235
1236
const double * const * x = c.coordinates;
1237
double result = 0.0;
1238
// Iterate over the points:
1239
// Evaluate basis functions for affine mapping
1240
const double w0 = 1.0 - X[i][0][0] - X[i][0][1] - X[i][0][2];
1241
const double w1 = X[i][0][0];
1242
const double w2 = X[i][0][1];
1243
const double w3 = X[i][0][2];
1244
1245
// Compute affine mapping y = F(X)
1246
double y[3];
1247
y[0] = w0*x[0][0] + w1*x[1][0] + w2*x[2][0] + w3*x[3][0];
1248
y[1] = w0*x[0][1] + w1*x[1][1] + w2*x[2][1] + w3*x[3][1];
1249
y[2] = w0*x[0][2] + w1*x[1][2] + w2*x[2][2] + w3*x[3][2];
1250
1251
// Evaluate function at physical points
1252
double values[1];
1253
f.evaluate(values, y, c);
1254
1255
// Map function values using appropriate mapping
1256
// Affine map: Do nothing
1257
1258
// Note that we do not map the weights (yet).
1259
1260
// Take directional components
1261
for(int k = 0; k < 1; k++)
1262
result += values[k]*D[i][0][k];
1263
// Multiply by weights
1264
result *= W[i][0];
1265
1266
return result;
1267
}
1268
1269
/// Evaluate linear functionals for all dofs on the function f
1270
virtual void evaluate_dofs(double* values,
1271
const ufc::function& f,
1272
const ufc::cell& c) const
1273
{
1274
throw std::runtime_error("Not implemented (introduced in UFC v1.1).");
1275
}
1276
1277
/// Interpolate vertex values from dof values
1278
virtual void interpolate_vertex_values(double* vertex_values,
1279
const double* dof_values,
1280
const ufc::cell& c) const
1281
{
1282
// Evaluate at vertices and use affine mapping
1283
vertex_values[0] = dof_values[0];
1284
vertex_values[1] = dof_values[1];
1285
vertex_values[2] = dof_values[2];
1286
vertex_values[3] = dof_values[3];
1287
}
1288
1289
/// Return the number of sub elements (for a mixed element)
1290
virtual unsigned int num_sub_elements() const
1291
{
1292
return 1;
1293
}
1294
1295
/// Create a new finite element for sub element i (for a mixed element)
1296
virtual ufc::finite_element* create_sub_element(unsigned int i) const
1297
{
1298
return new projection_0_finite_element_1();
1299
}
1300
1301
};
1302
1303
/// This class defines the interface for a local-to-global mapping of
1304
/// degrees of freedom (dofs).
1305
1306
class projection_0_dof_map_0: public ufc::dof_map
1307
{
1308
private:
1309
1310
unsigned int __global_dimension;
1311
1312
public:
1313
1314
/// Constructor
1315
projection_0_dof_map_0() : ufc::dof_map()
1316
{
1317
__global_dimension = 0;
1318
}
1319
1320
/// Destructor
1321
virtual ~projection_0_dof_map_0()
1322
{
1323
// Do nothing
1324
}
1325
1326
/// Return a string identifying the dof map
1327
virtual const char* signature() const
1328
{
1329
return "FFC dof map for FiniteElement('Lagrange', 'tetrahedron', 2)";
1330
}
1331
1332
/// Return true iff mesh entities of topological dimension d are needed
1333
virtual bool needs_mesh_entities(unsigned int d) const
1334
{
1335
switch ( d )
1336
{
1337
case 0:
1338
return true;
1339
break;
1340
case 1:
1341
return true;
1342
break;
1343
case 2:
1344
return false;
1345
break;
1346
case 3:
1347
return false;
1348
break;
1349
}
1350
return false;
1351
}
1352
1353
/// Initialize dof map for mesh (return true iff init_cell() is needed)
1354
virtual bool init_mesh(const ufc::mesh& m)
1355
{
1356
__global_dimension = m.num_entities[0] + m.num_entities[1];
1357
return false;
1358
}
1359
1360
/// Initialize dof map for given cell
1361
virtual void init_cell(const ufc::mesh& m,
1362
const ufc::cell& c)
1363
{
1364
// Do nothing
1365
}
1366
1367
/// Finish initialization of dof map for cells
1368
virtual void init_cell_finalize()
1369
{
1370
// Do nothing
1371
}
1372
1373
/// Return the dimension of the global finite element function space
1374
virtual unsigned int global_dimension() const
1375
{
1376
return __global_dimension;
1377
}
1378
1379
/// Return the dimension of the local finite element function space for a cell
1380
virtual unsigned int local_dimension(const ufc::cell& c) const
1381
{
1382
return 10;
1383
}
1384
1385
/// Return the maximum dimension of the local finite element function space
1386
virtual unsigned int max_local_dimension() const
1387
{
1388
return 10;
1389
}
1390
1391
// Return the geometric dimension of the coordinates this dof map provides
1392
virtual unsigned int geometric_dimension() const
1393
{
1394
return 3;
1395
}
1396
1397
/// Return the number of dofs on each cell facet
1398
virtual unsigned int num_facet_dofs() const
1399
{
1400
return 6;
1401
}
1402
1403
/// Return the number of dofs associated with each cell entity of dimension d
1404
virtual unsigned int num_entity_dofs(unsigned int d) const
1405
{
1406
throw std::runtime_error("Not implemented (introduced in UFC v1.1).");
1407
}
1408
1409
/// Tabulate the local-to-global mapping of dofs on a cell
1410
virtual void tabulate_dofs(unsigned int* dofs,
1411
const ufc::mesh& m,
1412
const ufc::cell& c) const
1413
{
1414
dofs[0] = c.entity_indices[0][0];
1415
dofs[1] = c.entity_indices[0][1];
1416
dofs[2] = c.entity_indices[0][2];
1417
dofs[3] = c.entity_indices[0][3];
1418
unsigned int offset = m.num_entities[0];
1419
dofs[4] = offset + c.entity_indices[1][0];
1420
dofs[5] = offset + c.entity_indices[1][1];
1421
dofs[6] = offset + c.entity_indices[1][2];
1422
dofs[7] = offset + c.entity_indices[1][3];
1423
dofs[8] = offset + c.entity_indices[1][4];
1424
dofs[9] = offset + c.entity_indices[1][5];
1425
}
1426
1427
/// Tabulate the local-to-local mapping from facet dofs to cell dofs
1428
virtual void tabulate_facet_dofs(unsigned int* dofs,
1429
unsigned int facet) const
1430
{
1431
switch ( facet )
1432
{
1433
case 0:
1434
dofs[0] = 1;
1435
dofs[1] = 2;
1436
dofs[2] = 3;
1437
dofs[3] = 4;
1438
dofs[4] = 5;
1439
dofs[5] = 6;
1440
break;
1441
case 1:
1442
dofs[0] = 0;
1443
dofs[1] = 2;
1444
dofs[2] = 3;
1445
dofs[3] = 4;
1446
dofs[4] = 7;
1447
dofs[5] = 8;
1448
break;
1449
case 2:
1450
dofs[0] = 0;
1451
dofs[1] = 1;
1452
dofs[2] = 3;
1453
dofs[3] = 5;
1454
dofs[4] = 7;
1455
dofs[5] = 9;
1456
break;
1457
case 3:
1458
dofs[0] = 0;
1459
dofs[1] = 1;
1460
dofs[2] = 2;
1461
dofs[3] = 6;
1462
dofs[4] = 8;
1463
dofs[5] = 9;
1464
break;
1465
}
1466
}
1467
1468
/// Tabulate the local-to-local mapping of dofs on entity (d, i)
1469
virtual void tabulate_entity_dofs(unsigned int* dofs,
1470
unsigned int d, unsigned int i) const
1471
{
1472
throw std::runtime_error("Not implemented (introduced in UFC v1.1).");
1473
}
1474
1475
/// Tabulate the coordinates of all dofs on a cell
1476
virtual void tabulate_coordinates(double** coordinates,
1477
const ufc::cell& c) const
1478
{
1479
const double * const * x = c.coordinates;
1480
coordinates[0][0] = x[0][0];
1481
coordinates[0][1] = x[0][1];
1482
coordinates[0][2] = x[0][2];
1483
coordinates[1][0] = x[1][0];
1484
coordinates[1][1] = x[1][1];
1485
coordinates[1][2] = x[1][2];
1486
coordinates[2][0] = x[2][0];
1487
coordinates[2][1] = x[2][1];
1488
coordinates[2][2] = x[2][2];
1489
coordinates[3][0] = x[3][0];
1490
coordinates[3][1] = x[3][1];
1491
coordinates[3][2] = x[3][2];
1492
coordinates[4][0] = 0.5*x[2][0] + 0.5*x[3][0];
1493
coordinates[4][1] = 0.5*x[2][1] + 0.5*x[3][1];
1494
coordinates[4][2] = 0.5*x[2][2] + 0.5*x[3][2];
1495
coordinates[5][0] = 0.5*x[1][0] + 0.5*x[3][0];
1496
coordinates[5][1] = 0.5*x[1][1] + 0.5*x[3][1];
1497
coordinates[5][2] = 0.5*x[1][2] + 0.5*x[3][2];
1498
coordinates[6][0] = 0.5*x[1][0] + 0.5*x[2][0];
1499
coordinates[6][1] = 0.5*x[1][1] + 0.5*x[2][1];
1500
coordinates[6][2] = 0.5*x[1][2] + 0.5*x[2][2];
1501
coordinates[7][0] = 0.5*x[0][0] + 0.5*x[3][0];
1502
coordinates[7][1] = 0.5*x[0][1] + 0.5*x[3][1];
1503
coordinates[7][2] = 0.5*x[0][2] + 0.5*x[3][2];
1504
coordinates[8][0] = 0.5*x[0][0] + 0.5*x[2][0];
1505
coordinates[8][1] = 0.5*x[0][1] + 0.5*x[2][1];
1506
coordinates[8][2] = 0.5*x[0][2] + 0.5*x[2][2];
1507
coordinates[9][0] = 0.5*x[0][0] + 0.5*x[1][0];
1508
coordinates[9][1] = 0.5*x[0][1] + 0.5*x[1][1];
1509
coordinates[9][2] = 0.5*x[0][2] + 0.5*x[1][2];
1510
}
1511
1512
/// Return the number of sub dof maps (for a mixed element)
1513
virtual unsigned int num_sub_dof_maps() const
1514
{
1515
return 1;
1516
}
1517
1518
/// Create a new dof_map for sub dof map i (for a mixed element)
1519
virtual ufc::dof_map* create_sub_dof_map(unsigned int i) const
1520
{
1521
return new projection_0_dof_map_0();
1522
}
1523
1524
};
1525
1526
/// This class defines the interface for a local-to-global mapping of
1527
/// degrees of freedom (dofs).
1528
1529
class projection_0_dof_map_1: public ufc::dof_map
1530
{
1531
private:
1532
1533
unsigned int __global_dimension;
1534
1535
public:
1536
1537
/// Constructor
1538
projection_0_dof_map_1() : ufc::dof_map()
1539
{
1540
__global_dimension = 0;
1541
}
1542
1543
/// Destructor
1544
virtual ~projection_0_dof_map_1()
1545
{
1546
// Do nothing
1547
}
1548
1549
/// Return a string identifying the dof map
1550
virtual const char* signature() const
1551
{
1552
return "FFC dof map for FiniteElement('Lagrange', 'tetrahedron', 2)";
1553
}
1554
1555
/// Return true iff mesh entities of topological dimension d are needed
1556
virtual bool needs_mesh_entities(unsigned int d) const
1557
{
1558
switch ( d )
1559
{
1560
case 0:
1561
return true;
1562
break;
1563
case 1:
1564
return true;
1565
break;
1566
case 2:
1567
return false;
1568
break;
1569
case 3:
1570
return false;
1571
break;
1572
}
1573
return false;
1574
}
1575
1576
/// Initialize dof map for mesh (return true iff init_cell() is needed)
1577
virtual bool init_mesh(const ufc::mesh& m)
1578
{
1579
__global_dimension = m.num_entities[0] + m.num_entities[1];
1580
return false;
1581
}
1582
1583
/// Initialize dof map for given cell
1584
virtual void init_cell(const ufc::mesh& m,
1585
const ufc::cell& c)
1586
{
1587
// Do nothing
1588
}
1589
1590
/// Finish initialization of dof map for cells
1591
virtual void init_cell_finalize()
1592
{
1593
// Do nothing
1594
}
1595
1596
/// Return the dimension of the global finite element function space
1597
virtual unsigned int global_dimension() const
1598
{
1599
return __global_dimension;
1600
}
1601
1602
/// Return the dimension of the local finite element function space for a cell
1603
virtual unsigned int local_dimension(const ufc::cell& c) const
1604
{
1605
return 10;
1606
}
1607
1608
/// Return the maximum dimension of the local finite element function space
1609
virtual unsigned int max_local_dimension() const
1610
{
1611
return 10;
1612
}
1613
1614
// Return the geometric dimension of the coordinates this dof map provides
1615
virtual unsigned int geometric_dimension() const
1616
{
1617
return 3;
1618
}
1619
1620
/// Return the number of dofs on each cell facet
1621
virtual unsigned int num_facet_dofs() const
1622
{
1623
return 6;
1624
}
1625
1626
/// Return the number of dofs associated with each cell entity of dimension d
1627
virtual unsigned int num_entity_dofs(unsigned int d) const
1628
{
1629
throw std::runtime_error("Not implemented (introduced in UFC v1.1).");
1630
}
1631
1632
/// Tabulate the local-to-global mapping of dofs on a cell
1633
virtual void tabulate_dofs(unsigned int* dofs,
1634
const ufc::mesh& m,
1635
const ufc::cell& c) const
1636
{
1637
dofs[0] = c.entity_indices[0][0];
1638
dofs[1] = c.entity_indices[0][1];
1639
dofs[2] = c.entity_indices[0][2];
1640
dofs[3] = c.entity_indices[0][3];
1641
unsigned int offset = m.num_entities[0];
1642
dofs[4] = offset + c.entity_indices[1][0];
1643
dofs[5] = offset + c.entity_indices[1][1];
1644
dofs[6] = offset + c.entity_indices[1][2];
1645
dofs[7] = offset + c.entity_indices[1][3];
1646
dofs[8] = offset + c.entity_indices[1][4];
1647
dofs[9] = offset + c.entity_indices[1][5];
1648
}
1649
1650
/// Tabulate the local-to-local mapping from facet dofs to cell dofs
1651
virtual void tabulate_facet_dofs(unsigned int* dofs,
1652
unsigned int facet) const
1653
{
1654
switch ( facet )
1655
{
1656
case 0:
1657
dofs[0] = 1;
1658
dofs[1] = 2;
1659
dofs[2] = 3;
1660
dofs[3] = 4;
1661
dofs[4] = 5;
1662
dofs[5] = 6;
1663
break;
1664
case 1:
1665
dofs[0] = 0;
1666
dofs[1] = 2;
1667
dofs[2] = 3;
1668
dofs[3] = 4;
1669
dofs[4] = 7;
1670
dofs[5] = 8;
1671
break;
1672
case 2:
1673
dofs[0] = 0;
1674
dofs[1] = 1;
1675
dofs[2] = 3;
1676
dofs[3] = 5;
1677
dofs[4] = 7;
1678
dofs[5] = 9;
1679
break;
1680
case 3:
1681
dofs[0] = 0;
1682
dofs[1] = 1;
1683
dofs[2] = 2;
1684
dofs[3] = 6;
1685
dofs[4] = 8;
1686
dofs[5] = 9;
1687
break;
1688
}
1689
}
1690
1691
/// Tabulate the local-to-local mapping of dofs on entity (d, i)
1692
virtual void tabulate_entity_dofs(unsigned int* dofs,
1693
unsigned int d, unsigned int i) const
1694
{
1695
throw std::runtime_error("Not implemented (introduced in UFC v1.1).");
1696
}
1697
1698
/// Tabulate the coordinates of all dofs on a cell
1699
virtual void tabulate_coordinates(double** coordinates,
1700
const ufc::cell& c) const
1701
{
1702
const double * const * x = c.coordinates;
1703
coordinates[0][0] = x[0][0];
1704
coordinates[0][1] = x[0][1];
1705
coordinates[0][2] = x[0][2];
1706
coordinates[1][0] = x[1][0];
1707
coordinates[1][1] = x[1][1];
1708
coordinates[1][2] = x[1][2];
1709
coordinates[2][0] = x[2][0];
1710
coordinates[2][1] = x[2][1];
1711
coordinates[2][2] = x[2][2];
1712
coordinates[3][0] = x[3][0];
1713
coordinates[3][1] = x[3][1];
1714
coordinates[3][2] = x[3][2];
1715
coordinates[4][0] = 0.5*x[2][0] + 0.5*x[3][0];
1716
coordinates[4][1] = 0.5*x[2][1] + 0.5*x[3][1];
1717
coordinates[4][2] = 0.5*x[2][2] + 0.5*x[3][2];
1718
coordinates[5][0] = 0.5*x[1][0] + 0.5*x[3][0];
1719
coordinates[5][1] = 0.5*x[1][1] + 0.5*x[3][1];
1720
coordinates[5][2] = 0.5*x[1][2] + 0.5*x[3][2];
1721
coordinates[6][0] = 0.5*x[1][0] + 0.5*x[2][0];
1722
coordinates[6][1] = 0.5*x[1][1] + 0.5*x[2][1];
1723
coordinates[6][2] = 0.5*x[1][2] + 0.5*x[2][2];
1724
coordinates[7][0] = 0.5*x[0][0] + 0.5*x[3][0];
1725
coordinates[7][1] = 0.5*x[0][1] + 0.5*x[3][1];
1726
coordinates[7][2] = 0.5*x[0][2] + 0.5*x[3][2];
1727
coordinates[8][0] = 0.5*x[0][0] + 0.5*x[2][0];
1728
coordinates[8][1] = 0.5*x[0][1] + 0.5*x[2][1];
1729
coordinates[8][2] = 0.5*x[0][2] + 0.5*x[2][2];
1730
coordinates[9][0] = 0.5*x[0][0] + 0.5*x[1][0];
1731
coordinates[9][1] = 0.5*x[0][1] + 0.5*x[1][1];
1732
coordinates[9][2] = 0.5*x[0][2] + 0.5*x[1][2];
1733
}
1734
1735
/// Return the number of sub dof maps (for a mixed element)
1736
virtual unsigned int num_sub_dof_maps() const
1737
{
1738
return 1;
1739
}
1740
1741
/// Create a new dof_map for sub dof map i (for a mixed element)
1742
virtual ufc::dof_map* create_sub_dof_map(unsigned int i) const
1743
{
1744
return new projection_0_dof_map_1();
1733
1745
}
1734
1746
1735
1747
};
1738
1750
/// tensor corresponding to the local contribution to a form from
1739
1751
/// the integral over a cell.
