~ubuntu-branches/ubuntu/natty/dolfin/natty
» Revision
19
: demo/undocumented/auto-adaptive-poisson/cpp/AdaptivePoisson.h
« back to all changes in this revision
Viewing changes to demo/undocumented/auto-adaptive-poisson/cpp/AdaptivePoisson.h
- browse files at revision 19
- compare with another revision
- download diff
- download tarball
- view history from revision 19
- Committer: Bazaar Package Importer
- Author(s): Johannes Ring
- Date: 2011-02-24 10:34:44 UTC
- mfrom: (1.1.7 upstream) (14.1.4 sid)
- Revision ID: james.westby@ubuntu.com-20110224103444-n3fwnmh32lfoske0
Tags: 0.9.10-1
* New upstream release. This release fixes bug "FTBFS: error:
'SCOTCH_Dgraph' was not declared in this scope" (closes: #612602).
* debian/control:
- Add libslepc3.1-dev and libboost-thread-dev to Build-Depends and
Depends field in binary package libdolfin0-dev.
- Bump build dependency on python-ufc to >= 2.0.0.
- Remove Build-Depends-Indep field as upstream no longer ships the
user manual.
- Remove old fields Conflicts, Provides, and Replaces from
libdolfin0-dev, libdolfin0, libdolfin0-dbg, and python-dolfin.
* Remove all patches as they are now incorporated upstream.
* Add dolfin-plot and dolfin-version to debian/dolfin-bin.install.
* Remove .doc-base file since the user manual is removed by upstream.
* Remove targets clean and install/dolfin-doc from debian/rules since
they are no longer needed.
'SCOTCH_Dgraph' was not declared in this scope" (closes: #612602).
* debian/control:
- Add libslepc3.1-dev and libboost-thread-dev to Build-Depends and
Depends field in binary package libdolfin0-dev.
- Bump build dependency on python-ufc to >= 2.0.0.
- Remove Build-Depends-Indep field as upstream no longer ships the
user manual.
- Remove old fields Conflicts, Provides, and Replaces from
libdolfin0-dev, libdolfin0, libdolfin0-dbg, and python-dolfin.
* Remove all patches as they are now incorporated upstream.
* Add dolfin-plot and dolfin-version to debian/dolfin-bin.install.
* Remove .doc-base file since the user manual is removed by upstream.
* Remove targets clean and install/dolfin-doc from debian/rules since
they are no longer needed.
- files added:
- bench/common/timing
- bench/common/timing/cpp
- bench/fem/multicore
- bench/fem/multicore/cpp
- bench/mesh/topology
- bench/mesh/topology/cpp
- demo/undocumented/auto-adaptive-navier-stokes
- demo/undocumented/auto-adaptive-navier-stokes/cpp
- demo/undocumented/auto-adaptive-navier-stokes/python
- demo/undocumented/auto-adaptive-poisson
- demo/undocumented/auto-adaptive-poisson/cpp
- demo/undocumented/auto-adaptive-poisson/python
- demo/undocumented/coloring
- demo/undocumented/coloring/cpp
- demo/undocumented/coloring/python
- demo/undocumented/elementplot
- demo/undocumented/elementplot/python
- demo/undocumented/generalized-eigenvalue
- demo/undocumented/generalized-eigenvalue/python
- demo/undocumented/stokes-iterative/cpp
- scripts
- scripts/dolfin-convert
- scripts/dolfin-order
- scripts/dolfin-plot
- site-packages/dolfin/importhandler
- site-packages/dolfin_utils/documentation
- files removed:
- .pc
- .pc/cmake_find_petsc_slepc.patch
- .pc/cmake_find_petsc_slepc.patch/cmake
- .pc/cmake_find_petsc_slepc.patch/cmake/modules
- .pc/cmake_find_trilinos.patch
- .pc/cmake_find_trilinos.patch/cmake
- .pc/cmake_find_trilinos.patch/cmake/modules
- .pc/install.patch
- .pc/library_location.patch
- .pc/library_location.patch/dolfin
- debian/patches
- demo/undocumented/adaptive-pde
- doc/manual
- doc/manual/chapters
- doc/manual/dia
- doc/manual/eps
- doc/progr_reference
- doc/progr_reference/html
- doc/progr_reference/tex
- dolfin/main
- site-packages/dolfin/adaptivity
- site-packages/dolfin/docstrings
- site-packages/dolfin/docstrings/dolfin
- utils/convert
- utils/order
- files modified:
- AUTHORS
added
removed
demo/undocumented/auto-adaptive-poisson/cpp/AdaptivePoisson.h
1
// This code conforms with the UFC specification version 1.4.2
2
// and was automatically generated by FFC version 0.9.4+.
3
//
4
// This code was generated with the option '-l dolfin' and
5
// contains DOLFIN-specific wrappers that depend on DOLFIN.
6
//
7
// This code was generated with the following parameters:
8
//
9
// cache_dir: ''
10
// convert_exceptions_to_warnings: False
11
// cpp_optimize: False
12
// cpp_optimize_flags: '-O2'
13
// epsilon: 1e-14
14
// error_control: True
15
// form_postfix: True
16
// format: 'dolfin'
17
// log_level: 10
18
// log_prefix: ''
19
// no_ferari: True
20
// optimize: True
21
// output_dir: '.'
22
// precision: 15
23
// quadrature_degree: 'auto'
24
// quadrature_rule: 'auto'
25
// representation: 'auto'
26
// split: False
27
28
#ifndef __ADAPTIVEPOISSON_H
29
#define __ADAPTIVEPOISSON_H
30
31
#include <cmath>
32
#include <stdexcept>
33
#include <fstream>
34
#include <ufc.h>
35
36
/// This class defines the interface for a finite element.
37
38
class adaptivepoisson_finite_element_0: public ufc::finite_element
39
{
40
public:
41
42
/// Constructor
43
adaptivepoisson_finite_element_0() : ufc::finite_element()
44
{
45
// Do nothing
46
}
47
48
/// Destructor
49
virtual ~adaptivepoisson_finite_element_0()
50
{
51
// Do nothing
52
}
53
54
/// Return a string identifying the finite element
55
virtual const char* signature() const
56
{
57
return "FiniteElement('Discontinuous Lagrange', Cell('triangle', 1, Space(2)), 0)";
58
}
59
60
/// Return the cell shape
61
virtual ufc::shape cell_shape() const
62
{
63
return ufc::triangle;
64
}
65
66
/// Return the topological dimension of the cell shape
67
virtual unsigned int topological_dimension() const
68
{
69
return 2;
70
}
71
72
/// Return the geometric dimension of the cell shape
73
virtual unsigned int geometric_dimension() const
74
{
75
return 2;
76
}
77
78
/// Return the dimension of the finite element function space
79
virtual unsigned int space_dimension() const
80
{
81
return 1;
82
}
83
84
/// Return the rank of the value space
85
virtual unsigned int value_rank() const
86
{
87
return 0;
88
}
89
90
/// Return the dimension of the value space for axis i
91
virtual unsigned int value_dimension(unsigned int i) const
92
{
93
return 1;
94
}
95
96
/// Evaluate basis function i at given point in cell
97
virtual void evaluate_basis(unsigned int i,
98
double* values,
99
const double* coordinates,
100
const ufc::cell& c) const
101
{
102
// Extract vertex coordinates
103
104
// Compute Jacobian of affine map from reference cell
105
106
// Compute determinant of Jacobian
107
108
// Compute inverse of Jacobian
109
110
// Compute constants
111
112
// Get coordinates and map to the reference (FIAT) element
113
114
// Reset values.
115
*values = 0.000000000000000;
116
117
// Array of basisvalues.
118
double basisvalues[1] = {0.000000000000000};
119
120
// Declare helper variables.
121
122
// Compute basisvalues.
123
basisvalues[0] = 1.000000000000000;
124
125
// Table(s) of coefficients.
126
static const double coefficients0[1] = \
127
{1.000000000000000};
128
129
// Compute value(s).
130
for (unsigned int r = 0; r < 1; r++)
131
{
132
*values += coefficients0[r]*basisvalues[r];
133
}// end loop over 'r'
134
}
135
136
/// Evaluate all basis functions at given point in cell
137
virtual void evaluate_basis_all(double* values,
138
const double* coordinates,
139
const ufc::cell& c) const
140
{
141
// Element is constant, calling evaluate_basis.
142
evaluate_basis(0, values, coordinates, c);
143
}
144
145
/// Evaluate order n derivatives of basis function i at given point in cell
146
virtual void evaluate_basis_derivatives(unsigned int i,
147
unsigned int n,
148
double* values,
149
const double* coordinates,
150
const ufc::cell& c) const
151
{
152
// Extract vertex coordinates
153
const double * const * x = c.coordinates;
154
155
// Compute Jacobian of affine map from reference cell
156
const double J_00 = x[1][0] - x[0][0];
157
const double J_01 = x[2][0] - x[0][0];
158
const double J_10 = x[1][1] - x[0][1];
159
const double J_11 = x[2][1] - x[0][1];
160
161
// Compute determinant of Jacobian
162
double detJ = J_00*J_11 - J_01*J_10;
163
164
// Compute inverse of Jacobian
165
const double K_00 = J_11 / detJ;
166
const double K_01 = -J_01 / detJ;
167
const double K_10 = -J_10 / detJ;
168
const double K_11 = J_00 / detJ;
169
170
// Compute constants
171
172
// Get coordinates and map to the reference (FIAT) element
173
174
// Compute number of derivatives.
175
unsigned int num_derivatives = 1;
176
for (unsigned int r = 0; r < n; r++)
177
{
178
num_derivatives *= 2;
179
}// end loop over 'r'
180
181
// Declare pointer to two dimensional array that holds combinations of derivatives and initialise
182
unsigned int **combinations = new unsigned int *[num_derivatives];
183
for (unsigned int row = 0; row < num_derivatives; row++)
184
{
185
combinations[row] = new unsigned int [n];
186
for (unsigned int col = 0; col < n; col++)
187
combinations[row][col] = 0;
188
}
189
190
// Generate combinations of derivatives
191
for (unsigned int row = 1; row < num_derivatives; row++)
192
{
193
for (unsigned int num = 0; num < row; num++)
194
{
195
for (unsigned int col = n-1; col+1 > 0; col--)
196
{
197
if (combinations[row][col] + 1 > 1)
198
combinations[row][col] = 0;
199
else
200
{
201
combinations[row][col] += 1;
202
break;
203
}
204
}
205
}
206
}
207
208
// Compute inverse of Jacobian
209
const double Jinv[2][2] = {{K_00, K_01}, {K_10, K_11}};
210
211
// Declare transformation matrix
212
// Declare pointer to two dimensional array and initialise
213
double **transform = new double *[num_derivatives];
214
215
for (unsigned int j = 0; j < num_derivatives; j++)
216
{
217
transform[j] = new double [num_derivatives];
218
for (unsigned int k = 0; k < num_derivatives; k++)
219
transform[j][k] = 1;
220
}
221
222
// Construct transformation matrix
223
for (unsigned int row = 0; row < num_derivatives; row++)
224
{
225
for (unsigned int col = 0; col < num_derivatives; col++)
226
{
227
for (unsigned int k = 0; k < n; k++)
228
transform[row][col] *= Jinv[combinations[col][k]][combinations[row][k]];
229
}
230
}
231
232
// Reset values. Assuming that values is always an array.
233
for (unsigned int r = 0; r < num_derivatives; r++)
234
{
235
values[r] = 0.000000000000000;
236
}// end loop over 'r'
237
238
239
// Array of basisvalues.
240
double basisvalues[1] = {0.000000000000000};
241
242
// Declare helper variables.
243
244
// Compute basisvalues.
245
basisvalues[0] = 1.000000000000000;
246
247
// Table(s) of coefficients.
248
static const double coefficients0[1] = \
249
{1.000000000000000};
250
251
// Tables of derivatives of the polynomial base (transpose).
252
static const double dmats0[1][1] = \
253
{{0.000000000000000}};
254
255
static const double dmats1[1][1] = \
256
{{0.000000000000000}};
257
258
// Compute reference derivatives.
259
// Declare pointer to array of derivatives on FIAT element.
260
double *derivatives = new double[num_derivatives];
261
for (unsigned int r = 0; r < num_derivatives; r++)
262
{
263
derivatives[r] = 0.000000000000000;
264
}// end loop over 'r'
265
266
// Declare derivative matrix (of polynomial basis).
267
double dmats[1][1] = \
268
{{1.000000000000000}};
269
270
// Declare (auxiliary) derivative matrix (of polynomial basis).
271
double dmats_old[1][1] = \
272
{{1.000000000000000}};
273
274
// Loop possible derivatives.
275
for (unsigned int r = 0; r < num_derivatives; r++)
276
{
277
// Resetting dmats values to compute next derivative.
278
for (unsigned int t = 0; t < 1; t++)
279
{
280
for (unsigned int u = 0; u < 1; u++)
281
{
282
dmats[t][u] = 0.000000000000000;
283
if (t == u)
284
{
285
dmats[t][u] = 1.000000000000000;
286
}
287
288
}// end loop over 'u'
289
}// end loop over 't'
290
291
// Looping derivative order to generate dmats.
292
for (unsigned int s = 0; s < n; s++)
293
{
294
// Updating dmats_old with new values and resetting dmats.
295
for (unsigned int t = 0; t < 1; t++)
296
{
297
for (unsigned int u = 0; u < 1; u++)
298
{
299
dmats_old[t][u] = dmats[t][u];
300
dmats[t][u] = 0.000000000000000;
301
}// end loop over 'u'
302
}// end loop over 't'
303
304
// Update dmats using an inner product.
305
if (combinations[r][s] == 0)
306
{
307
for (unsigned int t = 0; t < 1; t++)
308
{
309
for (unsigned int u = 0; u < 1; u++)
310
{
311
for (unsigned int tu = 0; tu < 1; tu++)
312
{
313
dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
314
}// end loop over 'tu'
315
}// end loop over 'u'
316
}// end loop over 't'
317
}
318
319
if (combinations[r][s] == 1)
320
{
321
for (unsigned int t = 0; t < 1; t++)
322
{
323
for (unsigned int u = 0; u < 1; u++)
324
{
325
for (unsigned int tu = 0; tu < 1; tu++)
326
{
327
dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
328
}// end loop over 'tu'
329
}// end loop over 'u'
330
}// end loop over 't'
331
}
332
333
}// end loop over 's'
334
for (unsigned int s = 0; s < 1; s++)
335
{
336
for (unsigned int t = 0; t < 1; t++)
337
{
338
derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
339
}// end loop over 't'
340
}// end loop over 's'
341
}// end loop over 'r'
342
343
// Transform derivatives back to physical element
344
for (unsigned int r = 0; r < num_derivatives; r++)
345
{
346
for (unsigned int s = 0; s < num_derivatives; s++)
347
{
348
values[r] += transform[r][s]*derivatives[s];
349
}// end loop over 's'
350
}// end loop over 'r'
351
352
// Delete pointer to array of derivatives on FIAT element
353
delete [] derivatives;
354
355
// Delete pointer to array of combinations of derivatives and transform
356
for (unsigned int r = 0; r < num_derivatives; r++)
357
{
358
delete [] combinations[r];
359
}// end loop over 'r'
360
delete [] combinations;
361
for (unsigned int r = 0; r < num_derivatives; r++)
362
{
363
delete [] transform[r];
364
}// end loop over 'r'
365
delete [] transform;
366
}
367
368
/// Evaluate order n derivatives of all basis functions at given point in cell
369
virtual void evaluate_basis_derivatives_all(unsigned int n,
370
double* values,
371
const double* coordinates,
372
const ufc::cell& c) const
373
{
374
// Element is constant, calling evaluate_basis_derivatives.
375
evaluate_basis_derivatives(0, n, values, coordinates, c);
376
}
377
378
/// Evaluate linear functional for dof i on the function f
379
virtual double evaluate_dof(unsigned int i,
380
const ufc::function& f,
381
const ufc::cell& c) const
382
{
383
// Declare variables for result of evaluation.
384
double vals[1];
385
386
// Declare variable for physical coordinates.
387
double y[2];
388
const double * const * x = c.coordinates;
389
switch (i)
390
{
391
case 0:
392
{
393
y[0] = 0.333333333333333*x[0][0] + 0.333333333333333*x[1][0] + 0.333333333333333*x[2][0];
394
y[1] = 0.333333333333333*x[0][1] + 0.333333333333333*x[1][1] + 0.333333333333333*x[2][1];
395
f.evaluate(vals, y, c);
396
return vals[0];
397
break;
398
}
399
}
400
401
return 0.000000000000000;
402
}
403
404
/// Evaluate linear functionals for all dofs on the function f
405
virtual void evaluate_dofs(double* values,
406
const ufc::function& f,
407
const ufc::cell& c) const
408
{
409
// Declare variables for result of evaluation.
410
double vals[1];
411
412
// Declare variable for physical coordinates.
413
double y[2];
414
const double * const * x = c.coordinates;
415
y[0] = 0.333333333333333*x[0][0] + 0.333333333333333*x[1][0] + 0.333333333333333*x[2][0];
416
y[1] = 0.333333333333333*x[0][1] + 0.333333333333333*x[1][1] + 0.333333333333333*x[2][1];
417
f.evaluate(vals, y, c);
418
values[0] = vals[0];
419
}
420
421
/// Interpolate vertex values from dof values
422
virtual void interpolate_vertex_values(double* vertex_values,
423
const double* dof_values,
424
const ufc::cell& c) const
425
{
426
// Evaluate function and change variables
427
vertex_values[0] = dof_values[0];
428
vertex_values[1] = dof_values[0];
429
vertex_values[2] = dof_values[0];
430
}
431
432
/// Map coordinate xhat from reference cell to coordinate x in cell
433
virtual void map_from_reference_cell(double* x,
434
const double* xhat,
435
const ufc::cell& c)
436
{
437
throw std::runtime_error("map_from_reference_cell not yet implemented (introduced in UFC 2.0).");
438
}
439
440
/// Map from coordinate x in cell to coordinate xhat in reference cell
441
virtual void map_to_reference_cell(double* xhat,
442
const double* x,
443
const ufc::cell& c)
444
{
445
throw std::runtime_error("map_to_reference_cell not yet implemented (introduced in UFC 2.0).");
446
}
447
448
/// Return the number of sub elements (for a mixed element)
449
virtual unsigned int num_sub_elements() const
450
{
451
return 0;
452
}
453
454
/// Create a new finite element for sub element i (for a mixed element)
455
virtual ufc::finite_element* create_sub_element(unsigned int i) const
456
{
457
return 0;
458
}
459
460
/// Create a new class instance
461
virtual ufc::finite_element* create() const
462
{
463
return new adaptivepoisson_finite_element_0();
464
}
465
466
};
467
468
/// This class defines the interface for a finite element.
