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- Committer: Bazaar Package Importer
- Author(s): Johannes Ring
- Date: 2010-02-03 20:22:35 UTC
- mfrom: (1.1.2 upstream)
- Revision ID: james.westby@ubuntu.com-20100203202235-fe8d0kajuvgy2sqn
Tags: 0.9.0-1
* New upstream release.
* debian/control: Bump Standards-Version (no changes needed).
* Update debian/copyright and debian/copyright_hints.
* debian/control: Bump Standards-Version (no changes needed).
* Update debian/copyright and debian/copyright_hints.
- files added:
- demo/VectorPoisson.ufl
- ffc/quadrature
- ffc/tensor
- test/evaluate_basis
- test/evaluate_basis_derivatives
- test/regression/references
- test/unit/evaluate_basis
- test/unit/misc
- test/unit/symbolics
- files removed:
- ffc/common
- ffc/compiler
- ffc/compiler/quadrature
- ffc/compiler/tensor
- ffc/fem
- ffc/jit
- test/benchmarks
- test/regression/reference
- test/regression/reference/quadrature
- test/regression/reference/tensor
- test/simple_verify_tensors
- test/verify_tensors
- test/verify_tensors/references
- test/verify_tensors/test_cache
- files modified:
- AUTHORS
added
removed
test/regression/references/SubDomains.h
1
// This code conforms with the UFC specification version 1.4
2
// and was automatically generated by FFC version 0.9.0.
3
4
#ifndef __SUBDOMAINS_H
5
#define __SUBDOMAINS_H
6
7
#include <cmath>
8
#include <stdexcept>
9
#include <fstream>
10
#include <ufc.h>
11
12
/// This class defines the interface for a finite element.
13
14
class subdomains_finite_element_0: public ufc::finite_element
15
{
16
public:
17
18
/// Constructor
19
subdomains_finite_element_0() : ufc::finite_element()
20
{
21
// Do nothing
22
}
23
24
/// Destructor
25
virtual ~subdomains_finite_element_0()
26
{
27
// Do nothing
28
}
29
30
/// Return a string identifying the finite element
31
virtual const char* signature() const
32
{
33
return "FiniteElement('Lagrange', Cell('tetrahedron', 1, Space(3)), 1)";
34
}
35
36
/// Return the cell shape
37
virtual ufc::shape cell_shape() const
38
{
39
return ufc::tetrahedron;
40
}
41
42
/// Return the dimension of the finite element function space
43
virtual unsigned int space_dimension() const
44
{
45
return 4;
46
}
47
48
/// Return the rank of the value space
49
virtual unsigned int value_rank() const
50
{
51
return 0;
52
}
53
54
/// Return the dimension of the value space for axis i
55
virtual unsigned int value_dimension(unsigned int i) const
56
{
57
return 1;
58
}
59
60
/// Evaluate basis function i at given point in cell
61
virtual void evaluate_basis(unsigned int i,
62
double* values,
63
const double* coordinates,
64
const ufc::cell& c) const
65
{
66
// Extract vertex coordinates
67
const double * const * x = c.coordinates;
68
69
// Compute Jacobian of affine map from reference cell
70
const double J_00 = x[1][0] - x[0][0];
71
const double J_01 = x[2][0] - x[0][0];
72
const double J_02 = x[3][0] - x[0][0];
73
const double J_10 = x[1][1] - x[0][1];
74
const double J_11 = x[2][1] - x[0][1];
75
const double J_12 = x[3][1] - x[0][1];
76
const double J_20 = x[1][2] - x[0][2];
77
const double J_21 = x[2][2] - x[0][2];
78
const double J_22 = x[3][2] - x[0][2];
79
80
// Compute sub determinants
81
const double d_00 = J_11*J_22 - J_12*J_21;
82
const double d_01 = J_12*J_20 - J_10*J_22;
83
const double d_02 = J_10*J_21 - J_11*J_20;
84
const double d_10 = J_02*J_21 - J_01*J_22;
85
const double d_11 = J_00*J_22 - J_02*J_20;
86
const double d_12 = J_01*J_20 - J_00*J_21;
87
const double d_20 = J_01*J_12 - J_02*J_11;
88
const double d_21 = J_02*J_10 - J_00*J_12;
89
const double d_22 = J_00*J_11 - J_01*J_10;
90
91
// Compute determinant of Jacobian
92
double detJ = J_00*d_00 + J_10*d_10 + J_20*d_20;
93
94
// Compute inverse of Jacobian
95
96
// Compute constants
97
const double C0 = x[3][0] + x[2][0] + x[1][0] - x[0][0];
98
const double C1 = x[3][1] + x[2][1] + x[1][1] - x[0][1];
99
const double C2 = x[3][2] + x[2][2] + x[1][2] - x[0][2];
100
101
// Get coordinates and map to the reference (FIAT) element
102
double X = (d_00*(2.0*coordinates[0] - C0) + d_10*(2.0*coordinates[1] - C1) + d_20*(2.0*coordinates[2] - C2)) / detJ;
103
double Y = (d_01*(2.0*coordinates[0] - C0) + d_11*(2.0*coordinates[1] - C1) + d_21*(2.0*coordinates[2] - C2)) / detJ;
104
double Z = (d_02*(2.0*coordinates[0] - C0) + d_12*(2.0*coordinates[1] - C1) + d_22*(2.0*coordinates[2] - C2)) / detJ;
105
106
107
// Reset values
108
*values = 0.00000000;
109
110
// Map degree of freedom to element degree of freedom
111
const unsigned int dof = i;
112
113
// Array of basisvalues
114
double basisvalues[4] = {0.00000000, 0.00000000, 0.00000000, 0.00000000};
115
116
// Declare helper variables
117
unsigned int rr = 0;
118
unsigned int ss = 0;
119
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
120
121
// Compute basisvalues
122
basisvalues[0] = 1.00000000;
123
basisvalues[1] = tmp0;
124
for (unsigned int r = 0; r < 1; r++)
125
{
126
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
127
ss = r*(r + 1)*(r + 2)/6;
128
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
129
}// end loop over 'r'
130
for (unsigned int r = 0; r < 1; r++)
131
{
132
for (unsigned int s = 0; s < 1 - r; s++)
133
{
134
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
135
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
136
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
137
}// end loop over 's'
138
}// end loop over 'r'
139
for (unsigned int r = 0; r < 2; r++)
140
{
141
for (unsigned int s = 0; s < 2 - r; s++)
142
{
143
for (unsigned int t = 0; t < 2 - r - s; t++)
144
{
145
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
146
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
147
}// end loop over 't'
148
}// end loop over 's'
149
}// end loop over 'r'
150
151
// Table(s) of coefficients
152
static const double coefficients0[4][4] = \
153
{{0.28867513, -0.18257419, -0.10540926, -0.07453560},
154
{0.28867513, 0.18257419, -0.10540926, -0.07453560},
155
{0.28867513, 0.00000000, 0.21081851, -0.07453560},
156
{0.28867513, 0.00000000, 0.00000000, 0.22360680}};
157
158
// Compute value(s).
159
for (unsigned int r = 0; r < 4; r++)
160
{
161
*values += coefficients0[dof][r]*basisvalues[r];
162
}// end loop over 'r'
163
}
164
165
/// Evaluate all basis functions at given point in cell
166
virtual void evaluate_basis_all(double* values,
167
const double* coordinates,
168
const ufc::cell& c) const
169
{
170
// Helper variable to hold values of a single dof.
171
double dof_values = 0.00000000;
172
173
// Loop dofs and call evaluate_basis.
174
for (unsigned int r = 0; r < 4; r++)
175
{
176
evaluate_basis(r, &dof_values, coordinates, c);
177
values[r] = dof_values;
178
}// end loop over 'r'
179
}
180
181
/// Evaluate order n derivatives of basis function i at given point in cell
182
virtual void evaluate_basis_derivatives(unsigned int i,
183
unsigned int n,
184
double* values,
185
const double* coordinates,
186
const ufc::cell& c) const
187
{
188
// Extract vertex coordinates
189
const double * const * x = c.coordinates;
190
191
// Compute Jacobian of affine map from reference cell
192
const double J_00 = x[1][0] - x[0][0];
193
const double J_01 = x[2][0] - x[0][0];
194
const double J_02 = x[3][0] - x[0][0];
195
const double J_10 = x[1][1] - x[0][1];
196
const double J_11 = x[2][1] - x[0][1];
197
const double J_12 = x[3][1] - x[0][1];
198
const double J_20 = x[1][2] - x[0][2];
199
const double J_21 = x[2][2] - x[0][2];
200
const double J_22 = x[3][2] - x[0][2];
201
202
// Compute sub determinants
203
const double d_00 = J_11*J_22 - J_12*J_21;
204
const double d_01 = J_12*J_20 - J_10*J_22;
205
const double d_02 = J_10*J_21 - J_11*J_20;
206
const double d_10 = J_02*J_21 - J_01*J_22;
207
const double d_11 = J_00*J_22 - J_02*J_20;
208
const double d_12 = J_01*J_20 - J_00*J_21;
209
const double d_20 = J_01*J_12 - J_02*J_11;
210
const double d_21 = J_02*J_10 - J_00*J_12;
211
const double d_22 = J_00*J_11 - J_01*J_10;
212
213
// Compute determinant of Jacobian
214
double detJ = J_00*d_00 + J_10*d_10 + J_20*d_20;
215
216
// Compute inverse of Jacobian
217
const double K_00 = d_00 / detJ;
218
const double K_01 = d_10 / detJ;
219
const double K_02 = d_20 / detJ;
220
const double K_10 = d_01 / detJ;
221
const double K_11 = d_11 / detJ;
222
const double K_12 = d_21 / detJ;
223
const double K_20 = d_02 / detJ;
224
const double K_21 = d_12 / detJ;
225
const double K_22 = d_22 / detJ;
226
227
// Compute constants
228
const double C0 = x[3][0] + x[2][0] + x[1][0] - x[0][0];
229
const double C1 = x[3][1] + x[2][1] + x[1][1] - x[0][1];
230
const double C2 = x[3][2] + x[2][2] + x[1][2] - x[0][2];
231
232
// Get coordinates and map to the reference (FIAT) element
233
double X = (d_00*(2.0*coordinates[0] - C0) + d_10*(2.0*coordinates[1] - C1) + d_20*(2.0*coordinates[2] - C2)) / detJ;
234
double Y = (d_01*(2.0*coordinates[0] - C0) + d_11*(2.0*coordinates[1] - C1) + d_21*(2.0*coordinates[2] - C2)) / detJ;
235
double Z = (d_02*(2.0*coordinates[0] - C0) + d_12*(2.0*coordinates[1] - C1) + d_22*(2.0*coordinates[2] - C2)) / detJ;
236
237
238
// Compute number of derivatives.
239
unsigned int num_derivatives = 1;
240
241
for (unsigned int r = 0; r < n; r++)
242
{
243
num_derivatives *= 3;
244
}// end loop over 'r'
245
246
// Declare pointer to two dimensional array that holds combinations of derivatives and initialise
247
unsigned int **combinations = new unsigned int *[num_derivatives];
248
for (unsigned int row = 0; row < num_derivatives; row++)
249
{
250
combinations[row] = new unsigned int [n];
251
for (unsigned int col = 0; col < n; col++)
252
combinations[row][col] = 0;
253
}
254
255
// Generate combinations of derivatives
256
for (unsigned int row = 1; row < num_derivatives; row++)
257
{
258
for (unsigned int num = 0; num < row; num++)
259
{
260
for (unsigned int col = n-1; col+1 > 0; col--)
261
{
262
if (combinations[row][col] + 1 > 2)
263
combinations[row][col] = 0;
264
else
265
{
266
combinations[row][col] += 1;
267
break;
268
}
269
}
270
}
271
}
272
273
// Compute inverse of Jacobian
274
const double Jinv[3][3] = {{K_00, K_01, K_02}, {K_10, K_11, K_12}, {K_20, K_21, K_22}};
275
276
// Declare transformation matrix
277
// Declare pointer to two dimensional array and initialise
278
double **transform = new double *[num_derivatives];
279
280
for (unsigned int j = 0; j < num_derivatives; j++)
281
{
282
transform[j] = new double [num_derivatives];
283
for (unsigned int k = 0; k < num_derivatives; k++)
284
transform[j][k] = 1;
285
}
286
287
// Construct transformation matrix
288
for (unsigned int row = 0; row < num_derivatives; row++)
289
{
290
for (unsigned int col = 0; col < num_derivatives; col++)
291
{
292
for (unsigned int k = 0; k < n; k++)
293
transform[row][col] *= Jinv[combinations[col][k]][combinations[row][k]];
294
}
295
}
296
297
// Reset values. Assuming that values is always an array.
298
for (unsigned int r = 0; r < num_derivatives; r++)
299
{
300
values[r] = 0.00000000;
301
}// end loop over 'r'
302
303
// Map degree of freedom to element degree of freedom
304
const unsigned int dof = i;
305
306
// Array of basisvalues
307
double basisvalues[4] = {0.00000000, 0.00000000, 0.00000000, 0.00000000};
308
309
// Declare helper variables
310
unsigned int rr = 0;
311
unsigned int ss = 0;
312
double tmp0 = 0.50000000*(2.00000000 + Y + Z + 2.00000000*X);
313
314
// Compute basisvalues
315
basisvalues[0] = 1.00000000;
316
basisvalues[1] = tmp0;
317
for (unsigned int r = 0; r < 1; r++)
318
{
319
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
320
ss = r*(r + 1)*(r + 2)/6;
321
basisvalues[rr] = basisvalues[ss]*(r*(1.00000000 + Y) + (2.00000000 + Z + 3.00000000*Y)/2.00000000);
322
}// end loop over 'r'
323
for (unsigned int r = 0; r < 1; r++)
324
{
325
for (unsigned int s = 0; s < 1 - r; s++)
326
{
327
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
328
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
329
basisvalues[rr] = basisvalues[ss]*(1.00000000 + r + s + Z*(2.00000000 + r + s));
330
}// end loop over 's'
331
}// end loop over 'r'
332
for (unsigned int r = 0; r < 2; r++)
333
{
334
for (unsigned int s = 0; s < 2 - r; s++)
335
{
336
for (unsigned int t = 0; t < 2 - r - s; t++)
337
{
338
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
339
basisvalues[rr] *= std::sqrt((0.50000000 + r)*(1.00000000 + r + s)*(1.50000000 + r + s + t));
340
}// end loop over 't'
341
}// end loop over 's'
342
}// end loop over 'r'
343
344
// Table(s) of coefficients
345
static const double coefficients0[4][4] = \
346
{{0.28867513, -0.18257419, -0.10540926, -0.07453560},
347
{0.28867513, 0.18257419, -0.10540926, -0.07453560},
348
{0.28867513, 0.00000000, 0.21081851, -0.07453560},
349
{0.28867513, 0.00000000, 0.00000000, 0.22360680}};
350
351
// Tables of derivatives of the polynomial base (transpose).
352
static const double dmats0[4][4] = \
353
{{0.00000000, 0.00000000, 0.00000000, 0.00000000},
354
{6.32455532, 0.00000000, 0.00000000, 0.00000000},
355
{0.00000000, 0.00000000, 0.00000000, 0.00000000},
356
{0.00000000, 0.00000000, 0.00000000, 0.00000000}};
357
358
static const double dmats1[4][4] = \
359
{{0.00000000, 0.00000000, 0.00000000, 0.00000000},
360
{3.16227766, 0.00000000, 0.00000000, 0.00000000},
361
{5.47722558, 0.00000000, 0.00000000, 0.00000000},
362
{0.00000000, 0.00000000, 0.00000000, 0.00000000}};
363
364
static const double dmats2[4][4] = \
365
{{0.00000000, 0.00000000, 0.00000000, 0.00000000},
366
{3.16227766, 0.00000000, 0.00000000, 0.00000000},
367
{1.82574186, 0.00000000, 0.00000000, 0.00000000},
368
{5.16397779, 0.00000000, 0.00000000, 0.00000000}};
369
370
// Compute reference derivatives
371
// Declare pointer to array of derivatives on FIAT element
372
double *derivatives = new double [num_derivatives];
373
for (unsigned int r = 0; r < num_derivatives; r++)
374
{
375
derivatives[r] = 0.00000000;
376
}// end loop over 'r'
377
378
// Declare derivative matrix (of polynomial basis).
379
double dmats[4][4] = \
380
{{1.00000000, 0.00000000, 0.00000000, 0.00000000},
381
{0.00000000, 1.00000000, 0.00000000, 0.00000000},
382
{0.00000000, 0.00000000, 1.00000000, 0.00000000},
383
{0.00000000, 0.00000000, 0.00000000, 1.00000000}};
384
385
// Declare (auxiliary) derivative matrix (of polynomial basis).
386
double dmats_old[4][4] = \
387
{{1.00000000, 0.00000000, 0.00000000, 0.00000000},
388
{0.00000000, 1.00000000, 0.00000000, 0.00000000},
389
{0.00000000, 0.00000000, 1.00000000, 0.00000000},
390
{0.00000000, 0.00000000, 0.00000000, 1.00000000}};
391
392
// Loop possible derivatives.
393
for (unsigned int r = 0; r < num_derivatives; r++)
394
{
395
// Resetting dmats values to compute next derivative.
396
for (unsigned int t = 0; t < 4; t++)
397
{
398
for (unsigned int u = 0; u < 4; u++)
399
{
400
dmats[t][u] = 0.00000000;
401
if (t == u)
402
{
403
dmats[t][u] = 1.00000000;
404
}
405
406
}// end loop over 'u'
407
}// end loop over 't'
408
409
// Looping derivative order to generate dmats.
410
for (unsigned int s = 0; s < n; s++)
411
{
412
// Updating dmats_old with new values and resetting dmats.
413
for (unsigned int t = 0; t < 4; t++)
414
{
415
for (unsigned int u = 0; u < 4; u++)
416
{
417
dmats_old[t][u] = dmats[t][u];
418
dmats[t][u] = 0.00000000;
419
}// end loop over 'u'
420
}// end loop over 't'
421
422
// Update dmats using an inner product.