1740
1752
1741
class UFC_ProjectionBilinearForm_cell_integral_0: public ufc::cell_integral
1753
class projection_0_cell_integral_0_quadrature: public ufc::cell_integral
1742
1754
{
1743
1755
public:
1744
1756
1745
1757
/// Constructor
1746
UFC_ProjectionBilinearForm_cell_integral_0() : ufc::cell_integral()
1758
projection_0_cell_integral_0_quadrature() : ufc::cell_integral()
1747
1759
{
1748
1760
// Do nothing
1749
1761
}
1750
1762
1751
1763
/// Destructor
1752
virtual ~UFC_ProjectionBilinearForm_cell_integral_0()
1764
virtual ~projection_0_cell_integral_0_quadrature()
1753
1765
{
1754
1766
// Do nothing
1755
1767
}
1772
1784
const double J_20 = x[1][2] - x[0][2];
1773
1785
const double J_21 = x[2][2] - x[0][2];
1774
1786
const double J_22 = x[3][2] - x[0][2];
1775
1787
1776
1788
// Compute sub determinants
1777
1789
const double d_00 = J_11*J_22 - J_12*J_21;
1778
1790
1779
1791
const double d_10 = J_02*J_21 - J_01*J_22;
1780
1792
1781
1793
const double d_20 = J_01*J_12 - J_02*J_11;
1782
1794
1783
1795
// Compute determinant of Jacobian
1784
1796
double detJ = J_00*d_00 + J_10*d_10 + J_20*d_20;
1785
1797
1786
1798
// Compute inverse of Jacobian
1787
1799
1788
1800
// Set scale factor
1789
1801
const double det = std::abs(detJ);
1790
1802
1791
// Number of operations to compute element tensor = 101
1792
// Compute geometry tensors
1793
// Number of operations to compute decalrations = 1
1794
const double G0_ = det;
1795
1796
// Compute element tensor
1797
// Number of operations to compute tensor = 100
1798
A[0] = 0.00238095238095237*G0_;
1799
A[1] = 0.000396825396825395*G0_;
1800
A[2] = 0.000396825396825396*G0_;
1801
A[3] = 0.000396825396825396*G0_;
1802
A[4] = -0.00238095238095238*G0_;
1803
A[5] = -0.00238095238095238*G0_;
1804
A[6] = -0.00238095238095238*G0_;
1805
A[7] = -0.00158730158730158*G0_;
1806
A[8] = -0.00158730158730158*G0_;
1807
A[9] = -0.00158730158730158*G0_;
1808
A[10] = 0.000396825396825395*G0_;
1809
A[11] = 0.00238095238095238*G0_;
1810
A[12] = 0.000396825396825396*G0_;
1811
A[13] = 0.000396825396825396*G0_;
1812
A[14] = -0.00238095238095238*G0_;
1813
A[15] = -0.00158730158730158*G0_;
1814
A[16] = -0.00158730158730158*G0_;
1815
A[17] = -0.00238095238095237*G0_;
1816
A[18] = -0.00238095238095237*G0_;
1817
A[19] = -0.00158730158730158*G0_;
1818
A[20] = 0.000396825396825396*G0_;
1819
A[21] = 0.000396825396825396*G0_;
1820
A[22] = 0.00238095238095238*G0_;
1821
A[23] = 0.000396825396825398*G0_;
1822
A[24] = -0.00158730158730159*G0_;
1823
A[25] = -0.00238095238095238*G0_;
1824
A[26] = -0.00158730158730159*G0_;
1825
A[27] = -0.00238095238095238*G0_;
1826
A[28] = -0.00158730158730159*G0_;
1827
A[29] = -0.00238095238095238*G0_;
1828
A[30] = 0.000396825396825397*G0_;
1829
A[31] = 0.000396825396825396*G0_;
1830
A[32] = 0.000396825396825398*G0_;
1831
A[33] = 0.00238095238095238*G0_;
1832
A[34] = -0.00158730158730159*G0_;
1833
A[35] = -0.00158730158730159*G0_;
1834
A[36] = -0.00238095238095238*G0_;
1835
A[37] = -0.00158730158730159*G0_;
1836
A[38] = -0.00238095238095238*G0_;
1837
A[39] = -0.00238095238095238*G0_;
1838
A[40] = -0.00238095238095238*G0_;
1839
A[41] = -0.00238095238095237*G0_;
1840
A[42] = -0.00158730158730159*G0_;
1841
A[43] = -0.00158730158730159*G0_;
1842
A[44] = 0.0126984126984127*G0_;
1843
A[45] = 0.00634920634920634*G0_;
1844
A[46] = 0.00634920634920635*G0_;
1845
A[47] = 0.00634920634920634*G0_;
1846
A[48] = 0.00634920634920634*G0_;
1847
A[49] = 0.00317460317460317*G0_;
1848
A[50] = -0.00238095238095238*G0_;
1849
A[51] = -0.00158730158730158*G0_;
1850
A[52] = -0.00238095238095238*G0_;
1851
A[53] = -0.00158730158730159*G0_;
1852
A[54] = 0.00634920634920634*G0_;
1853
A[55] = 0.0126984126984127*G0_;
1854
A[56] = 0.00634920634920635*G0_;
1855
A[57] = 0.00634920634920634*G0_;
1856
A[58] = 0.00317460317460317*G0_;
1857
A[59] = 0.00634920634920634*G0_;
1858
A[60] = -0.00238095238095238*G0_;
1859
A[61] = -0.00158730158730158*G0_;
1860
A[62] = -0.00158730158730159*G0_;
1861
A[63] = -0.00238095238095238*G0_;
1862
A[64] = 0.00634920634920635*G0_;
1863
A[65] = 0.00634920634920635*G0_;
1864
A[66] = 0.0126984126984127*G0_;
1865
A[67] = 0.00317460317460317*G0_;
1866
A[68] = 0.00634920634920634*G0_;
1867
A[69] = 0.00634920634920634*G0_;
1868
A[70] = -0.00158730158730158*G0_;
1869
A[71] = -0.00238095238095237*G0_;
1870
A[72] = -0.00238095238095238*G0_;
1871
A[73] = -0.00158730158730159*G0_;
1872
A[74] = 0.00634920634920634*G0_;
1873
A[75] = 0.00634920634920634*G0_;
1874
A[76] = 0.00317460317460317*G0_;
1875
A[77] = 0.0126984126984127*G0_;
1876
A[78] = 0.00634920634920634*G0_;
1877
A[79] = 0.00634920634920633*G0_;
1878
A[80] = -0.00158730158730158*G0_;
1879
A[81] = -0.00238095238095237*G0_;
1880
A[82] = -0.00158730158730159*G0_;
1881
A[83] = -0.00238095238095238*G0_;
1882
A[84] = 0.00634920634920634*G0_;
1883
A[85] = 0.00317460317460317*G0_;
1884
A[86] = 0.00634920634920634*G0_;
1885
A[87] = 0.00634920634920634*G0_;
1886
A[88] = 0.0126984126984127*G0_;
1887
A[89] = 0.00634920634920634*G0_;
1888
A[90] = -0.00158730158730158*G0_;
1889
A[91] = -0.00158730158730158*G0_;
1890
A[92] = -0.00238095238095238*G0_;
1891
A[93] = -0.00238095238095238*G0_;
1892
A[94] = 0.00317460317460317*G0_;
1893
A[95] = 0.00634920634920634*G0_;
1894
A[96] = 0.00634920634920634*G0_;
1895
A[97] = 0.00634920634920633*G0_;
1896
A[98] = 0.00634920634920634*G0_;
1897
A[99] = 0.0126984126984127*G0_;
1803
1804
// Array of quadrature weights
1805
static const double W27[27] = {0.00877047492965105, 0.00816265076654668, 0.0016716811314837, 0.0100061425721761, 0.00931268237947044, 0.00190720341498178, 0.00304787709051818, 0.00283664869563092, 0.000580935315837384, 0.0140327598874417, 0.0130602412264747, 0.00267468981037392, 0.0160098281154818, 0.0149002918071527, 0.00305152546397085, 0.0048766033448291, 0.00453863791300947, 0.000929496505339815, 0.00877047492965105, 0.00816265076654668, 0.0016716811314837, 0.0100061425721761, 0.00931268237947044, 0.00190720341498178, 0.00304787709051818, 0.00283664869563092, 0.000580935315837384};
1806
// Quadrature points on the UFC reference element: (0.0952198798417149, 0.0821215678634425, 0.0729940240731498), (0.0670742417520586, 0.0578476039361427, 0.347003766038352), (0.0303014811742758, 0.0261332522867349, 0.705002209888498), (0.0616960186091465, 0.379578230280591, 0.0729940240731498), (0.0434595556538024, 0.267380320411884, 0.347003766038352), (0.0196333029354845, 0.120791820133903, 0.705002209888498), (0.0221843026408197, 0.730165028047632, 0.0729940240731498), (0.0156269392579017, 0.514338662174092, 0.347003766038352), (0.00705963113955477, 0.232357800579865, 0.705002209888498), (0.422442204031704, 0.0821215678634425, 0.0729940240731498), (0.297574315012753, 0.0578476039361427, 0.347003766038352), (0.134432268912383, 0.0261332522867349, 0.705002209888498), (0.27371387282313, 0.379578230280591, 0.0729940240731498), (0.192807956774882, 0.267380320411884, 0.347003766038352), (0.0871029849887995, 0.120791820133903, 0.705002209888498), (0.0984204739396093, 0.730165028047632, 0.0729940240731498), (0.0693287858937781, 0.514338662174092, 0.347003766038352), (0.0313199947658185, 0.232357800579865, 0.705002209888498), (0.749664528221693, 0.0821215678634425, 0.0729940240731498), (0.528074388273447, 0.0578476039361427, 0.347003766038352), (0.238563056650491, 0.0261332522867349, 0.705002209888498), (0.485731727037113, 0.379578230280591, 0.0729940240731498), (0.342156357895961, 0.267380320411884, 0.347003766038352), (0.154572667042115, 0.120791820133903, 0.705002209888498), (0.174656645238399, 0.730165028047632, 0.0729940240731498), (0.123030632529655, 0.514338662174092, 0.347003766038352), (0.0555803583920821, 0.232357800579865, 0.705002209888498)
1807
1808
// Value of basis functions at quadrature points.
1809
static const double FE0[27][10] = \
1810
{{0.374329281526014, -0.0770862288075737, -0.0686336640467425, -0.0623377689723666, 0.0239775348061957, 0.0278019288056343, 0.031278423297481, 0.218884122479203, 0.246254505716693, 0.285531865195462},
1811
{0.0296507308273033, -0.0580763339388314, -0.051154913373837, -0.106180538748753, 0.0802933456885461, 0.0931000579685248, 0.0155203366847607, 0.73297520591714, 0.122191352246653, 0.141680756728494},
1812
{-0.12473839265364, -0.0284651216515658, -0.0247673585365706, 0.289054022006834, 0.073696002454887, 0.0854504447630366, 0.00316750500875638, 0.672749928545405, 0.0249377141829676, 0.0289152558798901},
1813
{-0.0138611057361999, -0.0540832211847061, -0.0914189644747004, -0.0623377689723666, 0.11082776991498, 0.0180137626702941, 0.0936738622360728, 0.141822053505759, 0.737492757359529, 0.119870854681338},
1814
{-0.108014411398703, -0.0396820896985505, -0.12439584892476, -0.106180538748753, 0.37112791258986, 0.0603225179288912, 0.0464809196626873, 0.474918179055459, 0.365943506420742, 0.0594798531131275},
1815
{-0.10678724824909, -0.0188623697671714, -0.0916104925113804, 0.289054022006834, 0.340634000523421, 0.0553660878277077, 0.00948616958726985, 0.435896287412199, 0.0746844551798748, 0.0121390879903345},
1816
{-0.113646757786535, -0.0212000160735007, 0.336116908319966, -0.0623377689723666, 0.213190734538724, 0.00647728608404013, 0.0647928078398051, 0.050995565468269, 0.510112697076803, 0.0154985435047957},
1817
{-0.0927575594483608, -0.0151385367967613, 0.0147498566399773, -0.106180538748753, 0.71390981117415, 0.0216904270965778, 0.0321501561271397, 0.170768371303483, 0.253117643766939, 0.00769036888560855},
1818
{-0.0494020059140976, -0.0069599543559016, -0.12437750559924, 0.289054022006834, 0.655251051574542, 0.0199082222175352, 0.00656144145796827, 0.156737101971251, 0.0516581193256993, 0.00156950731540946},
1819
{-0.0655273725373765, -0.0655273725373763, -0.0686336640467425, -0.0623377689723666, 0.0239775348061957, 0.123343025642419, 0.138766464507087, 0.123343025642418, 0.138766464507087, 0.713829662988655},
1820
{-0.120473369102135, -0.120473369102135, -0.051154913373837, -0.106180538748753, 0.080293345688546, 0.413037631942832, 0.0688558444657068, 0.413037631942832, 0.0688558444657067, 0.354201891821236},
1821
{-0.0982881990625207, -0.0982881990625206, -0.0247673585365706, 0.289054022006834, 0.073696002454887, 0.379100186654221, 0.014052609595862, 0.379100186654221, 0.014052609595862, 0.0722881396997254},
1822
{-0.123875304471457, -0.123875304471457, -0.0914189644747004, -0.0623377689723666, 0.11082776991498, 0.0799179080880264, 0.415583309797801, 0.0799179080880263, 0.415583309797801, 0.299677136703346},
1823
{-0.118458140383472, -0.118458140383472, -0.12439584892476, -0.106180538748753, 0.37112791258986, 0.267620348492175, 0.206212213041715, 0.267620348492175, 0.206212213041715, 0.148699632782819},
1824
{-0.0719291250008815, -0.0719291250008814, -0.0916104925113804, 0.289054022006834, 0.340634000523421, 0.245631187619954, 0.0420853123835723, 0.245631187619953, 0.0420853123835723, 0.0303477199758362},
1825
{-0.0790472945586147, -0.0790472945586147, 0.336116908319966, -0.0623377689723666, 0.213190734538724, 0.0287364257761546, 0.287452752458304, 0.0287364257761545, 0.287452752458304, 0.0387463587619893},
1826
{-0.0597158247867675, -0.0597158247867675, 0.0147498566399773, -0.106180538748753, 0.71390981117415, 0.0962293992000304, 0.14263389994704, 0.0962293992000302, 0.142633899947039, 0.0192259222140213},
1827
{-0.0293581106215567, -0.0293581106215567, -0.12437750559924, 0.289054022006834, 0.655251051574542, 0.088322662094393, 0.0291097803918338, 0.088322662094393, 0.0291097803918338, 0.00392376828852362},
1828
{-0.0770862288075737, 0.374329281526014, -0.0686336640467425, -0.0623377689723666, 0.0239775348061957, 0.218884122479203, 0.246254505716693, 0.0278019288056342, 0.031278423297481, 0.285531865195462},
1829
{-0.0580763339388313, 0.0296507308273035, -0.0511549133738371, -0.106180538748753, 0.080293345688546, 0.73297520591714, 0.122191352246653, 0.0931000579685245, 0.0155203366847607, 0.141680756728494},
1830
{-0.0284651216515658, -0.12473839265364, -0.0247673585365706, 0.289054022006834, 0.0736960024548869, 0.672749928545405, 0.0249377141829676, 0.0854504447630365, 0.00316750500875635, 0.0289152558798901},
1831
{-0.0540832211847061, -0.0138611057361997, -0.0914189644747005, -0.0623377689723666, 0.11082776991498, 0.141822053505759, 0.737492757359529, 0.018013762670294, 0.0936738622360726, 0.119870854681338},
1832
{-0.0396820896985505, -0.108014411398703, -0.12439584892476, -0.106180538748753, 0.37112791258986, 0.474918179055459, 0.365943506420742, 0.060322517928891, 0.0464809196626872, 0.0594798531131274},
1833
{-0.0188623697671715, -0.10678724824909, -0.0916104925113804, 0.289054022006834, 0.340634000523421, 0.435896287412199, 0.0746844551798748, 0.0553660878277076, 0.00948616958726982, 0.0121390879903345},
1834
{-0.0212000160735008, -0.113646757786535, 0.336116908319966, -0.0623377689723666, 0.213190734538724, 0.0509955654682691, 0.510112697076803, 0.00647728608404003, 0.064792807839805, 0.0154985435047956},
1835
{-0.0151385367967614, -0.0927575594483608, 0.0147498566399773, -0.106180538748753, 0.71390981117415, 0.170768371303483, 0.25311764376694, 0.0216904270965776, 0.0321501561271396, 0.00769036888560852},
1836
{-0.00695995435590172, -0.0494020059140975, -0.12437750559924, 0.289054022006834, 0.655251051574542, 0.156737101971251, 0.0516581193256993, 0.0199082222175353, 0.00656144145796829, 0.00156950731540947}};
1837
1838
1839
// Compute element tensor using UFL quadrature representation
1840
// Optimisations: ('simplify expressions', True), ('ignore zero tables', True), ('non zero columns', True), ('remove zero terms', True), ('ignore ones', True)
1841
// Total number of operations to compute element tensor: 8127
1842
1843
// Loop quadrature points for integral
1844
// Number of operations to compute element tensor for following IP loop = 8127
1845
for (unsigned int ip = 0; ip < 27; ip++)
1846
{
1847
1848
// Number of operations to compute ip constants: 1
1849
// Number of operations: 1
1850
const double Gip0 = W27[ip]*det;
1851
1852
1853
// Number of operations for primary indices = 300
1854
for (unsigned int j = 0; j < 10; j++)
1855
{
1856
for (unsigned int k = 0; k < 10; k++)
1857
{
1858
// Number of operations to compute entry = 3
1859
A[j*10 + k] += FE0[ip][j]*FE0[ip][k]*Gip0;
1860
}// end loop over 'k'
1861
}// end loop over 'j'
1862
}// end loop over 'ip'
1863
}
1864
1865
};
1866
1867
/// This class defines the interface for the tabulation of the cell
1868
/// tensor corresponding to the local contribution to a form from
1869
/// the integral over a cell.
1870
1871
class projection_0_cell_integral_0: public ufc::cell_integral
1872
{
1873
private:
1874
1875
projection_0_cell_integral_0_quadrature integral_0_quadrature;
1876
1877
public:
1878
1879
/// Constructor
1880
projection_0_cell_integral_0() : ufc::cell_integral()
1881
{
1882
// Do nothing
1883
}
1884
1885
/// Destructor
1886
virtual ~projection_0_cell_integral_0()
1887
{
1888
// Do nothing
1889
}
1890
1891
/// Tabulate the tensor for the contribution from a local cell
1892
virtual void tabulate_tensor(double* A,
1893
const double * const * w,
1894
const ufc::cell& c) const
1895
{
1896
// Reset values of the element tensor block
1897
for (unsigned int j = 0; j < 100; j++)
1898
A[j] = 0;
1899
1900
// Add all contributions to element tensor
1901
integral_0_quadrature.tabulate_tensor(A, w, c);
1898
1902
}
1899
1903
1900
1904
};
1914
1918
/// sequence of basis functions of Vj and w1, w2, ..., wn are given
1915
1919
/// fixed functions (coefficients).