469
470
class adaptivepoisson_finite_element_1: public ufc::finite_element
471
{
472
public:
473
474
/// Constructor
475
adaptivepoisson_finite_element_1() : ufc::finite_element()
476
{
477
// Do nothing
478
}
479
480
/// Destructor
481
virtual ~adaptivepoisson_finite_element_1()
482
{
483
// Do nothing
484
}
485
486
/// Return a string identifying the finite element
487
virtual const char* signature() const
488
{
489
return "FiniteElement('Lagrange', Cell('triangle', 1, Space(2)), 2)";
490
}
491
492
/// Return the cell shape
493
virtual ufc::shape cell_shape() const
494
{
495
return ufc::triangle;
496
}
497
498
/// Return the topological dimension of the cell shape
499
virtual unsigned int topological_dimension() const
500
{
501
return 2;
502
}
503
504
/// Return the geometric dimension of the cell shape
505
virtual unsigned int geometric_dimension() const
506
{
507
return 2;
508
}
509
510
/// Return the dimension of the finite element function space
511
virtual unsigned int space_dimension() const
512
{
513
return 6;
514
}
515
516
/// Return the rank of the value space
517
virtual unsigned int value_rank() const
518
{
519
return 0;
520
}
521
522
/// Return the dimension of the value space for axis i
523
virtual unsigned int value_dimension(unsigned int i) const
524
{
525
return 1;
526
}
527
528
/// Evaluate basis function i at given point in cell
529
virtual void evaluate_basis(unsigned int i,
530
double* values,
531
const double* coordinates,
532
const ufc::cell& c) const
533
{
534
// Extract vertex coordinates
535
const double * const * x = c.coordinates;
536
537
// Compute Jacobian of affine map from reference cell
538
const double J_00 = x[1][0] - x[0][0];
539
const double J_01 = x[2][0] - x[0][0];
540
const double J_10 = x[1][1] - x[0][1];
541
const double J_11 = x[2][1] - x[0][1];
542
543
// Compute determinant of Jacobian
544
double detJ = J_00*J_11 - J_01*J_10;
545
546
// Compute inverse of Jacobian
547
548
// Compute constants
549
const double C0 = x[1][0] + x[2][0];
550
const double C1 = x[1][1] + x[2][1];
551
552
// Get coordinates and map to the reference (FIAT) element
553
double X = (J_01*(C1 - 2.0*coordinates[1]) + J_11*(2.0*coordinates[0] - C0)) / detJ;
554
double Y = (J_00*(2.0*coordinates[1] - C1) + J_10*(C0 - 2.0*coordinates[0])) / detJ;
555
556
// Reset values.
557
*values = 0.000000000000000;
558
switch (i)
559
{
560
case 0:
561
{
562
563
// Array of basisvalues.
564
double basisvalues[6] = {0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000};
565
566
// Declare helper variables.
567
unsigned int rr = 0;
568
unsigned int ss = 0;
569
unsigned int tt = 0;
570
double tmp5 = 0.000000000000000;
571
double tmp6 = 0.000000000000000;
572
double tmp7 = 0.000000000000000;
573
double tmp0 = (1.000000000000000 + Y + 2.000000000000000*X)/2.000000000000000;
574
double tmp1 = (1.000000000000000 - Y)/2.000000000000000;
575
double tmp2 = tmp1*tmp1;
576
577
// Compute basisvalues.
578
basisvalues[0] = 1.000000000000000;
579
basisvalues[1] = tmp0;
580
for (unsigned int r = 1; r < 2; r++)
581
{
582
rr = (r + 1)*((r + 1) + 1)/2;
583
ss = r*(r + 1)/2;
584
tt = (r - 1)*((r - 1) + 1)/2;
585
tmp5 = (1.000000000000000 + 2.000000000000000*r)/(1.000000000000000 + r);
586
basisvalues[rr] = (basisvalues[ss]*tmp0*tmp5 - basisvalues[tt]*tmp2*r/(1.000000000000000 + r));
587
}// end loop over 'r'
588
for (unsigned int r = 0; r < 2; r++)
589
{
590
rr = (r + 1)*(r + 1 + 1)/2 + 1;
591
ss = r*(r + 1)/2;
592
basisvalues[rr] = basisvalues[ss]*(0.500000000000000 + r + Y*(1.500000000000000 + r));
593
}// end loop over 'r'
594
for (unsigned int r = 0; r < 1; r++)
595
{
596
for (unsigned int s = 1; s < 2 - r; s++)
597
{
598
rr = (r + s + 1)*(r + s + 1 + 1)/2 + s + 1;
599
ss = (r + s)*(r + s + 1)/2 + s;
600
tt = (r + s - 1)*(r + s - 1 + 1)/2 + s - 1;
601
tmp5 = (2.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)*(3.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)/(2.000000000000000*(1.000000000000000 + s)*(2.000000000000000 + s + 2.000000000000000*r));
602
tmp6 = (1.000000000000000 + 4.000000000000000*r*r + 4.000000000000000*r)*(2.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)/(2.000000000000000*(1.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)*(1.000000000000000 + s)*(2.000000000000000 + s + 2.000000000000000*r));
603
tmp7 = (1.000000000000000 + s + 2.000000000000000*r)*(3.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)*s/((1.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)*(1.000000000000000 + s)*(2.000000000000000 + s + 2.000000000000000*r));
604
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Y*tmp5) - basisvalues[tt]*tmp7);
605
}// end loop over 's'
606
}// end loop over 'r'
607
for (unsigned int r = 0; r < 3; r++)
608
{
609
for (unsigned int s = 0; s < 3 - r; s++)
610
{
611
rr = (r + s)*(r + s + 1)/2 + s;
612
basisvalues[rr] *= std::sqrt((0.500000000000000 + r)*(1.000000000000000 + r + s));
613
}// end loop over 's'
614
}// end loop over 'r'
615
616
// Table(s) of coefficients.
617
static const double coefficients0[6] = \
618
{0.000000000000000, -0.173205080756888, -0.100000000000000, 0.121716123890037, 0.094280904158206, 0.054433105395182};
619
620
// Compute value(s).
621
for (unsigned int r = 0; r < 6; r++)
622
{
623
*values += coefficients0[r]*basisvalues[r];
624
}// end loop over 'r'
625
break;
626
}
627
case 1:
628
{
629
630
// Array of basisvalues.
631
double basisvalues[6] = {0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000};
632
633
// Declare helper variables.
634
unsigned int rr = 0;
635
unsigned int ss = 0;
636
unsigned int tt = 0;
637
double tmp5 = 0.000000000000000;
638
double tmp6 = 0.000000000000000;
639
double tmp7 = 0.000000000000000;
640
double tmp0 = (1.000000000000000 + Y + 2.000000000000000*X)/2.000000000000000;
641
double tmp1 = (1.000000000000000 - Y)/2.000000000000000;
642
double tmp2 = tmp1*tmp1;
643
644
// Compute basisvalues.
645
basisvalues[0] = 1.000000000000000;
646
basisvalues[1] = tmp0;
647
for (unsigned int r = 1; r < 2; r++)
648
{
649
rr = (r + 1)*((r + 1) + 1)/2;
650
ss = r*(r + 1)/2;
651
tt = (r - 1)*((r - 1) + 1)/2;
652
tmp5 = (1.000000000000000 + 2.000000000000000*r)/(1.000000000000000 + r);
653
basisvalues[rr] = (basisvalues[ss]*tmp0*tmp5 - basisvalues[tt]*tmp2*r/(1.000000000000000 + r));
654
}// end loop over 'r'
655
for (unsigned int r = 0; r < 2; r++)
656
{
657
rr = (r + 1)*(r + 1 + 1)/2 + 1;
658
ss = r*(r + 1)/2;
659
basisvalues[rr] = basisvalues[ss]*(0.500000000000000 + r + Y*(1.500000000000000 + r));
660
}// end loop over 'r'
661
for (unsigned int r = 0; r < 1; r++)
662
{
663
for (unsigned int s = 1; s < 2 - r; s++)
664
{
665
rr = (r + s + 1)*(r + s + 1 + 1)/2 + s + 1;
666
ss = (r + s)*(r + s + 1)/2 + s;
667
tt = (r + s - 1)*(r + s - 1 + 1)/2 + s - 1;
668
tmp5 = (2.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)*(3.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)/(2.000000000000000*(1.000000000000000 + s)*(2.000000000000000 + s + 2.000000000000000*r));
669
tmp6 = (1.000000000000000 + 4.000000000000000*r*r + 4.000000000000000*r)*(2.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)/(2.000000000000000*(1.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)*(1.000000000000000 + s)*(2.000000000000000 + s + 2.000000000000000*r));
670
tmp7 = (1.000000000000000 + s + 2.000000000000000*r)*(3.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)*s/((1.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)*(1.000000000000000 + s)*(2.000000000000000 + s + 2.000000000000000*r));
671
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Y*tmp5) - basisvalues[tt]*tmp7);
672
}// end loop over 's'
673
}// end loop over 'r'
674
for (unsigned int r = 0; r < 3; r++)
675
{
676
for (unsigned int s = 0; s < 3 - r; s++)
677
{
678
rr = (r + s)*(r + s + 1)/2 + s;
679
basisvalues[rr] *= std::sqrt((0.500000000000000 + r)*(1.000000000000000 + r + s));
680
}// end loop over 's'
681
}// end loop over 'r'
682
683
// Table(s) of coefficients.
684
static const double coefficients0[6] = \
685
{0.000000000000000, 0.173205080756888, -0.100000000000000, 0.121716123890037, -0.094280904158206, 0.054433105395182};
686
687
// Compute value(s).
688
for (unsigned int r = 0; r < 6; r++)
689
{
690
*values += coefficients0[r]*basisvalues[r];
691
}// end loop over 'r'
692
break;
693
}
694
case 2:
695
{
696
697
// Array of basisvalues.
698
double basisvalues[6] = {0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000};
699
700
// Declare helper variables.
701
unsigned int rr = 0;
702
unsigned int ss = 0;
703
unsigned int tt = 0;
704
double tmp5 = 0.000000000000000;
705
double tmp6 = 0.000000000000000;
706
double tmp7 = 0.000000000000000;
707
double tmp0 = (1.000000000000000 + Y + 2.000000000000000*X)/2.000000000000000;
708
double tmp1 = (1.000000000000000 - Y)/2.000000000000000;
709
double tmp2 = tmp1*tmp1;
710
711
// Compute basisvalues.
712
basisvalues[0] = 1.000000000000000;
713
basisvalues[1] = tmp0;
714
for (unsigned int r = 1; r < 2; r++)
715
{
716
rr = (r + 1)*((r + 1) + 1)/2;
717
ss = r*(r + 1)/2;
718
tt = (r - 1)*((r - 1) + 1)/2;
719
tmp5 = (1.000000000000000 + 2.000000000000000*r)/(1.000000000000000 + r);
720
basisvalues[rr] = (basisvalues[ss]*tmp0*tmp5 - basisvalues[tt]*tmp2*r/(1.000000000000000 + r));
721
}// end loop over 'r'
722
for (unsigned int r = 0; r < 2; r++)
723
{
724
rr = (r + 1)*(r + 1 + 1)/2 + 1;
725
ss = r*(r + 1)/2;
726
basisvalues[rr] = basisvalues[ss]*(0.500000000000000 + r + Y*(1.500000000000000 + r));
727
}// end loop over 'r'
728
for (unsigned int r = 0; r < 1; r++)
729
{
730
for (unsigned int s = 1; s < 2 - r; s++)
731
{
732
rr = (r + s + 1)*(r + s + 1 + 1)/2 + s + 1;
733
ss = (r + s)*(r + s + 1)/2 + s;
734
tt = (r + s - 1)*(r + s - 1 + 1)/2 + s - 1;
735
tmp5 = (2.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)*(3.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)/(2.000000000000000*(1.000000000000000 + s)*(2.000000000000000 + s + 2.000000000000000*r));
736
tmp6 = (1.000000000000000 + 4.000000000000000*r*r + 4.000000000000000*r)*(2.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)/(2.000000000000000*(1.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)*(1.000000000000000 + s)*(2.000000000000000 + s + 2.000000000000000*r));
737
tmp7 = (1.000000000000000 + s + 2.000000000000000*r)*(3.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)*s/((1.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)*(1.000000000000000 + s)*(2.000000000000000 + s + 2.000000000000000*r));
738
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Y*tmp5) - basisvalues[tt]*tmp7);
739
}// end loop over 's'
740
}// end loop over 'r'
741
for (unsigned int r = 0; r < 3; r++)
742
{
743
for (unsigned int s = 0; s < 3 - r; s++)
744
{
745
rr = (r + s)*(r + s + 1)/2 + s;
746
basisvalues[rr] *= std::sqrt((0.500000000000000 + r)*(1.000000000000000 + r + s));
747
}// end loop over 's'
748
}// end loop over 'r'
749
750
// Table(s) of coefficients.
751
static const double coefficients0[6] = \
752
{0.000000000000000, 0.000000000000000, 0.200000000000000, 0.000000000000000, 0.000000000000000, 0.163299316185545};
753
754
// Compute value(s).
755
for (unsigned int r = 0; r < 6; r++)
756
{
757
*values += coefficients0[r]*basisvalues[r];
758
}// end loop over 'r'
759
break;
760
}
761
case 3:
762
{
763
764
// Array of basisvalues.
765
double basisvalues[6] = {0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000};
766
767
// Declare helper variables.
768
unsigned int rr = 0;
769
unsigned int ss = 0;
770
unsigned int tt = 0;
771
double tmp5 = 0.000000000000000;
772
double tmp6 = 0.000000000000000;
773
double tmp7 = 0.000000000000000;
774
double tmp0 = (1.000000000000000 + Y + 2.000000000000000*X)/2.000000000000000;
775
double tmp1 = (1.000000000000000 - Y)/2.000000000000000;
776
double tmp2 = tmp1*tmp1;
777
778
// Compute basisvalues.
779
basisvalues[0] = 1.000000000000000;
780
basisvalues[1] = tmp0;
781
for (unsigned int r = 1; r < 2; r++)
782
{
783
rr = (r + 1)*((r + 1) + 1)/2;
784
ss = r*(r + 1)/2;
785
tt = (r - 1)*((r - 1) + 1)/2;
786
tmp5 = (1.000000000000000 + 2.000000000000000*r)/(1.000000000000000 + r);
787
basisvalues[rr] = (basisvalues[ss]*tmp0*tmp5 - basisvalues[tt]*tmp2*r/(1.000000000000000 + r));
788
}// end loop over 'r'
789
for (unsigned int r = 0; r < 2; r++)
790
{
791
rr = (r + 1)*(r + 1 + 1)/2 + 1;
792
ss = r*(r + 1)/2;
793
basisvalues[rr] = basisvalues[ss]*(0.500000000000000 + r + Y*(1.500000000000000 + r));
794
}// end loop over 'r'
795
for (unsigned int r = 0; r < 1; r++)
796
{
797
for (unsigned int s = 1; s < 2 - r; s++)
798
{
799
rr = (r + s + 1)*(r + s + 1 + 1)/2 + s + 1;
800
ss = (r + s)*(r + s + 1)/2 + s;
801
tt = (r + s - 1)*(r + s - 1 + 1)/2 + s - 1;
802
tmp5 = (2.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)*(3.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)/(2.000000000000000*(1.000000000000000 + s)*(2.000000000000000 + s + 2.000000000000000*r));
803
tmp6 = (1.000000000000000 + 4.000000000000000*r*r + 4.000000000000000*r)*(2.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)/(2.000000000000000*(1.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)*(1.000000000000000 + s)*(2.000000000000000 + s + 2.000000000000000*r));
804
tmp7 = (1.000000000000000 + s + 2.000000000000000*r)*(3.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)*s/((1.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)*(1.000000000000000 + s)*(2.000000000000000 + s + 2.000000000000000*r));
805
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Y*tmp5) - basisvalues[tt]*tmp7);
806
}// end loop over 's'
807
}// end loop over 'r'
808
for (unsigned int r = 0; r < 3; r++)
809
{
810
for (unsigned int s = 0; s < 3 - r; s++)
811
{
812
rr = (r + s)*(r + s + 1)/2 + s;
813
basisvalues[rr] *= std::sqrt((0.500000000000000 + r)*(1.000000000000000 + r + s));
814
}// end loop over 's'
815
}// end loop over 'r'
816
817
// Table(s) of coefficients.
818
static const double coefficients0[6] = \
819
{0.471404520791032, 0.230940107675850, 0.133333333333333, 0.000000000000000, 0.188561808316413, -0.163299316185545};
820
821
// Compute value(s).
822
for (unsigned int r = 0; r < 6; r++)
823
{
824
*values += coefficients0[r]*basisvalues[r];
825
}// end loop over 'r'
826
break;
827
}
828
case 4:
829
{
830
831
// Array of basisvalues.
832
double basisvalues[6] = {0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000};
833
834
// Declare helper variables.
835
unsigned int rr = 0;
836
unsigned int ss = 0;
837
unsigned int tt = 0;
838
double tmp5 = 0.000000000000000;
839
double tmp6 = 0.000000000000000;
840
double tmp7 = 0.000000000000000;
841
double tmp0 = (1.000000000000000 + Y + 2.000000000000000*X)/2.000000000000000;
842
double tmp1 = (1.000000000000000 - Y)/2.000000000000000;
843
double tmp2 = tmp1*tmp1;
844
845
// Compute basisvalues.