423
if (combinations[r][s] == 0)
424
{
425
for (unsigned int t = 0; t < 4; t++)
426
{
427
for (unsigned int u = 0; u < 4; u++)
428
{
429
for (unsigned int tu = 0; tu < 4; tu++)
430
{
431
dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
432
}// end loop over 'tu'
433
}// end loop over 'u'
434
}// end loop over 't'
435
}
436
437
if (combinations[r][s] == 1)
438
{
439
for (unsigned int t = 0; t < 4; t++)
440
{
441
for (unsigned int u = 0; u < 4; u++)
442
{
443
for (unsigned int tu = 0; tu < 4; tu++)
444
{
445
dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
446
}// end loop over 'tu'
447
}// end loop over 'u'
448
}// end loop over 't'
449
}
450
451
if (combinations[r][s] == 2)
452
{
453
for (unsigned int t = 0; t < 4; t++)
454
{
455
for (unsigned int u = 0; u < 4; u++)
456
{
457
for (unsigned int tu = 0; tu < 4; tu++)
458
{
459
dmats[t][u] += dmats2[t][tu]*dmats_old[tu][u];
460
}// end loop over 'tu'
461
}// end loop over 'u'
462
}// end loop over 't'
463
}
464
465
}// end loop over 's'
466
for (unsigned int s = 0; s < 4; s++)
467
{
468
for (unsigned int t = 0; t < 4; t++)
469
{
470
derivatives[r] += coefficients0[dof][s]*dmats[s][t]*basisvalues[t];
471
}// end loop over 't'
472
}// end loop over 's'
473
}// end loop over 'r'
474
475
// Transform derivatives back to physical element
476
for (unsigned int row = 0; row < num_derivatives; row++)
477
{
478
for (unsigned int col = 0; col < num_derivatives; col++)
479
{
480
values[row] += transform[row][col]*derivatives[col];
481
}
482
}
483
484
// Delete pointer to array of derivatives on FIAT element
485
delete [] derivatives;
486
487
// Delete pointer to array of combinations of derivatives and transform
488
for (unsigned int r = 0; r < num_derivatives; r++)
489
{
490
delete [] combinations[r];
491
delete [] transform[r];
492
}// end loop over 'r'
493
delete [] combinations;
494
delete [] transform;
495
}
496
497
/// Evaluate order n derivatives of all basis functions at given point in cell
498
virtual void evaluate_basis_derivatives_all(unsigned int n,
499
double* values,
500
const double* coordinates,
501
const ufc::cell& c) const
502
{
503
// Compute number of derivatives.
504
unsigned int num_derivatives = 1;
505
506
for (unsigned int r = 0; r < n; r++)
507
{
508
num_derivatives *= 3;
509
}// end loop over 'r'
510
511
// Helper variable to hold values of a single dof.
512
double *dof_values = new double [num_derivatives];
513
for (unsigned int r = 0; r < num_derivatives; r++)
514
{
515
dof_values[r] = 0.00000000;
516
}// end loop over 'r'
517
518
// Loop dofs and call evaluate_basis_derivatives.
519
for (unsigned int r = 0; r < 4; r++)
520
{
521
evaluate_basis_derivatives(r, n, dof_values, coordinates, c);
522
for (unsigned int s = 0; s < num_derivatives; s++)
523
{
524
values[r*num_derivatives + s] = dof_values[s];
525
}// end loop over 's'
526
}// end loop over 'r'
527
528
// Delete pointer.
529
delete [] dof_values;
530
}
531
532
/// Evaluate linear functional for dof i on the function f
533
virtual double evaluate_dof(unsigned int i,
534
const ufc::function& f,
535
const ufc::cell& c) const
536
{
537
// Declare variables for result of evaluation
538
double vals[1];
539
540
// Declare variable for physical coordinates
541
double y[3];
542
543
const double * const * x = c.coordinates;
544
switch (i)
545
{
546
case 0:
547
{
548
y[0] = x[0][0];
549
y[1] = x[0][1];
550
y[2] = x[0][2];
551
f.evaluate(vals, y, c);
552
return vals[0];
553
break;
554
}
555
case 1:
556
{
557
y[0] = x[1][0];
558
y[1] = x[1][1];
559
y[2] = x[1][2];
560
f.evaluate(vals, y, c);
561
return vals[0];
562
break;
563
}
564
case 2:
565
{
566
y[0] = x[2][0];
567
y[1] = x[2][1];
568
y[2] = x[2][2];
569
f.evaluate(vals, y, c);
570
return vals[0];
571
break;
572
}
573
case 3:
574
{
575
y[0] = x[3][0];
576
y[1] = x[3][1];
577
y[2] = x[3][2];
578
f.evaluate(vals, y, c);
579
return vals[0];
580
break;
581
}
582
}
583
584
return 0.0;
585
}
586
587
/// Evaluate linear functionals for all dofs on the function f
588
virtual void evaluate_dofs(double* values,
589
const ufc::function& f,
590
const ufc::cell& c) const
591
{
592
// Declare variables for result of evaluation
593
double vals[1];
594
595
// Declare variable for physical coordinates
596
double y[3];
597
598
const double * const * x = c.coordinates;
599
y[0] = x[0][0];
600
y[1] = x[0][1];
601
y[2] = x[0][2];
602
f.evaluate(vals, y, c);
603
values[0] = vals[0];
604
y[0] = x[1][0];
605
y[1] = x[1][1];
606
y[2] = x[1][2];
607
f.evaluate(vals, y, c);
608
values[1] = vals[0];
609
y[0] = x[2][0];
610
y[1] = x[2][1];
611
y[2] = x[2][2];
612
f.evaluate(vals, y, c);
613
values[2] = vals[0];
614
y[0] = x[3][0];
615
y[1] = x[3][1];
616
y[2] = x[3][2];
617
f.evaluate(vals, y, c);
618
values[3] = vals[0];
619
}
620
621
/// Interpolate vertex values from dof values
622
virtual void interpolate_vertex_values(double* vertex_values,
623
const double* dof_values,
624
const ufc::cell& c) const
625
{
626
// Evaluate function and change variables
627
vertex_values[0] = dof_values[0];
628
vertex_values[1] = dof_values[1];
629
vertex_values[2] = dof_values[2];
630
vertex_values[3] = dof_values[3];
631
}
632
633
/// Return the number of sub elements (for a mixed element)
634
virtual unsigned int num_sub_elements() const
635
{
636
return 0;
637
}
638
639
/// Create a new finite element for sub element i (for a mixed element)
640
virtual ufc::finite_element* create_sub_element(unsigned int i) const
641
{
642
return 0;
643
}
644
645
};
646
647
/// This class defines the interface for a local-to-global mapping of
648
/// degrees of freedom (dofs).
649
650
class subdomains_dof_map_0: public ufc::dof_map
651
{
652
private:
653
654
unsigned int _global_dimension;
655
656
public:
657
658
/// Constructor
659
subdomains_dof_map_0() : ufc::dof_map()
660
{
661
_global_dimension = 0;
662
}
663
664
/// Destructor
665
virtual ~subdomains_dof_map_0()
666
{
667
// Do nothing
668
}
669
670
/// Return a string identifying the dof map
671
virtual const char* signature() const
672
{
673
return "FFC dofmap for FiniteElement('Lagrange', Cell('tetrahedron', 1, Space(3)), 1)";
674
}
675
676
/// Return true iff mesh entities of topological dimension d are needed
677
virtual bool needs_mesh_entities(unsigned int d) const
678
{
679
switch (d)
680
{
681
case 0:
682
{
683
return true;
684
break;
685
}
686
case 1:
687
{
688
return false;
689
break;
690
}
691
case 2:
692
{
693
return false;
694
break;
695
}
696
case 3:
697
{
698
return false;
699
break;
700
}
701
}
702
703
return false;
704
}
705
706
/// Initialize dof map for mesh (return true iff init_cell() is needed)
707
virtual bool init_mesh(const ufc::mesh& m)
708
{
709
_global_dimension = m.num_entities[0];
710
return false;
711
}
712
713
/// Initialize dof map for given cell
714
virtual void init_cell(const ufc::mesh& m,
715
const ufc::cell& c)
716
{
717
// Do nothing
718
}
719
720
/// Finish initialization of dof map for cells
721
virtual void init_cell_finalize()
722
{
723
// Do nothing
724
}
725
726
/// Return the dimension of the global finite element function space
727
virtual unsigned int global_dimension() const
728
{
729
return _global_dimension;
730
}
731
732
/// Return the dimension of the local finite element function space for a cell
733
virtual unsigned int local_dimension(const ufc::cell& c) const
734
{
735
return 4;
736
}
737
738
/// Return the maximum dimension of the local finite element function space
739
virtual unsigned int max_local_dimension() const
740
{
741
return 4;
742
}
743
744
// Return the geometric dimension of the coordinates this dof map provides
745
virtual unsigned int geometric_dimension() const
746
{
747
return 3;
748
}
749
750
/// Return the number of dofs on each cell facet
751
virtual unsigned int num_facet_dofs() const
752
{
753
return 3;
754
}
755
756
/// Return the number of dofs associated with each cell entity of dimension d
757
virtual unsigned int num_entity_dofs(unsigned int d) const
758
{
759
switch (d)
760
{
761
case 0:
762
{
763
return 1;
764
break;
765
}
766
case 1:
767
{
768
return 0;
769
break;
770
}
771
case 2:
772
{
773
return 0;
774
break;
775
}
776
case 3:
777
{
778
return 0;
779
break;
780
}
781
}
782
783
return 0;
784
}
785
786
/// Tabulate the local-to-global mapping of dofs on a cell
787
virtual void tabulate_dofs(unsigned int* dofs,
788
const ufc::mesh& m,
789
const ufc::cell& c) const
790
{
791
dofs[0] = c.entity_indices[0][0];
792
dofs[1] = c.entity_indices[0][1];
793
dofs[2] = c.entity_indices[0][2];
794
dofs[3] = c.entity_indices[0][3];
795
}
796
797
/// Tabulate the local-to-local mapping from facet dofs to cell dofs
798
virtual void tabulate_facet_dofs(unsigned int* dofs,
799
unsigned int facet) const
800
{
801
switch (facet)
802
{
803
case 0:
804
{
805
dofs[0] = 1;
806
dofs[1] = 2;
807
dofs[2] = 3;
808
break;
809
}
810
case 1:
811
{
812
dofs[0] = 0;
813
dofs[1] = 2;
814
dofs[2] = 3;
815
break;
816
}
817
case 2:
818
{
819
dofs[0] = 0;
820
dofs[1] = 1;
821
dofs[2] = 3;
822
break;
823
}
824
case 3:
825
{
826
dofs[0] = 0;
827
dofs[1] = 1;
828
dofs[2] = 2;
829
break;
830
}
831
}
832
833
}
834
835
/// Tabulate the local-to-local mapping of dofs on entity (d, i)
836
virtual void tabulate_entity_dofs(unsigned int* dofs,
837
unsigned int d, unsigned int i) const
838
{
839
if (d > 3)
840
{
841
std::cerr << "*** FFC warning: " << "d is larger than dimension (3)" << std::endl;
842
}
843
844
switch (d)
845
{
846
case 0:
847
{
848
if (i > 3)
849
{
850
std::cerr << "*** FFC warning: " << "i is larger than number of entities (3)" << std::endl;
851
}
852
853
switch (i)
854
{
855
case 0:
856
{
857
dofs[0] = 0;
858
break;
859
}
860
case 1:
861
{
862
dofs[0] = 1;
863
break;
864
}
865
case 2:
866
{
867
dofs[0] = 2;
868
break;
869
}
870
case 3:
871
{
872
dofs[0] = 3;
873
break;
874
}
875
}
876
877
break;
878
}
879
case 1:
880
{
881
882
break;
883
}
884
case 2:
885
{
886
887
break;
888
}
889
case 3:
890
{
891
892
break;
893
}
894
}
895
896
}
897
898
/// Tabulate the coordinates of all dofs on a cell
899
virtual void tabulate_coordinates(double** coordinates,
900
const ufc::cell& c) const
901
{
902
const double * const * x = c.coordinates;
903
904
coordinates[0][0] = x[0][0];
905
coordinates[0][1] = x[0][1];
906
coordinates[0][2] = x[0][2];
907
coordinates[1][0] = x[1][0];
908
coordinates[1][1] = x[1][1];
909
coordinates[1][2] = x[1][2];
910
coordinates[2][0] = x[2][0];
911
coordinates[2][1] = x[2][1];
912
coordinates[2][2] = x[2][2];
913
coordinates[3][0] = x[3][0];
914
coordinates[3][1] = x[3][1];
915
coordinates[3][2] = x[3][2];
916
}
917
918
/// Return the number of sub dof maps (for a mixed element)
919
virtual unsigned int num_sub_dof_maps() const
920
{
921
return 0;
922
}
923
924
/// Create a new dof_map for sub dof map i (for a mixed element)
925
virtual ufc::dof_map* create_sub_dof_map(unsigned int i) const
926
{
927
return 0;
928
}
929
930
};
931
932
/// This class defines the interface for the tabulation of the cell
933
/// tensor corresponding to the local contribution to a form from
934
/// the integral over a cell.
935
936
class subdomains_cell_integral_0_0: public ufc::cell_integral
937
{
938
public:
939
940
/// Constructor
941
subdomains_cell_integral_0_0() : ufc::cell_integral()
942
{
943
// Do nothing
944
}
945
946
/// Destructor
947
virtual ~subdomains_cell_integral_0_0()
948
{
949
// Do nothing
950
}
951
952
/// Tabulate the tensor for the contribution from a local cell
953
virtual void tabulate_tensor(double* A,
954
const double * const * w,
955
const ufc::cell& c) const
956
{
957
// Number of operations (multiply-add pairs) for Jacobian data: 32
958
// Number of operations (multiply-add pairs) for geometry tensor: 0
959
// Number of operations (multiply-add pairs) for tensor contraction: 8
960
// Total number of operations (multiply-add pairs): 40
961
962
// Extract vertex coordinates
963
const double * const * x = c.coordinates;
964
965
// Compute Jacobian of affine map from reference cell
966
const double J_00 = x[1][0] - x[0][0];
967
const double J_01 = x[2][0] - x[0][0];
968
const double J_02 = x[3][0] - x[0][0];
969
const double J_10 = x[1][1] - x[0][1];
970
const double J_11 = x[2][1] - x[0][1];
971
const double J_12 = x[3][1] - x[0][1];
972
const double J_20 = x[1][2] - x[0][2];
973
const double J_21 = x[2][2] - x[0][2];
974
const double J_22 = x[3][2] - x[0][2];
975
976
// Compute sub determinants
977
const double d_00 = J_11*J_22 - J_12*J_21;
978
const double d_10 = J_02*J_21 - J_01*J_22;
979
const double d_20 = J_01*J_12 - J_02*J_11;
980
981
// Compute determinant of Jacobian
982
double detJ = J_00*d_00 + J_10*d_10 + J_20*d_20;
983
984
// Compute inverse of Jacobian
985
986
// Set scale factor
987
const double det = std::abs(detJ);
988
989
// Compute geometry tensor
990
const double G0_ = det;
991
992
// Compute element tensor
993
A[0] = 0.01666667*G0_;
994
A[1] = 0.00833333*G0_;
995
A[2] = 0.00833333*G0_;
996
A[3] = 0.00833333*G0_;
997
A[4] = 0.00833333*G0_;
998
A[5] = 0.01666667*G0_;
999
A[6] = 0.00833333*G0_;
1000
A[7] = 0.00833333*G0_;
1001
A[8] = 0.00833333*G0_;
1002
A[9] = 0.00833333*G0_;
1003
A[10] = 0.01666667*G0_;
1004
A[11] = 0.00833333*G0_;
1005
A[12] = 0.00833333*G0_;
1006
A[13] = 0.00833333*G0_;
1007
A[14] = 0.00833333*G0_;
1008
A[15] = 0.01666667*G0_;
1009
}
1010
1011
};
1012
1013
/// This class defines the interface for the tabulation of the cell
1014
/// tensor corresponding to the local contribution to a form from
1015
/// the integral over a cell.
1016
1017
class subdomains_cell_integral_0_1: public ufc::cell_integral
1018
{
1019
public:
1020
1021
/// Constructor
1022
subdomains_cell_integral_0_1() : ufc::cell_integral()
1023
{
1024
// Do nothing
1025
}
1026
1027
/// Destructor
1028
virtual ~subdomains_cell_integral_0_1()
1029
{
1030
// Do nothing
1031
}
1032
1033
/// Tabulate the tensor for the contribution from a local cell
1034
virtual void tabulate_tensor(double* A,
1035
const double * const * w,
1036
const ufc::cell& c) const
1037
{
1038
// Number of operations (multiply-add pairs) for Jacobian data: 32
1039
// Number of operations (multiply-add pairs) for geometry tensor: 0
1040
// Number of operations (multiply-add pairs) for tensor contraction: 8
1041
// Total number of operations (multiply-add pairs): 40
1042
1043
// Extract vertex coordinates
1044
const double * const * x = c.coordinates;
1045
1046
// Compute Jacobian of affine map from reference cell
1047
const double J_00 = x[1][0] - x[0][0];
1048
const double J_01 = x[2][0] - x[0][0];
1049
const double J_02 = x[3][0] - x[0][0];
1050
const double J_10 = x[1][1] - x[0][1];
1051
const double J_11 = x[2][1] - x[0][1];
1052
const double J_12 = x[3][1] - x[0][1];
1053
const double J_20 = x[1][2] - x[0][2];
1054
const double J_21 = x[2][2] - x[0][2];
1055
const double J_22 = x[3][2] - x[0][2];
1056
1057
// Compute sub determinants
1058
const double d_00 = J_11*J_22 - J_12*J_21;
1059
const double d_10 = J_02*J_21 - J_01*J_22;
1060
const double d_20 = J_01*J_12 - J_02*J_11;
1061
1062
// Compute determinant of Jacobian
1063
double detJ = J_00*d_00 + J_10*d_10 + J_20*d_20;
1064
1065
// Compute inverse of Jacobian
1066
1067
// Set scale factor
1068
const double det = std::abs(detJ);
1069
1070
// Compute geometry tensor
1071
const double G0_ = det;
1072
1073
// Compute element tensor
1074
A[0] = 0.16666667*G0_;
1075
A[1] = 0.08333333*G0_;
1076
A[2] = 0.08333333*G0_;
1077
A[3] = 0.08333333*G0_;
1078
A[4] = 0.08333333*G0_;
1079
A[5] = 0.16666667*G0_;
1080
A[6] = 0.08333333*G0_;
1081
A[7] = 0.08333333*G0_;
1082
A[8] = 0.08333333*G0_;
1083
A[9] = 0.08333333*G0_;
1084
A[10] = 0.16666667*G0_;
1085
A[11] = 0.08333333*G0_;
1086
A[12] = 0.08333333*G0_;
1087
A[13] = 0.08333333*G0_;
1088
A[14] = 0.08333333*G0_;
1089
A[15] = 0.16666667*G0_;
1090
}
1091
1092
};
1093
1094
/// This class defines the interface for the tabulation of the
1095
/// exterior facet tensor corresponding to the local contribution to
1096
/// a form from the integral over an exterior facet.