1916
1920
1917
class UFC_ProjectionBilinearForm: public ufc::form
1921
class projection_form_0: public ufc::form
1918
1922
{
1919
1923
public:
1920
1924
1921
1925
/// Constructor
1922
UFC_ProjectionBilinearForm() : ufc::form()
1926
projection_form_0() : ufc::form()
1923
1927
{
1924
1928
// Do nothing
1925
1929
}
1926
1930
1927
1931
/// Destructor
1928
virtual ~UFC_ProjectionBilinearForm()
1932
virtual ~projection_form_0()
1929
1933
{
1930
1934
// Do nothing
1931
1935
}
1933
1937
/// Return a string identifying the form
1934
1938
virtual const char* signature() const
1935
1939
{
1936
return " | vi0[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]*vi1[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]*dX(0)";
1940
return "Form([Integral(Product(BasisFunction(FiniteElement('Lagrange', Cell('tetrahedron', 1, Space(3)), 2), 0), BasisFunction(FiniteElement('Lagrange', Cell('tetrahedron', 1, Space(3)), 2), 1)), Measure('cell', 0, None))])";
1937
1941
}
1938
1942
1939
1943
/// Return the rank of the global tensor (r)
1953
1957
{
1954
1958
return 1;
1955
1959
}
1956
1960
1957
1961
/// Return the number of exterior facet integrals
1958
1962
virtual unsigned int num_exterior_facet_integrals() const
1959
1963
{
1960
1964
return 0;
1961
1965
}
1962
1966
1963
1967
/// Return the number of interior facet integrals
1964
1968
virtual unsigned int num_interior_facet_integrals() const
1965
1969
{
1966
1970
return 0;
1967
1971
}
1968
1972
1969
1973
/// Create a new finite element for argument function i
1970
1974
virtual ufc::finite_element* create_finite_element(unsigned int i) const
1971
1975
{
1972
1976
switch ( i )
1973
1977
{
1974
1978
case 0:
1975
return new UFC_ProjectionBilinearForm_finite_element_0();
1979
return new projection_0_finite_element_0();
1976
1980
break;
1977
1981
case 1:
1978
return new UFC_ProjectionBilinearForm_finite_element_1();
1982
return new projection_0_finite_element_1();
1979
1983
break;
1980
1984
}
1981
1985
return 0;
1982
1986
}
1983
1987
1984
1988
/// Create a new dof map for argument function i
1985
1989
virtual ufc::dof_map* create_dof_map(unsigned int i) const
1986
1990
{
1987
1991
switch ( i )
1988
1992
{
1989
1993
case 0:
1990
return new UFC_ProjectionBilinearForm_dof_map_0();
1994
return new projection_0_dof_map_0();
1991
1995
break;
1992
1996
case 1:
1993
return new UFC_ProjectionBilinearForm_dof_map_1();
1997
return new projection_0_dof_map_1();
1994
1998
break;
1995
1999
}
1996
2000
return 0;
1999
2003
/// Create a new cell integral on sub domain i
2000
2004
virtual ufc::cell_integral* create_cell_integral(unsigned int i) const
2001
2005
{
2002
return new UFC_ProjectionBilinearForm_cell_integral_0();
2006
return new projection_0_cell_integral_0();
2003
2007
}
2004
2008
2005
2009
/// Create a new exterior facet integral on sub domain i
2018
2022
2019
2023
/// This class defines the interface for a finite element.
2020
2024
2021
class UFC_ProjectionLinearForm_finite_element_0: public ufc::finite_element
2025
class projection_1_finite_element_0: public ufc::finite_element
2022
2026
{
2023
2027
public:
2024
2028
2025
2029
/// Constructor
2026
UFC_ProjectionLinearForm_finite_element_0() : ufc::finite_element()
2030
projection_1_finite_element_0() : ufc::finite_element()
2027
2031
{
2028
2032
// Do nothing
2029
2033
}
2030
2034
2031
2035
/// Destructor
2032
virtual ~UFC_ProjectionLinearForm_finite_element_0()
2036
virtual ~projection_1_finite_element_0()
2033
2037
{
2034
2038
// Do nothing
2035
2039
}
2083
2087
const double J_20 = element_coordinates[1][2] - element_coordinates[0][2];
2084
2088
const double J_21 = element_coordinates[2][2] - element_coordinates[0][2];
2085
2089
const double J_22 = element_coordinates[3][2] - element_coordinates[0][2];
2086
2090
2087
2091
// Compute sub determinants
2088
2092
const double d00 = J_11*J_22 - J_12*J_21;
2089
2093
const double d01 = J_12*J_20 - J_10*J_22;
2096
2100
const double d20 = J_01*J_12 - J_02*J_11;
2097
2101
const double d21 = J_02*J_10 - J_00*J_12;
2098
2102
const double d22 = J_00*J_11 - J_01*J_10;
2099
2103
2100
2104
// Compute determinant of Jacobian
2101
2105
double detJ = J_00*d00 + J_10*d10 + J_20*d20;
2102
2106
2183
2187
const double basisvalue9 = 1.3228756555323*psitilde_a_0*scalings_y_0*psitilde_bs_0_0*scalings_z_0*psitilde_cs_00_2;
2184
2188
2185
2189
// Table(s) of coefficients
2186
const static double coefficients0[10][10] = \
2187
{{-0.0577350269189625, -0.0608580619450185, -0.0351364184463153, -0.0248451997499977, 0.0650600048632355, 0.050395263067897, 0.0290957186981323, 0.0411475599898912, 0.0237565548366599, 0.0167984210226323},
2188
{-0.0577350269189625, 0.0608580619450185, -0.0351364184463153, -0.0248451997499976, 0.0650600048632355, -0.050395263067897, 0.0290957186981323, -0.0411475599898912, 0.0237565548366599, 0.0167984210226323},
2189
{-0.0577350269189626, 0, 0.0702728368926306, -0.0248451997499976, 0, 0, 0.087287156094397, 0, -0.0475131096733199, 0.0167984210226323},
2190
static const double coefficients0[10][10] = \
2191
{{-0.0577350269189626, -0.0608580619450185, -0.0351364184463153, -0.0248451997499977, 0.0650600048632355, 0.0503952630678969, 0.0290957186981323, 0.0411475599898912, 0.0237565548366599, 0.0167984210226323},
2192
{-0.0577350269189625, 0.0608580619450185, -0.0351364184463153, -0.0248451997499977, 0.0650600048632355, -0.050395263067897, 0.0290957186981323, -0.0411475599898912, 0.0237565548366599, 0.0167984210226323},
2193
{-0.0577350269189626, 0, 0.0702728368926307, -0.0248451997499977, 0, 0, 0.0872871560943969, 0, -0.0475131096733199, 0.0167984210226323},
2190
2194
{-0.0577350269189626, 0, 0, 0.074535599249993, 0, 0, 0, 0, 0, 0.100790526135794},
2191
2195
{0.23094010767585, 0, 0.140545673785261, 0.0993807989999906, 0, 0, 0, 0, 0.1187827741833, -0.0671936840905293},
2192
{0.23094010767585, 0.121716123890037, -0.0702728368926306, 0.0993807989999907, 0, 0, 0, 0.102868899974728, -0.0593913870916499, -0.0671936840905293},
2193
{0.23094010767585, 0.121716123890037, 0.0702728368926307, -0.0993807989999907, 0, 0.100790526135794, -0.087287156094397, -0.0205737799949456, -0.01187827741833, 0.0167984210226323},
2194
{0.23094010767585, -0.121716123890037, -0.0702728368926307, 0.0993807989999906, 0, 0, 0, -0.102868899974728, -0.0593913870916499, -0.0671936840905293},
2196
{0.23094010767585, 0.121716123890037, -0.0702728368926307, 0.0993807989999907, 0, 0, 0, 0.102868899974728, -0.0593913870916499, -0.0671936840905293},
2197
{0.23094010767585, 0.121716123890037, 0.0702728368926306, -0.0993807989999906, 0, 0.100790526135794, -0.0872871560943969, -0.0205737799949456, -0.01187827741833, 0.0167984210226323},
2198
{0.23094010767585, -0.121716123890037, -0.0702728368926307, 0.0993807989999907, 0, 0, 0, -0.102868899974728, -0.0593913870916499, -0.0671936840905293},
2195
2199
{0.23094010767585, -0.121716123890037, 0.0702728368926306, -0.0993807989999907, 0, -0.100790526135794, -0.0872871560943969, 0.0205737799949456, -0.01187827741833, 0.0167984210226323},
2196
2200
{0.23094010767585, 0, -0.140545673785261, -0.0993807989999906, -0.130120009726471, 0, 0.0290957186981323, 0, 0.02375655483666, 0.0167984210226323}};
2197
2201
2239
2243
const double J_20 = element_coordinates[1][2] - element_coordinates[0][2];
2240
2244
const double J_21 = element_coordinates[2][2] - element_coordinates[0][2];
2241
2245
const double J_22 = element_coordinates[3][2] - element_coordinates[0][2];
2242
2246
2243
2247
// Compute sub determinants
2244
2248
const double d00 = J_11*J_22 - J_12*J_21;
2245
2249
const double d01 = J_12*J_20 - J_10*J_22;
2252
2256
const double d20 = J_01*J_12 - J_02*J_11;
2253
2257
const double d21 = J_02*J_10 - J_00*J_12;
2254
2258
const double d22 = J_00*J_11 - J_01*J_10;
2255
2259
2256
2260
// Compute determinant of Jacobian
2257
2261
double detJ = J_00*d00 + J_10*d10 + J_20*d20;
2258
2262
2296
2300
2297
2301
// Declare pointer to two dimensional array that holds combinations of derivatives and initialise
2298
2302
unsigned int **combinations = new unsigned int *[num_derivatives];
2299
2303
2300
2304
for (unsigned int j = 0; j < num_derivatives; j++)
2301
2305
{
2302
2306
combinations[j] = new unsigned int [n];
2303
2307
for (unsigned int k = 0; k < n; k++)
2304
2308
combinations[j][k] = 0;
2305
2309
}
2306
2310
2307
2311
// Generate combinations of derivatives
2308
2312
for (unsigned int row = 1; row < num_derivatives; row++)
2309
2313
{
2328
2332
// Declare transformation matrix
2329
2333
// Declare pointer to two dimensional array and initialise
2330
2334
double **transform = new double *[num_derivatives];
2331
2335
2332
2336
for (unsigned int j = 0; j < num_derivatives; j++)
2333
2337
{
2334
2338
transform[j] = new double [num_derivatives];
2399
2403
const double basisvalue9 = 1.3228756555323*psitilde_a_0*scalings_y_0*psitilde_bs_0_0*scalings_z_0*psitilde_cs_00_2;
2400
2404
2401
2405
// Table(s) of coefficients
2402
const static double coefficients0[10][10] = \
2403
{{-0.0577350269189625, -0.0608580619450185, -0.0351364184463153, -0.0248451997499977, 0.0650600048632355, 0.050395263067897, 0.0290957186981323, 0.0411475599898912, 0.0237565548366599, 0.0167984210226323},
2404
{-0.0577350269189625, 0.0608580619450185, -0.0351364184463153, -0.0248451997499976, 0.0650600048632355, -0.050395263067897, 0.0290957186981323, -0.0411475599898912, 0.0237565548366599, 0.0167984210226323},
2405
{-0.0577350269189626, 0, 0.0702728368926306, -0.0248451997499976, 0, 0, 0.087287156094397, 0, -0.0475131096733199, 0.0167984210226323},
2406
static const double coefficients0[10][10] = \
2407
{{-0.0577350269189626, -0.0608580619450185, -0.0351364184463153, -0.0248451997499977, 0.0650600048632355, 0.0503952630678969, 0.0290957186981323, 0.0411475599898912, 0.0237565548366599, 0.0167984210226323},
2408
{-0.0577350269189625, 0.0608580619450185, -0.0351364184463153, -0.0248451997499977, 0.0650600048632355, -0.050395263067897, 0.0290957186981323, -0.0411475599898912, 0.0237565548366599, 0.0167984210226323},
2409
{-0.0577350269189626, 0, 0.0702728368926307, -0.0248451997499977, 0, 0, 0.0872871560943969, 0, -0.0475131096733199, 0.0167984210226323},
2406
2410
{-0.0577350269189626, 0, 0, 0.074535599249993, 0, 0, 0, 0, 0, 0.100790526135794},
2407
2411
{0.23094010767585, 0, 0.140545673785261, 0.0993807989999906, 0, 0, 0, 0, 0.1187827741833, -0.0671936840905293},
2408
{0.23094010767585, 0.121716123890037, -0.0702728368926306, 0.0993807989999907, 0, 0, 0, 0.102868899974728, -0.0593913870916499, -0.0671936840905293},
2409
{0.23094010767585, 0.121716123890037, 0.0702728368926307, -0.0993807989999907, 0, 0.100790526135794, -0.087287156094397, -0.0205737799949456, -0.01187827741833, 0.0167984210226323},
2410
{0.23094010767585, -0.121716123890037, -0.0702728368926307, 0.0993807989999906, 0, 0, 0, -0.102868899974728, -0.0593913870916499, -0.0671936840905293},
2412
{0.23094010767585, 0.121716123890037, -0.0702728368926307, 0.0993807989999907, 0, 0, 0, 0.102868899974728, -0.0593913870916499, -0.0671936840905293},
2413
{0.23094010767585, 0.121716123890037, 0.0702728368926306, -0.0993807989999906, 0, 0.100790526135794, -0.0872871560943969, -0.0205737799949456, -0.01187827741833, 0.0167984210226323},
2414
{0.23094010767585, -0.121716123890037, -0.0702728368926307, 0.0993807989999907, 0, 0, 0, -0.102868899974728, -0.0593913870916499, -0.0671936840905293},
2411
2415
{0.23094010767585, -0.121716123890037, 0.0702728368926306, -0.0993807989999907, 0, -0.100790526135794, -0.0872871560943969, 0.0205737799949456, -0.01187827741833, 0.0167984210226323},
2412
2416
{0.23094010767585, 0, -0.140545673785261, -0.0993807989999906, -0.130120009726471, 0, 0.0290957186981323, 0, 0.02375655483666, 0.0167984210226323}};
2413
2417
2414
2418
// Interesting (new) part
2415
2419
// Tables of derivatives of the polynomial base (transpose)
2416
const static double dmats0[10][10] = \
2420
static const double dmats0[10][10] = \
2417
2421
{{0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
2418
2422
{6.32455532033676, 0, 0, 0, 0, 0, 0, 0, 0, 0},
2419
2423
{0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
2425
2429
{0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
2426
2430
{0, 0, 0, 0, 0, 0, 0, 0, 0, 0}};
2427
2431
2428
const static double dmats1[10][10] = \
2432
static const double dmats1[10][10] = \
2429
2433
{{0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
2430
2434
{3.16227766016838, 0, 0, 0, 0, 0, 0, 0, 0, 0},
2431
2435
{5.47722557505166, 0, 0, 0, 0, 0, 0, 0, 0, 0},
2432
2436
{0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
2433
{2.95803989154981, 5.61248608016091, -1.08012344973464, -0.763762615825974, 0, 0, 0, 0, 0, 0},
2437
{2.95803989154981, 5.61248608016091, -1.08012344973464, -0.763762615825973, 0, 0, 0, 0, 0, 0},
2434
2438
{2.29128784747792, 7.24568837309472, 4.18330013267038, -0.591607978309962, 0, 0, 0, 0, 0, 0},
2435
{-2.64575131106459, 0, 9.66091783079296, 0.683130051063974, 0, 0, 0, 0, 0, 0},
2439
{-2.64575131106459, 0, 9.66091783079296, 0.683130051063973, 0, 0, 0, 0, 0, 0},
2436
2440
{1.87082869338697, 0, 0, 4.34741302385683, 0, 0, 0, 0, 0, 0},
2437
2441
{3.24037034920393, 0, 0, 7.52994023880668, 0, 0, 0, 0, 0, 0},
2438
2442
{0, 0, 0, 0, 0, 0, 0, 0, 0, 0}};
2439
2443
2440
const static double dmats2[10][10] = \
2444
static const double dmats2[10][10] = \
2441
2445
{{0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
2442
2446
{3.16227766016838, 0, 0, 0, 0, 0, 0, 0, 0, 0},
2443
2447
{1.82574185835055, 0, 0, 0, 0, 0, 0, 0, 0, 0},
2444
2448
{5.16397779494322, 0, 0, 0, 0, 0, 0, 0, 0, 0},
2445
2449
{2.95803989154981, 5.61248608016091, -1.08012344973464, -0.763762615825973, 0, 0, 0, 0, 0, 0},
2446
2450
{2.29128784747792, 1.44913767461894, 4.18330013267038, -0.591607978309962, 0, 0, 0, 0, 0, 0},
2447
{1.32287565553229, 0, 3.86436713231718, -0.341565025531986, 0, 0, 0, 0, 0, 0},
2451
{1.3228756555323, 0, 3.86436713231718, -0.341565025531986, 0, 0, 0, 0, 0, 0},
2448
2452
{1.87082869338697, 7.09929573971954, 0, 4.34741302385683, 0, 0, 0, 0, 0, 0},
2449
2453
{1.08012344973464, 0, 7.09929573971954, 2.50998007960223, 0, 0, 0, 0, 0, 0},
2450
{-3.81881307912986, 0, 0, 8.87411967464942, 0, 0, 0, 0, 0, 0}};
2454
{-3.81881307912987, 0, 0, 8.87411967464942, 0, 0, 0, 0, 0, 0}};
2451
2455
2452
2456
// Compute reference derivatives
2453
2457
// Declare pointer to array of derivatives on FIAT element
2589
2593
const ufc::cell& c) const
2590
2594
{
2591
2595
// The reference points, direction and weights:
2592
const static double X[10][1][3] = {{{0, 0, 0}}, {{1, 0, 0}}, {{0, 1, 0}}, {{0, 0, 1}}, {{0, 0.5, 0.5}}, {{0.5, 0, 0.5}}, {{0.5, 0.5, 0}}, {{0, 0, 0.5}}, {{0, 0.5, 0}}, {{0.5, 0, 0}}};
2593
const static double W[10][1] = {{1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}};
2594
const static double D[10][1][1] = {{{1}}, {{1}}, {{1}}, {{1}}, {{1}}, {{1}}, {{1}}, {{1}}, {{1}}, {{1}}};
2596
static const double X[10][1][3] = {{{0, 0, 0}}, {{1, 0, 0}}, {{0, 1, 0}}, {{0, 0, 1}}, {{0, 0.5, 0.5}}, {{0.5, 0, 0.5}}, {{0.5, 0.5, 0}}, {{0, 0, 0.5}}, {{0, 0.5, 0}}, {{0.5, 0, 0}}};
2597
static const double W[10][1] = {{1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}};
2598
static const double D[10][1][1] = {{{1}}, {{1}}, {{1}}, {{1}}, {{1}}, {{1}}, {{1}}, {{1}}, {{1}}, {{1}}};
2595
2599
2596
2600
const double * const * x = c.coordinates;
2597
2601
double result = 0.0;
2620
2624
// Take directional components
2621
2625
for(int k = 0; k < 1; k++)
2622
2626
result += values[k]*D[i][0][k];
2623
// Multiply by weights
2627
// Multiply by weights
2624
2628
result *= W[i][0];
2625
2629
2626
2630
return result;
2655
2659
/// Create a new finite element for sub element i (for a mixed element)
2656
2660
virtual ufc::finite_element* create_sub_element(unsigned int i) const
2657
2661
{
2658
return new UFC_ProjectionLinearForm_finite_element_0();
2662
return new projection_1_finite_element_0();
2659
2663
}
2660
2664
2661
2665
};
2662
2666
2663
2667
/// This class defines the interface for a finite element.