846
basisvalues[0] = 1.000000000000000;
847
basisvalues[1] = tmp0;
848
for (unsigned int r = 1; r < 2; r++)
849
{
850
rr = (r + 1)*((r + 1) + 1)/2;
851
ss = r*(r + 1)/2;
852
tt = (r - 1)*((r - 1) + 1)/2;
853
tmp5 = (1.000000000000000 + 2.000000000000000*r)/(1.000000000000000 + r);
854
basisvalues[rr] = (basisvalues[ss]*tmp0*tmp5 - basisvalues[tt]*tmp2*r/(1.000000000000000 + r));
855
}// end loop over 'r'
856
for (unsigned int r = 0; r < 2; r++)
857
{
858
rr = (r + 1)*(r + 1 + 1)/2 + 1;
859
ss = r*(r + 1)/2;
860
basisvalues[rr] = basisvalues[ss]*(0.500000000000000 + r + Y*(1.500000000000000 + r));
861
}// end loop over 'r'
862
for (unsigned int r = 0; r < 1; r++)
863
{
864
for (unsigned int s = 1; s < 2 - r; s++)
865
{
866
rr = (r + s + 1)*(r + s + 1 + 1)/2 + s + 1;
867
ss = (r + s)*(r + s + 1)/2 + s;
868
tt = (r + s - 1)*(r + s - 1 + 1)/2 + s - 1;
869
tmp5 = (2.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)*(3.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)/(2.000000000000000*(1.000000000000000 + s)*(2.000000000000000 + s + 2.000000000000000*r));
870
tmp6 = (1.000000000000000 + 4.000000000000000*r*r + 4.000000000000000*r)*(2.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)/(2.000000000000000*(1.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)*(1.000000000000000 + s)*(2.000000000000000 + s + 2.000000000000000*r));
871
tmp7 = (1.000000000000000 + s + 2.000000000000000*r)*(3.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)*s/((1.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)*(1.000000000000000 + s)*(2.000000000000000 + s + 2.000000000000000*r));
872
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Y*tmp5) - basisvalues[tt]*tmp7);
873
}// end loop over 's'
874
}// end loop over 'r'
875
for (unsigned int r = 0; r < 3; r++)
876
{
877
for (unsigned int s = 0; s < 3 - r; s++)
878
{
879
rr = (r + s)*(r + s + 1)/2 + s;
880
basisvalues[rr] *= std::sqrt((0.500000000000000 + r)*(1.000000000000000 + r + s));
881
}// end loop over 's'
882
}// end loop over 'r'
883
884
// Table(s) of coefficients.
885
static const double coefficients0[6] = \
886
{0.471404520791032, -0.230940107675850, 0.133333333333333, 0.000000000000000, -0.188561808316413, -0.163299316185545};
887
888
// Compute value(s).
889
for (unsigned int r = 0; r < 6; r++)
890
{
891
*values += coefficients0[r]*basisvalues[r];
892
}// end loop over 'r'
893
break;
894
}
895
case 5:
896
{
897
898
// Array of basisvalues.
899
double basisvalues[6] = {0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000};
900
901
// Declare helper variables.
902
unsigned int rr = 0;
903
unsigned int ss = 0;
904
unsigned int tt = 0;
905
double tmp5 = 0.000000000000000;
906
double tmp6 = 0.000000000000000;
907
double tmp7 = 0.000000000000000;
908
double tmp0 = (1.000000000000000 + Y + 2.000000000000000*X)/2.000000000000000;
909
double tmp1 = (1.000000000000000 - Y)/2.000000000000000;
910
double tmp2 = tmp1*tmp1;
911
912
// Compute basisvalues.
913
basisvalues[0] = 1.000000000000000;
914
basisvalues[1] = tmp0;
915
for (unsigned int r = 1; r < 2; r++)
916
{
917
rr = (r + 1)*((r + 1) + 1)/2;
918
ss = r*(r + 1)/2;
919
tt = (r - 1)*((r - 1) + 1)/2;
920
tmp5 = (1.000000000000000 + 2.000000000000000*r)/(1.000000000000000 + r);
921
basisvalues[rr] = (basisvalues[ss]*tmp0*tmp5 - basisvalues[tt]*tmp2*r/(1.000000000000000 + r));
922
}// end loop over 'r'
923
for (unsigned int r = 0; r < 2; r++)
924
{
925
rr = (r + 1)*(r + 1 + 1)/2 + 1;
926
ss = r*(r + 1)/2;
927
basisvalues[rr] = basisvalues[ss]*(0.500000000000000 + r + Y*(1.500000000000000 + r));
928
}// end loop over 'r'
929
for (unsigned int r = 0; r < 1; r++)
930
{
931
for (unsigned int s = 1; s < 2 - r; s++)
932
{
933
rr = (r + s + 1)*(r + s + 1 + 1)/2 + s + 1;
934
ss = (r + s)*(r + s + 1)/2 + s;
935
tt = (r + s - 1)*(r + s - 1 + 1)/2 + s - 1;
936
tmp5 = (2.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)*(3.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)/(2.000000000000000*(1.000000000000000 + s)*(2.000000000000000 + s + 2.000000000000000*r));
937
tmp6 = (1.000000000000000 + 4.000000000000000*r*r + 4.000000000000000*r)*(2.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)/(2.000000000000000*(1.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)*(1.000000000000000 + s)*(2.000000000000000 + s + 2.000000000000000*r));
938
tmp7 = (1.000000000000000 + s + 2.000000000000000*r)*(3.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)*s/((1.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)*(1.000000000000000 + s)*(2.000000000000000 + s + 2.000000000000000*r));
939
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Y*tmp5) - basisvalues[tt]*tmp7);
940
}// end loop over 's'
941
}// end loop over 'r'
942
for (unsigned int r = 0; r < 3; r++)
943
{
944
for (unsigned int s = 0; s < 3 - r; s++)
945
{
946
rr = (r + s)*(r + s + 1)/2 + s;
947
basisvalues[rr] *= std::sqrt((0.500000000000000 + r)*(1.000000000000000 + r + s));
948
}// end loop over 's'
949
}// end loop over 'r'
950
951
// Table(s) of coefficients.
952
static const double coefficients0[6] = \
953
{0.471404520791032, 0.000000000000000, -0.266666666666667, -0.243432247780074, 0.000000000000000, 0.054433105395182};
954
955
// Compute value(s).
956
for (unsigned int r = 0; r < 6; r++)
957
{
958
*values += coefficients0[r]*basisvalues[r];
959
}// end loop over 'r'
960
break;
961
}
962
}
963
964
}
965
966
/// Evaluate all basis functions at given point in cell
967
virtual void evaluate_basis_all(double* values,
968
const double* coordinates,
969
const ufc::cell& c) const
970
{
971
// Helper variable to hold values of a single dof.
972
double dof_values = 0.000000000000000;
973
974
// Loop dofs and call evaluate_basis.
975
for (unsigned int r = 0; r < 6; r++)
976
{
977
evaluate_basis(r, &dof_values, coordinates, c);
978
values[r] = dof_values;
979
}// end loop over 'r'
980
}
981
982
/// Evaluate order n derivatives of basis function i at given point in cell
983
virtual void evaluate_basis_derivatives(unsigned int i,
984
unsigned int n,
985
double* values,
986
const double* coordinates,
987
const ufc::cell& c) const
988
{
989
// Extract vertex coordinates
990
const double * const * x = c.coordinates;
991
992
// Compute Jacobian of affine map from reference cell
993
const double J_00 = x[1][0] - x[0][0];
994
const double J_01 = x[2][0] - x[0][0];
995
const double J_10 = x[1][1] - x[0][1];
996
const double J_11 = x[2][1] - x[0][1];
997
998
// Compute determinant of Jacobian
999
double detJ = J_00*J_11 - J_01*J_10;
1000
1001
// Compute inverse of Jacobian
1002
const double K_00 = J_11 / detJ;
1003
const double K_01 = -J_01 / detJ;
1004
const double K_10 = -J_10 / detJ;
1005
const double K_11 = J_00 / detJ;
1006
1007
// Compute constants
1008
const double C0 = x[1][0] + x[2][0];
1009
const double C1 = x[1][1] + x[2][1];
1010
1011
// Get coordinates and map to the reference (FIAT) element
1012
double X = (J_01*(C1 - 2.0*coordinates[1]) + J_11*(2.0*coordinates[0] - C0)) / detJ;
1013
double Y = (J_00*(2.0*coordinates[1] - C1) + J_10*(C0 - 2.0*coordinates[0])) / detJ;
1014
1015
// Compute number of derivatives.
1016
unsigned int num_derivatives = 1;
1017
for (unsigned int r = 0; r < n; r++)
1018
{
1019
num_derivatives *= 2;
1020
}// end loop over 'r'
1021
1022
// Declare pointer to two dimensional array that holds combinations of derivatives and initialise
1023
unsigned int **combinations = new unsigned int *[num_derivatives];
1024
for (unsigned int row = 0; row < num_derivatives; row++)
1025
{
1026
combinations[row] = new unsigned int [n];
1027
for (unsigned int col = 0; col < n; col++)
1028
combinations[row][col] = 0;
1029
}
1030
1031
// Generate combinations of derivatives
1032
for (unsigned int row = 1; row < num_derivatives; row++)
1033
{
1034
for (unsigned int num = 0; num < row; num++)
1035
{
1036
for (unsigned int col = n-1; col+1 > 0; col--)
1037
{
1038
if (combinations[row][col] + 1 > 1)
1039
combinations[row][col] = 0;
1040
else
1041
{
1042
combinations[row][col] += 1;
1043
break;
1044
}
1045
}
1046
}
1047
}
1048
1049
// Compute inverse of Jacobian
1050
const double Jinv[2][2] = {{K_00, K_01}, {K_10, K_11}};
1051
1052
// Declare transformation matrix
1053
// Declare pointer to two dimensional array and initialise
1054
double **transform = new double *[num_derivatives];
1055
1056
for (unsigned int j = 0; j < num_derivatives; j++)
1057
{
1058
transform[j] = new double [num_derivatives];
1059
for (unsigned int k = 0; k < num_derivatives; k++)
1060
transform[j][k] = 1;
1061
}
1062
1063
// Construct transformation matrix
1064
for (unsigned int row = 0; row < num_derivatives; row++)
1065
{
1066
for (unsigned int col = 0; col < num_derivatives; col++)
1067
{
1068
for (unsigned int k = 0; k < n; k++)
1069
transform[row][col] *= Jinv[combinations[col][k]][combinations[row][k]];
1070
}
1071
}
1072
1073
// Reset values. Assuming that values is always an array.
1074
for (unsigned int r = 0; r < num_derivatives; r++)
1075
{
1076
values[r] = 0.000000000000000;
1077
}// end loop over 'r'
1078
1079
switch (i)
1080
{
1081
case 0:
1082
{
1083
1084
// Array of basisvalues.
1085
double basisvalues[6] = {0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000};
1086
1087
// Declare helper variables.
1088
unsigned int rr = 0;
1089
unsigned int ss = 0;
1090
unsigned int tt = 0;
1091
double tmp5 = 0.000000000000000;
1092
double tmp6 = 0.000000000000000;
1093
double tmp7 = 0.000000000000000;
1094
double tmp0 = (1.000000000000000 + Y + 2.000000000000000*X)/2.000000000000000;
1095
double tmp1 = (1.000000000000000 - Y)/2.000000000000000;
1096
double tmp2 = tmp1*tmp1;
1097
1098
// Compute basisvalues.
1099
basisvalues[0] = 1.000000000000000;
1100
basisvalues[1] = tmp0;
1101
for (unsigned int r = 1; r < 2; r++)
1102
{
1103
rr = (r + 1)*((r + 1) + 1)/2;
1104
ss = r*(r + 1)/2;
1105
tt = (r - 1)*((r - 1) + 1)/2;
1106
tmp5 = (1.000000000000000 + 2.000000000000000*r)/(1.000000000000000 + r);
1107
basisvalues[rr] = (basisvalues[ss]*tmp0*tmp5 - basisvalues[tt]*tmp2*r/(1.000000000000000 + r));
1108
}// end loop over 'r'
1109
for (unsigned int r = 0; r < 2; r++)
1110
{
1111
rr = (r + 1)*(r + 1 + 1)/2 + 1;
1112
ss = r*(r + 1)/2;
1113
basisvalues[rr] = basisvalues[ss]*(0.500000000000000 + r + Y*(1.500000000000000 + r));
1114
}// end loop over 'r'
1115
for (unsigned int r = 0; r < 1; r++)
1116
{
1117
for (unsigned int s = 1; s < 2 - r; s++)
1118
{
1119
rr = (r + s + 1)*(r + s + 1 + 1)/2 + s + 1;
1120
ss = (r + s)*(r + s + 1)/2 + s;
1121
tt = (r + s - 1)*(r + s - 1 + 1)/2 + s - 1;
1122
tmp5 = (2.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)*(3.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)/(2.000000000000000*(1.000000000000000 + s)*(2.000000000000000 + s + 2.000000000000000*r));
1123
tmp6 = (1.000000000000000 + 4.000000000000000*r*r + 4.000000000000000*r)*(2.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)/(2.000000000000000*(1.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)*(1.000000000000000 + s)*(2.000000000000000 + s + 2.000000000000000*r));
1124
tmp7 = (1.000000000000000 + s + 2.000000000000000*r)*(3.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)*s/((1.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)*(1.000000000000000 + s)*(2.000000000000000 + s + 2.000000000000000*r));
1125
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Y*tmp5) - basisvalues[tt]*tmp7);
1126
}// end loop over 's'
1127
}// end loop over 'r'
1128
for (unsigned int r = 0; r < 3; r++)
1129
{
1130
for (unsigned int s = 0; s < 3 - r; s++)
1131
{
1132
rr = (r + s)*(r + s + 1)/2 + s;
1133
basisvalues[rr] *= std::sqrt((0.500000000000000 + r)*(1.000000000000000 + r + s));
1134
}// end loop over 's'
1135
}// end loop over 'r'
1136
1137
// Table(s) of coefficients.
1138
static const double coefficients0[6] = \
1139
{0.000000000000000, -0.173205080756888, -0.100000000000000, 0.121716123890037, 0.094280904158206, 0.054433105395182};
1140
1141
// Tables of derivatives of the polynomial base (transpose).
1142
static const double dmats0[6][6] = \
1143
{{0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
1144
{4.898979485566355, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
1145
{0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
1146
{0.000000000000000, 9.486832980505138, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
1147
{3.999999999999999, 0.000000000000000, 7.071067811865476, 0.000000000000000, 0.000000000000000, 0.000000000000000},
1148
{0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000}};
1149
1150
static const double dmats1[6][6] = \
1151
{{0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
1152
{2.449489742783177, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
1153
{4.242640687119285, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
1154
{2.581988897471611, 4.743416490252570, -0.912870929175278, 0.000000000000000, 0.000000000000000, 0.000000000000000},
1155
{1.999999999999999, 6.123724356957944, 3.535533905932737, 0.000000000000000, 0.000000000000000, 0.000000000000000},
1156
{-2.309401076758502, 0.000000000000000, 8.164965809277259, 0.000000000000000, 0.000000000000000, 0.000000000000000}};
1157
1158
// Compute reference derivatives.
1159
// Declare pointer to array of derivatives on FIAT element.
1160
double *derivatives = new double[num_derivatives];
1161
for (unsigned int r = 0; r < num_derivatives; r++)
1162
{
1163
derivatives[r] = 0.000000000000000;
1164
}// end loop over 'r'
1165
1166
// Declare derivative matrix (of polynomial basis).
1167
double dmats[6][6] = \
1168
{{1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
1169
{0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
1170
{0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
1171
{0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000},
1172
{0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000},
1173
{0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000}};
1174
1175
// Declare (auxiliary) derivative matrix (of polynomial basis).
1176
double dmats_old[6][6] = \
1177
{{1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
1178
{0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
1179
{0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
1180
{0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000},
1181
{0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000},
1182
{0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000}};
1183
1184
// Loop possible derivatives.
1185
for (unsigned int r = 0; r < num_derivatives; r++)
1186
{
1187
// Resetting dmats values to compute next derivative.
1188
for (unsigned int t = 0; t < 6; t++)
1189
{
1190
for (unsigned int u = 0; u < 6; u++)
1191
{
1192
dmats[t][u] = 0.000000000000000;
1193
if (t == u)
1194
{
1195
dmats[t][u] = 1.000000000000000;
1196
}
1197
1198
}// end loop over 'u'
1199
}// end loop over 't'
1200
1201
// Looping derivative order to generate dmats.
1202
for (unsigned int s = 0; s < n; s++)
1203
{
1204
// Updating dmats_old with new values and resetting dmats.
1205
for (unsigned int t = 0; t < 6; t++)
1206
{
1207
for (unsigned int u = 0; u < 6; u++)
1208
{
1209
dmats_old[t][u] = dmats[t][u];
1210
dmats[t][u] = 0.000000000000000;
1211
}// end loop over 'u'
1212
}// end loop over 't'
1213
1214
// Update dmats using an inner product.
1215
if (combinations[r][s] == 0)
1216
{
1217
for (unsigned int t = 0; t < 6; t++)
1218
{
1219
for (unsigned int u = 0; u < 6; u++)
1220
{
1221
for (unsigned int tu = 0; tu < 6; tu++)
1222
{
1223
dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
1224
}// end loop over 'tu'
1225
}// end loop over 'u'
1226
}// end loop over 't'
1227
}
1228
1229
if (combinations[r][s] == 1)
1230
{
1231
for (unsigned int t = 0; t < 6; t++)
1232
{
1233
for (unsigned int u = 0; u < 6; u++)
1234
{
1235
for (unsigned int tu = 0; tu < 6; tu++)
1236
{
1237
dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
1238
}// end loop over 'tu'
1239
}// end loop over 'u'
1240
}// end loop over 't'
1241
}
1242
1243
}// end loop over 's'
1244
for (unsigned int s = 0; s < 6; s++)
1245
{
1246
for (unsigned int t = 0; t < 6; t++)
1247
{
1248
derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
1249
}// end loop over 't'
1250
}// end loop over 's'
1251
}// end loop over 'r'
1252
1253
// Transform derivatives back to physical element
1254
for (unsigned int r = 0; r < num_derivatives; r++)
1255
{
1256
for (unsigned int s = 0; s < num_derivatives; s++)
1257
{
1258
values[r] += transform[r][s]*derivatives[s];
1259
}// end loop over 's'
1260
}// end loop over 'r'
1261
1262
// Delete pointer to array of derivatives on FIAT element
1263
delete [] derivatives;
1264
1265
// Delete pointer to array of combinations of derivatives and transform
1266
for (unsigned int r = 0; r < num_derivatives; r++)
1267
{
1268
delete [] combinations[r];
1269
}// end loop over 'r'
1270
delete [] combinations;
1271
for (unsigned int r = 0; r < num_derivatives; r++)
1272
{
1273
delete [] transform[r];
1274
}// end loop over 'r'
1275
delete [] transform;
1276
break;
1277
}
1278
case 1:
1279
{
1280
1281
// Array of basisvalues.