1097
1098
class subdomains_exterior_facet_integral_0_0: public ufc::exterior_facet_integral
1099
{
1100
public:
1101
1102
/// Constructor
1103
subdomains_exterior_facet_integral_0_0() : ufc::exterior_facet_integral()
1104
{
1105
// Do nothing
1106
}
1107
1108
/// Destructor
1109
virtual ~subdomains_exterior_facet_integral_0_0()
1110
{
1111
// Do nothing
1112
}
1113
1114
/// Tabulate the tensor for the contribution from a local exterior facet
1115
virtual void tabulate_tensor(double* A,
1116
const double * const * w,
1117
const ufc::cell& c,
1118
unsigned int facet) const
1119
{
1120
// Number of operations (multiply-add pairs) for Jacobian data: 52
1121
// Number of operations (multiply-add pairs) for geometry tensor: 0
1122
// Number of operations (multiply-add pairs) for tensor contraction: 18
1123
// Total number of operations (multiply-add pairs): 70
1124
1125
// Extract vertex coordinates
1126
const double * const * x = c.coordinates;
1127
1128
// Compute Jacobian of affine map from reference cell
1129
1130
// Compute sub determinants
1131
1132
// Compute determinant of Jacobian
1133
1134
// Compute inverse of Jacobian
1135
1136
// Get vertices on face
1137
static unsigned int face_vertices[4][3] = {{1, 2, 3}, {0, 2, 3}, {0, 1, 3}, {0, 1, 2}};
1138
const unsigned int v0 = face_vertices[facet][0];
1139
const unsigned int v1 = face_vertices[facet][1];
1140
const unsigned int v2 = face_vertices[facet][2];
1141
1142
// Compute scale factor (area of face scaled by area of reference triangle)
1143
const double a0 = (x[v0][1]*x[v1][2]
1144
+ x[v0][2]*x[v2][1]
1145
+ x[v1][1]*x[v2][2])
1146
- (x[v2][1]*x[v1][2]
1147
+ x[v2][2]*x[v0][1]
1148
+ x[v1][1]*x[v0][2]);
1149
1150
const double a1 = (x[v0][2]*x[v1][0]
1151
+ x[v0][0]*x[v2][2]
1152
+ x[v1][2]*x[v2][0])
1153
- (x[v2][2]*x[v1][0]
1154
+ x[v2][0]*x[v0][2]
1155
+ x[v1][2]*x[v0][0]);
1156
1157
const double a2 = (x[v0][0]*x[v1][1]
1158
+ x[v0][1]*x[v2][0]
1159
+ x[v1][0]*x[v2][1])
1160
- (x[v2][0]*x[v1][1]
1161
+ x[v2][1]*x[v0][0]
1162
+ x[v1][0]*x[v0][1]);
1163
1164
const double det = std::sqrt(a0*a0 + a1*a1 + a2*a2);
1165
1166
// Compute geometry tensor
1167
const double G0_ = det;
1168
1169
// Compute element tensor
1170
switch (facet)
1171
{
1172
case 0:
1173
{
1174
A[0] = 0.00000000;
1175
A[1] = 0.00000000;
1176
A[2] = 0.00000000;
1177
A[3] = 0.00000000;
1178
A[4] = 0.00000000;
1179
A[5] = 0.08333333*G0_;
1180
A[6] = 0.04166667*G0_;
1181
A[7] = 0.04166667*G0_;
1182
A[8] = 0.00000000;
1183
A[9] = 0.04166667*G0_;
1184
A[10] = 0.08333333*G0_;
1185
A[11] = 0.04166667*G0_;
1186
A[12] = 0.00000000;
1187
A[13] = 0.04166667*G0_;
1188
A[14] = 0.04166667*G0_;
1189
A[15] = 0.08333333*G0_;
1190
break;
1191
}
1192
case 1:
1193
{
1194
A[0] = 0.08333333*G0_;
1195
A[1] = 0.00000000;
1196
A[2] = 0.04166667*G0_;
1197
A[3] = 0.04166667*G0_;
1198
A[4] = 0.00000000;
1199
A[5] = 0.00000000;
1200
A[6] = 0.00000000;
1201
A[7] = 0.00000000;
1202
A[8] = 0.04166667*G0_;
1203
A[9] = 0.00000000;
1204
A[10] = 0.08333333*G0_;
1205
A[11] = 0.04166667*G0_;
1206
A[12] = 0.04166667*G0_;
1207
A[13] = 0.00000000;
1208
A[14] = 0.04166667*G0_;
1209
A[15] = 0.08333333*G0_;
1210
break;
1211
}
1212
case 2:
1213
{
1214
A[0] = 0.08333333*G0_;
1215
A[1] = 0.04166667*G0_;
1216
A[2] = 0.00000000;
1217
A[3] = 0.04166667*G0_;
1218
A[4] = 0.04166667*G0_;
1219
A[5] = 0.08333333*G0_;
1220
A[6] = 0.00000000;
1221
A[7] = 0.04166667*G0_;
1222
A[8] = 0.00000000;
1223
A[9] = 0.00000000;
1224
A[10] = 0.00000000;
1225
A[11] = 0.00000000;
1226
A[12] = 0.04166667*G0_;
1227
A[13] = 0.04166667*G0_;
1228
A[14] = 0.00000000;
1229
A[15] = 0.08333333*G0_;
1230
break;
1231
}
1232
case 3:
1233
{
1234
A[0] = 0.08333333*G0_;
1235
A[1] = 0.04166667*G0_;
1236
A[2] = 0.04166667*G0_;
1237
A[3] = 0.00000000;
1238
A[4] = 0.04166667*G0_;
1239
A[5] = 0.08333333*G0_;
1240
A[6] = 0.04166667*G0_;
1241
A[7] = 0.00000000;
1242
A[8] = 0.04166667*G0_;
1243
A[9] = 0.04166667*G0_;
1244
A[10] = 0.08333333*G0_;
1245
A[11] = 0.00000000;
1246
A[12] = 0.00000000;
1247
A[13] = 0.00000000;
1248
A[14] = 0.00000000;
1249
A[15] = 0.00000000;
1250
break;
1251
}
1252
}
1253
1254
}
1255
1256
};
1257
1258
/// This class defines the interface for the tabulation of the
1259
/// exterior facet tensor corresponding to the local contribution to
1260
/// a form from the integral over an exterior facet.
1261
1262
class subdomains_exterior_facet_integral_0_1: public ufc::exterior_facet_integral
1263
{
1264
public:
1265
1266
/// Constructor
1267
subdomains_exterior_facet_integral_0_1() : ufc::exterior_facet_integral()
1268
{
1269
// Do nothing
1270
}
1271
1272
/// Destructor
1273
virtual ~subdomains_exterior_facet_integral_0_1()
1274
{
1275
// Do nothing
1276
}
1277
1278
/// Tabulate the tensor for the contribution from a local exterior facet
1279
virtual void tabulate_tensor(double* A,
1280
const double * const * w,
1281
const ufc::cell& c,
1282
unsigned int facet) const
1283
{
1284
// Number of operations (multiply-add pairs) for Jacobian data: 52
1285
// Number of operations (multiply-add pairs) for geometry tensor: 0
1286
// Number of operations (multiply-add pairs) for tensor contraction: 18
1287
// Total number of operations (multiply-add pairs): 70
1288
1289
// Extract vertex coordinates
1290
const double * const * x = c.coordinates;
1291
1292
// Compute Jacobian of affine map from reference cell
1293
1294
// Compute sub determinants
1295
1296
// Compute determinant of Jacobian
1297
1298
// Compute inverse of Jacobian
1299
1300
// Get vertices on face
1301
static unsigned int face_vertices[4][3] = {{1, 2, 3}, {0, 2, 3}, {0, 1, 3}, {0, 1, 2}};
1302
const unsigned int v0 = face_vertices[facet][0];
1303
const unsigned int v1 = face_vertices[facet][1];
1304
const unsigned int v2 = face_vertices[facet][2];
1305
1306
// Compute scale factor (area of face scaled by area of reference triangle)
1307
const double a0 = (x[v0][1]*x[v1][2]
1308
+ x[v0][2]*x[v2][1]
1309
+ x[v1][1]*x[v2][2])
1310
- (x[v2][1]*x[v1][2]
1311
+ x[v2][2]*x[v0][1]
1312
+ x[v1][1]*x[v0][2]);
1313
1314
const double a1 = (x[v0][2]*x[v1][0]
1315
+ x[v0][0]*x[v2][2]
1316
+ x[v1][2]*x[v2][0])
1317
- (x[v2][2]*x[v1][0]
1318
+ x[v2][0]*x[v0][2]
1319
+ x[v1][2]*x[v0][0]);
1320
1321
const double a2 = (x[v0][0]*x[v1][1]
1322
+ x[v0][1]*x[v2][0]
1323
+ x[v1][0]*x[v2][1])
1324
- (x[v2][0]*x[v1][1]
1325
+ x[v2][1]*x[v0][0]
1326
+ x[v1][0]*x[v0][1]);
1327
1328
const double det = std::sqrt(a0*a0 + a1*a1 + a2*a2);
1329
1330
// Compute geometry tensor
1331
const double G0_ = det;
1332
1333
// Compute element tensor
1334
switch (facet)
1335
{
1336
case 0:
1337
{
1338
A[0] = 0.00000000;
1339
A[1] = 0.00000000;
1340
A[2] = 0.00000000;
1341
A[3] = 0.00000000;
1342
A[4] = 0.00000000;
1343
A[5] = 0.16666667*G0_;
1344
A[6] = 0.08333333*G0_;
1345
A[7] = 0.08333333*G0_;
1346
A[8] = 0.00000000;
1347
A[9] = 0.08333333*G0_;
1348
A[10] = 0.16666667*G0_;
1349
A[11] = 0.08333333*G0_;
1350
A[12] = 0.00000000;
1351
A[13] = 0.08333333*G0_;
1352
A[14] = 0.08333333*G0_;
1353
A[15] = 0.16666667*G0_;
1354
break;
1355
}
1356
case 1:
1357
{
1358
A[0] = 0.16666667*G0_;
1359
A[1] = 0.00000000;
1360
A[2] = 0.08333333*G0_;
1361
A[3] = 0.08333333*G0_;
1362
A[4] = 0.00000000;
1363
A[5] = 0.00000000;
1364
A[6] = 0.00000000;
1365
A[7] = 0.00000000;
1366
A[8] = 0.08333333*G0_;
1367
A[9] = 0.00000000;
1368
A[10] = 0.16666667*G0_;
1369
A[11] = 0.08333333*G0_;
1370
A[12] = 0.08333333*G0_;
1371
A[13] = 0.00000000;
1372
A[14] = 0.08333333*G0_;
1373
A[15] = 0.16666667*G0_;
1374
break;
1375
}
1376
case 2:
1377
{
1378
A[0] = 0.16666667*G0_;
1379
A[1] = 0.08333333*G0_;
1380
A[2] = 0.00000000;
1381
A[3] = 0.08333333*G0_;
1382
A[4] = 0.08333333*G0_;
1383
A[5] = 0.16666667*G0_;
1384
A[6] = 0.00000000;
1385
A[7] = 0.08333333*G0_;
1386
A[8] = 0.00000000;
1387
A[9] = 0.00000000;
1388
A[10] = 0.00000000;
1389
A[11] = 0.00000000;
1390
A[12] = 0.08333333*G0_;
1391
A[13] = 0.08333333*G0_;
1392
A[14] = 0.00000000;
1393
A[15] = 0.16666667*G0_;
1394
break;
1395
}
1396
case 3:
1397
{
1398
A[0] = 0.16666667*G0_;
1399
A[1] = 0.08333333*G0_;
1400
A[2] = 0.08333333*G0_;
1401
A[3] = 0.00000000;
1402
A[4] = 0.08333333*G0_;
1403
A[5] = 0.16666667*G0_;
1404
A[6] = 0.08333333*G0_;
1405
A[7] = 0.00000000;
1406
A[8] = 0.08333333*G0_;
1407
A[9] = 0.08333333*G0_;
1408
A[10] = 0.16666667*G0_;
1409
A[11] = 0.00000000;
1410
A[12] = 0.00000000;
1411
A[13] = 0.00000000;
1412
A[14] = 0.00000000;
1413
A[15] = 0.00000000;
1414
break;
1415
}
1416
}
1417
1418
}
1419
1420
};
1421
1422
/// This class defines the interface for the tabulation of the
1423
/// interior facet tensor corresponding to the local contribution to
1424
/// a form from the integral over an interior facet.
1425
1426
class subdomains_interior_facet_integral_0_0: public ufc::interior_facet_integral
1427
{
1428
public:
1429
1430
/// Constructor
1431
subdomains_interior_facet_integral_0_0() : ufc::interior_facet_integral()
1432
{
1433
// Do nothing
1434
}
1435
1436
/// Destructor
1437
virtual ~subdomains_interior_facet_integral_0_0()
1438
{
1439
// Do nothing
1440
}
1441
1442
/// Tabulate the tensor for the contribution from a local interior facet
1443
virtual void tabulate_tensor(double* A,
1444
const double * const * w,
1445
const ufc::cell& c0,
1446
const ufc::cell& c1,
1447
unsigned int facet0,
1448
unsigned int facet1) const
1449
{
1450
// Number of operations (multiply-add pairs) for Jacobian data: 83
1451
// Number of operations (multiply-add pairs) for geometry tensor: 0
1452
// Number of operations (multiply-add pairs) for tensor contraction: 72
1453
// Total number of operations (multiply-add pairs): 155
1454
1455
// Extract vertex coordinates
1456
const double * const * x0 = c0.coordinates;
1457
1458
// Compute Jacobian of affine map from reference cell
1459
1460
// Compute sub determinants
1461
1462
// Compute determinant of Jacobian
1463
1464
// Compute inverse of Jacobian
1465
1466
// Compute Jacobian of affine map from reference cell
1467
1468
// Compute sub determinants
1469
1470
// Compute determinant of Jacobian
1471
1472
// Compute inverse of Jacobian
1473
1474
// Get vertices on face
1475
static unsigned int face_vertices[4][3] = {{1, 2, 3}, {0, 2, 3}, {0, 1, 3}, {0, 1, 2}};
1476
const unsigned int v0 = face_vertices[facet0][0];
1477
const unsigned int v1 = face_vertices[facet0][1];
1478
const unsigned int v2 = face_vertices[facet0][2];
1479
1480
// Compute scale factor (area of face scaled by area of reference triangle)
1481
const double a0 = (x0[v0][1]*x0[v1][2]
1482
+ x0[v0][2]*x0[v2][1]
1483
+ x0[v1][1]*x0[v2][2])
1484
- (x0[v2][1]*x0[v1][2]
1485
+ x0[v2][2]*x0[v0][1]
1486
+ x0[v1][1]*x0[v0][2]);
1487
1488
const double a1 = (x0[v0][2]*x0[v1][0]
1489
+ x0[v0][0]*x0[v2][2]
1490
+ x0[v1][2]*x0[v2][0])
1491
- (x0[v2][2]*x0[v1][0]
1492
+ x0[v2][0]*x0[v0][2]
1493
+ x0[v1][2]*x0[v0][0]);
1494
1495
const double a2 = (x0[v0][0]*x0[v1][1]
1496
+ x0[v0][1]*x0[v2][0]
1497
+ x0[v1][0]*x0[v2][1])
1498
- (x0[v2][0]*x0[v1][1]
1499
+ x0[v2][1]*x0[v0][0]
1500
+ x0[v1][0]*x0[v0][1]);
1501
1502
const double det = std::sqrt(a0*a0 + a1*a1 + a2*a2);
1503
1504
// Compute geometry tensor
1505
const double G0_ = det;
1506
1507
// Compute element tensor
1508
switch (facet0)
1509
{
1510
case 0:
1511
{
1512
switch (facet1)
1513
{
1514
case 0:
1515
{
1516
A[0] = 0.00000000;
1517
A[1] = 0.00000000;
1518
A[2] = 0.00000000;
1519
A[3] = 0.00000000;
1520
A[4] = 0.00000000;
1521
A[5] = 0.00000000;
1522
A[6] = 0.00000000;
1523
A[7] = 0.00000000;
1524
A[8] = 0.00000000;
1525
A[9] = 0.08333333*G0_;
1526
A[10] = 0.04166667*G0_;
1527
A[11] = 0.04166667*G0_;
1528
A[12] = 0.00000000;
1529
A[13] = 0.00000000;
1530
A[14] = 0.00000000;
1531
A[15] = 0.00000000;
1532
A[16] = 0.00000000;
1533
A[17] = 0.04166667*G0_;
1534
A[18] = 0.08333333*G0_;
1535
A[19] = 0.04166667*G0_;
1536
A[20] = 0.00000000;
1537
A[21] = 0.00000000;
1538
A[22] = 0.00000000;
1539
A[23] = 0.00000000;
1540
A[24] = 0.00000000;
1541
A[25] = 0.04166667*G0_;
1542
A[26] = 0.04166667*G0_;
1543
A[27] = 0.08333333*G0_;
1544
A[28] = 0.00000000;
1545
A[29] = 0.00000000;
1546
A[30] = 0.00000000;
1547
A[31] = 0.00000000;
1548
A[32] = 0.00000000;
1549
A[33] = 0.00000000;
1550
A[34] = 0.00000000;
1551
A[35] = 0.00000000;
1552
A[36] = 0.00000000;
1553
A[37] = 0.00000000;
1554
A[38] = 0.00000000;
1555
A[39] = 0.00000000;
1556
A[40] = 0.00000000;
1557
A[41] = 0.00000000;
1558
A[42] = 0.00000000;
1559
A[43] = 0.00000000;
1560
A[44] = 0.00000000;
1561
A[45] = 0.00000000;
1562
A[46] = 0.00000000;
1563
A[47] = 0.00000000;
1564
A[48] = 0.00000000;
1565
A[49] = 0.00000000;
1566
A[50] = 0.00000000;
1567
A[51] = 0.00000000;
1568
A[52] = 0.00000000;
1569
A[53] = 0.00000000;
1570
A[54] = 0.00000000;
1571
A[55] = 0.00000000;
1572
A[56] = 0.00000000;
1573
A[57] = 0.00000000;
1574
A[58] = 0.00000000;
1575
A[59] = 0.00000000;
1576
A[60] = 0.00000000;