2664
2668
2665
class UFC_ProjectionLinearForm_finite_element_1: public ufc::finite_element
2669
class projection_1_finite_element_1: public ufc::finite_element
2666
2670
{
2667
2671
public:
2668
2672
2669
2673
/// Constructor
2670
UFC_ProjectionLinearForm_finite_element_1() : ufc::finite_element()
2674
projection_1_finite_element_1() : ufc::finite_element()
2671
2675
{
2672
2676
// Do nothing
2673
2677
}
2674
2678
2675
2679
/// Destructor
2676
virtual ~UFC_ProjectionLinearForm_finite_element_1()
2680
virtual ~projection_1_finite_element_1()
2677
2681
{
2678
2682
// Do nothing
2679
2683
}
2727
2731
const double J_20 = element_coordinates[1][2] - element_coordinates[0][2];
2728
2732
const double J_21 = element_coordinates[2][2] - element_coordinates[0][2];
2729
2733
const double J_22 = element_coordinates[3][2] - element_coordinates[0][2];
2730
2734
2731
2735
// Compute sub determinants
2732
2736
const double d00 = J_11*J_22 - J_12*J_21;
2733
2737
const double d01 = J_12*J_20 - J_10*J_22;
2740
2744
const double d20 = J_01*J_12 - J_02*J_11;
2741
2745
const double d21 = J_02*J_10 - J_00*J_12;
2742
2746
const double d22 = J_00*J_11 - J_01*J_10;
2743
2747
2744
2748
// Compute determinant of Jacobian
2745
2749
double detJ = J_00*d00 + J_10*d10 + J_20*d20;
2746
2750
2827
2831
const double basisvalue9 = 1.3228756555323*psitilde_a_0*scalings_y_0*psitilde_bs_0_0*scalings_z_0*psitilde_cs_00_2;
2828
2832
2829
2833
// Table(s) of coefficients
2830
const static double coefficients0[10][10] = \
2831
{{-0.0577350269189625, -0.0608580619450185, -0.0351364184463153, -0.0248451997499977, 0.0650600048632355, 0.050395263067897, 0.0290957186981323, 0.0411475599898912, 0.0237565548366599, 0.0167984210226323},
2832
{-0.0577350269189625, 0.0608580619450185, -0.0351364184463153, -0.0248451997499976, 0.0650600048632355, -0.050395263067897, 0.0290957186981323, -0.0411475599898912, 0.0237565548366599, 0.0167984210226323},
2833
{-0.0577350269189626, 0, 0.0702728368926306, -0.0248451997499976, 0, 0, 0.087287156094397, 0, -0.0475131096733199, 0.0167984210226323},
2834
static const double coefficients0[10][10] = \
2835
{{-0.0577350269189626, -0.0608580619450185, -0.0351364184463153, -0.0248451997499977, 0.0650600048632355, 0.0503952630678969, 0.0290957186981323, 0.0411475599898912, 0.0237565548366599, 0.0167984210226323},
2836
{-0.0577350269189625, 0.0608580619450185, -0.0351364184463153, -0.0248451997499977, 0.0650600048632355, -0.050395263067897, 0.0290957186981323, -0.0411475599898912, 0.0237565548366599, 0.0167984210226323},
2837
{-0.0577350269189626, 0, 0.0702728368926307, -0.0248451997499977, 0, 0, 0.0872871560943969, 0, -0.0475131096733199, 0.0167984210226323},
2834
2838
{-0.0577350269189626, 0, 0, 0.074535599249993, 0, 0, 0, 0, 0, 0.100790526135794},
2835
2839
{0.23094010767585, 0, 0.140545673785261, 0.0993807989999906, 0, 0, 0, 0, 0.1187827741833, -0.0671936840905293},
2836
{0.23094010767585, 0.121716123890037, -0.0702728368926306, 0.0993807989999907, 0, 0, 0, 0.102868899974728, -0.0593913870916499, -0.0671936840905293},
2837
{0.23094010767585, 0.121716123890037, 0.0702728368926307, -0.0993807989999907, 0, 0.100790526135794, -0.087287156094397, -0.0205737799949456, -0.01187827741833, 0.0167984210226323},
2838
{0.23094010767585, -0.121716123890037, -0.0702728368926307, 0.0993807989999906, 0, 0, 0, -0.102868899974728, -0.0593913870916499, -0.0671936840905293},
2840
{0.23094010767585, 0.121716123890037, -0.0702728368926307, 0.0993807989999907, 0, 0, 0, 0.102868899974728, -0.0593913870916499, -0.0671936840905293},
2841
{0.23094010767585, 0.121716123890037, 0.0702728368926306, -0.0993807989999906, 0, 0.100790526135794, -0.0872871560943969, -0.0205737799949456, -0.01187827741833, 0.0167984210226323},
2842
{0.23094010767585, -0.121716123890037, -0.0702728368926307, 0.0993807989999907, 0, 0, 0, -0.102868899974728, -0.0593913870916499, -0.0671936840905293},
2839
2843
{0.23094010767585, -0.121716123890037, 0.0702728368926306, -0.0993807989999907, 0, -0.100790526135794, -0.0872871560943969, 0.0205737799949456, -0.01187827741833, 0.0167984210226323},
2840
2844
{0.23094010767585, 0, -0.140545673785261, -0.0993807989999906, -0.130120009726471, 0, 0.0290957186981323, 0, 0.02375655483666, 0.0167984210226323}};
2841
2845
2883
2887
const double J_20 = element_coordinates[1][2] - element_coordinates[0][2];
2884
2888
const double J_21 = element_coordinates[2][2] - element_coordinates[0][2];
2885
2889
const double J_22 = element_coordinates[3][2] - element_coordinates[0][2];
2886
2890
2887
2891
// Compute sub determinants
2888
2892
const double d00 = J_11*J_22 - J_12*J_21;
2889
2893
const double d01 = J_12*J_20 - J_10*J_22;
2896
2900
const double d20 = J_01*J_12 - J_02*J_11;
2897
2901
const double d21 = J_02*J_10 - J_00*J_12;
2898
2902
const double d22 = J_00*J_11 - J_01*J_10;
2899
2903
2900
2904
// Compute determinant of Jacobian
2901
2905
double detJ = J_00*d00 + J_10*d10 + J_20*d20;
2902
2906
2940
2944
2941
2945
// Declare pointer to two dimensional array that holds combinations of derivatives and initialise
2942
2946
unsigned int **combinations = new unsigned int *[num_derivatives];
2943
2947
2944
2948
for (unsigned int j = 0; j < num_derivatives; j++)
2945
2949
{
2946
2950
combinations[j] = new unsigned int [n];
2947
2951
for (unsigned int k = 0; k < n; k++)
2948
2952
combinations[j][k] = 0;
2949
2953
}
2950
2954
2951
2955
// Generate combinations of derivatives
2952
2956
for (unsigned int row = 1; row < num_derivatives; row++)
2953
2957
{
2972
2976
// Declare transformation matrix
2973
2977
// Declare pointer to two dimensional array and initialise
2974
2978
double **transform = new double *[num_derivatives];
2975
2979
2976
2980
for (unsigned int j = 0; j < num_derivatives; j++)
2977
2981
{
2978
2982
transform[j] = new double [num_derivatives];
3043
3047
const double basisvalue9 = 1.3228756555323*psitilde_a_0*scalings_y_0*psitilde_bs_0_0*scalings_z_0*psitilde_cs_00_2;
3044
3048
3045
3049
// Table(s) of coefficients
3046
const static double coefficients0[10][10] = \
3047
{{-0.0577350269189625, -0.0608580619450185, -0.0351364184463153, -0.0248451997499977, 0.0650600048632355, 0.050395263067897, 0.0290957186981323, 0.0411475599898912, 0.0237565548366599, 0.0167984210226323},
3048
{-0.0577350269189625, 0.0608580619450185, -0.0351364184463153, -0.0248451997499976, 0.0650600048632355, -0.050395263067897, 0.0290957186981323, -0.0411475599898912, 0.0237565548366599, 0.0167984210226323},
3049
{-0.0577350269189626, 0, 0.0702728368926306, -0.0248451997499976, 0, 0, 0.087287156094397, 0, -0.0475131096733199, 0.0167984210226323},
3050
static const double coefficients0[10][10] = \
3051
{{-0.0577350269189626, -0.0608580619450185, -0.0351364184463153, -0.0248451997499977, 0.0650600048632355, 0.0503952630678969, 0.0290957186981323, 0.0411475599898912, 0.0237565548366599, 0.0167984210226323},
3052
{-0.0577350269189625, 0.0608580619450185, -0.0351364184463153, -0.0248451997499977, 0.0650600048632355, -0.050395263067897, 0.0290957186981323, -0.0411475599898912, 0.0237565548366599, 0.0167984210226323},
3053
{-0.0577350269189626, 0, 0.0702728368926307, -0.0248451997499977, 0, 0, 0.0872871560943969, 0, -0.0475131096733199, 0.0167984210226323},
3050
3054
{-0.0577350269189626, 0, 0, 0.074535599249993, 0, 0, 0, 0, 0, 0.100790526135794},
3051
3055
{0.23094010767585, 0, 0.140545673785261, 0.0993807989999906, 0, 0, 0, 0, 0.1187827741833, -0.0671936840905293},
3052
{0.23094010767585, 0.121716123890037, -0.0702728368926306, 0.0993807989999907, 0, 0, 0, 0.102868899974728, -0.0593913870916499, -0.0671936840905293},
3053
{0.23094010767585, 0.121716123890037, 0.0702728368926307, -0.0993807989999907, 0, 0.100790526135794, -0.087287156094397, -0.0205737799949456, -0.01187827741833, 0.0167984210226323},
3054
{0.23094010767585, -0.121716123890037, -0.0702728368926307, 0.0993807989999906, 0, 0, 0, -0.102868899974728, -0.0593913870916499, -0.0671936840905293},
3056
{0.23094010767585, 0.121716123890037, -0.0702728368926307, 0.0993807989999907, 0, 0, 0, 0.102868899974728, -0.0593913870916499, -0.0671936840905293},
3057
{0.23094010767585, 0.121716123890037, 0.0702728368926306, -0.0993807989999906, 0, 0.100790526135794, -0.0872871560943969, -0.0205737799949456, -0.01187827741833, 0.0167984210226323},
3058
{0.23094010767585, -0.121716123890037, -0.0702728368926307, 0.0993807989999907, 0, 0, 0, -0.102868899974728, -0.0593913870916499, -0.0671936840905293},
3055
3059
{0.23094010767585, -0.121716123890037, 0.0702728368926306, -0.0993807989999907, 0, -0.100790526135794, -0.0872871560943969, 0.0205737799949456, -0.01187827741833, 0.0167984210226323},
3056
3060
{0.23094010767585, 0, -0.140545673785261, -0.0993807989999906, -0.130120009726471, 0, 0.0290957186981323, 0, 0.02375655483666, 0.0167984210226323}};
3057
3061
3058
3062
// Interesting (new) part
3059
3063
// Tables of derivatives of the polynomial base (transpose)
3060
const static double dmats0[10][10] = \
3064
static const double dmats0[10][10] = \
3061
3065
{{0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
3062
3066
{6.32455532033676, 0, 0, 0, 0, 0, 0, 0, 0, 0},
3063
3067
{0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
3069
3073
{0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
3070
3074
{0, 0, 0, 0, 0, 0, 0, 0, 0, 0}};
3071
3075
3072
const static double dmats1[10][10] = \
3076
static const double dmats1[10][10] = \
3073
3077
{{0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
3074
3078
{3.16227766016838, 0, 0, 0, 0, 0, 0, 0, 0, 0},
3075
3079
{5.47722557505166, 0, 0, 0, 0, 0, 0, 0, 0, 0},
3076
3080
{0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
3077
{2.95803989154981, 5.61248608016091, -1.08012344973464, -0.763762615825974, 0, 0, 0, 0, 0, 0},
3081
{2.95803989154981, 5.61248608016091, -1.08012344973464, -0.763762615825973, 0, 0, 0, 0, 0, 0},
3078
3082
{2.29128784747792, 7.24568837309472, 4.18330013267038, -0.591607978309962, 0, 0, 0, 0, 0, 0},
3079
{-2.64575131106459, 0, 9.66091783079296, 0.683130051063974, 0, 0, 0, 0, 0, 0},
3083
{-2.64575131106459, 0, 9.66091783079296, 0.683130051063973, 0, 0, 0, 0, 0, 0},
3080
3084
{1.87082869338697, 0, 0, 4.34741302385683, 0, 0, 0, 0, 0, 0},
3081
3085
{3.24037034920393, 0, 0, 7.52994023880668, 0, 0, 0, 0, 0, 0},
3082
3086
{0, 0, 0, 0, 0, 0, 0, 0, 0, 0}};
3083
3087
3084
const static double dmats2[10][10] = \
3088
static const double dmats2[10][10] = \
3085
3089
{{0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
3086
3090
{3.16227766016838, 0, 0, 0, 0, 0, 0, 0, 0, 0},
3087
3091
{1.82574185835055, 0, 0, 0, 0, 0, 0, 0, 0, 0},
3088
3092
{5.16397779494322, 0, 0, 0, 0, 0, 0, 0, 0, 0},
3089
3093
{2.95803989154981, 5.61248608016091, -1.08012344973464, -0.763762615825973, 0, 0, 0, 0, 0, 0},
3090
3094
{2.29128784747792, 1.44913767461894, 4.18330013267038, -0.591607978309962, 0, 0, 0, 0, 0, 0},
3091
{1.32287565553229, 0, 3.86436713231718, -0.341565025531986, 0, 0, 0, 0, 0, 0},
3095
{1.3228756555323, 0, 3.86436713231718, -0.341565025531986, 0, 0, 0, 0, 0, 0},
3092
3096
{1.87082869338697, 7.09929573971954, 0, 4.34741302385683, 0, 0, 0, 0, 0, 0},
3093
3097
{1.08012344973464, 0, 7.09929573971954, 2.50998007960223, 0, 0, 0, 0, 0, 0},
3094
{-3.81881307912986, 0, 0, 8.87411967464942, 0, 0, 0, 0, 0, 0}};
3098
{-3.81881307912987, 0, 0, 8.87411967464942, 0, 0, 0, 0, 0, 0}};
3095
3099
3096
3100
// Compute reference derivatives
3097
3101
// Declare pointer to array of derivatives on FIAT element
3233
3237
const ufc::cell& c) const
3234
3238
{
3235
3239
// The reference points, direction and weights:
3236
const static double X[10][1][3] = {{{0, 0, 0}}, {{1, 0, 0}}, {{0, 1, 0}}, {{0, 0, 1}}, {{0, 0.5, 0.5}}, {{0.5, 0, 0.5}}, {{0.5, 0.5, 0}}, {{0, 0, 0.5}}, {{0, 0.5, 0}}, {{0.5, 0, 0}}};
3237
const static double W[10][1] = {{1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}};
3238
const static double D[10][1][1] = {{{1}}, {{1}}, {{1}}, {{1}}, {{1}}, {{1}}, {{1}}, {{1}}, {{1}}, {{1}}};
3240
static const double X[10][1][3] = {{{0, 0, 0}}, {{1, 0, 0}}, {{0, 1, 0}}, {{0, 0, 1}}, {{0, 0.5, 0.5}}, {{0.5, 0, 0.5}}, {{0.5, 0.5, 0}}, {{0, 0, 0.5}}, {{0, 0.5, 0}}, {{0.5, 0, 0}}};
3241
static const double W[10][1] = {{1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}};
3242
static const double D[10][1][1] = {{{1}}, {{1}}, {{1}}, {{1}}, {{1}}, {{1}}, {{1}}, {{1}}, {{1}}, {{1}}};
3239
3243
3240
3244
const double * const * x = c.coordinates;
3241
3245
double result = 0.0;
3264
3268
// Take directional components
3265
3269
for(int k = 0; k < 1; k++)
3266
3270
result += values[k]*D[i][0][k];
3267
// Multiply by weights
3271
// Multiply by weights
3268
3272
result *= W[i][0];
3269
3273
3270
3274
return result;
3299
3303
/// Create a new finite element for sub element i (for a mixed element)
3300
3304
virtual ufc::finite_element* create_sub_element(unsigned int i) const
3301
3305
{
3302
return new UFC_ProjectionLinearForm_finite_element_1();
3303
}
3304
3305
};
3306
3307
/// This class defines the interface for a local-to-global mapping of
3308
/// degrees of freedom (dofs).