1282
double basisvalues[6] = {0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000};
1283
1284
// Declare helper variables.
1285
unsigned int rr = 0;
1286
unsigned int ss = 0;
1287
unsigned int tt = 0;
1288
double tmp5 = 0.000000000000000;
1289
double tmp6 = 0.000000000000000;
1290
double tmp7 = 0.000000000000000;
1291
double tmp0 = (1.000000000000000 + Y + 2.000000000000000*X)/2.000000000000000;
1292
double tmp1 = (1.000000000000000 - Y)/2.000000000000000;
1293
double tmp2 = tmp1*tmp1;
1294
1295
// Compute basisvalues.
1296
basisvalues[0] = 1.000000000000000;
1297
basisvalues[1] = tmp0;
1298
for (unsigned int r = 1; r < 2; r++)
1299
{
1300
rr = (r + 1)*((r + 1) + 1)/2;
1301
ss = r*(r + 1)/2;
1302
tt = (r - 1)*((r - 1) + 1)/2;
1303
tmp5 = (1.000000000000000 + 2.000000000000000*r)/(1.000000000000000 + r);
1304
basisvalues[rr] = (basisvalues[ss]*tmp0*tmp5 - basisvalues[tt]*tmp2*r/(1.000000000000000 + r));
1305
}// end loop over 'r'
1306
for (unsigned int r = 0; r < 2; r++)
1307
{
1308
rr = (r + 1)*(r + 1 + 1)/2 + 1;
1309
ss = r*(r + 1)/2;
1310
basisvalues[rr] = basisvalues[ss]*(0.500000000000000 + r + Y*(1.500000000000000 + r));
1311
}// end loop over 'r'
1312
for (unsigned int r = 0; r < 1; r++)
1313
{
1314
for (unsigned int s = 1; s < 2 - r; s++)
1315
{
1316
rr = (r + s + 1)*(r + s + 1 + 1)/2 + s + 1;
1317
ss = (r + s)*(r + s + 1)/2 + s;
1318
tt = (r + s - 1)*(r + s - 1 + 1)/2 + s - 1;
1319
tmp5 = (2.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)*(3.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)/(2.000000000000000*(1.000000000000000 + s)*(2.000000000000000 + s + 2.000000000000000*r));
1320
tmp6 = (1.000000000000000 + 4.000000000000000*r*r + 4.000000000000000*r)*(2.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)/(2.000000000000000*(1.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)*(1.000000000000000 + s)*(2.000000000000000 + s + 2.000000000000000*r));
1321
tmp7 = (1.000000000000000 + s + 2.000000000000000*r)*(3.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)*s/((1.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)*(1.000000000000000 + s)*(2.000000000000000 + s + 2.000000000000000*r));
1322
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Y*tmp5) - basisvalues[tt]*tmp7);
1323
}// end loop over 's'
1324
}// end loop over 'r'
1325
for (unsigned int r = 0; r < 3; r++)
1326
{
1327
for (unsigned int s = 0; s < 3 - r; s++)
1328
{
1329
rr = (r + s)*(r + s + 1)/2 + s;
1330
basisvalues[rr] *= std::sqrt((0.500000000000000 + r)*(1.000000000000000 + r + s));
1331
}// end loop over 's'
1332
}// end loop over 'r'
1333
1334
// Table(s) of coefficients.
1335
static const double coefficients0[6] = \
1336
{0.000000000000000, 0.173205080756888, -0.100000000000000, 0.121716123890037, -0.094280904158206, 0.054433105395182};
1337
1338
// Tables of derivatives of the polynomial base (transpose).
1339
static const double dmats0[6][6] = \
1340
{{0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
1341
{4.898979485566355, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
1342
{0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
1343
{0.000000000000000, 9.486832980505138, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
1344
{3.999999999999999, 0.000000000000000, 7.071067811865476, 0.000000000000000, 0.000000000000000, 0.000000000000000},
1345
{0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000}};
1346
1347
static const double dmats1[6][6] = \
1348
{{0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
1349
{2.449489742783177, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
1350
{4.242640687119285, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
1351
{2.581988897471611, 4.743416490252570, -0.912870929175278, 0.000000000000000, 0.000000000000000, 0.000000000000000},
1352
{1.999999999999999, 6.123724356957944, 3.535533905932737, 0.000000000000000, 0.000000000000000, 0.000000000000000},
1353
{-2.309401076758502, 0.000000000000000, 8.164965809277259, 0.000000000000000, 0.000000000000000, 0.000000000000000}};
1354
1355
// Compute reference derivatives.
1356
// Declare pointer to array of derivatives on FIAT element.
1357
double *derivatives = new double[num_derivatives];
1358
for (unsigned int r = 0; r < num_derivatives; r++)
1359
{
1360
derivatives[r] = 0.000000000000000;
1361
}// end loop over 'r'
1362
1363
// Declare derivative matrix (of polynomial basis).
1364
double dmats[6][6] = \
1365
{{1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
1366
{0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
1367
{0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
1368
{0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000},
1369
{0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000},
1370
{0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000}};
1371
1372
// Declare (auxiliary) derivative matrix (of polynomial basis).
1373
double dmats_old[6][6] = \
1374
{{1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
1375
{0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
1376
{0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
1377
{0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000},
1378
{0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000},
1379
{0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000}};
1380
1381
// Loop possible derivatives.
1382
for (unsigned int r = 0; r < num_derivatives; r++)
1383
{
1384
// Resetting dmats values to compute next derivative.
1385
for (unsigned int t = 0; t < 6; t++)
1386
{
1387
for (unsigned int u = 0; u < 6; u++)
1388
{
1389
dmats[t][u] = 0.000000000000000;
1390
if (t == u)
1391
{
1392
dmats[t][u] = 1.000000000000000;
1393
}
1394
1395
}// end loop over 'u'
1396
}// end loop over 't'
1397
1398
// Looping derivative order to generate dmats.
1399
for (unsigned int s = 0; s < n; s++)
1400
{
1401
// Updating dmats_old with new values and resetting dmats.
1402
for (unsigned int t = 0; t < 6; t++)
1403
{
1404
for (unsigned int u = 0; u < 6; u++)
1405
{
1406
dmats_old[t][u] = dmats[t][u];
1407
dmats[t][u] = 0.000000000000000;
1408
}// end loop over 'u'
1409
}// end loop over 't'
1410
1411
// Update dmats using an inner product.
1412
if (combinations[r][s] == 0)
1413
{
1414
for (unsigned int t = 0; t < 6; t++)
1415
{
1416
for (unsigned int u = 0; u < 6; u++)
1417
{
1418
for (unsigned int tu = 0; tu < 6; tu++)
1419
{
1420
dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
1421
}// end loop over 'tu'
1422
}// end loop over 'u'
1423
}// end loop over 't'
1424
}
1425
1426
if (combinations[r][s] == 1)
1427
{
1428
for (unsigned int t = 0; t < 6; t++)
1429
{
1430
for (unsigned int u = 0; u < 6; u++)
1431
{
1432
for (unsigned int tu = 0; tu < 6; tu++)
1433
{
1434
dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
1435
}// end loop over 'tu'
1436
}// end loop over 'u'
1437
}// end loop over 't'
1438
}
1439
1440
}// end loop over 's'
1441
for (unsigned int s = 0; s < 6; s++)
1442
{
1443
for (unsigned int t = 0; t < 6; t++)
1444
{
1445
derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
1446
}// end loop over 't'
1447
}// end loop over 's'
1448
}// end loop over 'r'
1449
1450
// Transform derivatives back to physical element
1451
for (unsigned int r = 0; r < num_derivatives; r++)
1452
{
1453
for (unsigned int s = 0; s < num_derivatives; s++)
1454
{
1455
values[r] += transform[r][s]*derivatives[s];
1456
}// end loop over 's'
1457
}// end loop over 'r'
1458
1459
// Delete pointer to array of derivatives on FIAT element
1460
delete [] derivatives;
1461
1462
// Delete pointer to array of combinations of derivatives and transform
1463
for (unsigned int r = 0; r < num_derivatives; r++)
1464
{
1465
delete [] combinations[r];
1466
}// end loop over 'r'
1467
delete [] combinations;
1468
for (unsigned int r = 0; r < num_derivatives; r++)
1469
{
1470
delete [] transform[r];
1471
}// end loop over 'r'
1472
delete [] transform;
1473
break;
1474
}
1475
case 2:
1476
{
1477
1478
// Array of basisvalues.
1479
double basisvalues[6] = {0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000};
1480
1481
// Declare helper variables.
1482
unsigned int rr = 0;
1483
unsigned int ss = 0;
1484
unsigned int tt = 0;
1485
double tmp5 = 0.000000000000000;
1486
double tmp6 = 0.000000000000000;
1487
double tmp7 = 0.000000000000000;
1488
double tmp0 = (1.000000000000000 + Y + 2.000000000000000*X)/2.000000000000000;
1489
double tmp1 = (1.000000000000000 - Y)/2.000000000000000;
1490
double tmp2 = tmp1*tmp1;
1491
1492
// Compute basisvalues.
1493
basisvalues[0] = 1.000000000000000;
1494
basisvalues[1] = tmp0;
1495
for (unsigned int r = 1; r < 2; r++)
1496
{
1497
rr = (r + 1)*((r + 1) + 1)/2;
1498
ss = r*(r + 1)/2;
1499
tt = (r - 1)*((r - 1) + 1)/2;
1500
tmp5 = (1.000000000000000 + 2.000000000000000*r)/(1.000000000000000 + r);
1501
basisvalues[rr] = (basisvalues[ss]*tmp0*tmp5 - basisvalues[tt]*tmp2*r/(1.000000000000000 + r));
1502
}// end loop over 'r'
1503
for (unsigned int r = 0; r < 2; r++)
1504
{
1505
rr = (r + 1)*(r + 1 + 1)/2 + 1;
1506
ss = r*(r + 1)/2;
1507
basisvalues[rr] = basisvalues[ss]*(0.500000000000000 + r + Y*(1.500000000000000 + r));
1508
}// end loop over 'r'
1509
for (unsigned int r = 0; r < 1; r++)
1510
{
1511
for (unsigned int s = 1; s < 2 - r; s++)
1512
{
1513
rr = (r + s + 1)*(r + s + 1 + 1)/2 + s + 1;
1514
ss = (r + s)*(r + s + 1)/2 + s;
1515
tt = (r + s - 1)*(r + s - 1 + 1)/2 + s - 1;
1516
tmp5 = (2.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)*(3.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)/(2.000000000000000*(1.000000000000000 + s)*(2.000000000000000 + s + 2.000000000000000*r));
1517
tmp6 = (1.000000000000000 + 4.000000000000000*r*r + 4.000000000000000*r)*(2.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)/(2.000000000000000*(1.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)*(1.000000000000000 + s)*(2.000000000000000 + s + 2.000000000000000*r));
1518
tmp7 = (1.000000000000000 + s + 2.000000000000000*r)*(3.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)*s/((1.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)*(1.000000000000000 + s)*(2.000000000000000 + s + 2.000000000000000*r));
1519
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Y*tmp5) - basisvalues[tt]*tmp7);
1520
}// end loop over 's'
1521
}// end loop over 'r'
1522
for (unsigned int r = 0; r < 3; r++)
1523
{
1524
for (unsigned int s = 0; s < 3 - r; s++)
1525
{
1526
rr = (r + s)*(r + s + 1)/2 + s;
1527
basisvalues[rr] *= std::sqrt((0.500000000000000 + r)*(1.000000000000000 + r + s));
1528
}// end loop over 's'
1529
}// end loop over 'r'
1530
1531
// Table(s) of coefficients.
1532
static const double coefficients0[6] = \
1533
{0.000000000000000, 0.000000000000000, 0.200000000000000, 0.000000000000000, 0.000000000000000, 0.163299316185545};
1534
1535
// Tables of derivatives of the polynomial base (transpose).
1536
static const double dmats0[6][6] = \
1537
{{0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
1538
{4.898979485566355, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
1539
{0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
1540
{0.000000000000000, 9.486832980505138, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
1541
{3.999999999999999, 0.000000000000000, 7.071067811865476, 0.000000000000000, 0.000000000000000, 0.000000000000000},
1542
{0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000}};
1543
1544
static const double dmats1[6][6] = \
1545
{{0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
1546
{2.449489742783177, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
1547
{4.242640687119285, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
1548
{2.581988897471611, 4.743416490252570, -0.912870929175278, 0.000000000000000, 0.000000000000000, 0.000000000000000},
1549
{1.999999999999999, 6.123724356957944, 3.535533905932737, 0.000000000000000, 0.000000000000000, 0.000000000000000},
1550
{-2.309401076758502, 0.000000000000000, 8.164965809277259, 0.000000000000000, 0.000000000000000, 0.000000000000000}};
1551
1552
// Compute reference derivatives.
1553
// Declare pointer to array of derivatives on FIAT element.
1554
double *derivatives = new double[num_derivatives];
1555
for (unsigned int r = 0; r < num_derivatives; r++)
1556
{
1557
derivatives[r] = 0.000000000000000;
1558
}// end loop over 'r'
1559
1560
// Declare derivative matrix (of polynomial basis).
1561
double dmats[6][6] = \
1562
{{1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
1563
{0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
1564
{0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
1565
{0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000},
1566
{0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000},
1567
{0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000}};
1568
1569
// Declare (auxiliary) derivative matrix (of polynomial basis).
1570
double dmats_old[6][6] = \
1571
{{1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
1572
{0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
1573
{0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
1574
{0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000},
1575
{0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000},
1576
{0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000}};
1577
1578
// Loop possible derivatives.
1579
for (unsigned int r = 0; r < num_derivatives; r++)
1580
{
1581
// Resetting dmats values to compute next derivative.
1582
for (unsigned int t = 0; t < 6; t++)
1583
{
1584
for (unsigned int u = 0; u < 6; u++)
1585
{
1586
dmats[t][u] = 0.000000000000000;
1587
if (t == u)
1588
{
1589
dmats[t][u] = 1.000000000000000;
1590
}
1591
1592
}// end loop over 'u'
1593
}// end loop over 't'
1594
1595
// Looping derivative order to generate dmats.
1596
for (unsigned int s = 0; s < n; s++)
1597
{
1598
// Updating dmats_old with new values and resetting dmats.
1599
for (unsigned int t = 0; t < 6; t++)
1600
{
1601
for (unsigned int u = 0; u < 6; u++)
1602
{
1603
dmats_old[t][u] = dmats[t][u];
1604
dmats[t][u] = 0.000000000000000;
1605
}// end loop over 'u'
1606
}// end loop over 't'
1607
1608
// Update dmats using an inner product.
1609
if (combinations[r][s] == 0)
1610
{
1611
for (unsigned int t = 0; t < 6; t++)
1612
{
1613
for (unsigned int u = 0; u < 6; u++)
1614
{
1615
for (unsigned int tu = 0; tu < 6; tu++)
1616
{
1617
dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
1618
}// end loop over 'tu'
1619
}// end loop over 'u'
1620
}// end loop over 't'
1621
}
1622
1623
if (combinations[r][s] == 1)
1624
{
1625
for (unsigned int t = 0; t < 6; t++)
1626
{
1627
for (unsigned int u = 0; u < 6; u++)
1628
{
1629
for (unsigned int tu = 0; tu < 6; tu++)
1630
{
1631
dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
1632
}// end loop over 'tu'
1633
}// end loop over 'u'
1634
}// end loop over 't'
1635
}
1636
1637
}// end loop over 's'
1638
for (unsigned int s = 0; s < 6; s++)
1639
{
1640
for (unsigned int t = 0; t < 6; t++)
1641
{
1642
derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
1643
}// end loop over 't'
1644
}// end loop over 's'
1645
}// end loop over 'r'
1646
1647
// Transform derivatives back to physical element
1648
for (unsigned int r = 0; r < num_derivatives; r++)
1649
{
1650
for (unsigned int s = 0; s < num_derivatives; s++)
1651
{
1652
values[r] += transform[r][s]*derivatives[s];
1653
}// end loop over 's'
1654
}// end loop over 'r'
1655
1656
// Delete pointer to array of derivatives on FIAT element
1657
delete [] derivatives;
1658
1659
// Delete pointer to array of combinations of derivatives and transform
1660
for (unsigned int r = 0; r < num_derivatives; r++)
1661
{
1662
delete [] combinations[r];
1663
}// end loop over 'r'
1664
delete [] combinations;
1665
for (unsigned int r = 0; r < num_derivatives; r++)
1666
{
1667
delete [] transform[r];
1668
}// end loop over 'r'
1669
delete [] transform;
1670
break;
1671
}
1672
case 3:
1673
{
1674
1675
// Array of basisvalues.
1676
double basisvalues[6] = {0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000};
1677
1678
// Declare helper variables.
1679
unsigned int rr = 0;
1680
unsigned int ss = 0;
1681
unsigned int tt = 0;
1682
double tmp5 = 0.000000000000000;
1683
double tmp6 = 0.000000000000000;
1684
double tmp7 = 0.000000000000000;
1685
double tmp0 = (1.000000000000000 + Y + 2.000000000000000*X)/2.000000000000000;
1686
double tmp1 = (1.000000000000000 - Y)/2.000000000000000;
1687
double tmp2 = tmp1*tmp1;
1688
1689
// Compute basisvalues.