1577
A[61] = 0.00000000;
1578
A[62] = 0.00000000;
1579
A[63] = 0.00000000;
1580
break;
1581
}
1582
case 1:
1583
{
1584
A[0] = 0.00000000;
1585
A[1] = 0.00000000;
1586
A[2] = 0.00000000;
1587
A[3] = 0.00000000;
1588
A[4] = 0.00000000;
1589
A[5] = 0.00000000;
1590
A[6] = 0.00000000;
1591
A[7] = 0.00000000;
1592
A[8] = 0.00000000;
1593
A[9] = 0.08333333*G0_;
1594
A[10] = 0.04166667*G0_;
1595
A[11] = 0.04166667*G0_;
1596
A[12] = 0.00000000;
1597
A[13] = 0.00000000;
1598
A[14] = 0.00000000;
1599
A[15] = 0.00000000;
1600
A[16] = 0.00000000;
1601
A[17] = 0.04166667*G0_;
1602
A[18] = 0.08333333*G0_;
1603
A[19] = 0.04166667*G0_;
1604
A[20] = 0.00000000;
1605
A[21] = 0.00000000;
1606
A[22] = 0.00000000;
1607
A[23] = 0.00000000;
1608
A[24] = 0.00000000;
1609
A[25] = 0.04166667*G0_;
1610
A[26] = 0.04166667*G0_;
1611
A[27] = 0.08333333*G0_;
1612
A[28] = 0.00000000;
1613
A[29] = 0.00000000;
1614
A[30] = 0.00000000;
1615
A[31] = 0.00000000;
1616
A[32] = 0.00000000;
1617
A[33] = 0.00000000;
1618
A[34] = 0.00000000;
1619
A[35] = 0.00000000;
1620
A[36] = 0.00000000;
1621
A[37] = 0.00000000;
1622
A[38] = 0.00000000;
1623
A[39] = 0.00000000;
1624
A[40] = 0.00000000;
1625
A[41] = 0.00000000;
1626
A[42] = 0.00000000;
1627
A[43] = 0.00000000;
1628
A[44] = 0.00000000;
1629
A[45] = 0.00000000;
1630
A[46] = 0.00000000;
1631
A[47] = 0.00000000;
1632
A[48] = 0.00000000;
1633
A[49] = 0.00000000;
1634
A[50] = 0.00000000;
1635
A[51] = 0.00000000;
1636
A[52] = 0.00000000;
1637
A[53] = 0.00000000;
1638
A[54] = 0.00000000;
1639
A[55] = 0.00000000;
1640
A[56] = 0.00000000;
1641
A[57] = 0.00000000;
1642
A[58] = 0.00000000;
1643
A[59] = 0.00000000;
1644
A[60] = 0.00000000;
1645
A[61] = 0.00000000;
1646
A[62] = 0.00000000;
1647
A[63] = 0.00000000;
1648
break;
1649
}
1650
case 2:
1651
{
1652
A[0] = 0.00000000;
1653
A[1] = 0.00000000;
1654
A[2] = 0.00000000;
1655
A[3] = 0.00000000;
1656
A[4] = 0.00000000;
1657
A[5] = 0.00000000;
1658
A[6] = 0.00000000;
1659
A[7] = 0.00000000;
1660
A[8] = 0.00000000;
1661
A[9] = 0.08333333*G0_;
1662
A[10] = 0.04166667*G0_;
1663
A[11] = 0.04166667*G0_;
1664
A[12] = 0.00000000;
1665
A[13] = 0.00000000;
1666
A[14] = 0.00000000;
1667
A[15] = 0.00000000;
1668
A[16] = 0.00000000;
1669
A[17] = 0.04166667*G0_;
1670
A[18] = 0.08333333*G0_;
1671
A[19] = 0.04166667*G0_;
1672
A[20] = 0.00000000;
1673
A[21] = 0.00000000;
1674
A[22] = 0.00000000;
1675
A[23] = 0.00000000;
1676
A[24] = 0.00000000;
1677
A[25] = 0.04166667*G0_;
1678
A[26] = 0.04166667*G0_;
1679
A[27] = 0.08333333*G0_;
1680
A[28] = 0.00000000;
1681
A[29] = 0.00000000;
1682
A[30] = 0.00000000;
1683
A[31] = 0.00000000;
1684
A[32] = 0.00000000;
1685
A[33] = 0.00000000;
1686
A[34] = 0.00000000;
1687
A[35] = 0.00000000;
1688
A[36] = 0.00000000;
1689
A[37] = 0.00000000;
1690
A[38] = 0.00000000;
1691
A[39] = 0.00000000;
1692
A[40] = 0.00000000;
1693
A[41] = 0.00000000;
1694
A[42] = 0.00000000;
1695
A[43] = 0.00000000;
1696
A[44] = 0.00000000;
1697
A[45] = 0.00000000;
1698
A[46] = 0.00000000;
1699
A[47] = 0.00000000;
1700
A[48] = 0.00000000;
1701
A[49] = 0.00000000;
1702
A[50] = 0.00000000;
1703
A[51] = 0.00000000;
1704
A[52] = 0.00000000;
1705
A[53] = 0.00000000;
1706
A[54] = 0.00000000;
1707
A[55] = 0.00000000;
1708
A[56] = 0.00000000;
1709
A[57] = 0.00000000;
1710
A[58] = 0.00000000;
1711
A[59] = 0.00000000;
1712
A[60] = 0.00000000;
1713
A[61] = 0.00000000;
1714
A[62] = 0.00000000;
1715
A[63] = 0.00000000;
1716
break;
1717
}
1718
case 3:
1719
{
1720
A[0] = 0.00000000;
1721
A[1] = 0.00000000;
1722
A[2] = 0.00000000;
1723
A[3] = 0.00000000;
1724
A[4] = 0.00000000;
1725
A[5] = 0.00000000;
1726
A[6] = 0.00000000;
1727
A[7] = 0.00000000;
1728
A[8] = 0.00000000;
1729
A[9] = 0.08333333*G0_;
1730
A[10] = 0.04166667*G0_;
1731
A[11] = 0.04166667*G0_;
1732
A[12] = 0.00000000;
1733
A[13] = 0.00000000;
1734
A[14] = 0.00000000;
1735
A[15] = 0.00000000;
1736
A[16] = 0.00000000;
1737
A[17] = 0.04166667*G0_;
1738
A[18] = 0.08333333*G0_;
1739
A[19] = 0.04166667*G0_;
1740
A[20] = 0.00000000;
1741
A[21] = 0.00000000;
1742
A[22] = 0.00000000;
1743
A[23] = 0.00000000;
1744
A[24] = 0.00000000;
1745
A[25] = 0.04166667*G0_;
1746
A[26] = 0.04166667*G0_;
1747
A[27] = 0.08333333*G0_;
1748
A[28] = 0.00000000;
1749
A[29] = 0.00000000;
1750
A[30] = 0.00000000;
1751
A[31] = 0.00000000;
1752
A[32] = 0.00000000;
1753
A[33] = 0.00000000;
1754
A[34] = 0.00000000;
1755
A[35] = 0.00000000;
1756
A[36] = 0.00000000;
1757
A[37] = 0.00000000;
1758
A[38] = 0.00000000;
1759
A[39] = 0.00000000;
1760
A[40] = 0.00000000;
1761
A[41] = 0.00000000;
1762
A[42] = 0.00000000;
1763
A[43] = 0.00000000;
1764
A[44] = 0.00000000;
1765
A[45] = 0.00000000;
1766
A[46] = 0.00000000;
1767
A[47] = 0.00000000;
1768
A[48] = 0.00000000;
1769
A[49] = 0.00000000;
1770
A[50] = 0.00000000;
1771
A[51] = 0.00000000;
1772
A[52] = 0.00000000;
1773
A[53] = 0.00000000;
1774
A[54] = 0.00000000;
1775
A[55] = 0.00000000;
1776
A[56] = 0.00000000;
1777
A[57] = 0.00000000;
1778
A[58] = 0.00000000;
1779
A[59] = 0.00000000;
1780
A[60] = 0.00000000;
1781
A[61] = 0.00000000;
1782
A[62] = 0.00000000;
1783
A[63] = 0.00000000;
1784
break;
1785
}
1786
}
1787
1788
break;
1789
}
1790
case 1:
1791
{
1792
switch (facet1)
1793
{
1794
case 0:
1795
{
1796
A[0] = 0.08333333*G0_;
1797
A[1] = 0.00000000;
1798
A[2] = 0.04166667*G0_;
1799
A[3] = 0.04166667*G0_;
1800
A[4] = 0.00000000;
1801
A[5] = 0.00000000;
1802
A[6] = 0.00000000;
1803
A[7] = 0.00000000;
1804
A[8] = 0.00000000;
1805
A[9] = 0.00000000;
1806
A[10] = 0.00000000;
1807
A[11] = 0.00000000;
1808
A[12] = 0.00000000;
1809
A[13] = 0.00000000;
1810
A[14] = 0.00000000;
1811
A[15] = 0.00000000;
1812
A[16] = 0.04166667*G0_;
1813
A[17] = 0.00000000;
1814
A[18] = 0.08333333*G0_;
1815
A[19] = 0.04166667*G0_;
1816
A[20] = 0.00000000;
1817
A[21] = 0.00000000;
1818
A[22] = 0.00000000;
1819
A[23] = 0.00000000;
1820
A[24] = 0.04166667*G0_;
1821
A[25] = 0.00000000;
1822
A[26] = 0.04166667*G0_;
1823
A[27] = 0.08333333*G0_;
1824
A[28] = 0.00000000;
1825
A[29] = 0.00000000;
1826
A[30] = 0.00000000;
1827
A[31] = 0.00000000;
1828
A[32] = 0.00000000;
1829
A[33] = 0.00000000;
1830
A[34] = 0.00000000;
1831
A[35] = 0.00000000;
1832
A[36] = 0.00000000;
1833
A[37] = 0.00000000;
1834
A[38] = 0.00000000;
1835
A[39] = 0.00000000;
1836
A[40] = 0.00000000;
1837
A[41] = 0.00000000;
1838
A[42] = 0.00000000;
1839
A[43] = 0.00000000;
1840
A[44] = 0.00000000;
1841
A[45] = 0.00000000;
1842
A[46] = 0.00000000;
1843
A[47] = 0.00000000;
1844
A[48] = 0.00000000;
1845
A[49] = 0.00000000;
1846
A[50] = 0.00000000;
1847
A[51] = 0.00000000;
1848
A[52] = 0.00000000;
1849
A[53] = 0.00000000;
1850
A[54] = 0.00000000;
1851
A[55] = 0.00000000;
1852
A[56] = 0.00000000;
1853
A[57] = 0.00000000;
1854
A[58] = 0.00000000;
1855
A[59] = 0.00000000;
1856
A[60] = 0.00000000;
1857
A[61] = 0.00000000;
1858
A[62] = 0.00000000;
1859
A[63] = 0.00000000;
1860
break;
1861
}
1862
case 1:
1863
{
1864
A[0] = 0.08333333*G0_;
1865
A[1] = 0.00000000;
1866
A[2] = 0.04166667*G0_;
1867
A[3] = 0.04166667*G0_;
1868
A[4] = 0.00000000;
1869
A[5] = 0.00000000;
1870
A[6] = 0.00000000;
1871
A[7] = 0.00000000;
1872
A[8] = 0.00000000;
1873
A[9] = 0.00000000;
1874
A[10] = 0.00000000;
1875
A[11] = 0.00000000;
1876
A[12] = 0.00000000;
1877
A[13] = 0.00000000;
1878
A[14] = 0.00000000;
1879
A[15] = 0.00000000;
1880
A[16] = 0.04166667*G0_;
1881
A[17] = 0.00000000;
1882
A[18] = 0.08333333*G0_;
1883
A[19] = 0.04166667*G0_;
1884
A[20] = 0.00000000;
1885
A[21] = 0.00000000;
1886
A[22] = 0.00000000;
1887
A[23] = 0.00000000;
1888
A[24] = 0.04166667*G0_;
1889
A[25] = 0.00000000;
1890
A[26] = 0.04166667*G0_;
1891
A[27] = 0.08333333*G0_;
1892
A[28] = 0.00000000;
1893
A[29] = 0.00000000;
1894
A[30] = 0.00000000;
1895
A[31] = 0.00000000;
1896
A[32] = 0.00000000;
1897
A[33] = 0.00000000;
1898
A[34] = 0.00000000;
1899
A[35] = 0.00000000;
1900
A[36] = 0.00000000;
1901
A[37] = 0.00000000;
1902
A[38] = 0.00000000;
1903
A[39] = 0.00000000;
1904
A[40] = 0.00000000;
1905
A[41] = 0.00000000;
1906
A[42] = 0.00000000;
1907
A[43] = 0.00000000;
1908
A[44] = 0.00000000;
1909
A[45] = 0.00000000;
1910
A[46] = 0.00000000;
1911
A[47] = 0.00000000;
1912
A[48] = 0.00000000;
1913
A[49] = 0.00000000;
1914
A[50] = 0.00000000;
1915
A[51] = 0.00000000;
1916
A[52] = 0.00000000;
1917
A[53] = 0.00000000;
1918
A[54] = 0.00000000;
1919
A[55] = 0.00000000;
1920
A[56] = 0.00000000;
1921
A[57] = 0.00000000;
1922
A[58] = 0.00000000;
1923
A[59] = 0.00000000;
1924
A[60] = 0.00000000;
1925
A[61] = 0.00000000;
1926
A[62] = 0.00000000;
1927
A[63] = 0.00000000;
1928
break;
1929
}
1930
case 2:
1931
{
1932
A[0] = 0.08333333*G0_;
1933
A[1] = 0.00000000;
1934
A[2] = 0.04166667*G0_;
1935
A[3] = 0.04166667*G0_;
1936
A[4] = 0.00000000;
1937
A[5] = 0.00000000;
1938
A[6] = 0.00000000;
1939
A[7] = 0.00000000;
1940
A[8] = 0.00000000;
1941
A[9] = 0.00000000;
1942
A[10] = 0.00000000;
1943
A[11] = 0.00000000;
1944
A[12] = 0.00000000;
1945
A[13] = 0.00000000;
1946
A[14] = 0.00000000;
1947
A[15] = 0.00000000;
1948
A[16] = 0.04166667*G0_;
1949
A[17] = 0.00000000;
1950
A[18] = 0.08333333*G0_;
1951
A[19] = 0.04166667*G0_;
1952
A[20] = 0.00000000;
1953
A[21] = 0.00000000;
1954
A[22] = 0.00000000;
1955
A[23] = 0.00000000;
1956
A[24] = 0.04166667*G0_;
1957
A[25] = 0.00000000;
1958
A[26] = 0.04166667*G0_;
1959
A[27] = 0.08333333*G0_;
1960
A[28] = 0.00000000;
1961
A[29] = 0.00000000;
1962
A[30] = 0.00000000;
1963
A[31] = 0.00000000;
1964
A[32] = 0.00000000;
1965
A[33] = 0.00000000;
1966
A[34] = 0.00000000;
1967
A[35] = 0.00000000;
1968
A[36] = 0.00000000;
1969
A[37] = 0.00000000;
1970
A[38] = 0.00000000;
1971
A[39] = 0.00000000;
1972
A[40] = 0.00000000;
1973
A[41] = 0.00000000;
1974
A[42] = 0.00000000;
1975
A[43] = 0.00000000;
1976
A[44] = 0.00000000;
1977
A[45] = 0.00000000;
1978
A[46] = 0.00000000;
1979
A[47] = 0.00000000;
1980
A[48] = 0.00000000;
1981
A[49] = 0.00000000;
1982
A[50] = 0.00000000;
1983
A[51] = 0.00000000;
1984
A[52] = 0.00000000;
1985
A[53] = 0.00000000;
1986
A[54] = 0.00000000;
1987
A[55] = 0.00000000;
1988
A[56] = 0.00000000;
1989
A[57] = 0.00000000;
1990
A[58] = 0.00000000;
1991
A[59] = 0.00000000;
1992
A[60] = 0.00000000;
1993
A[61] = 0.00000000;
1994
A[62] = 0.00000000;
1995
A[63] = 0.00000000;
1996
break;
1997
}
1998
case 3:
1999
{
2000
A[0] = 0.08333333*G0_;
2001
A[1] = 0.00000000;
2002
A[2] = 0.04166667*G0_;
2003
A[3] = 0.04166667*G0_;
2004
A[4] = 0.00000000;
2005
A[5] = 0.00000000;
2006
A[6] = 0.00000000;
2007
A[7] = 0.00000000;
2008
A[8] = 0.00000000;
2009
A[9] = 0.00000000;
2010
A[10] = 0.00000000;
2011
A[11] = 0.00000000;
2012
A[12] = 0.00000000;
2013
A[13] = 0.00000000;
2014
A[14] = 0.00000000;
2015
A[15] = 0.00000000;
2016
A[16] = 0.04166667*G0_;
2017
A[17] = 0.00000000;
2018
A[18] = 0.08333333*G0_;
2019
A[19] = 0.04166667*G0_;
2020
A[20] = 0.00000000;
2021
A[21] = 0.00000000;
2022
A[22] = 0.00000000;
2023
A[23] = 0.00000000;
2024
A[24] = 0.04166667*G0_;
2025
A[25] = 0.00000000;
2026
A[26] = 0.04166667*G0_;
2027
A[27] = 0.08333333*G0_;
2028
A[28] = 0.00000000;
2029
A[29] = 0.00000000;
2030
A[30] = 0.00000000;
2031
A[31] = 0.00000000;
2032
A[32] = 0.00000000;
2033
A[33] = 0.00000000;
2034
A[34] = 0.00000000;
2035
A[35] = 0.00000000;
2036
A[36] = 0.00000000;
2037
A[37] = 0.00000000;
2038
A[38] = 0.00000000;
2039
A[39] = 0.00000000;
2040
A[40] = 0.00000000;
2041
A[41] = 0.00000000;
2042
A[42] = 0.00000000;
2043
A[43] = 0.00000000;
2044
A[44] = 0.00000000;
2045
A[45] = 0.00000000;
2046
A[46] = 0.00000000;
2047
A[47] = 0.00000000;
2048
A[48] = 0.00000000;
2049
A[49] = 0.00000000;
2050
A[50] = 0.00000000;
2051
A[51] = 0.00000000;
2052
A[52] = 0.00000000;
2053
A[53] = 0.00000000;
2054
A[54] = 0.00000000;
2055
A[55] = 0.00000000;
2056
A[56] = 0.00000000;
2057
A[57] = 0.00000000;
2058
A[58] = 0.00000000;
2059
A[59] = 0.00000000;
2060
A[60] = 0.00000000;
2061
A[61] = 0.00000000;
2062
A[62] = 0.00000000;
2063
A[63] = 0.00000000;
2064
break;
2065
}
2066
}
2067
2068
break;
2069
}
2070
case 2:
2071
{
2072
switch (facet1)
2073
{
2074
case 0:
2075
{
2076
A[0] = 0.08333333*G0_;
2077
A[1] = 0.04166667*G0_;
2078
A[2] = 0.00000000;
2079
A[3] = 0.04166667*G0_;
2080
A[4] = 0.00000000;
2081
A[5] = 0.00000000;
2082
A[6] = 0.00000000;
2083
A[7] = 0.00000000;
2084
A[8] = 0.04166667*G0_;
2085
A[9] = 0.08333333*G0_;
2086
A[10] = 0.00000000;
2087
A[11] = 0.04166667*G0_;
2088
A[12] = 0.00000000;
2089
A[13] = 0.00000000;
2090
A[14] = 0.00000000;
2091
A[15] = 0.00000000;
2092
A[16] = 0.00000000;
2093
A[17] = 0.00000000;
2094
A[18] = 0.00000000;
2095
A[19] = 0.00000000;
2096
A[20] = 0.00000000;
2097
A[21] = 0.00000000;
2098
A[22] = 0.00000000;
2099
A[23] = 0.00000000;
2100
A[24] = 0.04166667*G0_;
2101
A[25] = 0.04166667*G0_;
2102
A[26] = 0.00000000;
2103
A[27] = 0.08333333*G0_;
2104
A[28] = 0.00000000;
2105
A[29] = 0.00000000;
2106
A[30] = 0.00000000;
2107
A[31] = 0.00000000;
2108
A[32] = 0.00000000;
2109