3309
3310
class UFC_ProjectionLinearForm_dof_map_0: public ufc::dof_map
3311
{
3312
private:
3313
3314
unsigned int __global_dimension;
3315
3316
public:
3317
3318
/// Constructor
3319
UFC_ProjectionLinearForm_dof_map_0() : ufc::dof_map()
3320
{
3321
__global_dimension = 0;
3322
}
3323
3324
/// Destructor
3325
virtual ~UFC_ProjectionLinearForm_dof_map_0()
3326
{
3327
// Do nothing
3328
}
3329
3330
/// Return a string identifying the dof map
3331
virtual const char* signature() const
3332
{
3333
return "FFC dof map for FiniteElement('Lagrange', 'tetrahedron', 2)";
3334
}
3335
3336
/// Return true iff mesh entities of topological dimension d are needed
3337
virtual bool needs_mesh_entities(unsigned int d) const
3338
{
3339
switch ( d )
3340
{
3341
case 0:
3342
return true;
3343
break;
3344
case 1:
3345
return true;
3346
break;
3347
case 2:
3348
return false;
3349
break;
3350
case 3:
3351
return false;
3352
break;
3353
}
3354
return false;
3355
}
3356
3357
/// Initialize dof map for mesh (return true iff init_cell() is needed)
3358
virtual bool init_mesh(const ufc::mesh& m)
3359
{
3360
__global_dimension = m.num_entities[0] + m.num_entities[1];
3361
return false;
3362
}
3363
3364
/// Initialize dof map for given cell
3365
virtual void init_cell(const ufc::mesh& m,
3366
const ufc::cell& c)
3367
{
3368
// Do nothing
3369
}
3370
3371
/// Finish initialization of dof map for cells
3372
virtual void init_cell_finalize()
3373
{
3374
// Do nothing
3375
}
3376
3377
/// Return the dimension of the global finite element function space
3378
virtual unsigned int global_dimension() const
3379
{
3380
return __global_dimension;
3381
}
3382
3383
/// Return the dimension of the local finite element function space
3384
virtual unsigned int local_dimension() const
3385
{
3386
return 10;
3387
}
3388
3389
// Return the geometric dimension of the coordinates this dof map provides
3390
virtual unsigned int geometric_dimension() const
3391
{
3392
return 3;
3393
}
3394
3395
/// Return the number of dofs on each cell facet
3396
virtual unsigned int num_facet_dofs() const
3397
{
3398
return 6;
3399
}
3400
3401
/// Return the number of dofs associated with each cell entity of dimension d
3402
virtual unsigned int num_entity_dofs(unsigned int d) const
3403
{
3404
throw std::runtime_error("Not implemented (introduced in UFC v1.1).");
3405
}
3406
3407
/// Tabulate the local-to-global mapping of dofs on a cell
3408
virtual void tabulate_dofs(unsigned int* dofs,
3409
const ufc::mesh& m,
3410
const ufc::cell& c) const
3411
{
3412
dofs[0] = c.entity_indices[0][0];
3413
dofs[1] = c.entity_indices[0][1];
3414
dofs[2] = c.entity_indices[0][2];
3415
dofs[3] = c.entity_indices[0][3];
3416
unsigned int offset = m.num_entities[0];
3417
dofs[4] = offset + c.entity_indices[1][0];
3418
dofs[5] = offset + c.entity_indices[1][1];
3419
dofs[6] = offset + c.entity_indices[1][2];
3420
dofs[7] = offset + c.entity_indices[1][3];
3421
dofs[8] = offset + c.entity_indices[1][4];
3422
dofs[9] = offset + c.entity_indices[1][5];
3423
}
3424
3425
/// Tabulate the local-to-local mapping from facet dofs to cell dofs
3426
virtual void tabulate_facet_dofs(unsigned int* dofs,
3427
unsigned int facet) const
3428
{
3429
switch ( facet )
3430
{
3431
case 0:
3432
dofs[0] = 1;
3433
dofs[1] = 2;
3434
dofs[2] = 3;
3435
dofs[3] = 4;
3436
dofs[4] = 5;
3437
dofs[5] = 6;
3438
break;
3439
case 1:
3440
dofs[0] = 0;
3441
dofs[1] = 2;
3442
dofs[2] = 3;
3443
dofs[3] = 4;
3444
dofs[4] = 7;
3445
dofs[5] = 8;
3446
break;
3447
case 2:
3448
dofs[0] = 0;
3449
dofs[1] = 1;
3450
dofs[2] = 3;
3451
dofs[3] = 5;
3452
dofs[4] = 7;
3453
dofs[5] = 9;
3454
break;
3455
case 3:
3456
dofs[0] = 0;
3457
dofs[1] = 1;
3458
dofs[2] = 2;
3459
dofs[3] = 6;
3460
dofs[4] = 8;
3461
dofs[5] = 9;
3462
break;
3463
}
3464
}
3465
3466
/// Tabulate the local-to-local mapping of dofs on entity (d, i)
3467
virtual void tabulate_entity_dofs(unsigned int* dofs,
3468
unsigned int d, unsigned int i) const
3469
{
3470
throw std::runtime_error("Not implemented (introduced in UFC v1.1).");
3471
}
3472
3473
/// Tabulate the coordinates of all dofs on a cell
3474
virtual void tabulate_coordinates(double** coordinates,
3475
const ufc::cell& c) const
3476
{
3477
const double * const * x = c.coordinates;
3478
coordinates[0][0] = x[0][0];
3479
coordinates[0][1] = x[0][1];
3480
coordinates[0][2] = x[0][2];
3481
coordinates[1][0] = x[1][0];
3482
coordinates[1][1] = x[1][1];
3483
coordinates[1][2] = x[1][2];
3484
coordinates[2][0] = x[2][0];
3485
coordinates[2][1] = x[2][1];
3486
coordinates[2][2] = x[2][2];
3487
coordinates[3][0] = x[3][0];
3488
coordinates[3][1] = x[3][1];
3489
coordinates[3][2] = x[3][2];
3490
coordinates[4][0] = 0.5*x[2][0] + 0.5*x[3][0];
3491
coordinates[4][1] = 0.5*x[2][1] + 0.5*x[3][1];
3492
coordinates[4][2] = 0.5*x[2][2] + 0.5*x[3][2];
3493
coordinates[5][0] = 0.5*x[1][0] + 0.5*x[3][0];
3494
coordinates[5][1] = 0.5*x[1][1] + 0.5*x[3][1];
3495
coordinates[5][2] = 0.5*x[1][2] + 0.5*x[3][2];
3496
coordinates[6][0] = 0.5*x[1][0] + 0.5*x[2][0];
3497
coordinates[6][1] = 0.5*x[1][1] + 0.5*x[2][1];
3498
coordinates[6][2] = 0.5*x[1][2] + 0.5*x[2][2];
3499
coordinates[7][0] = 0.5*x[0][0] + 0.5*x[3][0];
3500
coordinates[7][1] = 0.5*x[0][1] + 0.5*x[3][1];
3501
coordinates[7][2] = 0.5*x[0][2] + 0.5*x[3][2];
3502
coordinates[8][0] = 0.5*x[0][0] + 0.5*x[2][0];
3503
coordinates[8][1] = 0.5*x[0][1] + 0.5*x[2][1];
3504
coordinates[8][2] = 0.5*x[0][2] + 0.5*x[2][2];
3505
coordinates[9][0] = 0.5*x[0][0] + 0.5*x[1][0];
3506
coordinates[9][1] = 0.5*x[0][1] + 0.5*x[1][1];
3507
coordinates[9][2] = 0.5*x[0][2] + 0.5*x[1][2];
3508
}
3509
3510
/// Return the number of sub dof maps (for a mixed element)
3511
virtual unsigned int num_sub_dof_maps() const
3512
{
3513
return 1;
3514
}
3515
3516
/// Create a new dof_map for sub dof map i (for a mixed element)
3517
virtual ufc::dof_map* create_sub_dof_map(unsigned int i) const
3518
{
3519
return new UFC_ProjectionLinearForm_dof_map_0();
3520
}
3521
3522
};
3523
3524
/// This class defines the interface for a local-to-global mapping of
3525
/// degrees of freedom (dofs).
3526
3527
class UFC_ProjectionLinearForm_dof_map_1: public ufc::dof_map
3528
{
3529
private:
3530
3531
unsigned int __global_dimension;
3532
3533
public:
3534
3535
/// Constructor
3536
UFC_ProjectionLinearForm_dof_map_1() : ufc::dof_map()
3537
{
3538
__global_dimension = 0;
3539
}
3540
3541
/// Destructor
3542
virtual ~UFC_ProjectionLinearForm_dof_map_1()
3543
{
3544
// Do nothing
3545
}
3546
3547
/// Return a string identifying the dof map
3548
virtual const char* signature() const
3549
{
3550
return "FFC dof map for FiniteElement('Lagrange', 'tetrahedron', 2)";
3551
}
3552
3553
/// Return true iff mesh entities of topological dimension d are needed
3554
virtual bool needs_mesh_entities(unsigned int d) const
3555
{
3556
switch ( d )
3557
{
3558
case 0:
3559
return true;
3560
break;
3561
case 1:
3562
return true;
3563
break;
3564
case 2:
3565
return false;
3566
break;
3567
case 3:
3568
return false;
3569
break;
3570
}
3571
return false;
3572
}
3573
3574
/// Initialize dof map for mesh (return true iff init_cell() is needed)
3575
virtual bool init_mesh(const ufc::mesh& m)
3576
{
3577
__global_dimension = m.num_entities[0] + m.num_entities[1];
3578
return false;
3579
}
3580
3581
/// Initialize dof map for given cell
3582
virtual void init_cell(const ufc::mesh& m,
3583
const ufc::cell& c)
3584
{
3585
// Do nothing
3586
}
3587
3588
/// Finish initialization of dof map for cells
3589
virtual void init_cell_finalize()
3590
{
3591
// Do nothing
3592
}
3593
3594
/// Return the dimension of the global finite element function space
3595
virtual unsigned int global_dimension() const
3596
{
3597
return __global_dimension;
3598
}
3599
3600
/// Return the dimension of the local finite element function space
3601
virtual unsigned int local_dimension() const
3602
{
3603
return 10;
3604
}
3605
3606
// Return the geometric dimension of the coordinates this dof map provides
3607
virtual unsigned int geometric_dimension() const
3608
{
3609
return 3;
3610
}
3611
3612
/// Return the number of dofs on each cell facet
3613
virtual unsigned int num_facet_dofs() const
3614
{
3615
return 6;
3616
}
3617
3618
/// Return the number of dofs associated with each cell entity of dimension d
3619
virtual unsigned int num_entity_dofs(unsigned int d) const
3620
{
3621
throw std::runtime_error("Not implemented (introduced in UFC v1.1).");
3622
}
3623
3624
/// Tabulate the local-to-global mapping of dofs on a cell
3625
virtual void tabulate_dofs(unsigned int* dofs,
3626
const ufc::mesh& m,
3627
const ufc::cell& c) const
3628
{
3629
dofs[0] = c.entity_indices[0][0];
3630
dofs[1] = c.entity_indices[0][1];
3631
dofs[2] = c.entity_indices[0][2];
3632
dofs[3] = c.entity_indices[0][3];
3633
unsigned int offset = m.num_entities[0];
3634
dofs[4] = offset + c.entity_indices[1][0];
3635
dofs[5] = offset + c.entity_indices[1][1];
3636
dofs[6] = offset + c.entity_indices[1][2];
3637
dofs[7] = offset + c.entity_indices[1][3];
3638
dofs[8] = offset + c.entity_indices[1][4];
3639
dofs[9] = offset + c.entity_indices[1][5];
3640
}
3641
3642
/// Tabulate the local-to-local mapping from facet dofs to cell dofs
3643
virtual void tabulate_facet_dofs(unsigned int* dofs,
3644
unsigned int facet) const
3645
{
3646
switch ( facet )
3647
{
3648
case 0:
3649
dofs[0] = 1;
3650
dofs[1] = 2;
3651
dofs[2] = 3;
3652
dofs[3] = 4;
3653
dofs[4] = 5;
3654
dofs[5] = 6;
3655
break;
3656
case 1:
3657
dofs[0] = 0;
3658
dofs[1] = 2;
3659
dofs[2] = 3;
3660
dofs[3] = 4;
3661
dofs[4] = 7;
3662
dofs[5] = 8;
3663
break;
3664
case 2:
3665
dofs[0] = 0;
3666
dofs[1] = 1;
3667
dofs[2] = 3;
3668
dofs[3] = 5;
3669
dofs[4] = 7;
3670
dofs[5] = 9;
3671
break;
3672
case 3:
3673
dofs[0] = 0;
3674
dofs[1] = 1;
3675
dofs[2] = 2;
3676
dofs[3] = 6;
3677
dofs[4] = 8;
3678
dofs[5] = 9;
3679
break;
3680
}
3681
}
3682
3683
/// Tabulate the local-to-local mapping of dofs on entity (d, i)
3684
virtual void tabulate_entity_dofs(unsigned int* dofs,
3685
unsigned int d, unsigned int i) const
3686
{
3687
throw std::runtime_error("Not implemented (introduced in UFC v1.1).");
3688
}
3689
3690
/// Tabulate the coordinates of all dofs on a cell
3691
virtual void tabulate_coordinates(double** coordinates,
3692
const ufc::cell& c) const
3693
{
3694
const double * const * x = c.coordinates;
3695
coordinates[0][0] = x[0][0];
3696
coordinates[0][1] = x[0][1];
3697
coordinates[0][2] = x[0][2];
3698
coordinates[1][0] = x[1][0];
3699
coordinates[1][1] = x[1][1];
3700
coordinates[1][2] = x[1][2];
3701
coordinates[2][0] = x[2][0];
3702
coordinates[2][1] = x[2][1];
3703
coordinates[2][2] = x[2][2];
3704
coordinates[3][0] = x[3][0];
3705
coordinates[3][1] = x[3][1];
3706
coordinates[3][2] = x[3][2];
3707
coordinates[4][0] = 0.5*x[2][0] + 0.5*x[3][0];
3708
coordinates[4][1] = 0.5*x[2][1] + 0.5*x[3][1];
3709
coordinates[4][2] = 0.5*x[2][2] + 0.5*x[3][2];
3710
coordinates[5][0] = 0.5*x[1][0] + 0.5*x[3][0];
3711
coordinates[5][1] = 0.5*x[1][1] + 0.5*x[3][1];
3712
coordinates[5][2] = 0.5*x[1][2] + 0.5*x[3][2];
3713
coordinates[6][0] = 0.5*x[1][0] + 0.5*x[2][0];
3714
coordinates[6][1] = 0.5*x[1][1] + 0.5*x[2][1];
3715
coordinates[6][2] = 0.5*x[1][2] + 0.5*x[2][2];
3716
coordinates[7][0] = 0.5*x[0][0] + 0.5*x[3][0];
3717
coordinates[7][1] = 0.5*x[0][1] + 0.5*x[3][1];
3718
coordinates[7][2] = 0.5*x[0][2] + 0.5*x[3][2];
3719
coordinates[8][0] = 0.5*x[0][0] + 0.5*x[2][0];
3720
coordinates[8][1] = 0.5*x[0][1] + 0.5*x[2][1];
3721
coordinates[8][2] = 0.5*x[0][2] + 0.5*x[2][2];
3722
coordinates[9][0] = 0.5*x[0][0] + 0.5*x[1][0];
3723
coordinates[9][1] = 0.5*x[0][1] + 0.5*x[1][1];
3724
coordinates[9][2] = 0.5*x[0][2] + 0.5*x[1][2];
3725
}
3726
3727
/// Return the number of sub dof maps (for a mixed element)
3728
virtual unsigned int num_sub_dof_maps() const
3729
{
3730
return 1;
3731
}
3732
3733
/// Create a new dof_map for sub dof map i (for a mixed element)
3734
virtual ufc::dof_map* create_sub_dof_map(unsigned int i) const
3735
{
3736
return new UFC_ProjectionLinearForm_dof_map_1();
3306
return new projection_1_finite_element_1();
3307
}
3308
3309
};
3310
3311
/// This class defines the interface for a local-to-global mapping of
3312
/// degrees of freedom (dofs).
3313
3314
class projection_1_dof_map_0: public ufc::dof_map
3315
{
3316
private:
3317
3318
unsigned int __global_dimension;
3319
3320
public:
3321
3322
/// Constructor
3323
projection_1_dof_map_0() : ufc::dof_map()
3324
{
3325
__global_dimension = 0;
3326
}
3327
3328
/// Destructor
3329
virtual ~projection_1_dof_map_0()
3330
{
3331
// Do nothing
3332
}
3333
3334
/// Return a string identifying the dof map
3335
virtual const char* signature() const
3336
{
3337
return "FFC dof map for FiniteElement('Lagrange', 'tetrahedron', 2)";
3338
}
3339
3340
/// Return true iff mesh entities of topological dimension d are needed
3341
virtual bool needs_mesh_entities(unsigned int d) const
3342
{
3343
switch ( d )
3344
{
3345
case 0:
3346
return true;
3347
break;
3348
case 1:
3349
return true;
3350
break;
3351
case 2:
3352
return false;
3353
break;
3354
case 3:
3355
return false;
3356
break;
3357
}
3358
return false;
3359
}
3360
3361
/// Initialize dof map for mesh (return true iff init_cell() is needed)
3362
virtual bool init_mesh(const ufc::mesh& m)
3363
{
3364
__global_dimension = m.num_entities[0] + m.num_entities[1];
3365
return false;
3366
}
3367
3368
/// Initialize dof map for given cell
3369
virtual void init_cell(const ufc::mesh& m,
3370
const ufc::cell& c)
3371
{
3372
// Do nothing
3373
}
3374
3375
/// Finish initialization of dof map for cells
3376
virtual void init_cell_finalize()
3377
{
3378
// Do nothing
3379
}
3380
3381
/// Return the dimension of the global finite element function space
3382
virtual unsigned int global_dimension() const
3383
{
3384
return __global_dimension;
3385
}
3386
3387
/// Return the dimension of the local finite element function space for a cell
3388
virtual unsigned int local_dimension(const ufc::cell& c) const
3389
{
3390
return 10;
3391
}
3392
3393
/// Return the maximum dimension of the local finite element function space
3394
virtual unsigned int max_local_dimension() const
3395
{
3396
return 10;
3397
}
3398
3399
// Return the geometric dimension of the coordinates this dof map provides
3400
virtual unsigned int geometric_dimension() const
3401
{
3402
return 3;
3403
}
3404
3405
/// Return the number of dofs on each cell facet
3406
virtual unsigned int num_facet_dofs() const
3407
{
3408
return 6;
3409
}
3410
3411
/// Return the number of dofs associated with each cell entity of dimension d
3412
virtual unsigned int num_entity_dofs(unsigned int d) const
3413
{
3414
throw std::runtime_error("Not implemented (introduced in UFC v1.1).");
3415
}
3416
3417
/// Tabulate the local-to-global mapping of dofs on a cell
3418
virtual void tabulate_dofs(unsigned int* dofs,
3419
const ufc::mesh& m,
3420
const ufc::cell& c) const
3421
{
3422
dofs[0] = c.entity_indices[0][0];
3423
dofs[1] = c.entity_indices[0][1];
3424
dofs[2] = c.entity_indices[0][2];
3425
dofs[3] = c.entity_indices[0][3];
3426
unsigned int offset = m.num_entities[0];
3427
dofs[4] = offset + c.entity_indices[1][0];
3428
dofs[5] = offset + c.entity_indices[1][1];
3429
dofs[6] = offset + c.entity_indices[1][2];
3430
dofs[7] = offset + c.entity_indices[1][3];
3431
dofs[8] = offset + c.entity_indices[1][4];
3432
dofs[9] = offset + c.entity_indices[1][5];
3433
}
3434
3435
/// Tabulate the local-to-local mapping from facet dofs to cell dofs
3436
virtual void tabulate_facet_dofs(unsigned int* dofs,
3437
unsigned int facet) const
3438
{
3439
switch ( facet )
3440
{
3441
case 0:
3442
dofs[0] = 1;
3443
dofs[1] = 2;
3444
dofs[2] = 3;
3445
dofs[3] = 4;
3446
dofs[4] = 5;
3447
dofs[5] = 6;
3448
break;
3449
case 1:
3450
dofs[0] = 0;
3451
dofs[1] = 2;
3452
dofs[2] = 3;
3453
dofs[3] = 4;
3454
dofs[4] = 7;
3455
dofs[5] = 8;
3456
break;
3457
case 2:
3458
dofs[0] = 0;
3459
dofs[1] = 1;
3460
dofs[2] = 3;
3461
dofs[3] = 5;
3462
dofs[4] = 7;
3463
dofs[5] = 9;
3464
break;
3465
case 3:
3466
dofs[0] = 0;
3467
dofs[1] = 1;
3468
dofs[2] = 2;
3469
dofs[3] = 6;
3470
dofs[4] = 8;
3471
dofs[5] = 9;
3472
break;
3473
}
3474
}
3475
3476
/// Tabulate the local-to-local mapping of dofs on entity (d, i)
3477
virtual void tabulate_entity_dofs(unsigned int* dofs,
3478
unsigned int d, unsigned int i) const
3479
{
3480
throw std::runtime_error("Not implemented (introduced in UFC v1.1).");
3481
}
3482
3483
/// Tabulate the coordinates of all dofs on a cell
3484
virtual void tabulate_coordinates(double** coordinates,
3485
const ufc::cell& c) const
3486
{
3487
const double * const * x = c.coordinates;
3488
coordinates[0][0] = x[0][0];
3489
coordinates[0][1] = x[0][1];
3490
coordinates[0][2] = x[0][2];
3491
coordinates[1][0] = x[1][0];
3492
coordinates[1][1] = x[1][1];
3493
coordinates[1][2] = x[1][2];
3494
coordinates[2][0] = x[2][0];
3495
coordinates[2][1] = x[2][1];
3496
coordinates[2][2] = x[2][2];
3497
coordinates[3][0] = x[3][0];
3498
coordinates[3][1] = x[3][1];
3499
coordinates[3][2] = x[3][2];
3500
coordinates[4][0] = 0.5*x[2][0] + 0.5*x[3][0];
3501
coordinates[4][1] = 0.5*x[2][1] + 0.5*x[3][1];
3502
coordinates[4][2] = 0.5*x[2][2] + 0.5*x[3][2];
3503
coordinates[5][0] = 0.5*x[1][0] + 0.5*x[3][0];
3504
coordinates[5][1] = 0.5*x[1][1] + 0.5*x[3][1];
3505
coordinates[5][2] = 0.5*x[1][2] + 0.5*x[3][2];
3506
coordinates[6][0] = 0.5*x[1][0] + 0.5*x[2][0];
3507
coordinates[6][1] = 0.5*x[1][1] + 0.5*x[2][1];
3508
coordinates[6][2] = 0.5*x[1][2] + 0.5*x[2][2];
3509
coordinates[7][0] = 0.5*x[0][0] + 0.5*x[3][0];
3510
coordinates[7][1] = 0.5*x[0][1] + 0.5*x[3][1];
3511
coordinates[7][2] = 0.5*x[0][2] + 0.5*x[3][2];
3512
coordinates[8][0] = 0.5*x[0][0] + 0.5*x[2][0];
3513
coordinates[8][1] = 0.5*x[0][1] + 0.5*x[2][1];
3514
coordinates[8][2] = 0.5*x[0][2] + 0.5*x[2][2];
3515
coordinates[9][0] = 0.5*x[0][0] + 0.5*x[1][0];
3516
coordinates[9][1] = 0.5*x[0][1] + 0.5*x[1][1];
3517
coordinates[9][2] = 0.5*x[0][2] + 0.5*x[1][2];
3518
}
3519
3520
/// Return the number of sub dof maps (for a mixed element)
3521
virtual unsigned int num_sub_dof_maps() const
3522
{
3523
return 1;
3524
}
3525
3526
/// Create a new dof_map for sub dof map i (for a mixed element)
3527
virtual ufc::dof_map* create_sub_dof_map(unsigned int i) const
3528
{
3529
return new projection_1_dof_map_0();
3530
}
3531
3532
};
3533
3534
/// This class defines the interface for a local-to-global mapping of
3535
/// degrees of freedom (dofs).