1690
basisvalues[0] = 1.000000000000000;
1691
basisvalues[1] = tmp0;
1692
for (unsigned int r = 1; r < 2; r++)
1693
{
1694
rr = (r + 1)*((r + 1) + 1)/2;
1695
ss = r*(r + 1)/2;
1696
tt = (r - 1)*((r - 1) + 1)/2;
1697
tmp5 = (1.000000000000000 + 2.000000000000000*r)/(1.000000000000000 + r);
1698
basisvalues[rr] = (basisvalues[ss]*tmp0*tmp5 - basisvalues[tt]*tmp2*r/(1.000000000000000 + r));
1699
}// end loop over 'r'
1700
for (unsigned int r = 0; r < 2; r++)
1701
{
1702
rr = (r + 1)*(r + 1 + 1)/2 + 1;
1703
ss = r*(r + 1)/2;
1704
basisvalues[rr] = basisvalues[ss]*(0.500000000000000 + r + Y*(1.500000000000000 + r));
1705
}// end loop over 'r'
1706
for (unsigned int r = 0; r < 1; r++)
1707
{
1708
for (unsigned int s = 1; s < 2 - r; s++)
1709
{
1710
rr = (r + s + 1)*(r + s + 1 + 1)/2 + s + 1;
1711
ss = (r + s)*(r + s + 1)/2 + s;
1712
tt = (r + s - 1)*(r + s - 1 + 1)/2 + s - 1;
1713
tmp5 = (2.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)*(3.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)/(2.000000000000000*(1.000000000000000 + s)*(2.000000000000000 + s + 2.000000000000000*r));
1714
tmp6 = (1.000000000000000 + 4.000000000000000*r*r + 4.000000000000000*r)*(2.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)/(2.000000000000000*(1.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)*(1.000000000000000 + s)*(2.000000000000000 + s + 2.000000000000000*r));
1715
tmp7 = (1.000000000000000 + s + 2.000000000000000*r)*(3.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)*s/((1.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)*(1.000000000000000 + s)*(2.000000000000000 + s + 2.000000000000000*r));
1716
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Y*tmp5) - basisvalues[tt]*tmp7);
1717
}// end loop over 's'
1718
}// end loop over 'r'
1719
for (unsigned int r = 0; r < 3; r++)
1720
{
1721
for (unsigned int s = 0; s < 3 - r; s++)
1722
{
1723
rr = (r + s)*(r + s + 1)/2 + s;
1724
basisvalues[rr] *= std::sqrt((0.500000000000000 + r)*(1.000000000000000 + r + s));
1725
}// end loop over 's'
1726
}// end loop over 'r'
1727
1728
// Table(s) of coefficients.
1729
static const double coefficients0[6] = \
1730
{0.471404520791032, 0.230940107675850, 0.133333333333333, 0.000000000000000, 0.188561808316413, -0.163299316185545};
1731
1732
// Tables of derivatives of the polynomial base (transpose).
1733
static const double dmats0[6][6] = \
1734
{{0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
1735
{4.898979485566355, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
1736
{0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
1737
{0.000000000000000, 9.486832980505138, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
1738
{3.999999999999999, 0.000000000000000, 7.071067811865476, 0.000000000000000, 0.000000000000000, 0.000000000000000},
1739
{0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000}};
1740
1741
static const double dmats1[6][6] = \
1742
{{0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
1743
{2.449489742783177, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
1744
{4.242640687119285, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
1745
{2.581988897471611, 4.743416490252570, -0.912870929175278, 0.000000000000000, 0.000000000000000, 0.000000000000000},
1746
{1.999999999999999, 6.123724356957944, 3.535533905932737, 0.000000000000000, 0.000000000000000, 0.000000000000000},
1747
{-2.309401076758502, 0.000000000000000, 8.164965809277259, 0.000000000000000, 0.000000000000000, 0.000000000000000}};
1748
1749
// Compute reference derivatives.
1750
// Declare pointer to array of derivatives on FIAT element.
1751
double *derivatives = new double[num_derivatives];
1752
for (unsigned int r = 0; r < num_derivatives; r++)
1753
{
1754
derivatives[r] = 0.000000000000000;
1755
}// end loop over 'r'
1756
1757
// Declare derivative matrix (of polynomial basis).
1758
double dmats[6][6] = \
1759
{{1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
1760
{0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
1761
{0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
1762
{0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000},
1763
{0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000},
1764
{0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000}};
1765
1766
// Declare (auxiliary) derivative matrix (of polynomial basis).
1767
double dmats_old[6][6] = \
1768
{{1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
1769
{0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
1770
{0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
1771
{0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000},
1772
{0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000},
1773
{0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000}};
1774
1775
// Loop possible derivatives.
1776
for (unsigned int r = 0; r < num_derivatives; r++)
1777
{
1778
// Resetting dmats values to compute next derivative.
1779
for (unsigned int t = 0; t < 6; t++)
1780
{
1781
for (unsigned int u = 0; u < 6; u++)
1782
{
1783
dmats[t][u] = 0.000000000000000;
1784
if (t == u)
1785
{
1786
dmats[t][u] = 1.000000000000000;
1787
}
1788
1789
}// end loop over 'u'
1790
}// end loop over 't'
1791
1792
// Looping derivative order to generate dmats.
1793
for (unsigned int s = 0; s < n; s++)
1794
{
1795
// Updating dmats_old with new values and resetting dmats.
1796
for (unsigned int t = 0; t < 6; t++)
1797
{
1798
for (unsigned int u = 0; u < 6; u++)
1799
{
1800
dmats_old[t][u] = dmats[t][u];
1801
dmats[t][u] = 0.000000000000000;
1802
}// end loop over 'u'
1803
}// end loop over 't'
1804
1805
// Update dmats using an inner product.
1806
if (combinations[r][s] == 0)
1807
{
1808
for (unsigned int t = 0; t < 6; t++)
1809
{
1810
for (unsigned int u = 0; u < 6; u++)
1811
{
1812
for (unsigned int tu = 0; tu < 6; tu++)
1813
{
1814
dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
1815
}// end loop over 'tu'
1816
}// end loop over 'u'
1817
}// end loop over 't'
1818
}
1819
1820
if (combinations[r][s] == 1)
1821
{
1822
for (unsigned int t = 0; t < 6; t++)
1823
{
1824
for (unsigned int u = 0; u < 6; u++)
1825
{
1826
for (unsigned int tu = 0; tu < 6; tu++)
1827
{
1828
dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
1829
}// end loop over 'tu'
1830
}// end loop over 'u'
1831
}// end loop over 't'
1832
}
1833
1834
}// end loop over 's'
1835
for (unsigned int s = 0; s < 6; s++)
1836
{
1837
for (unsigned int t = 0; t < 6; t++)
1838
{
1839
derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
1840
}// end loop over 't'
1841
}// end loop over 's'
1842
}// end loop over 'r'
1843
1844
// Transform derivatives back to physical element
1845
for (unsigned int r = 0; r < num_derivatives; r++)
1846
{
1847
for (unsigned int s = 0; s < num_derivatives; s++)
1848
{
1849
values[r] += transform[r][s]*derivatives[s];
1850
}// end loop over 's'
1851
}// end loop over 'r'
1852
1853
// Delete pointer to array of derivatives on FIAT element
1854
delete [] derivatives;
1855
1856
// Delete pointer to array of combinations of derivatives and transform
1857
for (unsigned int r = 0; r < num_derivatives; r++)
1858
{
1859
delete [] combinations[r];
1860
}// end loop over 'r'
1861
delete [] combinations;
1862
for (unsigned int r = 0; r < num_derivatives; r++)
1863
{
1864
delete [] transform[r];
1865
}// end loop over 'r'
1866
delete [] transform;
1867
break;
1868
}
1869
case 4:
1870
{
1871
1872
// Array of basisvalues.
1873
double basisvalues[6] = {0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000};
1874
1875
// Declare helper variables.
1876
unsigned int rr = 0;
1877
unsigned int ss = 0;
1878
unsigned int tt = 0;
1879
double tmp5 = 0.000000000000000;
1880
double tmp6 = 0.000000000000000;
1881
double tmp7 = 0.000000000000000;
1882
double tmp0 = (1.000000000000000 + Y + 2.000000000000000*X)/2.000000000000000;
1883
double tmp1 = (1.000000000000000 - Y)/2.000000000000000;
1884
double tmp2 = tmp1*tmp1;
1885
1886
// Compute basisvalues.
1887
basisvalues[0] = 1.000000000000000;
1888
basisvalues[1] = tmp0;
1889
for (unsigned int r = 1; r < 2; r++)
1890
{
1891
rr = (r + 1)*((r + 1) + 1)/2;
1892
ss = r*(r + 1)/2;
1893
tt = (r - 1)*((r - 1) + 1)/2;
1894
tmp5 = (1.000000000000000 + 2.000000000000000*r)/(1.000000000000000 + r);
1895
basisvalues[rr] = (basisvalues[ss]*tmp0*tmp5 - basisvalues[tt]*tmp2*r/(1.000000000000000 + r));
1896
}// end loop over 'r'
1897
for (unsigned int r = 0; r < 2; r++)
1898
{
1899
rr = (r + 1)*(r + 1 + 1)/2 + 1;
1900
ss = r*(r + 1)/2;
1901
basisvalues[rr] = basisvalues[ss]*(0.500000000000000 + r + Y*(1.500000000000000 + r));
1902
}// end loop over 'r'
1903
for (unsigned int r = 0; r < 1; r++)
1904
{
1905
for (unsigned int s = 1; s < 2 - r; s++)
1906
{
1907
rr = (r + s + 1)*(r + s + 1 + 1)/2 + s + 1;
1908
ss = (r + s)*(r + s + 1)/2 + s;
1909
tt = (r + s - 1)*(r + s - 1 + 1)/2 + s - 1;
1910
tmp5 = (2.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)*(3.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)/(2.000000000000000*(1.000000000000000 + s)*(2.000000000000000 + s + 2.000000000000000*r));
1911
tmp6 = (1.000000000000000 + 4.000000000000000*r*r + 4.000000000000000*r)*(2.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)/(2.000000000000000*(1.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)*(1.000000000000000 + s)*(2.000000000000000 + s + 2.000000000000000*r));
1912
tmp7 = (1.000000000000000 + s + 2.000000000000000*r)*(3.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)*s/((1.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)*(1.000000000000000 + s)*(2.000000000000000 + s + 2.000000000000000*r));
1913
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Y*tmp5) - basisvalues[tt]*tmp7);
1914
}// end loop over 's'
1915
}// end loop over 'r'
1916
for (unsigned int r = 0; r < 3; r++)
1917
{
1918
for (unsigned int s = 0; s < 3 - r; s++)
1919
{
1920
rr = (r + s)*(r + s + 1)/2 + s;
1921
basisvalues[rr] *= std::sqrt((0.500000000000000 + r)*(1.000000000000000 + r + s));
1922
}// end loop over 's'
1923
}// end loop over 'r'
1924
1925
// Table(s) of coefficients.
1926
static const double coefficients0[6] = \
1927
{0.471404520791032, -0.230940107675850, 0.133333333333333, 0.000000000000000, -0.188561808316413, -0.163299316185545};
1928
1929
// Tables of derivatives of the polynomial base (transpose).
1930
static const double dmats0[6][6] = \
1931
{{0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
1932
{4.898979485566355, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
1933
{0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
1934
{0.000000000000000, 9.486832980505138, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
1935
{3.999999999999999, 0.000000000000000, 7.071067811865476, 0.000000000000000, 0.000000000000000, 0.000000000000000},
1936
{0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000}};
1937
1938
static const double dmats1[6][6] = \
1939
{{0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
1940
{2.449489742783177, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
1941
{4.242640687119285, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
1942
{2.581988897471611, 4.743416490252570, -0.912870929175278, 0.000000000000000, 0.000000000000000, 0.000000000000000},
1943
{1.999999999999999, 6.123724356957944, 3.535533905932737, 0.000000000000000, 0.000000000000000, 0.000000000000000},
1944
{-2.309401076758502, 0.000000000000000, 8.164965809277259, 0.000000000000000, 0.000000000000000, 0.000000000000000}};
1945
1946
// Compute reference derivatives.
1947
// Declare pointer to array of derivatives on FIAT element.
1948
double *derivatives = new double[num_derivatives];
1949
for (unsigned int r = 0; r < num_derivatives; r++)
1950
{
1951
derivatives[r] = 0.000000000000000;
1952
}// end loop over 'r'
1953
1954
// Declare derivative matrix (of polynomial basis).
1955
double dmats[6][6] = \
1956
{{1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
1957
{0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
1958
{0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
1959
{0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000},
1960
{0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000},
1961
{0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000}};
1962
1963
// Declare (auxiliary) derivative matrix (of polynomial basis).
1964
double dmats_old[6][6] = \
1965
{{1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
1966
{0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
1967
{0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
1968
{0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000},
1969
{0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000},
1970
{0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000}};
1971
1972
// Loop possible derivatives.
1973
for (unsigned int r = 0; r < num_derivatives; r++)
1974
{
1975
// Resetting dmats values to compute next derivative.
1976
for (unsigned int t = 0; t < 6; t++)
1977
{
1978
for (unsigned int u = 0; u < 6; u++)
1979
{
1980
dmats[t][u] = 0.000000000000000;
1981
if (t == u)
1982
{
1983
dmats[t][u] = 1.000000000000000;
1984
}
1985
1986
}// end loop over 'u'
1987
}// end loop over 't'
1988
1989
// Looping derivative order to generate dmats.
1990
for (unsigned int s = 0; s < n; s++)
1991
{
1992
// Updating dmats_old with new values and resetting dmats.
1993
for (unsigned int t = 0; t < 6; t++)
1994
{
1995
for (unsigned int u = 0; u < 6; u++)
1996
{
1997
dmats_old[t][u] = dmats[t][u];
1998
dmats[t][u] = 0.000000000000000;
1999
}// end loop over 'u'
2000
}// end loop over 't'
2001
2002
// Update dmats using an inner product.
2003
if (combinations[r][s] == 0)
2004
{
2005
for (unsigned int t = 0; t < 6; t++)
2006
{
2007
for (unsigned int u = 0; u < 6; u++)
2008
{
2009
for (unsigned int tu = 0; tu < 6; tu++)
2010
{
2011
dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
2012
}// end loop over 'tu'
2013
}// end loop over 'u'
2014
}// end loop over 't'
2015
}
2016
2017
if (combinations[r][s] == 1)
2018
{
2019
for (unsigned int t = 0; t < 6; t++)
2020
{
2021
for (unsigned int u = 0; u < 6; u++)
2022
{
2023
for (unsigned int tu = 0; tu < 6; tu++)
2024
{
2025
dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
2026
}// end loop over 'tu'
2027
}// end loop over 'u'
2028
}// end loop over 't'
2029
}
2030
2031
}// end loop over 's'
2032
for (unsigned int s = 0; s < 6; s++)
2033
{
2034
for (unsigned int t = 0; t < 6; t++)
2035
{
2036
derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
2037
}// end loop over 't'
2038
}// end loop over 's'
2039
}// end loop over 'r'
2040
2041
// Transform derivatives back to physical element
2042
for (unsigned int r = 0; r < num_derivatives; r++)
2043
{
2044
for (unsigned int s = 0; s < num_derivatives; s++)
2045
{
2046
values[r] += transform[r][s]*derivatives[s];
2047
}// end loop over 's'
2048
}// end loop over 'r'
2049
2050
// Delete pointer to array of derivatives on FIAT element
2051
delete [] derivatives;
2052
2053
// Delete pointer to array of combinations of derivatives and transform
2054
for (unsigned int r = 0; r < num_derivatives; r++)
2055
{
2056
delete [] combinations[r];
2057
}// end loop over 'r'
2058
delete [] combinations;
2059
for (unsigned int r = 0; r < num_derivatives; r++)
2060
{
2061
delete [] transform[r];
2062
}// end loop over 'r'
2063
delete [] transform;
2064
break;
2065
}
2066
case 5:
2067
{
2068
2069
// Array of basisvalues.
2070
double basisvalues[6] = {0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000};
2071
2072
// Declare helper variables.
2073
unsigned int rr = 0;
2074
unsigned int ss = 0;
2075
unsigned int tt = 0;
2076
double tmp5 = 0.000000000000000;
2077
double tmp6 = 0.000000000000000;
2078
double tmp7 = 0.000000000000000;
2079
double tmp0 = (1.000000000000000 + Y + 2.000000000000000*X)/2.000000000000000;
2080
double tmp1 = (1.000000000000000 - Y)/2.000000000000000;
2081
double tmp2 = tmp1*tmp1;
2082
2083
// Compute basisvalues.
2084
basisvalues[0] = 1.000000000000000;
2085
basisvalues[1] = tmp0;
2086
for (unsigned int r = 1; r < 2; r++)
2087
{
2088
rr = (r + 1)*((r + 1) + 1)/2;
2089
ss = r*(r + 1)/2;
2090
tt = (r - 1)*((r - 1) + 1)/2;
2091
tmp5 = (1.000000000000000 + 2.000000000000000*r)/(1.000000000000000 + r);
2092
basisvalues[rr] = (basisvalues[ss]*tmp0*tmp5 - basisvalues[tt]*tmp2*r/(1.000000000000000 + r));
2093
}// end loop over 'r'
2094
for (unsigned int r = 0; r < 2; r++)
2095
{
2096
rr = (r + 1)*(r + 1 + 1)/2 + 1;
2097
ss = r*(r + 1)/2;
2098
basisvalues[rr] = basisvalues[ss]*(0.500000000000000 + r + Y*(1.500000000000000 + r));
2099
}// end loop over 'r'
2100
for (unsigned int r = 0; r < 1; r++)
2101
{
2102
for (unsigned int s = 1; s < 2 - r; s++)
2103
{
2104
rr = (r + s + 1)*(r + s + 1 + 1)/2 + s + 1;
2105
ss = (r + s)*(r + s + 1)/2 + s;
2106
tt = (r + s - 1)*(r + s - 1 + 1)/2 + s - 1;
2107
tmp5 = (2.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)*(3.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)/(2.000000000000000*(1.000000000000000 + s)*(2.000000000000000 + s + 2.000000000000000*r));
2108
tmp6 = (1.000000000000000 + 4.000000000000000*r*r + 4.000000000000000*r)*(2.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)/(2.000000000000000*(1.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)*(1.000000000000000 + s)*(2.000000000000000 + s + 2.000000000000000*r));
2109
tmp7 = (1.000000000000000 + s + 2.000000000000000*r)*(3.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)*s/((1.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)*(1.000000000000000 + s)*(2.000000000000000 + s + 2.000000000000000*r));
2110
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Y*tmp5) - basisvalues[tt]*tmp7);
2111
}// end loop over 's'
2112
}// end loop over 'r'
2113
for (unsigned int r = 0; r < 3; r++)
2114
{
2115
for (unsigned int s = 0; s < 3 - r; s++)
2116
{
2117
rr = (r + s)*(r + s + 1)/2 + s;
2118
basisvalues[rr] *= std::sqrt((0.500000000000000 + r)*(1.000000000000000 + r + s));
2119
}// end loop over 's'
2120
}// end loop over 'r'
2121
2122
// Table(s) of coefficients.