A[33] = 0.00000000;
2110
A[34] = 0.00000000;
2111
A[35] = 0.00000000;
2112
A[36] = 0.00000000;
2113
A[37] = 0.00000000;
2114
A[38] = 0.00000000;
2115
A[39] = 0.00000000;
2116
A[40] = 0.00000000;
2117
A[41] = 0.00000000;
2118
A[42] = 0.00000000;
2119
A[43] = 0.00000000;
2120
A[44] = 0.00000000;
2121
A[45] = 0.00000000;
2122
A[46] = 0.00000000;
2123
A[47] = 0.00000000;
2124
A[48] = 0.00000000;
2125
A[49] = 0.00000000;
2126
A[50] = 0.00000000;
2127
A[51] = 0.00000000;
2128
A[52] = 0.00000000;
2129
A[53] = 0.00000000;
2130
A[54] = 0.00000000;
2131
A[55] = 0.00000000;
2132
A[56] = 0.00000000;
2133
A[57] = 0.00000000;
2134
A[58] = 0.00000000;
2135
A[59] = 0.00000000;
2136
A[60] = 0.00000000;
2137
A[61] = 0.00000000;
2138
A[62] = 0.00000000;
2139
A[63] = 0.00000000;
2140
break;
2141
}
2142
case 1:
2143
{
2144
A[0] = 0.08333333*G0_;
2145
A[1] = 0.04166667*G0_;
2146
A[2] = 0.00000000;
2147
A[3] = 0.04166667*G0_;
2148
A[4] = 0.00000000;
2149
A[5] = 0.00000000;
2150
A[6] = 0.00000000;
2151
A[7] = 0.00000000;
2152
A[8] = 0.04166667*G0_;
2153
A[9] = 0.08333333*G0_;
2154
A[10] = 0.00000000;
2155
A[11] = 0.04166667*G0_;
2156
A[12] = 0.00000000;
2157
A[13] = 0.00000000;
2158
A[14] = 0.00000000;
2159
A[15] = 0.00000000;
2160
A[16] = 0.00000000;
2161
A[17] = 0.00000000;
2162
A[18] = 0.00000000;
2163
A[19] = 0.00000000;
2164
A[20] = 0.00000000;
2165
A[21] = 0.00000000;
2166
A[22] = 0.00000000;
2167
A[23] = 0.00000000;
2168
A[24] = 0.04166667*G0_;
2169
A[25] = 0.04166667*G0_;
2170
A[26] = 0.00000000;
2171
A[27] = 0.08333333*G0_;
2172
A[28] = 0.00000000;
2173
A[29] = 0.00000000;
2174
A[30] = 0.00000000;
2175
A[31] = 0.00000000;
2176
A[32] = 0.00000000;
2177
A[33] = 0.00000000;
2178
A[34] = 0.00000000;
2179
A[35] = 0.00000000;
2180
A[36] = 0.00000000;
2181
A[37] = 0.00000000;
2182
A[38] = 0.00000000;
2183
A[39] = 0.00000000;
2184
A[40] = 0.00000000;
2185
A[41] = 0.00000000;
2186
A[42] = 0.00000000;
2187
A[43] = 0.00000000;
2188
A[44] = 0.00000000;
2189
A[45] = 0.00000000;
2190
A[46] = 0.00000000;
2191
A[47] = 0.00000000;
2192
A[48] = 0.00000000;
2193
A[49] = 0.00000000;
2194
A[50] = 0.00000000;
2195
A[51] = 0.00000000;
2196
A[52] = 0.00000000;
2197
A[53] = 0.00000000;
2198
A[54] = 0.00000000;
2199
A[55] = 0.00000000;
2200
A[56] = 0.00000000;
2201
A[57] = 0.00000000;
2202
A[58] = 0.00000000;
2203
A[59] = 0.00000000;
2204
A[60] = 0.00000000;
2205
A[61] = 0.00000000;
2206
A[62] = 0.00000000;
2207
A[63] = 0.00000000;
2208
break;
2209
}
2210
case 2:
2211
{
2212
A[0] = 0.08333333*G0_;
2213
A[1] = 0.04166667*G0_;
2214
A[2] = 0.00000000;
2215
A[3] = 0.04166667*G0_;
2216
A[4] = 0.00000000;
2217
A[5] = 0.00000000;
2218
A[6] = 0.00000000;
2219
A[7] = 0.00000000;
2220
A[8] = 0.04166667*G0_;
2221
A[9] = 0.08333333*G0_;
2222
A[10] = 0.00000000;
2223
A[11] = 0.04166667*G0_;
2224
A[12] = 0.00000000;
2225
A[13] = 0.00000000;
2226
A[14] = 0.00000000;
2227
A[15] = 0.00000000;
2228
A[16] = 0.00000000;
2229
A[17] = 0.00000000;
2230
A[18] = 0.00000000;
2231
A[19] = 0.00000000;
2232
A[20] = 0.00000000;
2233
A[21] = 0.00000000;
2234
A[22] = 0.00000000;
2235
A[23] = 0.00000000;
2236
A[24] = 0.04166667*G0_;
2237
A[25] = 0.04166667*G0_;
2238
A[26] = 0.00000000;
2239
A[27] = 0.08333333*G0_;
2240
A[28] = 0.00000000;
2241
A[29] = 0.00000000;
2242
A[30] = 0.00000000;
2243
A[31] = 0.00000000;
2244
A[32] = 0.00000000;
2245
A[33] = 0.00000000;
2246
A[34] = 0.00000000;
2247
A[35] = 0.00000000;
2248
A[36] = 0.00000000;
2249
A[37] = 0.00000000;
2250
A[38] = 0.00000000;
2251
A[39] = 0.00000000;
2252
A[40] = 0.00000000;
2253
A[41] = 0.00000000;
2254
A[42] = 0.00000000;
2255
A[43] = 0.00000000;
2256
A[44] = 0.00000000;
2257
A[45] = 0.00000000;
2258
A[46] = 0.00000000;
2259
A[47] = 0.00000000;
2260
A[48] = 0.00000000;
2261
A[49] = 0.00000000;
2262
A[50] = 0.00000000;
2263
A[51] = 0.00000000;
2264
A[52] = 0.00000000;
2265
A[53] = 0.00000000;
2266
A[54] = 0.00000000;
2267
A[55] = 0.00000000;
2268
A[56] = 0.00000000;
2269
A[57] = 0.00000000;
2270
A[58] = 0.00000000;
2271
A[59] = 0.00000000;
2272
A[60] = 0.00000000;
2273
A[61] = 0.00000000;
2274
A[62] = 0.00000000;
2275
A[63] = 0.00000000;
2276
break;
2277
}
2278
case 3:
2279
{
2280
A[0] = 0.08333333*G0_;
2281
A[1] = 0.04166667*G0_;
2282
A[2] = 0.00000000;
2283
A[3] = 0.04166667*G0_;
2284
A[4] = 0.00000000;
2285
A[5] = 0.00000000;
2286
A[6] = 0.00000000;
2287
A[7] = 0.00000000;
2288
A[8] = 0.04166667*G0_;
2289
A[9] = 0.08333333*G0_;
2290
A[10] = 0.00000000;
2291
A[11] = 0.04166667*G0_;
2292
A[12] = 0.00000000;
2293
A[13] = 0.00000000;
2294
A[14] = 0.00000000;
2295
A[15] = 0.00000000;
2296
A[16] = 0.00000000;
2297
A[17] = 0.00000000;
2298
A[18] = 0.00000000;
2299
A[19] = 0.00000000;
2300
A[20] = 0.00000000;
2301
A[21] = 0.00000000;
2302
A[22] = 0.00000000;
2303
A[23] = 0.00000000;
2304
A[24] = 0.04166667*G0_;
2305
A[25] = 0.04166667*G0_;
2306
A[26] = 0.00000000;
2307
A[27] = 0.08333333*G0_;
2308
A[28] = 0.00000000;
2309
A[29] = 0.00000000;
2310
A[30] = 0.00000000;
2311
A[31] = 0.00000000;
2312
A[32] = 0.00000000;
2313
A[33] = 0.00000000;
2314
A[34] = 0.00000000;
2315
A[35] = 0.00000000;
2316
A[36] = 0.00000000;
2317
A[37] = 0.00000000;
2318
A[38] = 0.00000000;
2319
A[39] = 0.00000000;
2320
A[40] = 0.00000000;
2321
A[41] = 0.00000000;
2322
A[42] = 0.00000000;
2323
A[43] = 0.00000000;
2324
A[44] = 0.00000000;
2325
A[45] = 0.00000000;
2326
A[46] = 0.00000000;
2327
A[47] = 0.00000000;
2328
A[48] = 0.00000000;
2329
A[49] = 0.00000000;
2330
A[50] = 0.00000000;
2331
A[51] = 0.00000000;
2332
A[52] = 0.00000000;
2333
A[53] = 0.00000000;
2334
A[54] = 0.00000000;
2335
A[55] = 0.00000000;
2336
A[56] = 0.00000000;
2337
A[57] = 0.00000000;
2338
A[58] = 0.00000000;
2339
A[59] = 0.00000000;
2340
A[60] = 0.00000000;
2341
A[61] = 0.00000000;
2342
A[62] = 0.00000000;
2343
A[63] = 0.00000000;
2344
break;
2345
}
2346
}
2347
2348
break;
2349
}
2350
case 3:
2351
{
2352
switch (facet1)
2353
{
2354
case 0:
2355
{
2356
A[0] = 0.08333333*G0_;
2357
A[1] = 0.04166667*G0_;
2358
A[2] = 0.04166667*G0_;
2359
A[3] = 0.00000000;
2360
A[4] = 0.00000000;
2361
A[5] = 0.00000000;
2362
A[6] = 0.00000000;
2363
A[7] = 0.00000000;
2364
A[8] = 0.04166667*G0_;
2365
A[9] = 0.08333333*G0_;
2366
A[10] = 0.04166667*G0_;
2367
A[11] = 0.00000000;
2368
A[12] = 0.00000000;
2369
A[13] = 0.00000000;
2370
A[14] = 0.00000000;
2371
A[15] = 0.00000000;
2372
A[16] = 0.04166667*G0_;
2373
A[17] = 0.04166667*G0_;
2374
A[18] = 0.08333333*G0_;
2375
A[19] = 0.00000000;
2376
A[20] = 0.00000000;
2377
A[21] = 0.00000000;
2378
A[22] = 0.00000000;
2379
A[23] = 0.00000000;
2380
A[24] = 0.00000000;
2381
A[25] = 0.00000000;
2382
A[26] = 0.00000000;
2383
A[27] = 0.00000000;
2384
A[28] = 0.00000000;
2385
A[29] = 0.00000000;
2386
A[30] = 0.00000000;
2387
A[31] = 0.00000000;
2388
A[32] = 0.00000000;
2389
A[33] = 0.00000000;
2390
A[34] = 0.00000000;
2391
A[35] = 0.00000000;
2392
A[36] = 0.00000000;
2393
A[37] = 0.00000000;
2394
A[38] = 0.00000000;
2395
A[39] = 0.00000000;
2396
A[40] = 0.00000000;
2397
A[41] = 0.00000000;
2398
A[42] = 0.00000000;
2399
A[43] = 0.00000000;
2400
A[44] = 0.00000000;
2401
A[45] = 0.00000000;
2402
A[46] = 0.00000000;
2403
A[47] = 0.00000000;
2404
A[48] = 0.00000000;
2405
A[49] = 0.00000000;
2406
A[50] = 0.00000000;
2407
A[51] = 0.00000000;
2408
A[52] = 0.00000000;
2409
A[53] = 0.00000000;
2410
A[54] = 0.00000000;
2411
A[55] = 0.00000000;
2412
A[56] = 0.00000000;
2413
A[57] = 0.00000000;
2414
A[58] = 0.00000000;
2415
A[59] = 0.00000000;
2416
A[60] = 0.00000000;
2417
A[61] = 0.00000000;
2418
A[62] = 0.00000000;
2419
A[63] = 0.00000000;
2420
break;
2421
}
2422
case 1:
2423
{
2424
A[0] = 0.08333333*G0_;
2425
A[1] = 0.04166667*G0_;
2426
A[2] = 0.04166667*G0_;
2427
A[3] = 0.00000000;
2428
A[4] = 0.00000000;
2429
A[5] = 0.00000000;
2430
A[6] = 0.00000000;
2431
A[7] = 0.00000000;
2432
A[8] = 0.04166667*G0_;
2433
A[9] = 0.08333333*G0_;
2434
A[10] = 0.04166667*G0_;
2435
A[11] = 0.00000000;
2436
A[12] = 0.00000000;
2437
A[13] = 0.00000000;
2438
A[14] = 0.00000000;
2439
A[15] = 0.00000000;
2440
A[16] = 0.04166667*G0_;
2441
A[17] = 0.04166667*G0_;
2442
A[18] = 0.08333333*G0_;
2443
A[19] = 0.00000000;
2444
A[20] = 0.00000000;
2445
A[21] = 0.00000000;
2446
A[22] = 0.00000000;
2447
A[23] = 0.00000000;
2448
A[24] = 0.00000000;
2449
A[25] = 0.00000000;
2450
A[26] = 0.00000000;
2451
A[27] = 0.00000000;
2452
A[28] = 0.00000000;
2453
A[29] = 0.00000000;
2454
A[30] = 0.00000000;
2455
A[31] = 0.00000000;
2456
A[32] = 0.00000000;
2457
A[33] = 0.00000000;
2458
A[34] = 0.00000000;
2459
A[35] = 0.00000000;
2460
A[36] = 0.00000000;
2461
A[37] = 0.00000000;
2462
A[38] = 0.00000000;
2463
A[39] = 0.00000000;
2464
A[40] = 0.00000000;
2465
A[41] = 0.00000000;
2466
A[42] = 0.00000000;
2467
A[43] = 0.00000000;
2468
A[44] = 0.00000000;
2469
A[45] = 0.00000000;
2470
A[46] = 0.00000000;
2471
A[47] = 0.00000000;
2472
A[48] = 0.00000000;
2473
A[49] = 0.00000000;
2474
A[50] = 0.00000000;
2475
A[51] = 0.00000000;
2476
A[52] = 0.00000000;
2477
A[53] = 0.00000000;
2478
A[54] = 0.00000000;
2479
A[55] = 0.00000000;
2480
A[56] = 0.00000000;
2481
A[57] = 0.00000000;
2482
A[58] = 0.00000000;
2483
A[59] = 0.00000000;
2484
A[60] = 0.00000000;
2485
A[61] = 0.00000000;
2486
A[62] = 0.00000000;
2487
A[63] = 0.00000000;
2488
break;
2489
}
2490
case 2:
2491
{
2492
A[0] = 0.08333333*G0_;
2493
A[1] = 0.04166667*G0_;
2494
A[2] = 0.04166667*G0_;
2495
A[3] = 0.00000000;
2496
A[4] = 0.00000000;
2497
A[5] = 0.00000000;
2498
A[6] = 0.00000000;
2499
A[7] = 0.00000000;
2500
A[8] = 0.04166667*G0_;
2501
A[9] = 0.08333333*G0_;
2502
A[10] = 0.04166667*G0_;
2503
A[11] = 0.00000000;
2504
A[12] = 0.00000000;
2505
A[13] = 0.00000000;
2506
A[14] = 0.00000000;
2507
A[15] = 0.00000000;
2508
A[16] = 0.04166667*G0_;
2509
A[17] = 0.04166667*G0_;
2510
A[18] = 0.08333333*G0_;
2511
A[19] = 0.00000000;
2512
A[20] = 0.00000000;
2513
A[21] = 0.00000000;
2514
A[22] = 0.00000000;
2515
A[23] = 0.00000000;
2516
A[24] = 0.00000000;
2517
A[25] = 0.00000000;
2518
A[26] = 0.00000000;
2519
A[27] = 0.00000000;
2520
A[28] = 0.00000000;
2521
A[29] = 0.00000000;
2522
A[30] = 0.00000000;
2523
A[31] = 0.00000000;
2524
A[32] = 0.00000000;
2525
A[33] = 0.00000000;
2526
A[34] = 0.00000000;
2527
A[35] = 0.00000000;
2528
A[36] = 0.00000000;
2529
A[37] = 0.00000000;
2530
A[38] = 0.00000000;
2531
A[39] = 0.00000000;
2532
A[40] = 0.00000000;
2533
A[41] = 0.00000000;
2534
A[42] = 0.00000000;
2535
A[43] = 0.00000000;
2536
A[44] = 0.00000000;
2537
A[45] = 0.00000000;
2538
A[46] = 0.00000000;
2539
A[47] = 0.00000000;
2540
A[48] = 0.00000000;
2541
A[49] = 0.00000000;
2542
A[50] = 0.00000000;
2543
A[51] = 0.00000000;
2544
A[52] = 0.00000000;
2545
A[53] = 0.00000000;
2546
A[54] = 0.00000000;
2547
A[55] = 0.00000000;
2548
A[56] = 0.00000000;
2549
A[57] = 0.00000000;
2550
A[58] = 0.00000000;
2551
A[59] = 0.00000000;
2552
A[60] = 0.00000000;
2553
A[61] = 0.00000000;
2554
A[62] = 0.00000000;
2555
A[63] = 0.00000000;
2556
break;
2557
}
2558
case 3:
2559
{
2560
A[0] = 0.08333333*G0_;
2561
A[1] = 0.04166667*G0_;
2562
A[2] = 0.04166667*G0_;
2563
A[3] = 0.00000000;
2564
A[4] = 0.00000000;
2565
A[5] = 0.00000000;
2566
A[6] = 0.00000000;
2567
A[7] = 0.00000000;
2568
A[8] = 0.04166667*G0_;
2569
A[9] = 0.08333333*G0_;
2570
A[10] = 0.04166667*G0_;
2571
A[11] = 0.00000000;
2572
A[12] = 0.00000000;
2573
A[13] = 0.00000000;
2574
A[14] = 0.00000000;
2575
A[15] = 0.00000000;
2576
A[16] = 0.04166667*G0_;
2577
A[17] = 0.04166667*G0_;
2578
A[18] = 0.08333333*G0_;
2579
A[19] = 0.00000000;
2580
A[20] = 0.00000000;
2581
A[21] = 0.00000000;
2582
A[22] = 0.00000000;
2583
A[23] = 0.00000000;
2584
A[24] = 0.00000000;
2585
A[25] = 0.00000000;
2586
A[26] = 0.00000000;
2587
A[27] = 0.00000000;
2588
A[28] = 0.00000000;
2589
A[29] = 0.00000000;
2590
A[30] = 0.00000000;
2591
A[31] = 0.00000000;
2592
A[32] = 0.00000000;
2593
A[33] = 0.00000000;
2594
A[34] = 0.00000000;
2595
A[35] = 0.00000000;
2596
A[36] = 0.00000000;
2597
A[37] = 0.00000000;
2598
A[38] = 0.00000000;
2599
A[39] = 0.00000000;
2600
A[40] = 0.00000000;
2601
A[41] = 0.00000000;
2602
A[42] = 0.00000000;
2603
A[43] = 0.00000000;
2604
A[44] = 0.00000000;
2605
A[45] = 0.00000000;
2606
A[46] = 0.00000000;
2607
A[47] = 0.00000000;
2608
A[48] = 0.00000000;
2609
A[49] = 0.00000000;
2610
A[50] = 0.00000000;
2611
A[51] = 0.00000000;
2612
A[52] = 0.00000000;
2613
A[53] = 0.00000000;
2614
A[54] = 0.00000000;
2615
A[55] = 0.00000000;
2616
A[56] = 0.00000000;
2617
A[57] = 0.00000000;
2618
A[58] = 0.00000000;
2619
A[59] = 0.00000000;
2620
A[60] = 0.00000000;
2621
A[61] = 0.00000000;
2622
A[62] = 0.00000000;
2623
A[63] = 0.00000000;
2624
break;
2625
}
2626
}
2627
2628
break;
2629
}
2630
}
2631
2632
}
2633
2634
};
2635
2636
/// This class defines the interface for the tabulation of the
2637
/// interior facet tensor corresponding to the local contribution to
2638
/// a form from the integral over an interior facet.