3536
3537
class projection_1_dof_map_1: public ufc::dof_map
3538
{
3539
private:
3540
3541
unsigned int __global_dimension;
3542
3543
public:
3544
3545
/// Constructor
3546
projection_1_dof_map_1() : ufc::dof_map()
3547
{
3548
__global_dimension = 0;
3549
}
3550
3551
/// Destructor
3552
virtual ~projection_1_dof_map_1()
3553
{
3554
// Do nothing
3555
}
3556
3557
/// Return a string identifying the dof map
3558
virtual const char* signature() const
3559
{
3560
return "FFC dof map for FiniteElement('Lagrange', 'tetrahedron', 2)";
3561
}
3562
3563
/// Return true iff mesh entities of topological dimension d are needed
3564
virtual bool needs_mesh_entities(unsigned int d) const
3565
{
3566
switch ( d )
3567
{
3568
case 0:
3569
return true;
3570
break;
3571
case 1:
3572
return true;
3573
break;
3574
case 2:
3575
return false;
3576
break;
3577
case 3:
3578
return false;
3579
break;
3580
}
3581
return false;
3582
}
3583
3584
/// Initialize dof map for mesh (return true iff init_cell() is needed)
3585
virtual bool init_mesh(const ufc::mesh& m)
3586
{
3587
__global_dimension = m.num_entities[0] + m.num_entities[1];
3588
return false;
3589
}
3590
3591
/// Initialize dof map for given cell
3592
virtual void init_cell(const ufc::mesh& m,
3593
const ufc::cell& c)
3594
{
3595
// Do nothing
3596
}
3597
3598
/// Finish initialization of dof map for cells
3599
virtual void init_cell_finalize()
3600
{
3601
// Do nothing
3602
}
3603
3604
/// Return the dimension of the global finite element function space
3605
virtual unsigned int global_dimension() const
3606
{
3607
return __global_dimension;
3608
}
3609
3610
/// Return the dimension of the local finite element function space for a cell
3611
virtual unsigned int local_dimension(const ufc::cell& c) const
3612
{
3613
return 10;
3614
}
3615
3616
/// Return the maximum dimension of the local finite element function space
3617
virtual unsigned int max_local_dimension() const
3618
{
3619
return 10;
3620
}
3621
3622
// Return the geometric dimension of the coordinates this dof map provides
3623
virtual unsigned int geometric_dimension() const
3624
{
3625
return 3;
3626
}
3627
3628
/// Return the number of dofs on each cell facet
3629
virtual unsigned int num_facet_dofs() const
3630
{
3631
return 6;
3632
}
3633
3634
/// Return the number of dofs associated with each cell entity of dimension d
3635
virtual unsigned int num_entity_dofs(unsigned int d) const
3636
{
3637
throw std::runtime_error("Not implemented (introduced in UFC v1.1).");
3638
}
3639
3640
/// Tabulate the local-to-global mapping of dofs on a cell
3641
virtual void tabulate_dofs(unsigned int* dofs,
3642
const ufc::mesh& m,
3643
const ufc::cell& c) const
3644
{
3645
dofs[0] = c.entity_indices[0][0];
3646
dofs[1] = c.entity_indices[0][1];
3647
dofs[2] = c.entity_indices[0][2];
3648
dofs[3] = c.entity_indices[0][3];
3649
unsigned int offset = m.num_entities[0];
3650
dofs[4] = offset + c.entity_indices[1][0];
3651
dofs[5] = offset + c.entity_indices[1][1];
3652
dofs[6] = offset + c.entity_indices[1][2];
3653
dofs[7] = offset + c.entity_indices[1][3];
3654
dofs[8] = offset + c.entity_indices[1][4];
3655
dofs[9] = offset + c.entity_indices[1][5];
3656
}
3657
3658
/// Tabulate the local-to-local mapping from facet dofs to cell dofs
3659
virtual void tabulate_facet_dofs(unsigned int* dofs,
3660
unsigned int facet) const
3661
{
3662
switch ( facet )
3663
{
3664
case 0:
3665
dofs[0] = 1;
3666
dofs[1] = 2;
3667
dofs[2] = 3;
3668
dofs[3] = 4;
3669
dofs[4] = 5;
3670
dofs[5] = 6;
3671
break;
3672
case 1:
3673
dofs[0] = 0;
3674
dofs[1] = 2;
3675
dofs[2] = 3;
3676
dofs[3] = 4;
3677
dofs[4] = 7;
3678
dofs[5] = 8;
3679
break;
3680
case 2:
3681
dofs[0] = 0;
3682
dofs[1] = 1;
3683
dofs[2] = 3;
3684
dofs[3] = 5;
3685
dofs[4] = 7;
3686
dofs[5] = 9;
3687
break;
3688
case 3:
3689
dofs[0] = 0;
3690
dofs[1] = 1;
3691
dofs[2] = 2;
3692
dofs[3] = 6;
3693
dofs[4] = 8;
3694
dofs[5] = 9;
3695
break;
3696
}
3697
}
3698
3699
/// Tabulate the local-to-local mapping of dofs on entity (d, i)
3700
virtual void tabulate_entity_dofs(unsigned int* dofs,
3701
unsigned int d, unsigned int i) const
3702
{
3703
throw std::runtime_error("Not implemented (introduced in UFC v1.1).");
3704
}
3705
3706
/// Tabulate the coordinates of all dofs on a cell
3707
virtual void tabulate_coordinates(double** coordinates,
3708
const ufc::cell& c) const
3709
{
3710
const double * const * x = c.coordinates;
3711
coordinates[0][0] = x[0][0];
3712
coordinates[0][1] = x[0][1];
3713
coordinates[0][2] = x[0][2];
3714
coordinates[1][0] = x[1][0];
3715
coordinates[1][1] = x[1][1];
3716
coordinates[1][2] = x[1][2];
3717
coordinates[2][0] = x[2][0];
3718
coordinates[2][1] = x[2][1];
3719
coordinates[2][2] = x[2][2];
3720
coordinates[3][0] = x[3][0];
3721
coordinates[3][1] = x[3][1];
3722
coordinates[3][2] = x[3][2];
3723
coordinates[4][0] = 0.5*x[2][0] + 0.5*x[3][0];
3724
coordinates[4][1] = 0.5*x[2][1] + 0.5*x[3][1];
3725
coordinates[4][2] = 0.5*x[2][2] + 0.5*x[3][2];
3726
coordinates[5][0] = 0.5*x[1][0] + 0.5*x[3][0];
3727
coordinates[5][1] = 0.5*x[1][1] + 0.5*x[3][1];
3728
coordinates[5][2] = 0.5*x[1][2] + 0.5*x[3][2];
3729
coordinates[6][0] = 0.5*x[1][0] + 0.5*x[2][0];
3730
coordinates[6][1] = 0.5*x[1][1] + 0.5*x[2][1];
3731
coordinates[6][2] = 0.5*x[1][2] + 0.5*x[2][2];
3732
coordinates[7][0] = 0.5*x[0][0] + 0.5*x[3][0];
3733
coordinates[7][1] = 0.5*x[0][1] + 0.5*x[3][1];
3734
coordinates[7][2] = 0.5*x[0][2] + 0.5*x[3][2];
3735
coordinates[8][0] = 0.5*x[0][0] + 0.5*x[2][0];
3736
coordinates[8][1] = 0.5*x[0][1] + 0.5*x[2][1];
3737
coordinates[8][2] = 0.5*x[0][2] + 0.5*x[2][2];
3738
coordinates[9][0] = 0.5*x[0][0] + 0.5*x[1][0];
3739
coordinates[9][1] = 0.5*x[0][1] + 0.5*x[1][1];
3740
coordinates[9][2] = 0.5*x[0][2] + 0.5*x[1][2];
3741
}
3742
3743
/// Return the number of sub dof maps (for a mixed element)
3744
virtual unsigned int num_sub_dof_maps() const
3745
{
3746
return 1;
3747
}
3748
3749
/// Create a new dof_map for sub dof map i (for a mixed element)
3750
virtual ufc::dof_map* create_sub_dof_map(unsigned int i) const
3751
{
3752
return new projection_1_dof_map_1();
3737
3753
}
3738
3754
3739
3755
};
3742
3758
/// tensor corresponding to the local contribution to a form from
3743
3759
/// the integral over a cell.
3744
3760
3745
class UFC_ProjectionLinearForm_cell_integral_0: public ufc::cell_integral
3761
class projection_1_cell_integral_0_quadrature: public ufc::cell_integral
3746
3762
{
3747
3763
public:
3748
3764
3749
3765
/// Constructor
3750
UFC_ProjectionLinearForm_cell_integral_0() : ufc::cell_integral()
3766
projection_1_cell_integral_0_quadrature() : ufc::cell_integral()
3751
3767
{
3752
3768
// Do nothing
3753
3769
}
3754
3770
3755
3771
/// Destructor
3756
virtual ~UFC_ProjectionLinearForm_cell_integral_0()
3772
virtual ~projection_1_cell_integral_0_quadrature()
3757
3773
{
3758
3774
// Do nothing
3759
3775
}
3776
3792
const double J_20 = x[1][2] - x[0][2];
3777
3793
const double J_21 = x[2][2] - x[0][2];
3778
3794
const double J_22 = x[3][2] - x[0][2];
3779
3795
3780
3796
// Compute sub determinants
3781
3797
const double d_00 = J_11*J_22 - J_12*J_21;
3782
3798
3783
3799
const double d_10 = J_02*J_21 - J_01*J_22;
3784
3800
3785
3801
const double d_20 = J_01*J_12 - J_02*J_11;
3786
3802
3787
3803
// Compute determinant of Jacobian
3788
3804
double detJ = J_00*d_00 + J_10*d_10 + J_20*d_20;
3789
3805
3790
3806
// Compute inverse of Jacobian
3791
3807
3792
3808
// Set scale factor
3793
3809
const double det = std::abs(detJ);
3794
3810
3795
// Number of operations to compute element tensor = 200
3796
// Compute coefficients
3797
const double c0_0_0_0 = w[0][0];
3798
const double c0_0_0_1 = w[0][1];
3799
const double c0_0_0_2 = w[0][2];
3800
const double c0_0_0_3 = w[0][3];
3801
const double c0_0_0_4 = w[0][4];
3802
const double c0_0_0_5 = w[0][5];
3803
const double c0_0_0_6 = w[0][6];
3804
const double c0_0_0_7 = w[0][7];
3805
const double c0_0_0_8 = w[0][8];
3806
const double c0_0_0_9 = w[0][9];
3807
3808
// Compute geometry tensors
3809
// Number of operations to compute decalrations = 10
3810
const double G0_0 = det*c0_0_0_0;
3811
const double G0_1 = det*c0_0_0_1;
3812
const double G0_2 = det*c0_0_0_2;
3813
const double G0_3 = det*c0_0_0_3;
3814
const double G0_4 = det*c0_0_0_4;
3815
const double G0_5 = det*c0_0_0_5;
3816
const double G0_6 = det*c0_0_0_6;
3817
const double G0_7 = det*c0_0_0_7;
3818
const double G0_8 = det*c0_0_0_8;
3819
const double G0_9 = det*c0_0_0_9;
3820
3821
// Compute element tensor
3822
// Number of operations to compute tensor = 190
3823
A[0] = 0.00238095238095237*G0_0 + 0.000396825396825395*G0_1 + 0.000396825396825396*G0_2 + 0.000396825396825396*G0_3 - 0.00238095238095238*G0_4 - 0.00238095238095238*G0_5 - 0.00238095238095238*G0_6 - 0.00158730158730158*G0_7 - 0.00158730158730158*G0_8 - 0.00158730158730158*G0_9;
3824
A[1] = 0.000396825396825395*G0_0 + 0.00238095238095238*G0_1 + 0.000396825396825396*G0_2 + 0.000396825396825396*G0_3 - 0.00238095238095238*G0_4 - 0.00158730158730158*G0_5 - 0.00158730158730158*G0_6 - 0.00238095238095237*G0_7 - 0.00238095238095237*G0_8 - 0.00158730158730158*G0_9;
3825
A[2] = 0.000396825396825396*G0_0 + 0.000396825396825396*G0_1 + 0.00238095238095238*G0_2 + 0.000396825396825398*G0_3 - 0.00158730158730159*G0_4 - 0.00238095238095238*G0_5 - 0.00158730158730159*G0_6 - 0.00238095238095238*G0_7 - 0.00158730158730159*G0_8 - 0.00238095238095238*G0_9;
3826
A[3] = 0.000396825396825396*G0_0 + 0.000396825396825396*G0_1 + 0.000396825396825398*G0_2 + 0.00238095238095238*G0_3 - 0.00158730158730159*G0_4 - 0.00158730158730159*G0_5 - 0.00238095238095238*G0_6 - 0.00158730158730159*G0_7 - 0.00238095238095238*G0_8 - 0.00238095238095238*G0_9;
3827
A[4] = -0.00238095238095238*G0_0 - 0.00238095238095237*G0_1 - 0.00158730158730159*G0_2 - 0.00158730158730159*G0_3 + 0.0126984126984127*G0_4 + 0.00634920634920634*G0_5 + 0.00634920634920635*G0_6 + 0.00634920634920634*G0_7 + 0.00634920634920634*G0_8 + 0.00317460317460317*G0_9;
3828
A[5] = -0.00238095238095238*G0_0 - 0.00158730158730158*G0_1 - 0.00238095238095238*G0_2 - 0.00158730158730159*G0_3 + 0.00634920634920634*G0_4 + 0.0126984126984127*G0_5 + 0.00634920634920635*G0_6 + 0.00634920634920634*G0_7 + 0.00317460317460317*G0_8 + 0.00634920634920634*G0_9;
3829
A[6] = -0.00238095238095238*G0_0 - 0.00158730158730158*G0_1 - 0.00158730158730159*G0_2 - 0.00238095238095238*G0_3 + 0.00634920634920635*G0_4 + 0.00634920634920635*G0_5 + 0.0126984126984127*G0_6 + 0.00317460317460317*G0_7 + 0.00634920634920634*G0_8 + 0.00634920634920634*G0_9;
3830
A[7] = -0.00158730158730158*G0_0 - 0.00238095238095237*G0_1 - 0.00238095238095238*G0_2 - 0.00158730158730159*G0_3 + 0.00634920634920634*G0_4 + 0.00634920634920634*G0_5 + 0.00317460317460317*G0_6 + 0.0126984126984127*G0_7 + 0.00634920634920634*G0_8 + 0.00634920634920633*G0_9;
3831
A[8] = -0.00158730158730158*G0_0 - 0.00238095238095237*G0_1 - 0.00158730158730159*G0_2 - 0.00238095238095238*G0_3 + 0.00634920634920634*G0_4 + 0.00317460317460317*G0_5 + 0.00634920634920634*G0_6 + 0.00634920634920634*G0_7 + 0.0126984126984127*G0_8 + 0.00634920634920634*G0_9;
3832
A[9] = -0.00158730158730158*G0_0 - 0.00158730158730158*G0_1 - 0.00238095238095238*G0_2 - 0.00238095238095238*G0_3 + 0.00317460317460317*G0_4 + 0.00634920634920634*G0_5 + 0.00634920634920634*G0_6 + 0.00634920634920633*G0_7 + 0.00634920634920634*G0_8 + 0.0126984126984127*G0_9;
3811
3812
// Array of quadrature weights
3813
static const double W27[27] = {0.00877047492965105, 0.00816265076654668, 0.0016716811314837, 0.0100061425721761, 0.00931268237947044, 0.00190720341498178, 0.00304787709051818, 0.00283664869563092, 0.000580935315837384, 0.0140327598874417, 0.0130602412264747, 0.00267468981037392, 0.0160098281154818, 0.0149002918071527, 0.00305152546397085, 0.0048766033448291, 0.00453863791300947, 0.000929496505339815, 0.00877047492965105, 0.00816265076654668, 0.0016716811314837, 0.0100061425721761, 0.00931268237947044, 0.00190720341498178, 0.00304787709051818, 0.00283664869563092, 0.000580935315837384};
3814
// Quadrature points on the UFC reference element: (0.0952198798417149, 0.0821215678634425, 0.0729940240731498), (0.0670742417520586, 0.0578476039361427, 0.347003766038352), (0.0303014811742758, 0.0261332522867349, 0.705002209888498), (0.0616960186091465, 0.379578230280591, 0.0729940240731498), (0.0434595556538024, 0.267380320411884, 0.347003766038352), (0.0196333029354845, 0.120791820133903, 0.705002209888498), (0.0221843026408197, 0.730165028047632, 0.0729940240731498), (0.0156269392579017, 0.514338662174092, 0.347003766038352), (0.00705963113955477, 0.232357800579865, 0.705002209888498), (0.422442204031704, 0.0821215678634425, 0.0729940240731498), (0.297574315012753, 0.0578476039361427, 0.347003766038352), (0.134432268912383, 0.0261332522867349, 0.705002209888498), (0.27371387282313, 0.379578230280591, 0.0729940240731498), (0.192807956774882, 0.267380320411884, 0.347003766038352), (0.0871029849887995, 0.120791820133903, 0.705002209888498), (0.0984204739396093, 0.730165028047632, 0.0729940240731498), (0.0693287858937781, 0.514338662174092, 0.347003766038352), (0.0313199947658185, 0.232357800579865, 0.705002209888498), (0.749664528221693, 0.0821215678634425, 0.0729940240731498), (0.528074388273447, 0.0578476039361427, 0.347003766038352), (0.238563056650491, 0.0261332522867349, 0.705002209888498), (0.485731727037113, 0.379578230280591, 0.0729940240731498), (0.342156357895961, 0.267380320411884, 0.347003766038352), (0.154572667042115, 0.120791820133903, 0.705002209888498), (0.174656645238399, 0.730165028047632, 0.0729940240731498), (0.123030632529655, 0.514338662174092, 0.347003766038352), (0.0555803583920821, 0.232357800579865, 0.705002209888498)
3815
3816
// Value of basis functions at quadrature points.