2123
static const double coefficients0[6] = \
2124
{0.471404520791032, 0.000000000000000, -0.266666666666667, -0.243432247780074, 0.000000000000000, 0.054433105395182};
2125
2126
// Tables of derivatives of the polynomial base (transpose).
2127
static const double dmats0[6][6] = \
2128
{{0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
2129
{4.898979485566355, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
2130
{0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
2131
{0.000000000000000, 9.486832980505138, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
2132
{3.999999999999999, 0.000000000000000, 7.071067811865476, 0.000000000000000, 0.000000000000000, 0.000000000000000},
2133
{0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000}};
2134
2135
static const double dmats1[6][6] = \
2136
{{0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
2137
{2.449489742783177, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
2138
{4.242640687119285, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
2139
{2.581988897471611, 4.743416490252570, -0.912870929175278, 0.000000000000000, 0.000000000000000, 0.000000000000000},
2140
{1.999999999999999, 6.123724356957944, 3.535533905932737, 0.000000000000000, 0.000000000000000, 0.000000000000000},
2141
{-2.309401076758502, 0.000000000000000, 8.164965809277259, 0.000000000000000, 0.000000000000000, 0.000000000000000}};
2142
2143
// Compute reference derivatives.
2144
// Declare pointer to array of derivatives on FIAT element.
2145
double *derivatives = new double[num_derivatives];
2146
for (unsigned int r = 0; r < num_derivatives; r++)
2147
{
2148
derivatives[r] = 0.000000000000000;
2149
}// end loop over 'r'
2150
2151
// Declare derivative matrix (of polynomial basis).
2152
double dmats[6][6] = \
2153
{{1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
2154
{0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
2155
{0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
2156
{0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000},
2157
{0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000},
2158
{0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000}};
2159
2160
// Declare (auxiliary) derivative matrix (of polynomial basis).
2161
double dmats_old[6][6] = \
2162
{{1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
2163
{0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
2164
{0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
2165
{0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000},
2166
{0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000},
2167
{0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000}};
2168
2169
// Loop possible derivatives.
2170
for (unsigned int r = 0; r < num_derivatives; r++)
2171
{
2172
// Resetting dmats values to compute next derivative.
2173
for (unsigned int t = 0; t < 6; t++)
2174
{
2175
for (unsigned int u = 0; u < 6; u++)
2176
{
2177
dmats[t][u] = 0.000000000000000;
2178
if (t == u)
2179
{
2180
dmats[t][u] = 1.000000000000000;
2181
}
2182
2183
}// end loop over 'u'
2184
}// end loop over 't'
2185
2186
// Looping derivative order to generate dmats.
2187
for (unsigned int s = 0; s < n; s++)
2188
{
2189
// Updating dmats_old with new values and resetting dmats.
2190
for (unsigned int t = 0; t < 6; t++)
2191
{
2192
for (unsigned int u = 0; u < 6; u++)
2193
{
2194
dmats_old[t][u] = dmats[t][u];
2195
dmats[t][u] = 0.000000000000000;
2196
}// end loop over 'u'
2197
}// end loop over 't'
2198
2199
// Update dmats using an inner product.
2200
if (combinations[r][s] == 0)
2201
{
2202
for (unsigned int t = 0; t < 6; t++)
2203
{
2204
for (unsigned int u = 0; u < 6; u++)
2205
{
2206
for (unsigned int tu = 0; tu < 6; tu++)
2207
{
2208
dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
2209
}// end loop over 'tu'
2210
}// end loop over 'u'
2211
}// end loop over 't'
2212
}
2213
2214
if (combinations[r][s] == 1)
2215
{
2216
for (unsigned int t = 0; t < 6; t++)
2217
{
2218
for (unsigned int u = 0; u < 6; u++)
2219
{
2220
for (unsigned int tu = 0; tu < 6; tu++)
2221
{
2222
dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
2223
}// end loop over 'tu'
2224
}// end loop over 'u'
2225
}// end loop over 't'
2226
}
2227
2228
}// end loop over 's'
2229
for (unsigned int s = 0; s < 6; s++)
2230
{
2231
for (unsigned int t = 0; t < 6; t++)
2232
{
2233
derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
2234
}// end loop over 't'
2235
}// end loop over 's'
2236
}// end loop over 'r'
2237
2238
// Transform derivatives back to physical element
2239
for (unsigned int r = 0; r < num_derivatives; r++)
2240
{
2241
for (unsigned int s = 0; s < num_derivatives; s++)
2242
{
2243
values[r] += transform[r][s]*derivatives[s];
2244
}// end loop over 's'
2245
}// end loop over 'r'
2246
2247
// Delete pointer to array of derivatives on FIAT element
2248
delete [] derivatives;
2249
2250
// Delete pointer to array of combinations of derivatives and transform
2251
for (unsigned int r = 0; r < num_derivatives; r++)
2252
{
2253
delete [] combinations[r];
2254
}// end loop over 'r'
2255
delete [] combinations;
2256
for (unsigned int r = 0; r < num_derivatives; r++)
2257
{
2258
delete [] transform[r];
2259
}// end loop over 'r'
2260
delete [] transform;
2261
break;
2262
}
2263
}
2264
2265
}
2266
2267
/// Evaluate order n derivatives of all basis functions at given point in cell
2268
virtual void evaluate_basis_derivatives_all(unsigned int n,
2269
double* values,
2270
const double* coordinates,
2271
const ufc::cell& c) const
2272
{
2273
// Compute number of derivatives.
2274
unsigned int num_derivatives = 1;
2275
for (unsigned int r = 0; r < n; r++)
2276
{
2277
num_derivatives *= 2;
2278
}// end loop over 'r'
2279
2280
// Helper variable to hold values of a single dof.
2281
double *dof_values = new double[num_derivatives];
2282
for (unsigned int r = 0; r < num_derivatives; r++)
2283
{
2284
dof_values[r] = 0.000000000000000;
2285
}// end loop over 'r'
2286
2287
// Loop dofs and call evaluate_basis_derivatives.
2288
for (unsigned int r = 0; r < 6; r++)
2289
{
2290
evaluate_basis_derivatives(r, n, dof_values, coordinates, c);
2291
for (unsigned int s = 0; s < num_derivatives; s++)
2292
{
2293
values[r*num_derivatives + s] = dof_values[s];
2294
}// end loop over 's'
2295
}// end loop over 'r'
2296
2297
// Delete pointer.
2298
delete [] dof_values;
2299
}
2300
2301
/// Evaluate linear functional for dof i on the function f
2302
virtual double evaluate_dof(unsigned int i,
2303
const ufc::function& f,
2304
const ufc::cell& c) const
2305
{
2306
// Declare variables for result of evaluation.
2307
double vals[1];
2308
2309
// Declare variable for physical coordinates.
2310
double y[2];
2311
const double * const * x = c.coordinates;
2312
switch (i)
2313
{
2314
case 0:
2315
{
2316
y[0] = x[0][0];
2317
y[1] = x[0][1];
2318
f.evaluate(vals, y, c);
2319
return vals[0];
2320
break;
2321
}
2322
case 1:
2323
{
2324
y[0] = x[1][0];
2325
y[1] = x[1][1];
2326
f.evaluate(vals, y, c);
2327
return vals[0];
2328
break;
2329
}
2330
case 2:
2331
{
2332
y[0] = x[2][0];
2333
y[1] = x[2][1];
2334
f.evaluate(vals, y, c);
2335
return vals[0];
2336
break;
2337
}
2338
case 3:
2339
{
2340
y[0] = 0.500000000000000*x[1][0] + 0.500000000000000*x[2][0];
2341
y[1] = 0.500000000000000*x[1][1] + 0.500000000000000*x[2][1];
2342
f.evaluate(vals, y, c);
2343
return vals[0];
2344
break;
2345
}
2346
case 4:
2347
{
2348
y[0] = 0.500000000000000*x[0][0] + 0.500000000000000*x[2][0];
2349
y[1] = 0.500000000000000*x[0][1] + 0.500000000000000*x[2][1];
2350
f.evaluate(vals, y, c);
2351
return vals[0];
2352
break;
2353
}
2354
case 5:
2355
{
2356
y[0] = 0.500000000000000*x[0][0] + 0.500000000000000*x[1][0];
2357
y[1] = 0.500000000000000*x[0][1] + 0.500000000000000*x[1][1];
2358
f.evaluate(vals, y, c);
2359
return vals[0];
2360
break;
2361
}
2362
}
2363
2364
return 0.000000000000000;
2365
}
2366
2367
/// Evaluate linear functionals for all dofs on the function f
2368
virtual void evaluate_dofs(double* values,
2369
const ufc::function& f,
2370
const ufc::cell& c) const
2371
{
2372
// Declare variables for result of evaluation.
2373
double vals[1];
2374
2375
// Declare variable for physical coordinates.
2376
double y[2];
2377
const double * const * x = c.coordinates;
2378
y[0] = x[0][0];
2379
y[1] = x[0][1];
2380
f.evaluate(vals, y, c);
2381
values[0] = vals[0];
2382
y[0] = x[1][0];
2383
y[1] = x[1][1];
2384
f.evaluate(vals, y, c);
2385
values[1] = vals[0];
2386
y[0] = x[2][0];
2387
y[1] = x[2][1];
2388
f.evaluate(vals, y, c);
2389
values[2] = vals[0];
2390
y[0] = 0.500000000000000*x[1][0] + 0.500000000000000*x[2][0];
2391
y[1] = 0.500000000000000*x[1][1] + 0.500000000000000*x[2][1];
2392
f.evaluate(vals, y, c);
2393
values[3] = vals[0];
2394
y[0] = 0.500000000000000*x[0][0] + 0.500000000000000*x[2][0];
2395
y[1] = 0.500000000000000*x[0][1] + 0.500000000000000*x[2][1];
2396
f.evaluate(vals, y, c);
2397
values[4] = vals[0];
2398
y[0] = 0.500000000000000*x[0][0] + 0.500000000000000*x[1][0];
2399
y[1] = 0.500000000000000*x[0][1] + 0.500000000000000*x[1][1];
2400
f.evaluate(vals, y, c);
2401
values[5] = vals[0];
2402
}
2403
2404
/// Interpolate vertex values from dof values
2405
virtual void interpolate_vertex_values(double* vertex_values,
2406
const double* dof_values,
2407
const ufc::cell& c) const
2408
{
2409
// Evaluate function and change variables
2410
vertex_values[0] = dof_values[0];
2411
vertex_values[1] = dof_values[1];
2412
vertex_values[2] = dof_values[2];
2413
}
2414
2415
/// Map coordinate xhat from reference cell to coordinate x in cell
2416
virtual void map_from_reference_cell(double* x,
2417
const double* xhat,
2418
const ufc::cell& c)
2419
{
2420
throw std::runtime_error("map_from_reference_cell not yet implemented (introduced in UFC 2.0).");
2421
}
2422
2423
/// Map from coordinate x in cell to coordinate xhat in reference cell
2424
virtual void map_to_reference_cell(double* xhat,
2425
const double* x,
2426
const ufc::cell& c)
2427
{
2428
throw std::runtime_error("map_to_reference_cell not yet implemented (introduced in UFC 2.0).");
2429
}
2430
2431
/// Return the number of sub elements (for a mixed element)
2432
virtual unsigned int num_sub_elements() const
2433
{
2434
return 0;
2435
}
2436
2437
/// Create a new finite element for sub element i (for a mixed element)
2438
virtual ufc::finite_element* create_sub_element(unsigned int i) const
2439
{
2440
return 0;
2441
}
2442
2443
/// Create a new class instance
2444
virtual ufc::finite_element* create() const
2445
{
2446
return new adaptivepoisson_finite_element_1();
2447
}
2448
2449
};
2450
2451
/// This class defines the interface for a finite element.
2452
2453
class adaptivepoisson_finite_element_2: public ufc::finite_element
2454
{
2455
public:
2456
2457
/// Constructor
2458
adaptivepoisson_finite_element_2() : ufc::finite_element()
2459
{
2460
// Do nothing
2461
}
2462
2463
/// Destructor
2464
virtual ~adaptivepoisson_finite_element_2()
2465
{
2466
// Do nothing
2467
}
2468
2469
/// Return a string identifying the finite element
2470
virtual const char* signature() const
2471
{
2472
return "FiniteElement('Discontinuous Lagrange', Cell('triangle', 1, Space(2)), 2)";
2473
}
2474
2475
/// Return the cell shape
2476
virtual ufc::shape cell_shape() const
2477
{
2478
return ufc::triangle;
2479
}
2480
2481
/// Return the topological dimension of the cell shape
2482
virtual unsigned int topological_dimension() const
2483
{
2484
return 2;
2485
}
2486
2487
/// Return the geometric dimension of the cell shape
2488
virtual unsigned int geometric_dimension() const
2489
{
2490
return 2;
2491
}
2492
2493
/// Return the dimension of the finite element function space
2494
virtual unsigned int space_dimension() const
2495
{
2496
return 6;
2497
}
2498
2499
/// Return the rank of the value space
2500
virtual unsigned int value_rank() const
2501
{
2502
return 0;
2503
}
2504
2505
/// Return the dimension of the value space for axis i
2506
virtual unsigned int value_dimension(unsigned int i) const
2507
{
2508
return 1;
2509
}
2510
2511
/// Evaluate basis function i at given point in cell
2512
virtual void evaluate_basis(unsigned int i,
2513
double* values,
2514
const double* coordinates,
2515
const ufc::cell& c) const
2516
{
2517
// Extract vertex coordinates
2518
const double * const * x = c.coordinates;
2519
2520
// Compute Jacobian of affine map from reference cell
2521
const double J_00 = x[1][0] - x[0][0];
2522
const double J_01 = x[2][0] - x[0][0];
2523
const double J_10 = x[1][1] - x[0][1];
2524
const double J_11 = x[2][1] - x[0][1];
2525
2526
// Compute determinant of Jacobian
2527
double detJ = J_00*J_11 - J_01*J_10;
2528
2529
// Compute inverse of Jacobian
2530
2531
// Compute constants
2532
const double C0 = x[1][0] + x[2][0];
2533
const double C1 = x[1][1] + x[2][1];
2534
2535
// Get coordinates and map to the reference (FIAT) element
2536
double X = (J_01*(C1 - 2.0*coordinates[1]) + J_11*(2.0*coordinates[0] - C0)) / detJ;
2537
double Y = (J_00*(2.0*coordinates[1] - C1) + J_10*(C0 - 2.0*coordinates[0])) / detJ;
2538
2539
// Reset values.
2540
*values = 0.000000000000000;
2541
switch (i)
2542
{
2543
case 0:
2544
{
2545
2546
// Array of basisvalues.
2547
double basisvalues[6] = {0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000};
2548
2549
// Declare helper variables.
2550
unsigned int rr = 0;
2551
unsigned int ss = 0;
2552
unsigned int tt = 0;
2553
double tmp5 = 0.000000000000000;
2554
double tmp6 = 0.000000000000000;
2555
double tmp7 = 0.000000000000000;
2556
double tmp0 = (1.000000000000000 + Y + 2.000000000000000*X)/2.000000000000000;
2557
double tmp1 = (1.000000000000000 - Y)/2.000000000000000;
2558
double tmp2 = tmp1*tmp1;
2559
2560
// Compute basisvalues.
2561
basisvalues[0] = 1.000000000000000;
2562
basisvalues[1] = tmp0;
2563
for (unsigned int r = 1; r < 2; r++)
2564
{
2565
rr = (r + 1)*((r + 1) + 1)/2;
2566
ss = r*(r + 1)/2;
2567
tt = (r - 1)*((r - 1) + 1)/2;
2568
tmp5 = (1.000000000000000 + 2.000000000000000*r)/(1.000000000000000 + r);
2569
basisvalues[rr] = (basisvalues[ss]*tmp0*tmp5 - basisvalues[tt]*tmp2*r/(1.000000000000000 + r));
2570
}// end loop over 'r'
2571
for (unsigned int r = 0; r < 2; r++)
2572
{
2573
rr = (r + 1)*(r + 1 + 1)/2 + 1;
2574
ss = r*(r + 1)/2;
2575
basisvalues[rr] = basisvalues[ss]*(0.500000000000000 + r + Y*(1.500000000000000 + r));
2576
}// end loop over 'r'
2577
for (unsigned int r = 0; r < 1; r++)
2578
{
2579
for (unsigned int s = 1; s < 2 - r; s++)
2580
{
2581
rr = (r + s + 1)*(r + s + 1 + 1)/2 + s + 1;
2582
ss = (r + s)*(r + s + 1)/2 + s;
2583
tt = (r + s - 1)*(r + s - 1 + 1)/2 + s - 1;
2584
tmp5 = (2.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)*(3.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)/(2.000000000000000*(1.000000000000000 + s)*(2.000000000000000 + s + 2.000000000000000*r));
2585
tmp6 = (1.000000000000000 + 4.000000000000000*r*r + 4.000000000000000*r)*(2.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)/(2.000000000000000*(1.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)*(1.000000000000000 + s)*(2.000000000000000 + s + 2.000000000000000*r));
2586
tmp7 = (1.000000000000000 + s + 2.000000000000000*r)*(3.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)*s/((1.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)*(1.000000000000000 + s)*(2.000000000000000 + s + 2.000000000000000*r));
2587
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Y*tmp5) - basisvalues[tt]*tmp7);
2588
}// end loop over 's'
2589
}// end loop over 'r'
2590
for (unsigned int r = 0; r < 3; r++)
2591
{
2592
for (unsigned int s = 0; s < 3 - r; s++)
2593
{
2594
rr = (r + s)*(r + s + 1)/2 + s;
2595
basisvalues[rr] *= std::sqrt((0.500000000000000 + r)*(1.000000000000000 + r + s));
2596
}// end loop over 's'
2597
}// end loop over 'r'
2598
2599
// Table(s) of coefficients.