2639
2640
class subdomains_interior_facet_integral_0_1: public ufc::interior_facet_integral
2641
{
2642
public:
2643
2644
/// Constructor
2645
subdomains_interior_facet_integral_0_1() : ufc::interior_facet_integral()
2646
{
2647
// Do nothing
2648
}
2649
2650
/// Destructor
2651
virtual ~subdomains_interior_facet_integral_0_1()
2652
{
2653
// Do nothing
2654
}
2655
2656
/// Tabulate the tensor for the contribution from a local interior facet
2657
virtual void tabulate_tensor(double* A,
2658
const double * const * w,
2659
const ufc::cell& c0,
2660
const ufc::cell& c1,
2661
unsigned int facet0,
2662
unsigned int facet1) const
2663
{
2664
// Number of operations (multiply-add pairs) for Jacobian data: 83
2665
// Number of operations (multiply-add pairs) for geometry tensor: 0
2666
// Number of operations (multiply-add pairs) for tensor contraction: 72
2667
// Total number of operations (multiply-add pairs): 155
2668
2669
// Extract vertex coordinates
2670
const double * const * x0 = c0.coordinates;
2671
2672
// Compute Jacobian of affine map from reference cell
2673
2674
// Compute sub determinants
2675
2676
// Compute determinant of Jacobian
2677
2678
// Compute inverse of Jacobian
2679
2680
// Compute Jacobian of affine map from reference cell
2681
2682
// Compute sub determinants
2683
2684
// Compute determinant of Jacobian
2685
2686
// Compute inverse of Jacobian
2687
2688
// Get vertices on face
2689
static unsigned int face_vertices[4][3] = {{1, 2, 3}, {0, 2, 3}, {0, 1, 3}, {0, 1, 2}};
2690
const unsigned int v0 = face_vertices[facet0][0];
2691
const unsigned int v1 = face_vertices[facet0][1];
2692
const unsigned int v2 = face_vertices[facet0][2];
2693
2694
// Compute scale factor (area of face scaled by area of reference triangle)
2695
const double a0 = (x0[v0][1]*x0[v1][2]
2696
+ x0[v0][2]*x0[v2][1]
2697
+ x0[v1][1]*x0[v2][2])
2698
- (x0[v2][1]*x0[v1][2]
2699
+ x0[v2][2]*x0[v0][1]
2700
+ x0[v1][1]*x0[v0][2]);
2701
2702
const double a1 = (x0[v0][2]*x0[v1][0]
2703
+ x0[v0][0]*x0[v2][2]
2704
+ x0[v1][2]*x0[v2][0])
2705
- (x0[v2][2]*x0[v1][0]
2706
+ x0[v2][0]*x0[v0][2]
2707
+ x0[v1][2]*x0[v0][0]);
2708
2709
const double a2 = (x0[v0][0]*x0[v1][1]
2710
+ x0[v0][1]*x0[v2][0]
2711
+ x0[v1][0]*x0[v2][1])
2712
- (x0[v2][0]*x0[v1][1]
2713
+ x0[v2][1]*x0[v0][0]
2714
+ x0[v1][0]*x0[v0][1]);
2715
2716
const double det = std::sqrt(a0*a0 + a1*a1 + a2*a2);
2717
2718
// Compute geometry tensor
2719
const double G0_ = det;
2720
2721
// Compute element tensor
2722
switch (facet0)
2723
{
2724
case 0:
2725
{
2726
switch (facet1)
2727
{
2728
case 0:
2729
{
2730
A[0] = 0.00000000;
2731
A[1] = 0.00000000;
2732
A[2] = 0.00000000;
2733
A[3] = 0.00000000;
2734
A[4] = 0.00000000;
2735
A[5] = 0.00000000;
2736
A[6] = 0.00000000;
2737
A[7] = 0.00000000;
2738
A[8] = 0.00000000;
2739
A[9] = 0.35833333*G0_;
2740
A[10] = 0.17916667*G0_;
2741
A[11] = 0.17916667*G0_;
2742
A[12] = 0.00000000;
2743
A[13] = 0.00000000;
2744
A[14] = 0.00000000;
2745
A[15] = 0.00000000;
2746
A[16] = 0.00000000;
2747
A[17] = 0.17916667*G0_;
2748
A[18] = 0.35833333*G0_;
2749
A[19] = 0.17916667*G0_;
2750
A[20] = 0.00000000;
2751
A[21] = 0.00000000;
2752
A[22] = 0.00000000;
2753
A[23] = 0.00000000;
2754
A[24] = 0.00000000;
2755
A[25] = 0.17916667*G0_;
2756
A[26] = 0.17916667*G0_;
2757
A[27] = 0.35833333*G0_;
2758
A[28] = 0.00000000;
2759
A[29] = 0.00000000;
2760
A[30] = 0.00000000;
2761
A[31] = 0.00000000;
2762
A[32] = 0.00000000;
2763
A[33] = 0.00000000;
2764
A[34] = 0.00000000;
2765
A[35] = 0.00000000;
2766
A[36] = 0.00000000;
2767
A[37] = 0.00000000;
2768
A[38] = 0.00000000;
2769
A[39] = 0.00000000;
2770
A[40] = 0.00000000;
2771
A[41] = 0.00000000;
2772
A[42] = 0.00000000;
2773
A[43] = 0.00000000;
2774
A[44] = 0.00000000;
2775
A[45] = 0.00000000;
2776
A[46] = 0.00000000;
2777
A[47] = 0.00000000;
2778
A[48] = 0.00000000;
2779
A[49] = 0.00000000;
2780
A[50] = 0.00000000;
2781
A[51] = 0.00000000;
2782
A[52] = 0.00000000;
2783
A[53] = 0.00000000;
2784
A[54] = 0.00000000;
2785
A[55] = 0.00000000;
2786
A[56] = 0.00000000;
2787
A[57] = 0.00000000;
2788
A[58] = 0.00000000;
2789
A[59] = 0.00000000;
2790
A[60] = 0.00000000;
2791
A[61] = 0.00000000;
2792
A[62] = 0.00000000;
2793
A[63] = 0.00000000;
2794
break;
2795
}
2796
case 1:
2797
{
2798
A[0] = 0.00000000;
2799
A[1] = 0.00000000;
2800
A[2] = 0.00000000;
2801
A[3] = 0.00000000;
2802
A[4] = 0.00000000;
2803
A[5] = 0.00000000;
2804
A[6] = 0.00000000;
2805
A[7] = 0.00000000;
2806
A[8] = 0.00000000;
2807
A[9] = 0.35833333*G0_;
2808
A[10] = 0.17916667*G0_;
2809
A[11] = 0.17916667*G0_;
2810
A[12] = 0.00000000;
2811
A[13] = 0.00000000;
2812
A[14] = 0.00000000;
2813
A[15] = 0.00000000;
2814
A[16] = 0.00000000;
2815
A[17] = 0.17916667*G0_;
2816
A[18] = 0.35833333*G0_;
2817
A[19] = 0.17916667*G0_;
2818
A[20] = 0.00000000;
2819
A[21] = 0.00000000;
2820
A[22] = 0.00000000;
2821
A[23] = 0.00000000;
2822
A[24] = 0.00000000;
2823
A[25] = 0.17916667*G0_;
2824
A[26] = 0.17916667*G0_;
2825
A[27] = 0.35833333*G0_;
2826
A[28] = 0.00000000;
2827
A[29] = 0.00000000;
2828
A[30] = 0.00000000;
2829
A[31] = 0.00000000;
2830
A[32] = 0.00000000;
2831
A[33] = 0.00000000;
2832
A[34] = 0.00000000;
2833
A[35] = 0.00000000;
2834
A[36] = 0.00000000;
2835
A[37] = 0.00000000;
2836
A[38] = 0.00000000;
2837
A[39] = 0.00000000;
2838
A[40] = 0.00000000;
2839
A[41] = 0.00000000;
2840
A[42] = 0.00000000;
2841
A[43] = 0.00000000;
2842
A[44] = 0.00000000;
2843
A[45] = 0.00000000;
2844
A[46] = 0.00000000;
2845
A[47] = 0.00000000;
2846
A[48] = 0.00000000;
2847
A[49] = 0.00000000;
2848
A[50] = 0.00000000;
2849
A[51] = 0.00000000;
2850
A[52] = 0.00000000;
2851
A[53] = 0.00000000;
2852
A[54] = 0.00000000;
2853
A[55] = 0.00000000;
2854
A[56] = 0.00000000;
2855
A[57] = 0.00000000;
2856
A[58] = 0.00000000;
2857
A[59] = 0.00000000;
2858
A[60] = 0.00000000;
2859
A[61] = 0.00000000;
2860
A[62] = 0.00000000;
2861
A[63] = 0.00000000;
2862
break;
2863
}
2864
case 2:
2865
{
2866
A[0] = 0.00000000;
2867
A[1] = 0.00000000;
2868
A[2] = 0.00000000;
2869
A[3] = 0.00000000;
2870
A[4] = 0.00000000;
2871
A[5] = 0.00000000;
2872
A[6] = 0.00000000;
2873
A[7] = 0.00000000;
2874
A[8] = 0.00000000;
2875
A[9] = 0.35833333*G0_;
2876
A[10] = 0.17916667*G0_;
2877
A[11] = 0.17916667*G0_;
2878
A[12] = 0.00000000;
2879
A[13] = 0.00000000;
2880
A[14] = 0.00000000;
2881
A[15] = 0.00000000;
2882
A[16] = 0.00000000;
2883
A[17] = 0.17916667*G0_;
2884
A[18] = 0.35833333*G0_;
2885
A[19] = 0.17916667*G0_;
2886
A[20] = 0.00000000;
2887
A[21] = 0.00000000;
2888
A[22] = 0.00000000;
2889
A[23] = 0.00000000;
2890
A[24] = 0.00000000;
2891
A[25] = 0.17916667*G0_;
2892
A[26] = 0.17916667*G0_;
2893
A[27] = 0.35833333*G0_;
2894
A[28] = 0.00000000;
2895
A[29] = 0.00000000;
2896
A[30] = 0.00000000;
2897
A[31] = 0.00000000;
2898
A[32] = 0.00000000;
2899
A[33] = 0.00000000;
2900
A[34] = 0.00000000;
2901
A[35] = 0.00000000;
2902
A[36] = 0.00000000;
2903
A[37] = 0.00000000;
2904
A[38] = 0.00000000;
2905
A[39] = 0.00000000;
2906
A[40] = 0.00000000;
2907
A[41] = 0.00000000;
2908
A[42] = 0.00000000;
2909
A[43] = 0.00000000;
2910
A[44] = 0.00000000;
2911
A[45] = 0.00000000;
2912
A[46] = 0.00000000;
2913
A[47] = 0.00000000;
2914
A[48] = 0.00000000;
2915
A[49] = 0.00000000;
2916
A[50] = 0.00000000;
2917
A[51] = 0.00000000;
2918
A[52] = 0.00000000;
2919
A[53] = 0.00000000;
2920
A[54] = 0.00000000;
2921
A[55] = 0.00000000;
2922
A[56] = 0.00000000;
2923
A[57] = 0.00000000;
2924
A[58] = 0.00000000;
2925
A[59] = 0.00000000;
2926
A[60] = 0.00000000;
2927
A[61] = 0.00000000;
2928
A[62] = 0.00000000;
2929
A[63] = 0.00000000;
2930
break;
2931
}
2932
case 3:
2933
{
2934
A[0] = 0.00000000;
2935
A[1] = 0.00000000;
2936
A[2] = 0.00000000;
2937
A[3] = 0.00000000;
2938
A[4] = 0.00000000;
2939
A[5] = 0.00000000;
2940
A[6] = 0.00000000;
2941
A[7] = 0.00000000;
2942
A[8] = 0.00000000;
2943
A[9] = 0.35833333*G0_;
2944
A[10] = 0.17916667*G0_;
2945
A[11] = 0.17916667*G0_;
2946
A[12] = 0.00000000;
2947
A[13] = 0.00000000;
2948
A[14] = 0.00000000;
2949
A[15] = 0.00000000;
2950
A[16] = 0.00000000;
2951
A[17] = 0.17916667*G0_;
2952
A[18] = 0.35833333*G0_;
2953
A[19] = 0.17916667*G0_;
2954
A[20] = 0.00000000;
2955
A[21] = 0.00000000;
2956
A[22] = 0.00000000;
2957
A[23] = 0.00000000;
2958
A[24] = 0.00000000;
2959
A[25] = 0.17916667*G0_;
2960
A[26] = 0.17916667*G0_;
2961
A[27] = 0.35833333*G0_;
2962
A[28] = 0.00000000;
2963
A[29] = 0.00000000;
2964
A[30] = 0.00000000;
2965
A[31] = 0.00000000;
2966
A[32] = 0.00000000;
2967
A[33] = 0.00000000;
2968
A[34] = 0.00000000;
2969
A[35] = 0.00000000;
2970
A[36] = 0.00000000;
2971
A[37] = 0.00000000;
2972
A[38] = 0.00000000;
2973
A[39] = 0.00000000;
2974
A[40] = 0.00000000;
2975
A[41] = 0.00000000;
2976
A[42] = 0.00000000;
2977
A[43] = 0.00000000;
2978
A[44] = 0.00000000;
2979
A[45] = 0.00000000;
2980
A[46] = 0.00000000;
2981
A[47] = 0.00000000;
2982
A[48] = 0.00000000;
2983
A[49] = 0.00000000;
2984
A[50] = 0.00000000;
2985
A[51] = 0.00000000;
2986
A[52] = 0.00000000;
2987
A[53] = 0.00000000;
2988
A[54] = 0.00000000;
2989
A[55] = 0.00000000;
2990
A[56] = 0.00000000;
2991
A[57] = 0.00000000;
2992
A[58] = 0.00000000;
2993
A[59] = 0.00000000;
2994
A[60] = 0.00000000;
2995
A[61] = 0.00000000;
2996
A[62] = 0.00000000;
2997
A[63] = 0.00000000;
2998
break;
2999
}
3000
}
3001
3002
break;
3003
}
3004
case 1:
3005
{
3006
switch (facet1)
3007
{
3008
case 0:
3009
{
3010
A[0] = 0.35833333*G0_;
3011
A[1] = 0.00000000;
3012
A[2] = 0.17916667*G0_;
3013
A[3] = 0.17916667*G0_;
3014
A[4] = 0.00000000;
3015
A[5] = 0.00000000;
3016
A[6] = 0.00000000;
3017
A[7] = 0.00000000;
3018
A[8] = 0.00000000;
3019
A[9] = 0.00000000;
3020
A[10] = 0.00000000;
3021
A[11] = 0.00000000;
3022
A[12] = 0.00000000;
3023
A[13] = 0.00000000;
3024
A[14] = 0.00000000;
3025
A[15] = 0.00000000;
3026
A[16] = 0.17916667*G0_;
3027
A[17] = 0.00000000;
3028
A[18] = 0.35833333*G0_;
3029
A[19] = 0.17916667*G0_;
3030
A[20] = 0.00000000;
3031
A[21] = 0.00000000;
3032
A[22] = 0.00000000;
3033
A[23] = 0.00000000;
3034
A[24] = 0.17916667*G0_;
3035
A[25] = 0.00000000;
3036
A[26] = 0.17916667*G0_;
3037
A[27] = 0.35833333*G0_;
3038
A[28] = 0.00000000;
3039
A[29] = 0.00000000;
3040
A[30] = 0.00000000;
3041
A[31] = 0.00000000;
3042
A[32] = 0.00000000;
3043
A[33] = 0.00000000;
3044
A[34] = 0.00000000;
3045
A[35] = 0.00000000;
3046
A[36] = 0.00000000;
3047
A[37] = 0.00000000;
3048
A[38] = 0.00000000;
3049
A[39] = 0.00000000;
3050
A[40] = 0.00000000;
3051
A[41] = 0.00000000;
3052
A[42] = 0.00000000;
3053
A[43] = 0.00000000;
3054
A[44] = 0.00000000;
3055
A[45] = 0.00000000;
3056
A[46] = 0.00000000;
3057
A[47] = 0.00000000;
3058
A[48] = 0.00000000;
3059
A[49] = 0.00000000;
3060
A[50] = 0.00000000;
3061
A[51] = 0.00000000;
3062
A[52] = 0.00000000;
3063
A[53] = 0.00000000;
3064
A[54] = 0.00000000;
3065
A[55] = 0.00000000;
3066
A[56] = 0.00000000;
3067
A[57] = 0.00000000;
3068
A[58] = 0.00000000;
3069
A[59] = 0.00000000;
3070
A[60] = 0.00000000;
3071
A[61] = 0.00000000;
3072
A[62] = 0.00000000;
3073
A[63] = 0.00000000;
3074
break;
3075
}
3076
case 1:
3077
{
3078
A[0] = 0.35833333*G0_;
3079
A[1] = 0.00000000;
3080
A[2] = 0.17916667*G0_;
3081
A[3] = 0.17916667*G0_;
3082
A[4] = 0.00000000;
3083
A[5] = 0.00000000;
3084
A[6] = 0.00000000;
3085
A[7] = 0.00000000;
3086
A[8] = 0.00000000;
3087
A[9] = 0.00000000;
3088
A[10] = 0.00000000;
3089
A[11] = 0.00000000;
3090
A[12] = 0.00000000;
3091
A[13] = 0.00000000;
3092
A[14] = 0.00000000;
3093
A[15] = 0.00000000;
3094
A[16] = 0.17916667*G0_;
3095
A[17] = 0.00000000;
3096
A[18] = 0.35833333*G0_;
3097
A[19] = 0.17916667*G0_;
3098
A[20] = 0.00000000;
3099
A[21] = 0.00000000;