3817
static const double FE0[27][10] = \
3818
{{0.374329281526014, -0.0770862288075737, -0.0686336640467425, -0.0623377689723666, 0.0239775348061957, 0.0278019288056343, 0.031278423297481, 0.218884122479203, 0.246254505716693, 0.285531865195462},
3819
{0.0296507308273033, -0.0580763339388314, -0.051154913373837, -0.106180538748753, 0.080293345688546, 0.0931000579685248, 0.0155203366847607, 0.73297520591714, 0.122191352246653, 0.141680756728494},
3820
{-0.12473839265364, -0.0284651216515658, -0.0247673585365706, 0.289054022006834, 0.073696002454887, 0.0854504447630366, 0.00316750500875638, 0.672749928545405, 0.0249377141829676, 0.0289152558798901},
3821
{-0.0138611057361999, -0.0540832211847061, -0.0914189644747004, -0.0623377689723666, 0.11082776991498, 0.0180137626702941, 0.0936738622360728, 0.141822053505759, 0.737492757359529, 0.119870854681338},
3822
{-0.108014411398703, -0.0396820896985505, -0.12439584892476, -0.106180538748753, 0.37112791258986, 0.0603225179288912, 0.0464809196626873, 0.474918179055459, 0.365943506420742, 0.0594798531131275},
3823
{-0.10678724824909, -0.0188623697671714, -0.0916104925113804, 0.289054022006834, 0.340634000523421, 0.0553660878277077, 0.00948616958726985, 0.435896287412199, 0.0746844551798748, 0.0121390879903345},
3824
{-0.113646757786535, -0.0212000160735007, 0.336116908319966, -0.0623377689723666, 0.213190734538724, 0.00647728608404015, 0.0647928078398051, 0.050995565468269, 0.510112697076803, 0.0154985435047957},
3825
{-0.0927575594483608, -0.0151385367967613, 0.0147498566399773, -0.106180538748753, 0.71390981117415, 0.0216904270965778, 0.0321501561271397, 0.170768371303483, 0.253117643766939, 0.00769036888560855},
3826
{-0.0494020059140976, -0.0069599543559016, -0.12437750559924, 0.289054022006834, 0.655251051574542, 0.0199082222175352, 0.00656144145796827, 0.156737101971251, 0.0516581193256993, 0.00156950731540946},
3827
{-0.0655273725373765, -0.0655273725373763, -0.0686336640467425, -0.0623377689723666, 0.0239775348061957, 0.123343025642419, 0.138766464507087, 0.123343025642418, 0.138766464507087, 0.713829662988655},
3828
{-0.120473369102135, -0.120473369102135, -0.051154913373837, -0.106180538748753, 0.080293345688546, 0.413037631942832, 0.0688558444657068, 0.413037631942832, 0.0688558444657067, 0.354201891821236},
3829
{-0.0982881990625207, -0.0982881990625206, -0.0247673585365706, 0.289054022006834, 0.073696002454887, 0.379100186654221, 0.014052609595862, 0.379100186654221, 0.014052609595862, 0.0722881396997254},
3830
{-0.123875304471457, -0.123875304471457, -0.0914189644747004, -0.0623377689723666, 0.11082776991498, 0.0799179080880264, 0.415583309797801, 0.0799179080880263, 0.415583309797801, 0.299677136703346},
3831
{-0.118458140383472, -0.118458140383472, -0.12439584892476, -0.106180538748753, 0.37112791258986, 0.267620348492175, 0.206212213041715, 0.267620348492175, 0.206212213041715, 0.148699632782819},
3832
{-0.0719291250008815, -0.0719291250008814, -0.0916104925113804, 0.289054022006834, 0.340634000523421, 0.245631187619954, 0.0420853123835723, 0.245631187619954, 0.0420853123835723, 0.0303477199758362},
3833
{-0.0790472945586147, -0.0790472945586147, 0.336116908319966, -0.0623377689723666, 0.213190734538724, 0.0287364257761546, 0.287452752458304, 0.0287364257761545, 0.287452752458304, 0.0387463587619893},
3834
{-0.0597158247867675, -0.0597158247867675, 0.0147498566399773, -0.106180538748753, 0.71390981117415, 0.0962293992000304, 0.14263389994704, 0.0962293992000302, 0.142633899947039, 0.0192259222140213},
3835
{-0.0293581106215567, -0.0293581106215567, -0.12437750559924, 0.289054022006834, 0.655251051574542, 0.088322662094393, 0.0291097803918338, 0.088322662094393, 0.0291097803918338, 0.00392376828852362},
3836
{-0.0770862288075737, 0.374329281526014, -0.0686336640467425, -0.0623377689723666, 0.0239775348061957, 0.218884122479203, 0.246254505716693, 0.0278019288056342, 0.031278423297481, 0.285531865195462},
3837
{-0.0580763339388313, 0.0296507308273035, -0.051154913373837, -0.106180538748753, 0.080293345688546, 0.73297520591714, 0.122191352246653, 0.0931000579685245, 0.0155203366847607, 0.141680756728494},
3838
{-0.0284651216515658, -0.12473839265364, -0.0247673585365706, 0.289054022006834, 0.073696002454887, 0.672749928545405, 0.0249377141829676, 0.0854504447630365, 0.00316750500875635, 0.0289152558798901},
3839
{-0.0540832211847061, -0.0138611057361997, -0.0914189644747004, -0.0623377689723666, 0.11082776991498, 0.141822053505759, 0.737492757359529, 0.018013762670294, 0.0936738622360726, 0.119870854681338},
3840
{-0.0396820896985505, -0.108014411398703, -0.12439584892476, -0.106180538748753, 0.37112791258986, 0.474918179055459, 0.365943506420742, 0.060322517928891, 0.0464809196626872, 0.0594798531131274},
3841
{-0.0188623697671715, -0.10678724824909, -0.0916104925113804, 0.289054022006834, 0.340634000523421, 0.435896287412199, 0.0746844551798748, 0.0553660878277076, 0.00948616958726982, 0.0121390879903345},
3842
{-0.0212000160735008, -0.113646757786535, 0.336116908319966, -0.0623377689723666, 0.213190734538724, 0.0509955654682691, 0.510112697076803, 0.00647728608404003, 0.064792807839805, 0.0154985435047956},
3843
{-0.0151385367967614, -0.0927575594483608, 0.0147498566399773, -0.106180538748753, 0.71390981117415, 0.170768371303483, 0.25311764376694, 0.0216904270965776, 0.0321501561271396, 0.00769036888560852},
3844
{-0.00695995435590172, -0.0494020059140975, -0.12437750559924, 0.289054022006834, 0.655251051574542, 0.156737101971251, 0.0516581193256993, 0.0199082222175353, 0.00656144145796829, 0.00156950731540947}};
3845
3846
3847
// Compute element tensor using UFL quadrature representation
3848
// Optimisations: ('simplify expressions', True), ('ignore zero tables', True), ('non zero columns', True), ('remove zero terms', True), ('ignore ones', True)
3849
// Total number of operations to compute element tensor: 1134
3850
3851
// Loop quadrature points for integral
3852
// Number of operations to compute element tensor for following IP loop = 1134
3853
for (unsigned int ip = 0; ip < 27; ip++)
3854
{
3855
3856
// Function declarations
3857
double F0 = 0;
3858
3859
// Total number of operations to compute function values = 20
3860
for (unsigned int r = 0; r < 10; r++)
3861
{
3862
F0 += FE0[ip][r]*w[0][r];
3863
}// end loop over 'r'
3864
3865
// Number of operations to compute ip constants: 2
3866
// Number of operations: 2
3867
const double Gip0 = F0*W27[ip]*det;
3868
3869
3870
// Number of operations for primary indices = 20
3871
for (unsigned int j = 0; j < 10; j++)
3872
{
3873
// Number of operations to compute entry = 2
3874
A[j] += FE0[ip][j]*Gip0;
3875
}// end loop over 'j'
3876
}// end loop over 'ip'
3877
}
3878
3879
};
3880
3881
/// This class defines the interface for the tabulation of the cell
3882
/// tensor corresponding to the local contribution to a form from
3883
/// the integral over a cell.
3884
3885
class projection_1_cell_integral_0: public ufc::cell_integral
3886
{
3887
private:
3888
3889
projection_1_cell_integral_0_quadrature integral_0_quadrature;
3890
3891
public:
3892
3893
/// Constructor
3894
projection_1_cell_integral_0() : ufc::cell_integral()
3895
{
3896
// Do nothing
3897
}
3898
3899
/// Destructor
3900
virtual ~projection_1_cell_integral_0()
3901
{
3902
// Do nothing
3903
}
3904
3905
/// Tabulate the tensor for the contribution from a local cell
3906
virtual void tabulate_tensor(double* A,
3907
const double * const * w,
3908
const ufc::cell& c) const
3909
{
3910
// Reset values of the element tensor block
3911
for (unsigned int j = 0; j < 10; j++)
3912
A[j] = 0;
3913
3914
// Add all contributions to element tensor
3915
integral_0_quadrature.tabulate_tensor(A, w, c);
3833
3916
}
3834
3917
3835
3918
};
3849
3932
/// sequence of basis functions of Vj and w1, w2, ..., wn are given
3850
3933
/// fixed functions (coefficients).
3851
3934
3852
class UFC_ProjectionLinearForm: public ufc::form
3935
class projection_form_1: public ufc::form
3853
3936
{
3854
3937
public:
3855
3938
3856
3939
/// Constructor
3857
UFC_ProjectionLinearForm() : ufc::form()
3940
projection_form_1() : ufc::form()
3858
3941
{
3859
3942
// Do nothing
3860
3943
}
3861
3944
3862
3945
/// Destructor
3863
virtual ~UFC_ProjectionLinearForm()
3946
virtual ~projection_form_1()
3864
3947
{
3865
3948
// Do nothing
3866
3949
}
3868
3951
/// Return a string identifying the form
3869
3952
virtual const char* signature() const
3870
3953
{
3871
return "w0_a0[0, 1, 2, 3, 4, 5, 6, 7, 8, 9] | vi0[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]*va0[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]*dX(0)";
3954
return "Form([Integral(Product(BasisFunction(FiniteElement('Lagrange', Cell('tetrahedron', 1, Space(3)), 2), 0), Function(FiniteElement('Lagrange', Cell('tetrahedron', 1, Space(3)), 2), 0)), Measure('cell', 0, None))])";
3872
3955
}
3873
3956
3874
3957
/// Return the rank of the global tensor (r)
3888
3971
{
3889
3972
return 1;
3890
3973
}
3891
3974
3892
3975
/// Return the number of exterior facet integrals
3893
3976
virtual unsigned int num_exterior_facet_integrals() const
3894
3977
{
3895
3978
return 0;
3896
3979
}
3897
3980
3898
3981
/// Return the number of interior facet integrals
3899
3982
virtual unsigned int num_interior_facet_integrals() const
3900
3983
{
3901
3984
return 0;
3902
3985
}
3903
3986
3904
3987
/// Create a new finite element for argument function i
3905
3988
virtual ufc::finite_element* create_finite_element(unsigned int i) const
3906
3989
{
3907
3990
switch ( i )
3908
3991
{
3909
3992
case 0:
3910
return new UFC_ProjectionLinearForm_finite_element_0();
3993
return new projection_1_finite_element_0();
3911
3994
break;
3912
3995
case 1:
3913
return new UFC_ProjectionLinearForm_finite_element_1();
3996
return new projection_1_finite_element_1();
3914
3997
break;
3915
3998
}
3916
3999
return 0;
3917
4000
}
3918
4001
3919
4002
/// Create a new dof map for argument function i
3920
4003
virtual ufc::dof_map* create_dof_map(unsigned int i) const
3921
4004
{
3922
4005
switch ( i )
3923
4006
{
3924
4007
case 0:
3925
return new UFC_ProjectionLinearForm_dof_map_0();
4008
return new projection_1_dof_map_0();
3926
4009
break;
3927
4010
case 1:
3928
return new UFC_ProjectionLinearForm_dof_map_1();
4011
return new projection_1_dof_map_1();
3929
4012
break;
3930
4013
}
3931
4014
return 0;
3934
4017
/// Create a new cell integral on sub domain i
3935
4018
virtual ufc::cell_integral* create_cell_integral(unsigned int i) const
3936
4019
{
3937
return new UFC_ProjectionLinearForm_cell_integral_0();
4020
return new projection_1_cell_integral_0();
3938
4021
}
3939
4022
3940
4023
/// Create a new exterior facet integral on sub domain i
3953
4036
3954
4037
// DOLFIN wrappers
3955
4038
3956
#include <dolfin/fem/Form.h>
4039
// Standard library includes
4040
#include <string>
4041
4042
// DOLFIN includes
4043
#include <dolfin/common/NoDeleter.h>
3957
4044
#include <dolfin/fem/FiniteElement.h>
3958
4045
#include <dolfin/fem/DofMap.h>
3959
#include <dolfin/function/Coefficient.h>
3960
#include <dolfin/function/Function.h>
4046
#include <dolfin/fem/Form.h>
3961
4047
#include <dolfin/function/FunctionSpace.h>
3962
3963
class ProjectionBilinearFormFunctionSpace0 : public dolfin::FunctionSpace
3964
{
3965
public:
3966
3967
ProjectionBilinearFormFunctionSpace0(const dolfin::Mesh& mesh)
3968
: dolfin::FunctionSpace(boost::shared_ptr<const dolfin::Mesh>(&mesh, dolfin::NoDeleter<const dolfin::Mesh>()),
3969
boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new UFC_ProjectionLinearForm_finite_element_1()))),
3970
boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dof_map>(new UFC_ProjectionLinearForm_dof_map_1()), mesh)))
3971
{
3972
// Do nothing
3973
}
3974
3975
};
3976
3977
class ProjectionBilinearFormFunctionSpace1 : public dolfin::FunctionSpace
3978
{
3979
public:
3980
3981
ProjectionBilinearFormFunctionSpace1(const dolfin::Mesh& mesh)
3982
: dolfin::FunctionSpace(boost::shared_ptr<const dolfin::Mesh>(&mesh, dolfin::NoDeleter<const dolfin::Mesh>()),
3983
boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new UFC_ProjectionLinearForm_finite_element_1()))),
3984
boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dof_map>(new UFC_ProjectionLinearForm_dof_map_1()), mesh)))
3985
{
3986
// Do nothing
3987
}
3988
3989
};
3990
3991
class ProjectionLinearFormFunctionSpace0 : public dolfin::FunctionSpace
3992
{
3993
public:
3994
3995
ProjectionLinearFormFunctionSpace0(const dolfin::Mesh& mesh)
3996
: dolfin::FunctionSpace(boost::shared_ptr<const dolfin::Mesh>(&mesh, dolfin::NoDeleter<const dolfin::Mesh>()),
3997
boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new UFC_ProjectionLinearForm_finite_element_1()))),
3998
boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dof_map>(new UFC_ProjectionLinearForm_dof_map_1()), mesh)))
3999
{
4000
// Do nothing
4001
}
4002
4003
};
4004
4005
class ProjectionLinearFormCoefficientSpace0 : public dolfin::FunctionSpace
4006
{
4007
public:
4008
4009
ProjectionLinearFormCoefficientSpace0(const dolfin::Mesh& mesh)
4010
: dolfin::FunctionSpace(boost::shared_ptr<const dolfin::Mesh>(&mesh, dolfin::NoDeleter<const dolfin::Mesh>()),
4011
boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new UFC_ProjectionLinearForm_finite_element_1()))),
4012
boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dof_map>(new UFC_ProjectionLinearForm_dof_map_1()), mesh)))
4013
{
4014
// Do nothing
4015
}
4016
4017
};
4018
4019
class ProjectionTestSpace : public dolfin::FunctionSpace
4020
{
4021
public:
4022
4023
ProjectionTestSpace(const dolfin::Mesh& mesh)
4024
: dolfin::FunctionSpace(boost::shared_ptr<const dolfin::Mesh>(&mesh, dolfin::NoDeleter<const dolfin::Mesh>()),
4025
boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new UFC_ProjectionLinearForm_finite_element_1()))),
4026
boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dof_map>(new UFC_ProjectionLinearForm_dof_map_1()), mesh)))
4027
{
4028
// Do nothing
4029
}
4030
4031
};
4032
4033
class ProjectionTrialSpace : public dolfin::FunctionSpace
4034
{
4035
public:
4036
4037
ProjectionTrialSpace(const dolfin::Mesh& mesh)
4038
: dolfin::FunctionSpace(boost::shared_ptr<const dolfin::Mesh>(&mesh, dolfin::NoDeleter<const dolfin::Mesh>()),
4039
boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new UFC_ProjectionLinearForm_finite_element_1()))),
4040
boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dof_map>(new UFC_ProjectionLinearForm_dof_map_1()), mesh)))
4041
{
4042
// Do nothing
4043
}
4044
4045
};
4046
4047
class ProjectionCoefficientSpace : public dolfin::FunctionSpace
4048
{
4049
public:
4050
4051
ProjectionCoefficientSpace(const dolfin::Mesh& mesh)
4052
: dolfin::FunctionSpace(boost::shared_ptr<const dolfin::Mesh>(&mesh, dolfin::NoDeleter<const dolfin::Mesh>()),
4053
boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new UFC_ProjectionLinearForm_finite_element_1()))),
4054
boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dof_map>(new UFC_ProjectionLinearForm_dof_map_1()), mesh)))
4055
{
4056
// Do nothing
4057
}
4058
4059
};
4060
4061
class ProjectionFunctionSpace : public dolfin::FunctionSpace
4062
{
4063
public:
4064
4065
ProjectionFunctionSpace(const dolfin::Mesh& mesh)
4066
: dolfin::FunctionSpace(boost::shared_ptr<const dolfin::Mesh>(&mesh, dolfin::NoDeleter<const dolfin::Mesh>()),
4067
boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new UFC_ProjectionLinearForm_finite_element_1()))),
4068
boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dof_map>(new UFC_ProjectionLinearForm_dof_map_1()), mesh)))
4069
{
4070
// Do nothing
4071
}
4072
4073
};
4074
4075
class ProjectionBilinearForm : public dolfin::Form
4076
{
4077
public:
4078
4079
// Create form on given function space(s)
4080
ProjectionBilinearForm(const dolfin::FunctionSpace& V0, const dolfin::FunctionSpace& V1) : dolfin::Form()
4081
{
4082
boost::shared_ptr<const dolfin::FunctionSpace> _V0(&V0, dolfin::NoDeleter<const dolfin::FunctionSpace>());
4083
_function_spaces.push_back(_V0);
4084
boost::shared_ptr<const dolfin::FunctionSpace> _V1(&V1, dolfin::NoDeleter<const dolfin::FunctionSpace>());
4085
_function_spaces.push_back(_V1);
4086
4087
_ufc_form = boost::shared_ptr<const ufc::form>(new UFC_ProjectionBilinearForm());
4088
}
4089
4090
// Create form on given function space(s) (shared data)
4091
ProjectionBilinearForm(boost::shared_ptr<const dolfin::FunctionSpace> V0, boost::shared_ptr<const dolfin::FunctionSpace> V1) : dolfin::Form()
4092
{
4093
_function_spaces.push_back(V0);
4094
_function_spaces.push_back(V1);
4095
4096
_ufc_form = boost::shared_ptr<const ufc::form>(new UFC_ProjectionBilinearForm());
4097
}
4098
4099
// Destructor
4100
~ProjectionBilinearForm() {}
4101
4102
};
4103
4104
class ProjectionLinearFormCoefficient0 : public dolfin::Coefficient
4105
{
4106
public:
4107
4108
// Constructor
4109
ProjectionLinearFormCoefficient0(dolfin::Form& form) : dolfin::Coefficient(form) {}
4110
4111
// Destructor
4112
~ProjectionLinearFormCoefficient0() {}
4113
4114
// Attach function to coefficient
4115
const ProjectionLinearFormCoefficient0& operator= (dolfin::Function& v)
4116
{
4117
attach(v);
4118
return *this;
4119
}
4120
4121
/// Create function space for coefficient
4122
const dolfin::FunctionSpace* create_function_space() const
4123
{
4124
return new ProjectionLinearFormCoefficientSpace0(form.mesh());
4125
}
4126
4127
/// Return coefficient number
4128
dolfin::uint number() const
4129
{
4130
return 0;
4131
}
4132
4133
/// Return coefficient name
4134
virtual std::string name() const
4135
{
4136
return "f";
4137
}
4138
4139
};
4140
class ProjectionLinearForm : public dolfin::Form
4141
{
4142
public:
4143
4144
// Create form on given function space(s)
4145
ProjectionLinearForm(const dolfin::FunctionSpace& V0) : dolfin::Form(), f(*this)
4146
{
4147
boost::shared_ptr<const dolfin::FunctionSpace> _V0(&V0, dolfin::NoDeleter<const dolfin::FunctionSpace>());
4148
_function_spaces.push_back(_V0);
4149
4150
_coefficients.push_back(boost::shared_ptr<const dolfin::Function>(static_cast<const dolfin::Function*>(0)));
4151
4152
_ufc_form = boost::shared_ptr<const ufc::form>(new UFC_ProjectionLinearForm());
4153
}
4154
4155
// Create form on given function space(s) (shared data)
4156
ProjectionLinearForm(boost::shared_ptr<const dolfin::FunctionSpace> V0) : dolfin::Form(), f(*this)
4157
{
4158
_function_spaces.push_back(V0);
4159
4160
_coefficients.push_back(boost::shared_ptr<const dolfin::Function>(static_cast<const dolfin::Function*>(0)));
4161
4162
_ufc_form = boost::shared_ptr<const ufc::form>(new UFC_ProjectionLinearForm());
4163
}
4164
4165
// Create form on given function space(s) with given coefficient(s)
4166
ProjectionLinearForm(const dolfin::FunctionSpace& V0, dolfin::Function& w0) : dolfin::Form(), f(*this)
4167
{
4168
boost::shared_ptr<const dolfin::FunctionSpace> _V0(&V0, dolfin::NoDeleter<const dolfin::FunctionSpace>());
4169
_function_spaces.push_back(_V0);
4170
4171
_coefficients.push_back(boost::shared_ptr<const dolfin::Function>(static_cast<const dolfin::Function*>(0)));
4172
4173
this->f = w0;
4174
4175
_ufc_form = boost::shared_ptr<const ufc::form>(new UFC_ProjectionLinearForm());
4176
}
4177
4178
// Create form on given function space(s) with given coefficient(s) (shared data)
4179
ProjectionLinearForm(boost::shared_ptr<const dolfin::FunctionSpace> V0, dolfin::Function& w0) : dolfin::Form(), f(*this)
4180
{
4181
_function_spaces.push_back(V0);
4182
4183
_coefficients.push_back(boost::shared_ptr<const dolfin::Function>(static_cast<const dolfin::Function*>(0)));
4184
4185
this->f = w0;
4186
4187
_ufc_form = boost::shared_ptr<const ufc::form>(new UFC_ProjectionLinearForm());
4188
}
4189
4190
// Destructor
4191
~ProjectionLinearForm() {}
4192
4193
// Coefficients
4194
ProjectionLinearFormCoefficient0 f;
4195
4196
};
4048
#include <dolfin/function/GenericFunction.h>
4049
#include <dolfin/function/CoefficientAssigner.h>
4050
4051
namespace Projection
4052
{
4053
4054
class CoefficientSpace_f: public dolfin::FunctionSpace
4055
{
4056
public:
4057
4058
CoefficientSpace_f(const dolfin::Mesh& mesh):
4059
dolfin::FunctionSpace(dolfin::reference_to_no_delete_pointer(mesh),
4060
boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new projection_1_finite_element_1()))),
4061
boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dof_map>(new projection_1_dof_map_1()), dolfin::reference_to_no_delete_pointer(mesh))))
4062
{
4063
// Do nothing
4064
}
4065
4066
CoefficientSpace_f(dolfin::Mesh& mesh):
4067
dolfin::FunctionSpace(dolfin::reference_to_no_delete_pointer(mesh),
4068
boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new projection_1_finite_element_1()))),
4069
boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dof_map>(new projection_1_dof_map_1()), dolfin::reference_to_no_delete_pointer(mesh))))
4070
{
4071
// Do nothing
4072
}
4073
4074
CoefficientSpace_f(boost::shared_ptr<dolfin::Mesh> mesh):
4075
dolfin::FunctionSpace(mesh,
4076
boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new projection_1_finite_element_1()))),
4077
boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dof_map>(new projection_1_dof_map_1()), mesh)))
4078
{
4079
// Do nothing
4080
}
4081
4082
CoefficientSpace_f(boost::shared_ptr<const dolfin::Mesh> mesh):
4083
dolfin::FunctionSpace(mesh,
4084
boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new projection_1_finite_element_1()))),
4085
boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dof_map>(new projection_1_dof_map_1()), mesh)))
4086
{
4087
// Do nothing
4088
}
4089
4090
4091
~CoefficientSpace_f()
4092
{
4093
}
4094
4095
};
4096
4097
class Form_0_FunctionSpace_0: public dolfin::FunctionSpace
4098
{
4099
public:
4100
4101
Form_0_FunctionSpace_0(const dolfin::Mesh& mesh):
4102
dolfin::FunctionSpace(dolfin::reference_to_no_delete_pointer(mesh),
4103
boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new projection_0_finite_element_0()))),
4104
boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dof_map>(new projection_0_dof_map_0()), dolfin::reference_to_no_delete_pointer(mesh))))
4105
{
4106
// Do nothing
4107
}
4108
4109
Form_0_FunctionSpace_0(dolfin::Mesh& mesh):
4110
dolfin::FunctionSpace(dolfin::reference_to_no_delete_pointer(mesh),
4111
boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new projection_0_finite_element_0()))),
4112
boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dof_map>(new projection_0_dof_map_0()), dolfin::reference_to_no_delete_pointer(mesh))))
4113
{
4114
// Do nothing
4115
}
4116
4117
Form_0_FunctionSpace_0(boost::shared_ptr<dolfin::Mesh> mesh):
4118
dolfin::FunctionSpace(mesh,
4119
boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new projection_0_finite_element_0()))),
4120
boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dof_map>(new projection_0_dof_map_0()), mesh)))
4121
{
4122
// Do nothing
4123
}
4124
4125
Form_0_FunctionSpace_0(boost::shared_ptr<const dolfin::Mesh> mesh):
4126
dolfin::FunctionSpace(mesh,
4127
boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new projection_0_finite_element_0()))),
4128
boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dof_map>(new projection_0_dof_map_0()), mesh)))
4129
{
4130
// Do nothing
4131
}
4132
4133
4134
~Form_0_FunctionSpace_0()
4135
{
4136
}
4137
4138
};
4139
4140
class Form_0_FunctionSpace_1: public dolfin::FunctionSpace
4141
{
4142
public:
4143
4144
Form_0_FunctionSpace_1(const dolfin::Mesh& mesh):
4145
dolfin::FunctionSpace(dolfin::reference_to_no_delete_pointer(mesh),
4146
boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new projection_0_finite_element_1()))),
4147
boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dof_map>(new projection_0_dof_map_1()), dolfin::reference_to_no_delete_pointer(mesh))))
4148
{
4149
// Do nothing
4150
}
4151
4152
Form_0_FunctionSpace_1(dolfin::Mesh& mesh):
4153
dolfin::FunctionSpace(dolfin::reference_to_no_delete_pointer(mesh),
4154
boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new projection_0_finite_element_1()))),
4155
boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dof_map>(new projection_0_dof_map_1()), dolfin::reference_to_no_delete_pointer(mesh))))
4156
{
4157
// Do nothing
4158
}
4159
4160
Form_0_FunctionSpace_1(boost::shared_ptr<dolfin::Mesh> mesh):
4161
dolfin::FunctionSpace(mesh,
4162
boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new projection_0_finite_element_1()))),
4163
boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dof_map>(new projection_0_dof_map_1()), mesh)))
4164
{
4165
// Do nothing
4166
}
4167
4168
Form_0_FunctionSpace_1(boost::shared_ptr<const dolfin::Mesh> mesh):
4169
dolfin::FunctionSpace(mesh,
4170
boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new projection_0_finite_element_1()))),
4171
boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dof_map>(new projection_0_dof_map_1()), mesh)))
4172
{
4173
// Do nothing
4174
}
4175
4176
4177
~Form_0_FunctionSpace_1()
4178
{
4179
}
4180
4181
};
4182
4183
class Form_0: public dolfin::Form
4184
{
4185
public:
4186
4187
// Constructor
4188
Form_0(const dolfin::FunctionSpace& V0, const dolfin::FunctionSpace& V1):
4189
dolfin::Form(2, 0)
4190
{
4191
_function_spaces[0] = reference_to_no_delete_pointer(V0);
4192
_function_spaces[1] = reference_to_no_delete_pointer(V1);
4193
4194
_ufc_form = boost::shared_ptr<const ufc::form>(new projection_form_0());
4195
}
4196
4197
// Constructor
4198
Form_0(boost::shared_ptr<const dolfin::FunctionSpace> V0, boost::shared_ptr<const dolfin::FunctionSpace> V1):
4199
dolfin::Form(2, 0)
4200
{
4201
_function_spaces[0] = V0;
4202
_function_spaces[1] = V1;
4203
4204
_ufc_form = boost::shared_ptr<const ufc::form>(new projection_form_0());
4205
}
4206
4207
// Destructor
4208
~Form_0()
4209
{}
4210
4211
/// Return the number of the coefficient with this name
4212
virtual dolfin::uint coefficient_number(const std::string& name) const
4213
{
4214
4215
dolfin::error("No coefficients.");
4216
return 0;
4217
}
4218
4219
/// Return the name of the coefficient with this number
4220
virtual std::string coefficient_name(dolfin::uint i) const
4221
{
4222
4223
dolfin::error("No coefficients.");
4224
return "unnamed";
4225
}
4226
4227
// Typedefs
4228
typedef Form_0_FunctionSpace_0 TestSpace;
4229
typedef Form_0_FunctionSpace_1 TrialSpace;
4230
4231
// Coefficients
4232
};
4233
4234
class Form_1_FunctionSpace_0: public dolfin::FunctionSpace
4235
{
4236
public:
4237
4238
Form_1_FunctionSpace_0(const dolfin::Mesh& mesh):
4239
dolfin::FunctionSpace(dolfin::reference_to_no_delete_pointer(mesh),
4240
boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new projection_1_finite_element_0()))),
4241
boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dof_map>(new projection_1_dof_map_0()), dolfin::reference_to_no_delete_pointer(mesh))))
4242
{
4243
// Do nothing
4244
}
4245
4246
Form_1_FunctionSpace_0(dolfin::Mesh& mesh):
4247
dolfin::FunctionSpace(dolfin::reference_to_no_delete_pointer(mesh),
4248
boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new projection_1_finite_element_0()))),
4249
boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dof_map>(new projection_1_dof_map_0()), dolfin::reference_to_no_delete_pointer(mesh))))
4250
{
4251
// Do nothing
4252
}
4253
4254
Form_1_FunctionSpace_0(boost::shared_ptr<dolfin::Mesh> mesh):
4255
dolfin::FunctionSpace(mesh,
4256
boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new projection_1_finite_element_0()))),
4257
boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dof_map>(new projection_1_dof_map_0()), mesh)))
4258
{
4259
// Do nothing
4260
}
4261
4262
Form_1_FunctionSpace_0(boost::shared_ptr<const dolfin::Mesh> mesh):
4263
dolfin::FunctionSpace(mesh,
4264
boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new projection_1_finite_element_0()))),
4265
boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dof_map>(new projection_1_dof_map_0()), mesh)))
4266
{
4267
// Do nothing
4268
}
4269
4270
4271
~Form_1_FunctionSpace_0()
4272
{
4273
}
4274
4275
};
4276
4277
typedef CoefficientSpace_f Form_1_FunctionSpace_1;
4278
4279
class Form_1: public dolfin::Form
4280
{
4281
public:
4282
4283
// Constructor
4284
Form_1(const dolfin::FunctionSpace& V0):
4285
dolfin::Form(1, 1), f(*this, 0)
4286
{
4287
_function_spaces[0] = reference_to_no_delete_pointer(V0);
4288
4289
_ufc_form = boost::shared_ptr<const ufc::form>(new projection_form_1());
4290
}
4291
4292
// Constructor
4293
Form_1(const dolfin::FunctionSpace& V0, const dolfin::GenericFunction& f):
4294
dolfin::Form(1, 1), f(*this, 0)
4295
{
4296
_function_spaces[0] = reference_to_no_delete_pointer(V0);
4297
4298
this->f = f;
4299
4300
_ufc_form = boost::shared_ptr<const ufc::form>(new projection_form_1());
4301
}
4302
4303
// Constructor
4304
Form_1(const dolfin::FunctionSpace& V0, boost::shared_ptr<const dolfin::GenericFunction> f):
4305
dolfin::Form(1, 1), f(*this, 0)
4306
{
4307
_function_spaces[0] = reference_to_no_delete_pointer(V0);
4308
4309
this->f = *f;
4310
4311
_ufc_form = boost::shared_ptr<const ufc::form>(new projection_form_1());
4312
}
4313
4314
// Constructor
4315
Form_1(boost::shared_ptr<const dolfin::FunctionSpace> V0):
4316
dolfin::Form(1, 1), f(*this, 0)
4317
{
4318
_function_spaces[0] = V0;
4319
4320
_ufc_form = boost::shared_ptr<const ufc::form>(new projection_form_1());
4321
}
4322
4323
// Constructor
4324
Form_1(boost::shared_ptr<const dolfin::FunctionSpace> V0, const dolfin::GenericFunction& f):
4325
dolfin::Form(1, 1), f(*this, 0)
4326
{
4327
_function_spaces[0] = V0;
4328
4329
this->f = f;
4330
4331
_ufc_form = boost::shared_ptr<const ufc::form>(new projection_form_1());
4332
}
4333
4334
// Constructor
4335
Form_1(boost::shared_ptr<const dolfin::FunctionSpace> V0, boost::shared_ptr<const dolfin::GenericFunction> f):
4336
dolfin::Form(1, 1), f(*this, 0)
4337
{
4338
_function_spaces[0] = V0;
4339
4340
this->f = *f;
4341
4342
_ufc_form = boost::shared_ptr<const ufc::form>(new projection_form_1());
4343
}
4344
4345
// Destructor
4346
~Form_1()
4347
{}
4348
4349
/// Return the number of the coefficient with this name
4350
virtual dolfin::uint coefficient_number(const std::string& name) const
4351
{
4352
if (name == "f")
4353
return 0;
4354
4355
dolfin::error("Invalid coefficient.");
4356
return 0;
4357
}
4358
4359
/// Return the name of the coefficient with this number
4360
virtual std::string coefficient_name(dolfin::uint i) const
4361
{
4362
switch (i)
4363
{
4364
case 0:
4365
return "f";
4366
}
4367
4368
dolfin::error("Invalid coefficient.");
4369
return "unnamed";
4370
}
4371
4372
// Typedefs
4373
typedef Form_1_FunctionSpace_0 TestSpace;
4374
typedef Form_1_FunctionSpace_1 CoefficientSpace_f;
4375
4376
// Coefficients
4377
dolfin::CoefficientAssigner f;
4378
};
4379
4380
// Class typedefs
4381
typedef Form_0 BilinearForm;
4382
typedef Form_1 LinearForm;
4383
typedef Form_0::TestSpace FunctionSpace;
4384
4385
} // namespace Projection
4197
4386
4198
4387
#endif
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