2600
static const double coefficients0[6] = \
2601
{0.000000000000000, -0.173205080756888, -0.100000000000000, 0.121716123890037, 0.094280904158206, 0.054433105395182};
2602
2603
// Compute value(s).
2604
for (unsigned int r = 0; r < 6; r++)
2605
{
2606
*values += coefficients0[r]*basisvalues[r];
2607
}// end loop over 'r'
2608
break;
2609
}
2610
case 1:
2611
{
2612
2613
// Array of basisvalues.
2614
double basisvalues[6] = {0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000};
2615
2616
// Declare helper variables.
2617
unsigned int rr = 0;
2618
unsigned int ss = 0;
2619
unsigned int tt = 0;
2620
double tmp5 = 0.000000000000000;
2621
double tmp6 = 0.000000000000000;
2622
double tmp7 = 0.000000000000000;
2623
double tmp0 = (1.000000000000000 + Y + 2.000000000000000*X)/2.000000000000000;
2624
double tmp1 = (1.000000000000000 - Y)/2.000000000000000;
2625
double tmp2 = tmp1*tmp1;
2626
2627
// Compute basisvalues.
2628
basisvalues[0] = 1.000000000000000;
2629
basisvalues[1] = tmp0;
2630
for (unsigned int r = 1; r < 2; r++)
2631
{
2632
rr = (r + 1)*((r + 1) + 1)/2;
2633
ss = r*(r + 1)/2;
2634
tt = (r - 1)*((r - 1) + 1)/2;
2635
tmp5 = (1.000000000000000 + 2.000000000000000*r)/(1.000000000000000 + r);
2636
basisvalues[rr] = (basisvalues[ss]*tmp0*tmp5 - basisvalues[tt]*tmp2*r/(1.000000000000000 + r));
2637
}// end loop over 'r'
2638
for (unsigned int r = 0; r < 2; r++)
2639
{
2640
rr = (r + 1)*(r + 1 + 1)/2 + 1;
2641
ss = r*(r + 1)/2;
2642
basisvalues[rr] = basisvalues[ss]*(0.500000000000000 + r + Y*(1.500000000000000 + r));
2643
}// end loop over 'r'
2644
for (unsigned int r = 0; r < 1; r++)
2645
{
2646
for (unsigned int s = 1; s < 2 - r; s++)
2647
{
2648
rr = (r + s + 1)*(r + s + 1 + 1)/2 + s + 1;
2649
ss = (r + s)*(r + s + 1)/2 + s;
2650
tt = (r + s - 1)*(r + s - 1 + 1)/2 + s - 1;
2651
tmp5 = (2.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)*(3.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)/(2.000000000000000*(1.000000000000000 + s)*(2.000000000000000 + s + 2.000000000000000*r));
2652
tmp6 = (1.000000000000000 + 4.000000000000000*r*r + 4.000000000000000*r)*(2.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)/(2.000000000000000*(1.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)*(1.000000000000000 + s)*(2.000000000000000 + s + 2.000000000000000*r));
2653
tmp7 = (1.000000000000000 + s + 2.000000000000000*r)*(3.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)*s/((1.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)*(1.000000000000000 + s)*(2.000000000000000 + s + 2.000000000000000*r));
2654
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Y*tmp5) - basisvalues[tt]*tmp7);
2655
}// end loop over 's'
2656
}// end loop over 'r'
2657
for (unsigned int r = 0; r < 3; r++)
2658
{
2659
for (unsigned int s = 0; s < 3 - r; s++)
2660
{
2661
rr = (r + s)*(r + s + 1)/2 + s;
2662
basisvalues[rr] *= std::sqrt((0.500000000000000 + r)*(1.000000000000000 + r + s));
2663
}// end loop over 's'
2664
}// end loop over 'r'
2665
2666
// Table(s) of coefficients.
2667
static const double coefficients0[6] = \
2668
{0.000000000000000, 0.173205080756888, -0.100000000000000, 0.121716123890037, -0.094280904158206, 0.054433105395182};
2669
2670
// Compute value(s).
2671
for (unsigned int r = 0; r < 6; r++)
2672
{
2673
*values += coefficients0[r]*basisvalues[r];
2674
}// end loop over 'r'
2675
break;
2676
}
2677
case 2:
2678
{
2679
2680
// Array of basisvalues.
2681
double basisvalues[6] = {0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000};
2682
2683
// Declare helper variables.
2684
unsigned int rr = 0;
2685
unsigned int ss = 0;
2686
unsigned int tt = 0;
2687
double tmp5 = 0.000000000000000;
2688
double tmp6 = 0.000000000000000;
2689
double tmp7 = 0.000000000000000;
2690
double tmp0 = (1.000000000000000 + Y + 2.000000000000000*X)/2.000000000000000;
2691
double tmp1 = (1.000000000000000 - Y)/2.000000000000000;
2692
double tmp2 = tmp1*tmp1;
2693
2694
// Compute basisvalues.
2695
basisvalues[0] = 1.000000000000000;
2696
basisvalues[1] = tmp0;
2697
for (unsigned int r = 1; r < 2; r++)
2698
{
2699
rr = (r + 1)*((r + 1) + 1)/2;
2700
ss = r*(r + 1)/2;
2701
tt = (r - 1)*((r - 1) + 1)/2;
2702
tmp5 = (1.000000000000000 + 2.000000000000000*r)/(1.000000000000000 + r);
2703
basisvalues[rr] = (basisvalues[ss]*tmp0*tmp5 - basisvalues[tt]*tmp2*r/(1.000000000000000 + r));
2704
}// end loop over 'r'
2705
for (unsigned int r = 0; r < 2; r++)
2706
{
2707
rr = (r + 1)*(r + 1 + 1)/2 + 1;
2708
ss = r*(r + 1)/2;
2709
basisvalues[rr] = basisvalues[ss]*(0.500000000000000 + r + Y*(1.500000000000000 + r));
2710
}// end loop over 'r'
2711
for (unsigned int r = 0; r < 1; r++)
2712
{
2713
for (unsigned int s = 1; s < 2 - r; s++)
2714
{
2715
rr = (r + s + 1)*(r + s + 1 + 1)/2 + s + 1;
2716
ss = (r + s)*(r + s + 1)/2 + s;
2717
tt = (r + s - 1)*(r + s - 1 + 1)/2 + s - 1;
2718
tmp5 = (2.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)*(3.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)/(2.000000000000000*(1.000000000000000 + s)*(2.000000000000000 + s + 2.000000000000000*r));
2719
tmp6 = (1.000000000000000 + 4.000000000000000*r*r + 4.000000000000000*r)*(2.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)/(2.000000000000000*(1.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)*(1.000000000000000 + s)*(2.000000000000000 + s + 2.000000000000000*r));
2720
tmp7 = (1.000000000000000 + s + 2.000000000000000*r)*(3.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)*s/((1.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)*(1.000000000000000 + s)*(2.000000000000000 + s + 2.000000000000000*r));
2721
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Y*tmp5) - basisvalues[tt]*tmp7);
2722
}// end loop over 's'
2723
}// end loop over 'r'
2724
for (unsigned int r = 0; r < 3; r++)
2725
{
2726
for (unsigned int s = 0; s < 3 - r; s++)
2727
{
2728
rr = (r + s)*(r + s + 1)/2 + s;
2729
basisvalues[rr] *= std::sqrt((0.500000000000000 + r)*(1.000000000000000 + r + s));
2730
}// end loop over 's'
2731
}// end loop over 'r'
2732
2733
// Table(s) of coefficients.
2734
static const double coefficients0[6] = \
2735
{0.000000000000000, 0.000000000000000, 0.200000000000000, 0.000000000000000, 0.000000000000000, 0.163299316185545};
2736
2737
// Compute value(s).
2738
for (unsigned int r = 0; r < 6; r++)
2739
{
2740
*values += coefficients0[r]*basisvalues[r];
2741
}// end loop over 'r'
2742
break;
2743
}
2744
case 3:
2745
{
2746
2747
// Array of basisvalues.
2748
double basisvalues[6] = {0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000};
2749
2750
// Declare helper variables.
2751
unsigned int rr = 0;
2752
unsigned int ss = 0;
2753
unsigned int tt = 0;
2754
double tmp5 = 0.000000000000000;
2755
double tmp6 = 0.000000000000000;
2756
double tmp7 = 0.000000000000000;
2757
double tmp0 = (1.000000000000000 + Y + 2.000000000000000*X)/2.000000000000000;
2758
double tmp1 = (1.000000000000000 - Y)/2.000000000000000;
2759
double tmp2 = tmp1*tmp1;
2760
2761
// Compute basisvalues.
2762
basisvalues[0] = 1.000000000000000;
2763
basisvalues[1] = tmp0;
2764
for (unsigned int r = 1; r < 2; r++)
2765
{
2766
rr = (r + 1)*((r + 1) + 1)/2;
2767
ss = r*(r + 1)/2;
2768
tt = (r - 1)*((r - 1) + 1)/2;
2769
tmp5 = (1.000000000000000 + 2.000000000000000*r)/(1.000000000000000 + r);
2770
basisvalues[rr] = (basisvalues[ss]*tmp0*tmp5 - basisvalues[tt]*tmp2*r/(1.000000000000000 + r));
2771
}// end loop over 'r'
2772
for (unsigned int r = 0; r < 2; r++)
2773
{
2774
rr = (r + 1)*(r + 1 + 1)/2 + 1;
2775
ss = r*(r + 1)/2;
2776
basisvalues[rr] = basisvalues[ss]*(0.500000000000000 + r + Y*(1.500000000000000 + r));
2777
}// end loop over 'r'
2778
for (unsigned int r = 0; r < 1; r++)
2779
{
2780
for (unsigned int s = 1; s < 2 - r; s++)
2781
{
2782
rr = (r + s + 1)*(r + s + 1 + 1)/2 + s + 1;
2783
ss = (r + s)*(r + s + 1)/2 + s;
2784
tt = (r + s - 1)*(r + s - 1 + 1)/2 + s - 1;
2785
tmp5 = (2.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)*(3.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)/(2.000000000000000*(1.000000000000000 + s)*(2.000000000000000 + s + 2.000000000000000*r));
2786
tmp6 = (1.000000000000000 + 4.000000000000000*r*r + 4.000000000000000*r)*(2.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)/(2.000000000000000*(1.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)*(1.000000000000000 + s)*(2.000000000000000 + s + 2.000000000000000*r));
2787
tmp7 = (1.000000000000000 + s + 2.000000000000000*r)*(3.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)*s/((1.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)*(1.000000000000000 + s)*(2.000000000000000 + s + 2.000000000000000*r));
2788
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Y*tmp5) - basisvalues[tt]*tmp7);
2789
}// end loop over 's'
2790
}// end loop over 'r'
2791
for (unsigned int r = 0; r < 3; r++)
2792
{
2793
for (unsigned int s = 0; s < 3 - r; s++)
2794
{
2795
rr = (r + s)*(r + s + 1)/2 + s;
2796
basisvalues[rr] *= std::sqrt((0.500000000000000 + r)*(1.000000000000000 + r + s));
2797
}// end loop over 's'
2798
}// end loop over 'r'
2799
2800
// Table(s) of coefficients.
2801
static const double coefficients0[6] = \
2802
{0.471404520791032, 0.230940107675850, 0.133333333333333, 0.000000000000000, 0.188561808316413, -0.163299316185545};
2803
2804
// Compute value(s).
2805
for (unsigned int r = 0; r < 6; r++)
2806
{
2807
*values += coefficients0[r]*basisvalues[r];
2808
}// end loop over 'r'
2809
break;
2810
}
2811
case 4:
2812
{
2813
2814
// Array of basisvalues.
2815
double basisvalues[6] = {0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000};
2816
2817
// Declare helper variables.
2818
unsigned int rr = 0;
2819
unsigned int ss = 0;
2820
unsigned int tt = 0;
2821
double tmp5 = 0.000000000000000;
2822
double tmp6 = 0.000000000000000;
2823
double tmp7 = 0.000000000000000;
2824
double tmp0 = (1.000000000000000 + Y + 2.000000000000000*X)/2.000000000000000;
2825
double tmp1 = (1.000000000000000 - Y)/2.000000000000000;
2826
double tmp2 = tmp1*tmp1;
2827
2828
// Compute basisvalues.
2829
basisvalues[0] = 1.000000000000000;
2830
basisvalues[1] = tmp0;
2831
for (unsigned int r = 1; r < 2; r++)
2832
{
2833
rr = (r + 1)*((r + 1) + 1)/2;
2834
ss = r*(r + 1)/2;
2835
tt = (r - 1)*((r - 1) + 1)/2;
2836
tmp5 = (1.000000000000000 + 2.000000000000000*r)/(1.000000000000000 + r);
2837
basisvalues[rr] = (basisvalues[ss]*tmp0*tmp5 - basisvalues[tt]*tmp2*r/(1.000000000000000 + r));
2838
}// end loop over 'r'
2839
for (unsigned int r = 0; r < 2; r++)
2840
{
2841
rr = (r + 1)*(r + 1 + 1)/2 + 1;
2842
ss = r*(r + 1)/2;
2843
basisvalues[rr] = basisvalues[ss]*(0.500000000000000 + r + Y*(1.500000000000000 + r));
2844
}// end loop over 'r'
2845
for (unsigned int r = 0; r < 1; r++)
2846
{
2847
for (unsigned int s = 1; s < 2 - r; s++)
2848
{
2849
rr = (r + s + 1)*(r + s + 1 + 1)/2 + s + 1;
2850
ss = (r + s)*(r + s + 1)/2 + s;
2851
tt = (r + s - 1)*(r + s - 1 + 1)/2 + s - 1;
2852
tmp5 = (2.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)*(3.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)/(2.000000000000000*(1.000000000000000 + s)*(2.000000000000000 + s + 2.000000000000000*r));
2853
tmp6 = (1.000000000000000 + 4.000000000000000*r*r + 4.000000000000000*r)*(2.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)/(2.000000000000000*(1.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)*(1.000000000000000 + s)*(2.000000000000000 + s + 2.000000000000000*r));
2854
tmp7 = (1.000000000000000 + s + 2.000000000000000*r)*(3.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)*s/((1.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)*(1.000000000000000 + s)*(2.000000000000000 + s + 2.000000000000000*r));
2855
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Y*tmp5) - basisvalues[tt]*tmp7);
2856
}// end loop over 's'
2857
}// end loop over 'r'
2858
for (unsigned int r = 0; r < 3; r++)
2859
{
2860
for (unsigned int s = 0; s < 3 - r; s++)
2861
{
2862
rr = (r + s)*(r + s + 1)/2 + s;
2863
basisvalues[rr] *= std::sqrt((0.500000000000000 + r)*(1.000000000000000 + r + s));
2864
}// end loop over 's'
2865
}// end loop over 'r'
2866
2867
// Table(s) of coefficients.
2868
static const double coefficients0[6] = \
2869
{0.471404520791032, -0.230940107675850, 0.133333333333333, 0.000000000000000, -0.188561808316413, -0.163299316185545};
2870
2871
// Compute value(s).
2872
for (unsigned int r = 0; r < 6; r++)
2873
{
2874
*values += coefficients0[r]*basisvalues[r];
2875
}// end loop over 'r'
2876
break;
2877
}
2878
case 5:
2879
{
2880
2881
// Array of basisvalues.
2882
double basisvalues[6] = {0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000};
2883
2884
// Declare helper variables.
2885
unsigned int rr = 0;
2886
unsigned int ss = 0;
2887
unsigned int tt = 0;
2888
double tmp5 = 0.000000000000000;
2889
double tmp6 = 0.000000000000000;
2890
double tmp7 = 0.000000000000000;
2891
double tmp0 = (1.000000000000000 + Y + 2.000000000000000*X)/2.000000000000000;
2892
double tmp1 = (1.000000000000000 - Y)/2.000000000000000;
2893
double tmp2 = tmp1*tmp1;
2894
2895
// Compute basisvalues.
2896
basisvalues[0] = 1.000000000000000;
2897
basisvalues[1] = tmp0;
2898
for (unsigned int r = 1; r < 2; r++)
2899
{
2900
rr = (r + 1)*((r + 1) + 1)/2;
2901
ss = r*(r + 1)/2;
2902
tt = (r - 1)*((r - 1) + 1)/2;
2903
tmp5 = (1.000000000000000 + 2.000000000000000*r)/(1.000000000000000 + r);
2904
basisvalues[rr] = (basisvalues[ss]*tmp0*tmp5 - basisvalues[tt]*tmp2*r/(1.000000000000000 + r));
2905
}// end loop over 'r'
2906
for (unsigned int r = 0; r < 2; r++)
2907
{
2908
rr = (r + 1)*(r + 1 + 1)/2 + 1;
2909
ss = r*(r + 1)/2;
2910
basisvalues[rr] = basisvalues[ss]*(0.500000000000000 + r + Y*(1.500000000000000 + r));
2911
}// end loop over 'r'
2912
for (unsigned int r = 0; r < 1; r++)
2913
{
2914
for (unsigned int s = 1; s < 2 - r; s++)
2915
{
2916
rr = (r + s + 1)*(r + s + 1 + 1)/2 + s + 1;
2917
ss = (r + s)*(r + s + 1)/2 + s;
2918
tt = (r + s - 1)*(r + s - 1 + 1)/2 + s - 1;
2919
tmp5 = (2.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)*(3.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)/(2.000000000000000*(1.000000000000000 + s)*(2.000000000000000 + s + 2.000000000000000*r));
2920
tmp6 = (1.000000000000000 + 4.000000000000000*r*r + 4.000000000000000*r)*(2.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)/(2.000000000000000*(1.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)*(1.000000000000000 + s)*(2.000000000000000 + s + 2.000000000000000*r));
2921
tmp7 = (1.000000000000000 + s + 2.000000000000000*r)*(3.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)*s/((1.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)*(1.000000000000000 + s)*(2.000000000000000 + s + 2.000000000000000*r));
2922
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Y*tmp5) - basisvalues[tt]*tmp7);
2923
}// end loop over 's'
2924
}// end loop over 'r'
2925
for (unsigned int r = 0; r < 3; r++)
2926
{
2927
for (unsigned int s = 0; s < 3 - r; s++)
2928
{
2929
rr = (r + s)*(r + s + 1)/2 + s;
2930
basisvalues[rr] *= std::sqrt((0.500000000000000 + r)*(1.000000000000000 + r + s));
2931
}// end loop over 's'
2932
}// end loop over 'r'
2933
2934
// Table(s) of coefficients.