3100
A[22] = 0.00000000;
3101
A[23] = 0.00000000;
3102
A[24] = 0.17916667*G0_;
3103
A[25] = 0.00000000;
3104
A[26] = 0.17916667*G0_;
3105
A[27] = 0.35833333*G0_;
3106
A[28] = 0.00000000;
3107
A[29] = 0.00000000;
3108
A[30] = 0.00000000;
3109
A[31] = 0.00000000;
3110
A[32] = 0.00000000;
3111
A[33] = 0.00000000;
3112
A[34] = 0.00000000;
3113
A[35] = 0.00000000;
3114
A[36] = 0.00000000;
3115
A[37] = 0.00000000;
3116
A[38] = 0.00000000;
3117
A[39] = 0.00000000;
3118
A[40] = 0.00000000;
3119
A[41] = 0.00000000;
3120
A[42] = 0.00000000;
3121
A[43] = 0.00000000;
3122
A[44] = 0.00000000;
3123
A[45] = 0.00000000;
3124
A[46] = 0.00000000;
3125
A[47] = 0.00000000;
3126
A[48] = 0.00000000;
3127
A[49] = 0.00000000;
3128
A[50] = 0.00000000;
3129
A[51] = 0.00000000;
3130
A[52] = 0.00000000;
3131
A[53] = 0.00000000;
3132
A[54] = 0.00000000;
3133
A[55] = 0.00000000;
3134
A[56] = 0.00000000;
3135
A[57] = 0.00000000;
3136
A[58] = 0.00000000;
3137
A[59] = 0.00000000;
3138
A[60] = 0.00000000;
3139
A[61] = 0.00000000;
3140
A[62] = 0.00000000;
3141
A[63] = 0.00000000;
3142
break;
3143
}
3144
case 2:
3145
{
3146
A[0] = 0.35833333*G0_;
3147
A[1] = 0.00000000;
3148
A[2] = 0.17916667*G0_;
3149
A[3] = 0.17916667*G0_;
3150
A[4] = 0.00000000;
3151
A[5] = 0.00000000;
3152
A[6] = 0.00000000;
3153
A[7] = 0.00000000;
3154
A[8] = 0.00000000;
3155
A[9] = 0.00000000;
3156
A[10] = 0.00000000;
3157
A[11] = 0.00000000;
3158
A[12] = 0.00000000;
3159
A[13] = 0.00000000;
3160
A[14] = 0.00000000;
3161
A[15] = 0.00000000;
3162
A[16] = 0.17916667*G0_;
3163
A[17] = 0.00000000;
3164
A[18] = 0.35833333*G0_;
3165
A[19] = 0.17916667*G0_;
3166
A[20] = 0.00000000;
3167
A[21] = 0.00000000;
3168
A[22] = 0.00000000;
3169
A[23] = 0.00000000;
3170
A[24] = 0.17916667*G0_;
3171
A[25] = 0.00000000;
3172
A[26] = 0.17916667*G0_;
3173
A[27] = 0.35833333*G0_;
3174
A[28] = 0.00000000;
3175
A[29] = 0.00000000;
3176
A[30] = 0.00000000;
3177
A[31] = 0.00000000;
3178
A[32] = 0.00000000;
3179
A[33] = 0.00000000;
3180
A[34] = 0.00000000;
3181
A[35] = 0.00000000;
3182
A[36] = 0.00000000;
3183
A[37] = 0.00000000;
3184
A[38] = 0.00000000;
3185
A[39] = 0.00000000;
3186
A[40] = 0.00000000;
3187
A[41] = 0.00000000;
3188
A[42] = 0.00000000;
3189
A[43] = 0.00000000;
3190
A[44] = 0.00000000;
3191
A[45] = 0.00000000;
3192
A[46] = 0.00000000;
3193
A[47] = 0.00000000;
3194
A[48] = 0.00000000;
3195
A[49] = 0.00000000;
3196
A[50] = 0.00000000;
3197
A[51] = 0.00000000;
3198
A[52] = 0.00000000;
3199
A[53] = 0.00000000;
3200
A[54] = 0.00000000;
3201
A[55] = 0.00000000;
3202
A[56] = 0.00000000;
3203
A[57] = 0.00000000;
3204
A[58] = 0.00000000;
3205
A[59] = 0.00000000;
3206
A[60] = 0.00000000;
3207
A[61] = 0.00000000;
3208
A[62] = 0.00000000;
3209
A[63] = 0.00000000;
3210
break;
3211
}
3212
case 3:
3213
{
3214
A[0] = 0.35833333*G0_;
3215
A[1] = 0.00000000;
3216
A[2] = 0.17916667*G0_;
3217
A[3] = 0.17916667*G0_;
3218
A[4] = 0.00000000;
3219
A[5] = 0.00000000;
3220
A[6] = 0.00000000;
3221
A[7] = 0.00000000;
3222
A[8] = 0.00000000;
3223
A[9] = 0.00000000;
3224
A[10] = 0.00000000;
3225
A[11] = 0.00000000;
3226
A[12] = 0.00000000;
3227
A[13] = 0.00000000;
3228
A[14] = 0.00000000;
3229
A[15] = 0.00000000;
3230
A[16] = 0.17916667*G0_;
3231
A[17] = 0.00000000;
3232
A[18] = 0.35833333*G0_;
3233
A[19] = 0.17916667*G0_;
3234
A[20] = 0.00000000;
3235
A[21] = 0.00000000;
3236
A[22] = 0.00000000;
3237
A[23] = 0.00000000;
3238
A[24] = 0.17916667*G0_;
3239
A[25] = 0.00000000;
3240
A[26] = 0.17916667*G0_;
3241
A[27] = 0.35833333*G0_;
3242
A[28] = 0.00000000;
3243
A[29] = 0.00000000;
3244
A[30] = 0.00000000;
3245
A[31] = 0.00000000;
3246
A[32] = 0.00000000;
3247
A[33] = 0.00000000;
3248
A[34] = 0.00000000;
3249
A[35] = 0.00000000;
3250
A[36] = 0.00000000;
3251
A[37] = 0.00000000;
3252
A[38] = 0.00000000;
3253
A[39] = 0.00000000;
3254
A[40] = 0.00000000;
3255
A[41] = 0.00000000;
3256
A[42] = 0.00000000;
3257
A[43] = 0.00000000;
3258
A[44] = 0.00000000;
3259
A[45] = 0.00000000;
3260
A[46] = 0.00000000;
3261
A[47] = 0.00000000;
3262
A[48] = 0.00000000;
3263
A[49] = 0.00000000;
3264
A[50] = 0.00000000;
3265
A[51] = 0.00000000;
3266
A[52] = 0.00000000;
3267
A[53] = 0.00000000;
3268
A[54] = 0.00000000;
3269
A[55] = 0.00000000;
3270
A[56] = 0.00000000;
3271
A[57] = 0.00000000;
3272
A[58] = 0.00000000;
3273
A[59] = 0.00000000;
3274
A[60] = 0.00000000;
3275
A[61] = 0.00000000;
3276
A[62] = 0.00000000;
3277
A[63] = 0.00000000;
3278
break;
3279
}
3280
}
3281
3282
break;
3283
}
3284
case 2:
3285
{
3286
switch (facet1)
3287
{
3288
case 0:
3289
{
3290
A[0] = 0.35833333*G0_;
3291
A[1] = 0.17916667*G0_;
3292
A[2] = 0.00000000;
3293
A[3] = 0.17916667*G0_;
3294
A[4] = 0.00000000;
3295
A[5] = 0.00000000;
3296
A[6] = 0.00000000;
3297
A[7] = 0.00000000;
3298
A[8] = 0.17916667*G0_;
3299
A[9] = 0.35833333*G0_;
3300
A[10] = 0.00000000;
3301
A[11] = 0.17916667*G0_;
3302
A[12] = 0.00000000;
3303
A[13] = 0.00000000;
3304
A[14] = 0.00000000;
3305
A[15] = 0.00000000;
3306
A[16] = 0.00000000;
3307
A[17] = 0.00000000;
3308
A[18] = 0.00000000;
3309
A[19] = 0.00000000;
3310
A[20] = 0.00000000;
3311
A[21] = 0.00000000;
3312
A[22] = 0.00000000;
3313
A[23] = 0.00000000;
3314
A[24] = 0.17916667*G0_;
3315
A[25] = 0.17916667*G0_;
3316
A[26] = 0.00000000;
3317
A[27] = 0.35833333*G0_;
3318
A[28] = 0.00000000;
3319
A[29] = 0.00000000;
3320
A[30] = 0.00000000;
3321
A[31] = 0.00000000;
3322
A[32] = 0.00000000;
3323
A[33] = 0.00000000;
3324
A[34] = 0.00000000;
3325
A[35] = 0.00000000;
3326
A[36] = 0.00000000;
3327
A[37] = 0.00000000;
3328
A[38] = 0.00000000;
3329
A[39] = 0.00000000;
3330
A[40] = 0.00000000;
3331
A[41] = 0.00000000;
3332
A[42] = 0.00000000;
3333
A[43] = 0.00000000;
3334
A[44] = 0.00000000;
3335
A[45] = 0.00000000;
3336
A[46] = 0.00000000;
3337
A[47] = 0.00000000;
3338
A[48] = 0.00000000;
3339
A[49] = 0.00000000;
3340
A[50] = 0.00000000;
3341
A[51] = 0.00000000;
3342
A[52] = 0.00000000;
3343
A[53] = 0.00000000;
3344
A[54] = 0.00000000;
3345
A[55] = 0.00000000;
3346
A[56] = 0.00000000;
3347
A[57] = 0.00000000;
3348
A[58] = 0.00000000;
3349
A[59] = 0.00000000;
3350
A[60] = 0.00000000;
3351
A[61] = 0.00000000;
3352
A[62] = 0.00000000;
3353
A[63] = 0.00000000;
3354
break;
3355
}
3356
case 1:
3357
{
3358
A[0] = 0.35833333*G0_;
3359
A[1] = 0.17916667*G0_;
3360
A[2] = 0.00000000;
3361
A[3] = 0.17916667*G0_;
3362
A[4] = 0.00000000;
3363
A[5] = 0.00000000;
3364
A[6] = 0.00000000;
3365
A[7] = 0.00000000;
3366
A[8] = 0.17916667*G0_;
3367
A[9] = 0.35833333*G0_;
3368
A[10] = 0.00000000;
3369
A[11] = 0.17916667*G0_;
3370
A[12] = 0.00000000;
3371
A[13] = 0.00000000;
3372
A[14] = 0.00000000;
3373
A[15] = 0.00000000;
3374
A[16] = 0.00000000;
3375
A[17] = 0.00000000;
3376
A[18] = 0.00000000;
3377
A[19] = 0.00000000;
3378
A[20] = 0.00000000;
3379
A[21] = 0.00000000;
3380
A[22] = 0.00000000;
3381
A[23] = 0.00000000;
3382
A[24] = 0.17916667*G0_;
3383
A[25] = 0.17916667*G0_;
3384
A[26] = 0.00000000;
3385
A[27] = 0.35833333*G0_;
3386
A[28] = 0.00000000;
3387
A[29] = 0.00000000;
3388
A[30] = 0.00000000;
3389
A[31] = 0.00000000;
3390
A[32] = 0.00000000;
3391
A[33] = 0.00000000;
3392
A[34] = 0.00000000;
3393
A[35] = 0.00000000;
3394
A[36] = 0.00000000;
3395
A[37] = 0.00000000;
3396
A[38] = 0.00000000;
3397
A[39] = 0.00000000;
3398
A[40] = 0.00000000;
3399
A[41] = 0.00000000;
3400
A[42] = 0.00000000;
3401
A[43] = 0.00000000;
3402
A[44] = 0.00000000;
3403
A[45] = 0.00000000;
3404
A[46] = 0.00000000;
3405
A[47] = 0.00000000;
3406
A[48] = 0.00000000;
3407
A[49] = 0.00000000;
3408
A[50] = 0.00000000;
3409
A[51] = 0.00000000;
3410
A[52] = 0.00000000;
3411
A[53] = 0.00000000;
3412
A[54] = 0.00000000;
3413
A[55] = 0.00000000;
3414
A[56] = 0.00000000;
3415
A[57] = 0.00000000;
3416
A[58] = 0.00000000;
3417
A[59] = 0.00000000;
3418
A[60] = 0.00000000;
3419
A[61] = 0.00000000;
3420
A[62] = 0.00000000;
3421
A[63] = 0.00000000;
3422
break;
3423
}
3424
case 2:
3425
{
3426
A[0] = 0.35833333*G0_;
3427
A[1] = 0.17916667*G0_;
3428
A[2] = 0.00000000;
3429
A[3] = 0.17916667*G0_;
3430
A[4] = 0.00000000;
3431
A[5] = 0.00000000;
3432
A[6] = 0.00000000;
3433
A[7] = 0.00000000;
3434
A[8] = 0.17916667*G0_;
3435
A[9] = 0.35833333*G0_;
3436
A[10] = 0.00000000;
3437
A[11] = 0.17916667*G0_;
3438
A[12] = 0.00000000;
3439
A[13] = 0.00000000;
3440
A[14] = 0.00000000;
3441
A[15] = 0.00000000;
3442
A[16] = 0.00000000;
3443
A[17] = 0.00000000;
3444
A[18] = 0.00000000;
3445
A[19] = 0.00000000;
3446
A[20] = 0.00000000;
3447
A[21] = 0.00000000;
3448
A[22] = 0.00000000;
3449
A[23] = 0.00000000;
3450
A[24] = 0.17916667*G0_;
3451
A[25] = 0.17916667*G0_;
3452
A[26] = 0.00000000;
3453
A[27] = 0.35833333*G0_;
3454
A[28] = 0.00000000;
3455
A[29] = 0.00000000;
3456
A[30] = 0.00000000;
3457
A[31] = 0.00000000;
3458
A[32] = 0.00000000;
3459
A[33] = 0.00000000;
3460
A[34] = 0.00000000;
3461
A[35] = 0.00000000;
3462
A[36] = 0.00000000;
3463
A[37] = 0.00000000;
3464
A[38] = 0.00000000;
3465
A[39] = 0.00000000;
3466
A[40] = 0.00000000;
3467
A[41] = 0.00000000;
3468
A[42] = 0.00000000;
3469
A[43] = 0.00000000;
3470
A[44] = 0.00000000;
3471
A[45] = 0.00000000;
3472
A[46] = 0.00000000;
3473
A[47] = 0.00000000;
3474
A[48] = 0.00000000;
3475
A[49] = 0.00000000;
3476
A[50] = 0.00000000;
3477
A[51] = 0.00000000;
3478
A[52] = 0.00000000;
3479
A[53] = 0.00000000;
3480
A[54] = 0.00000000;
3481
A[55] = 0.00000000;
3482
A[56] = 0.00000000;
3483
A[57] = 0.00000000;
3484
A[58] = 0.00000000;
3485
A[59] = 0.00000000;
3486
A[60] = 0.00000000;
3487
A[61] = 0.00000000;
3488
A[62] = 0.00000000;
3489
A[63] = 0.00000000;
3490
break;
3491
}
3492
case 3:
3493
{
3494
A[0] = 0.35833333*G0_;
3495
A[1] = 0.17916667*G0_;
3496
A[2] = 0.00000000;
3497
A[3] = 0.17916667*G0_;
3498
A[4] = 0.00000000;
3499
A[5] = 0.00000000;
3500
A[6] = 0.00000000;
3501
A[7] = 0.00000000;
3502
A[8] = 0.17916667*G0_;
3503
A[9] = 0.35833333*G0_;
3504
A[10] = 0.00000000;
3505
A[11] = 0.17916667*G0_;
3506
A[12] = 0.00000000;
3507
A[13] = 0.00000000;
3508
A[14] = 0.00000000;
3509
A[15] = 0.00000000;
3510
A[16] = 0.00000000;
3511
A[17] = 0.00000000;
3512
A[18] = 0.00000000;
3513
A[19] = 0.00000000;
3514
A[20] = 0.00000000;
3515
A[21] = 0.00000000;
3516
A[22] = 0.00000000;
3517
A[23] = 0.00000000;
3518
A[24] = 0.17916667*G0_;
3519
A[25] = 0.17916667*G0_;
3520
A[26] = 0.00000000;
3521
A[27] = 0.35833333*G0_;
3522
A[28] = 0.00000000;
3523
A[29] = 0.00000000;
3524
A[30] = 0.00000000;
3525
A[31] = 0.00000000;
3526
A[32] = 0.00000000;
3527
A[33] = 0.00000000;
3528
A[34] = 0.00000000;
3529
A[35] = 0.00000000;
3530
A[36] = 0.00000000;
3531
A[37] = 0.00000000;
3532
A[38] = 0.00000000;
3533
A[39] = 0.00000000;
3534
A[40] = 0.00000000;
3535
A[41] = 0.00000000;
3536
A[42] = 0.00000000;
3537
A[43] = 0.00000000;
3538
A[44] = 0.00000000;
3539
A[45] = 0.00000000;
3540
A[46] = 0.00000000;
3541
A[47] = 0.00000000;
3542
A[48] = 0.00000000;
3543
A[49] = 0.00000000;
3544
A[50] = 0.00000000;
3545
A[51] = 0.00000000;
3546
A[52] = 0.00000000;
3547
A[53] = 0.00000000;
3548
A[54] = 0.00000000;
3549
A[55] = 0.00000000;
3550
A[56] = 0.00000000;
3551
A[57] = 0.00000000;
3552
A[58] = 0.00000000;
3553
A[59] = 0.00000000;
3554
A[60] = 0.00000000;
3555
A[61] = 0.00000000;
3556
A[62] = 0.00000000;
3557
A[63] = 0.00000000;
3558
break;
3559
}
3560
}
3561
3562
break;
3563
}
3564
case 3:
3565
{
3566
switch (facet1)
3567
{
3568
case 0:
3569
{
3570
A[0] = 0.35833333*G0_;
3571
A[1] = 0.17916667*G0_;
3572
A[2] = 0.17916667*G0_;
3573
A[3] = 0.00000000;
3574
A[4] = 0.00000000;
3575
A[5] = 0.00000000;
3576
A[6] = 0.00000000;
3577
A[7] = 0.00000000;
3578
A[8] = 0.17916667*G0_;
3579
A[9] = 0.35833333*G0_;
3580
A[10] = 0.17916667*G0_;
3581
A[11] = 0.00000000;
3582
A[12] = 0.00000000;
3583
A[13] = 0.00000000;
3584
A[14] = 0.00000000;
3585
A[15] = 0.00000000;
3586
A[16] = 0.17916667*G0_;
3587
A[17] = 0.17916667*G0_;
3588
A[18] = 0.35833333*G0_;
3589
A[19] = 0.00000000;
3590
A[20] = 0.00000000;
3591
A[21] = 0.00000000;
3592
A[22] = 0.00000000;
3593
A[23] = 0.00000000;
3594
A[24] = 0.00000000;
3595
A[25] = 0.00000000;
3596
A[26] = 0.00000000;
3597
A[27] = 0.00000000;
3598
A[28] = 0.00000000;
3599
A[29] = 0.00000000;
3600
A[30] = 0.00000000;
3601
A[31] = 0.00000000;
3602
A[32] = 0.00000000;
3603
A[33] = 0.00000000;
3604
A[34] = 0.00000000;
3605
A[35] = 0.00000000;
3606
A[36] = 0.00000000;
3607
A[37] = 0.00000000;
3608
A[38] = 0.00000000;
3609
A[39] = 0.00000000;
3610
A[40] = 0.00000000;
3611
A[41] = 0.00000000;
3612
A[42] = 0.00000000;
3613
A[43] = 0.00000000;
3614
A[44] = 0.00000000;
3615
A[45] = 0.00000000;
3616
A[46] = 0.00000000;
3617
A[47] = 0.00000000;
3618
A[48] = 0.00000000;
3619
A[49] = 0.00000000;
3620
A[50] = 0.00000000;
3621
A[51] = 0.00000000;
3622
A[52] = 0.00000000;
3623
A[53] = 0.00000000;
3624
A[54] = 0.00000000;
3625
A[55] = 0.00000000;
3626
A[56] = 0.00000000;
3627
A[57] = 0.00000000;
3628
A[58] = 0.00000000;
3629
A[59] = 0.00000000;
3630
A[60] = 0.00000000;
3631
A[61] = 0.00000000;
3632
A[62] = 0.00000000;
3633
A[63] = 0.00000000;
3634
break;
3635
}
3636
case 1:
3637
{
3638
A[0] = 0.35833333*G0_;
3639
A[1] = 0.17916667*G0_;
3640
A[2] = 0.17916667*G0_;
3641
A[3] = 0.00000000;
3642
A[4] = 0.00000000;
3643
A[5] = 0.00000000;
3644
A[6] = 0.00000000;
3645
A[7] = 0.00000000;
3646
A[8] = 0.17916667*G0_;
3647
A[9] = 0.35833333*G0_;
3648
A[10] = 0.17916667*G0_;
3649
A[11] = 0.00000000;
3650
A[12] = 0.00000000;
3651
A[13] = 0.00000000;
3652
A[14] = 0.00000000;
3653
A[15] = 0.00000000;
3654
A[16] = 0.17916667*G0_;
3655
A[17] = 0.17916667*G0_;
3656
A[18] = 0.35833333*G0_;
3657
A[19] = 0.00000000;
3658
A[20] = 0.00000000;
3659
A[21] = 0.00000000;
3660
A[22] = 0.00000000;
3661
A[23] = 0.00000000;
3662
A[24] = 0.00000000;
3663
A[25] = 0.00000000;
3664
A[26] = 0.00000000;
3665
A[27] = 0.00000000;
3666
A[28] = 0.00000000;
3667
A[29] = 0.00000000;
3668
A[30] = 0.00000000;
3669
A[31] = 0.00000000;
3670
A[32] = 0.00000000;
3671
A[33] = 0.00000000;
3672
A[34] = 0.00000000;
3673
A[35] = 0.00000000;
3674
A[36] = 0.00000000;
3675
A[37] = 0.00000000;
3676
A[38] = 0.00000000;
3677
A[39] = 0.00000000;
3678
A[40] = 0.00000000;
3679
A[41] = 0.00000000;
3680
A[42] = 0.00000000;
3681
A[43] = 0.00000000;
3682
A[44] = 0.00000000;
3683
A[45] = 0.00000000;
3684
A[46] = 0.00000000;
3685
A[47] = 0.00000000;
3686
A[48] = 0.00000000;
3687
A[49] = 0.00000000;
3688
A[50] = 0.00000000;
3689
A[51] = 0.00000000;
3690
A[52] = 0.00000000;
3691
A[53] = 0.00000000;
3692
A[54] = 0.00000000;
3693
A[55] = 0.00000000;
3694
A[56] = 0.00000000;
3695
A[57] = 0.00000000;
3696
A[58] = 0.00000000;
3697
A[59] = 0.00000000;
3698
A[60] = 0.00000000;
3699
A[61] = 0.00000000;
3700
A[62] = 0.00000000;
3701
A[63] = 0.00000000;
3702
break;
3703
}
3704
case 2:
3705
{
3706
A[0] = 0.35833333*G0_;
3707
A[1] = 0.17916667*G0_;
3708
A[2] = 0.17916667*G0_;
3709
A[3] = 0.00000000;
3710
A[4] = 0.00000000;
3711
A[5] = 0.00000000;
3712
A[6] = 0.00000000;
3713
A[7] = 0.00000000;
3714
A[8] = 0.17916667*G0_;
3715
A[9] = 0.35833333*G0_;
3716
A[10] = 0.17916667*G0_;
3717
A[11] = 0.00000000;
3718
A[12] = 0.00000000;
3719
A[13] = 0.00000000;
3720
A[14] = 0.00000000;
3721
A[15] = 0.00000000;
3722
A[16] = 0.17916667*G0_;
3723
A[17] = 0.17916667*G0_;
3724
A[18] = 0.35833333*G0_;
3725
A[19] = 0.00000000;
3726
A[20] = 0.00000000;
3727
A[21] = 0.00000000;
3728
A[22] = 0.00000000;
3729
A[23] = 0.00000000;
3730
A[24] = 0.00000000;
3731
A[25] = 0.00000000;
3732
A[26] = 0.00000000;
3733
A[27] = 0.00000000;
3734
A[28] = 0.00000000;
3735
A[29] = 0.00000000;
3736
A[30] = 0.00000000;
3737
A[31] = 0.00000000;
3738
A[32] = 0.00000000;
3739
A[33] = 0.00000000;
3740
A[34] = 0.00000000;
3741
A[35] = 0.00000000;
3742
A[36] = 0.00000000;
3743
A[37] = 0.00000000;
3744
A[38] = 0.00000000;
3745
A[39] = 0.00000000;
3746
A[40] = 0.00000000;
3747
A[41] = 0.00000000;
3748
A[42] = 0.00000000;
3749
A[43] = 0.00000000;
3750
A[44] = 0.00000000;
3751
A[45] = 0.00000000;
3752
A[46] = 0.00000000;
3753
A[47] = 0.00000000;
3754
A[48] = 0.00000000;
3755
A[49] = 0.00000000;
3756
A[50] = 0.00000000;
3757
A[51] = 0.00000000;
3758
A[52] = 0.00000000;
3759
A[53] = 0.00000000;
3760
A[54] = 0.00000000;
3761
A[55] = 0.00000000;
3762
A[56] = 0.00000000;
3763
A[57] = 0.00000000;
3764
A[58] = 0.00000000;
3765
A[59] = 0.00000000;
3766
A[60] = 0.00000000;
3767
A[61] = 0.00000000;
3768
A[62] = 0.00000000;
3769
A[63] = 0.00000000;
3770
break;
3771
}
3772
case 3:
3773
{
3774
A[0] = 0.35833333*G0_;
3775
A[1] = 0.17916667*G0_;
3776
A[2] = 0.17916667*G0_;
3777
A[3] = 0.00000000;
3778
A[4] = 0.00000000;
3779
A[5] = 0.00000000;
3780
A[6] = 0.00000000;
3781
A[7] = 0.00000000;
3782
A[8] = 0.17916667*G0_;
3783
A[9] = 0.35833333*G0_;
3784
A[10] = 0.17916667*G0_;
3785
A[11] = 0.00000000;
3786
A[12] = 0.00000000;
3787
A[13] = 0.00000000;
3788
A[14] = 0.00000000;
3789
A[15] = 0.00000000;
3790
A[16] = 0.17916667*G0_;
3791
A[17] = 0.17916667*G0_;
3792
A[18] = 0.35833333*G0_;
3793
A[19] = 0.00000000;
3794
A[20] = 0.00000000;
3795
A[21] = 0.00000000;
3796
A[22] = 0.00000000;
3797
A[23] = 0.00000000;
3798
A[24] = 0.00000000;
3799
A[25] = 0.00000000;
3800
A[26] = 0.00000000;
3801
A[27] = 0.00000000;
3802
A[28] = 0.00000000;
3803
A[29] = 0.00000000;
3804
A[30] = 0.00000000;
3805
A[31] = 0.00000000;
3806
A[32] = 0.00000000;
3807
A[33] = 0.00000000;
3808
A[34] = 0.00000000;
3809
A[35] = 0.00000000;
3810
A[36] = 0.00000000;
3811
A[37] = 0.00000000;
3812
A[38] = 0.00000000;
3813
A[39] = 0.00000000;
3814
A[40] = 0.00000000;
3815
A[41] = 0.00000000;
3816
A[42] = 0.00000000;
3817
A[43] = 0.00000000;
3818
A[44] = 0.00000000;
3819
A[45] = 0.00000000;
3820
A[46] = 0.00000000;
3821
A[47] = 0.00000000;
3822
A[48] = 0.00000000;
3823
A[49] = 0.00000000;
3824
A[50] = 0.00000000;
3825
A[51] = 0.00000000;
3826
A[52] = 0.00000000;
3827
A[53] = 0.00000000;
3828
A[54] = 0.00000000;
3829
A[55] = 0.00000000;
3830
A[56] = 0.00000000;
3831
A[57] = 0.00000000;
3832
A[58] = 0.00000000;
3833
A[59] = 0.00000000;
3834
A[60] = 0.00000000;
3835
A[61] = 0.00000000;
3836
A[62] = 0.00000000;
3837
A[63] = 0.00000000;
3838
break;
3839
}
3840
}
3841
3842
break;
3843
}
3844
}
3845
3846
}
3847
3848
};
3849
3850
/// This class defines the interface for the assembly of the global
3851
/// tensor corresponding to a form with r + n arguments, that is, a
3852
/// mapping
3853
///
3854
/// a : V1 x V2 x ... Vr x W1 x W2 x ... x Wn -> R
3855
///
3856
/// with arguments v1, v2, ..., vr, w1, w2, ..., wn. The rank r
3857
/// global tensor A is defined by
3858
///
3859
/// A = a(V1, V2, ..., Vr, w1, w2, ..., wn),
3860
///
3861
/// where each argument Vj represents the application to the
3862
/// sequence of basis functions of Vj and w1, w2, ..., wn are given
3863
/// fixed functions (coefficients).
3864
3865
class subdomains_form_0: public ufc::form
3866
{
3867
public:
3868
3869
/// Constructor
3870
subdomains_form_0() : ufc::form()
3871
{
3872
// Do nothing
3873
}
3874
3875
/// Destructor
3876
virtual ~subdomains_form_0()
3877
{
3878
// Do nothing
3879
}
3880
3881
/// Return a string identifying the form
3882
virtual const char* signature() const
3883
{
3884
return "Form([Integral(Product(Argument(FiniteElement('Lagrange', Cell('tetrahedron', 1, Space(3)), 1), 0), Argument(FiniteElement('Lagrange', Cell('tetrahedron', 1, Space(3)), 1), 1)), Measure('cell', 0, None)), Integral(Product(Argument(FiniteElement('Lagrange', Cell('tetrahedron', 1, Space(3)), 1), 1), Product(FloatValue(10.0, (), (), {}), Argument(FiniteElement('Lagrange', Cell('tetrahedron', 1, Space(3)), 1), 0))), Measure('cell', 1, None)), Integral(Product(Argument(FiniteElement('Lagrange', Cell('tetrahedron', 1, Space(3)), 1), 0), Argument(FiniteElement('Lagrange', Cell('tetrahedron', 1, Space(3)), 1), 1)), Measure('exterior_facet', 0, None)), Integral(Product(Argument(FiniteElement('Lagrange', Cell('tetrahedron', 1, Space(3)), 1), 1), Product(FloatValue(2.0, (), (), {}), Argument(FiniteElement('Lagrange', Cell('tetrahedron', 1, Space(3)), 1), 0))), Measure('exterior_facet', 1, None)), Integral(Product(PositiveRestricted(Argument(FiniteElement('Lagrange', Cell('tetrahedron', 1, Space(3)), 1), 0)), PositiveRestricted(Argument(FiniteElement('Lagrange', Cell('tetrahedron', 1, Space(3)), 1), 1))), Measure('interior_facet', 0, None)), Integral(Product(PositiveRestricted(Argument(FiniteElement('Lagrange', Cell('tetrahedron', 1, Space(3)), 1), 1)), Product(FloatValue(4.2999999999999998, (), (), {}), PositiveRestricted(Argument(FiniteElement('Lagrange', Cell('tetrahedron', 1, Space(3)), 1), 0)))), Measure('interior_facet', 1, None))])";
3885
}
3886
3887
/// Return the rank of the global tensor (r)
3888
virtual unsigned int rank() const
3889
{
3890
return 2;
3891
}
3892
3893
/// Return the number of coefficients (n)
3894
virtual unsigned int num_coefficients() const
3895
{
3896
return 0;
3897
}
3898
3899
/// Return the number of cell integrals
3900
virtual unsigned int num_cell_integrals() const
3901
{
3902
return 2;
3903
}
3904
3905
/// Return the number of exterior facet integrals
3906
virtual unsigned int num_exterior_facet_integrals() const
3907
{
3908
return 2;
3909
}
3910
3911
/// Return the number of interior facet integrals
3912
virtual unsigned int num_interior_facet_integrals() const
3913
{
3914
return 2;
3915
}
3916
3917
/// Create a new finite element for argument function i
3918
virtual ufc::finite_element* create_finite_element(unsigned int i) const
3919
{
3920
switch (i)
3921
{
3922
case 0:
3923
{
3924
return new subdomains_finite_element_0();
3925
break;
3926
}
3927
case 1:
3928
{
3929
return new subdomains_finite_element_0();
3930
break;
3931
}
3932
}
3933
3934
return 0;
3935
}
3936
3937
/// Create a new dof map for argument function i
3938
virtual ufc::dof_map* create_dof_map(unsigned int i) const
3939
{
3940
switch (i)
3941
{
3942
case 0:
3943
{
3944
return new subdomains_dof_map_0();
3945
break;
3946
}
3947
case 1:
3948
{
3949
return new subdomains_dof_map_0();
3950
break;
3951
}
3952
}
3953
3954
return 0;
3955
}
3956
3957
/// Create a new cell integral on sub domain i
3958
virtual ufc::cell_integral* create_cell_integral(unsigned int i) const
3959
{
3960
switch (i)
3961
{
3962
case 0:
3963
{
3964
return new subdomains_cell_integral_0_0();
3965
break;
3966
}
3967
case 1:
3968
{
3969
return new subdomains_cell_integral_0_1();
3970
break;
3971
}
3972
}
3973
3974
return 0;
3975
}
3976
3977
/// Create a new exterior facet integral on sub domain i
3978
virtual ufc::exterior_facet_integral* create_exterior_facet_integral(unsigned int i) const
3979
{
3980
switch (i)
3981
{
3982
case 0:
3983
{
3984
return new subdomains_exterior_facet_integral_0_0();
3985
break;
3986
}
3987
case 1:
3988
{
3989
return new subdomains_exterior_facet_integral_0_1();
3990
break;
3991
}
3992
}
3993
3994
return 0;
3995
}
3996
3997
/// Create a new interior facet integral on sub domain i
3998
virtual ufc::interior_facet_integral* create_interior_facet_integral(unsigned int i) const
3999
{
4000
switch (i)
4001
{
4002
case 0:
4003
{
4004
return new subdomains_interior_facet_integral_0_0();
4005
break;
4006
}
4007
case 1:
4008
{
4009
return new subdomains_interior_facet_integral_0_1();
4010
break;
4011
}
4012
}
4013
4014
return 0;
4015
}
4016
4017
};
4018
4019
#endif
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