2935
static const double coefficients0[6] = \
2936
{0.471404520791032, 0.000000000000000, -0.266666666666667, -0.243432247780074, 0.000000000000000, 0.054433105395182};
2937
2938
// Compute value(s).
2939
for (unsigned int r = 0; r < 6; r++)
2940
{
2941
*values += coefficients0[r]*basisvalues[r];
2942
}// end loop over 'r'
2943
break;
2944
}
2945
}
2946
2947
}
2948
2949
/// Evaluate all basis functions at given point in cell
2950
virtual void evaluate_basis_all(double* values,
2951
const double* coordinates,
2952
const ufc::cell& c) const
2953
{
2954
// Helper variable to hold values of a single dof.
2955
double dof_values = 0.000000000000000;
2956
2957
// Loop dofs and call evaluate_basis.
2958
for (unsigned int r = 0; r < 6; r++)
2959
{
2960
evaluate_basis(r, &dof_values, coordinates, c);
2961
values[r] = dof_values;
2962
}// end loop over 'r'
2963
}
2964
2965
/// Evaluate order n derivatives of basis function i at given point in cell
2966
virtual void evaluate_basis_derivatives(unsigned int i,
2967
unsigned int n,
2968
double* values,
2969
const double* coordinates,
2970
const ufc::cell& c) const
2971
{
2972
// Extract vertex coordinates
2973
const double * const * x = c.coordinates;
2974
2975
// Compute Jacobian of affine map from reference cell
2976
const double J_00 = x[1][0] - x[0][0];
2977
const double J_01 = x[2][0] - x[0][0];
2978
const double J_10 = x[1][1] - x[0][1];
2979
const double J_11 = x[2][1] - x[0][1];
2980
2981
// Compute determinant of Jacobian
2982
double detJ = J_00*J_11 - J_01*J_10;
2983
2984
// Compute inverse of Jacobian
2985
const double K_00 = J_11 / detJ;
2986
const double K_01 = -J_01 / detJ;
2987
const double K_10 = -J_10 / detJ;
2988
const double K_11 = J_00 / detJ;
2989
2990
// Compute constants
2991
const double C0 = x[1][0] + x[2][0];
2992
const double C1 = x[1][1] + x[2][1];
2993
2994
// Get coordinates and map to the reference (FIAT) element
2995
double X = (J_01*(C1 - 2.0*coordinates[1]) + J_11*(2.0*coordinates[0] - C0)) / detJ;
2996
double Y = (J_00*(2.0*coordinates[1] - C1) + J_10*(C0 - 2.0*coordinates[0])) / detJ;
2997
2998
// Compute number of derivatives.
2999
unsigned int num_derivatives = 1;
3000
for (unsigned int r = 0; r < n; r++)
3001
{
3002
num_derivatives *= 2;
3003
}// end loop over 'r'
3004
3005
// Declare pointer to two dimensional array that holds combinations of derivatives and initialise
3006
unsigned int **combinations = new unsigned int *[num_derivatives];
3007
for (unsigned int row = 0; row < num_derivatives; row++)
3008
{
3009
combinations[row] = new unsigned int [n];
3010
for (unsigned int col = 0; col < n; col++)
3011
combinations[row][col] = 0;
3012
}
3013
3014
// Generate combinations of derivatives
3015
for (unsigned int row = 1; row < num_derivatives; row++)
3016
{
3017
for (unsigned int num = 0; num < row; num++)
3018
{
3019
for (unsigned int col = n-1; col+1 > 0; col--)
3020
{
3021
if (combinations[row][col] + 1 > 1)
3022
combinations[row][col] = 0;
3023
else
3024
{
3025
combinations[row][col] += 1;
3026
break;
3027
}
3028
}
3029
}
3030
}
3031
3032
// Compute inverse of Jacobian
3033
const double Jinv[2][2] = {{K_00, K_01}, {K_10, K_11}};
3034
3035
// Declare transformation matrix
3036
// Declare pointer to two dimensional array and initialise
3037
double **transform = new double *[num_derivatives];
3038
3039
for (unsigned int j = 0; j < num_derivatives; j++)
3040
{
3041
transform[j] = new double [num_derivatives];
3042
for (unsigned int k = 0; k < num_derivatives; k++)
3043
transform[j][k] = 1;
3044
}
3045
3046
// Construct transformation matrix
3047
for (unsigned int row = 0; row < num_derivatives; row++)
3048
{
3049
for (unsigned int col = 0; col < num_derivatives; col++)
3050
{
3051
for (unsigned int k = 0; k < n; k++)
3052
transform[row][col] *= Jinv[combinations[col][k]][combinations[row][k]];
3053
}
3054
}
3055
3056
// Reset values. Assuming that values is always an array.
3057
for (unsigned int r = 0; r < num_derivatives; r++)
3058
{
3059
values[r] = 0.000000000000000;
3060
}// end loop over 'r'
3061
3062
switch (i)
3063
{
3064
case 0:
3065
{
3066
3067
// Array of basisvalues.
3068
double basisvalues[6] = {0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000};
3069
3070
// Declare helper variables.
3071
unsigned int rr = 0;
3072
unsigned int ss = 0;
3073
unsigned int tt = 0;
3074
double tmp5 = 0.000000000000000;
3075
double tmp6 = 0.000000000000000;
3076
double tmp7 = 0.000000000000000;
3077
double tmp0 = (1.000000000000000 + Y + 2.000000000000000*X)/2.000000000000000;
3078
double tmp1 = (1.000000000000000 - Y)/2.000000000000000;
3079
double tmp2 = tmp1*tmp1;
3080
3081
// Compute basisvalues.
3082
basisvalues[0] = 1.000000000000000;
3083
basisvalues[1] = tmp0;
3084
for (unsigned int r = 1; r < 2; r++)
3085
{
3086
rr = (r + 1)*((r + 1) + 1)/2;
3087
ss = r*(r + 1)/2;
3088
tt = (r - 1)*((r - 1) + 1)/2;
3089
tmp5 = (1.000000000000000 + 2.000000000000000*r)/(1.000000000000000 + r);
3090
basisvalues[rr] = (basisvalues[ss]*tmp0*tmp5 - basisvalues[tt]*tmp2*r/(1.000000000000000 + r));
3091
}// end loop over 'r'
3092
for (unsigned int r = 0; r < 2; r++)
3093
{
3094
rr = (r + 1)*(r + 1 + 1)/2 + 1;
3095
ss = r*(r + 1)/2;
3096
basisvalues[rr] = basisvalues[ss]*(0.500000000000000 + r + Y*(1.500000000000000 + r));
3097
}// end loop over 'r'
3098
for (unsigned int r = 0; r < 1; r++)
3099
{
3100
for (unsigned int s = 1; s < 2 - r; s++)
3101
{
3102
rr = (r + s + 1)*(r + s + 1 + 1)/2 + s + 1;
3103
ss = (r + s)*(r + s + 1)/2 + s;
3104
tt = (r + s - 1)*(r + s - 1 + 1)/2 + s - 1;
3105
tmp5 = (2.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)*(3.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)/(2.000000000000000*(1.000000000000000 + s)*(2.000000000000000 + s + 2.000000000000000*r));
3106
tmp6 = (1.000000000000000 + 4.000000000000000*r*r + 4.000000000000000*r)*(2.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)/(2.000000000000000*(1.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)*(1.000000000000000 + s)*(2.000000000000000 + s + 2.000000000000000*r));
3107
tmp7 = (1.000000000000000 + s + 2.000000000000000*r)*(3.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)*s/((1.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)*(1.000000000000000 + s)*(2.000000000000000 + s + 2.000000000000000*r));
3108
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Y*tmp5) - basisvalues[tt]*tmp7);
3109
}// end loop over 's'
3110
}// end loop over 'r'
3111
for (unsigned int r = 0; r < 3; r++)
3112
{
3113
for (unsigned int s = 0; s < 3 - r; s++)
3114
{
3115
rr = (r + s)*(r + s + 1)/2 + s;
3116
basisvalues[rr] *= std::sqrt((0.500000000000000 + r)*(1.000000000000000 + r + s));
3117
}// end loop over 's'
3118
}// end loop over 'r'
3119
3120
// Table(s) of coefficients.
3121
static const double coefficients0[6] = \
3122
{0.000000000000000, -0.173205080756888, -0.100000000000000, 0.121716123890037, 0.094280904158206, 0.054433105395182};
3123
3124
// Tables of derivatives of the polynomial base (transpose).
3125
static const double dmats0[6][6] = \
3126
{{0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
3127
{4.898979485566355, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
3128
{0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
3129
{0.000000000000000, 9.486832980505138, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
3130
{3.999999999999999, 0.000000000000000, 7.071067811865476, 0.000000000000000, 0.000000000000000, 0.000000000000000},
3131
{0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000}};
3132
3133
static const double dmats1[6][6] = \
3134
{{0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
3135
{2.449489742783177, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
3136
{4.242640687119285, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
3137
{2.581988897471611, 4.743416490252570, -0.912870929175278, 0.000000000000000, 0.000000000000000, 0.000000000000000},
3138
{1.999999999999999, 6.123724356957944, 3.535533905932737, 0.000000000000000, 0.000000000000000, 0.000000000000000},
3139
{-2.309401076758502, 0.000000000000000, 8.164965809277259, 0.000000000000000, 0.000000000000000, 0.000000000000000}};
3140
3141
// Compute reference derivatives.
3142
// Declare pointer to array of derivatives on FIAT element.
3143
double *derivatives = new double[num_derivatives];
3144
for (unsigned int r = 0; r < num_derivatives; r++)
3145
{
3146
derivatives[r] = 0.000000000000000;
3147
}// end loop over 'r'
3148
3149
// Declare derivative matrix (of polynomial basis).
3150
double dmats[6][6] = \
3151
{{1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
3152
{0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
3153
{0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
3154
{0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000},
3155
{0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000},
3156
{0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000}};
3157
3158
// Declare (auxiliary) derivative matrix (of polynomial basis).
3159
double dmats_old[6][6] = \
3160
{{1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
3161
{0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
3162
{0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
3163
{0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000},
3164
{0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000},
3165
{0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000}};
3166
3167
// Loop possible derivatives.
3168
for (unsigned int r = 0; r < num_derivatives; r++)
3169
{
3170
// Resetting dmats values to compute next derivative.
3171
for (unsigned int t = 0; t < 6; t++)
3172
{
3173
for (unsigned int u = 0; u < 6; u++)
3174
{
3175
dmats[t][u] = 0.000000000000000;
3176
if (t == u)
3177
{
3178
dmats[t][u] = 1.000000000000000;
3179
}
3180
3181
}// end loop over 'u'
3182
}// end loop over 't'
3183
3184
// Looping derivative order to generate dmats.
3185
for (unsigned int s = 0; s < n; s++)
3186
{
3187
// Updating dmats_old with new values and resetting dmats.
3188
for (unsigned int t = 0; t < 6; t++)
3189
{
3190
for (unsigned int u = 0; u < 6; u++)
3191
{
3192
dmats_old[t][u] = dmats[t][u];
3193
dmats[t][u] = 0.000000000000000;
3194
}// end loop over 'u'
3195
}// end loop over 't'
3196
3197
// Update dmats using an inner product.
3198
if (combinations[r][s] == 0)
3199
{
3200
for (unsigned int t = 0; t < 6; t++)
3201
{
3202
for (unsigned int u = 0; u < 6; u++)
3203
{
3204
for (unsigned int tu = 0; tu < 6; tu++)
3205
{
3206
dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
3207
}// end loop over 'tu'
3208
}// end loop over 'u'
3209
}// end loop over 't'
3210
}
3211
3212
if (combinations[r][s] == 1)
3213
{
3214
for (unsigned int t = 0; t < 6; t++)
3215
{
3216
for (unsigned int u = 0; u < 6; u++)
3217
{
3218
for (unsigned int tu = 0; tu < 6; tu++)
3219
{
3220
dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
3221
}// end loop over 'tu'
3222
}// end loop over 'u'
3223
}// end loop over 't'
3224
}
3225
3226
}// end loop over 's'
3227
for (unsigned int s = 0; s < 6; s++)
3228
{
3229
for (unsigned int t = 0; t < 6; t++)
3230
{
3231
derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
3232
}// end loop over 't'
3233
}// end loop over 's'
3234
}// end loop over 'r'
3235
3236
// Transform derivatives back to physical element
3237
for (unsigned int r = 0; r < num_derivatives; r++)
3238
{
3239
for (unsigned int s = 0; s < num_derivatives; s++)
3240
{
3241
values[r] += transform[r][s]*derivatives[s];
3242
}// end loop over 's'
3243
}// end loop over 'r'
3244
3245
// Delete pointer to array of derivatives on FIAT element
3246
delete [] derivatives;
3247
3248
// Delete pointer to array of combinations of derivatives and transform
3249
for (unsigned int r = 0; r < num_derivatives; r++)
3250
{
3251
delete [] combinations[r];
3252
}// end loop over 'r'
3253
delete [] combinations;
3254
for (unsigned int r = 0; r < num_derivatives; r++)
3255
{
3256
delete [] transform[r];
3257
}// end loop over 'r'
3258
delete [] transform;
3259
break;
3260
}
3261
case 1:
3262
{
3263
3264
// Array of basisvalues.
3265
double basisvalues[6] = {0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000};
3266
3267
// Declare helper variables.
3268
unsigned int rr = 0;
3269
unsigned int ss = 0;
3270
unsigned int tt = 0;
3271
double tmp5 = 0.000000000000000;
3272
double tmp6 = 0.000000000000000;
3273
double tmp7 = 0.000000000000000;
3274
double tmp0 = (1.000000000000000 + Y + 2.000000000000000*X)/2.000000000000000;
3275
double tmp1 = (1.000000000000000 - Y)/2.000000000000000;
3276
double tmp2 = tmp1*tmp1;
3277
3278
// Compute basisvalues.
3279
basisvalues[0] = 1.000000000000000;
3280
basisvalues[1] = tmp0;
3281
for (unsigned int r = 1; r < 2; r++)
3282
{
3283
rr = (r + 1)*((r + 1) + 1)/2;
3284
ss = r*(r + 1)/2;
3285
tt = (r - 1)*((r - 1) + 1)/2;
3286
tmp5 = (1.000000000000000 + 2.000000000000000*r)/(1.000000000000000 + r);
3287
basisvalues[rr] = (basisvalues[ss]*tmp0*tmp5 - basisvalues[tt]*tmp2*r/(1.000000000000000 + r));
3288
}// end loop over 'r'
3289
for (unsigned int r = 0; r < 2; r++)
3290
{
3291
rr = (r + 1)*(r + 1 + 1)/2 + 1;
3292
ss = r*(r + 1)/2;
3293
basisvalues[rr] = basisvalues[ss]*(0.500000000000000 + r + Y*(1.500000000000000 + r));
3294
}// end loop over 'r'
3295
for (unsigned int r = 0; r < 1; r++)
3296
{
3297
for (unsigned int s = 1; s < 2 - r; s++)
3298
{
3299
rr = (r + s + 1)*(r + s + 1 + 1)/2 + s + 1;
3300
ss = (r + s)*(r + s + 1)/2 + s;
3301
tt = (r + s - 1)*(r + s - 1 + 1)/2 + s - 1;
3302
tmp5 = (2.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)*(3.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)/(2.000000000000000*(1.000000000000000 + s)*(2.000000000000000 + s + 2.000000000000000*r));
3303
tmp6 = (1.000000000000000 + 4.000000000000000*r*r + 4.000000000000000*r)*(2.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)/(2.000000000000000*(1.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)*(1.000000000000000 + s)*(2.000000000000000 + s + 2.000000000000000*r));
3304
tmp7 = (1.000000000000000 + s + 2.000000000000000*r)*(3.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)*s/((1.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)*(1.000000000000000 + s)*(2.000000000000000 + s + 2.000000000000000*r));
3305
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Y*tmp5) - basisvalues[tt]*tmp7);
3306
}// end loop over 's'
3307
}// end loop over 'r'
3308
for (unsigned int r = 0; r < 3; r++)
3309
{
3310
for (unsigned int s = 0; s < 3 - r; s++)
3311
{
3312
rr = (r + s)*(r + s + 1)/2 + s;
3313
basisvalues[rr] *= std::sqrt((0.500000000000000 + r)*(1.000000000000000 + r + s));
3314
}// end loop over 's'
3315
}// end loop over 'r'
3316
3317
// Table(s) of coefficients.
3318
static const double coefficients0[6] = \
3319
{0.000000000000000, 0.173205080756888, -0.100000000000000, 0.121716123890037, -0.094280904158206, 0.054433105395182};
3320
3321
// Tables of derivatives of the polynomial base (transpose).
3322
static const double dmats0[6][6] = \
3323
{{0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
3324
{4.898979485566355, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
3325
{0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
3326
{0.000000000000000, 9.486832980505138, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
3327
{3.999999999999999, 0.000000000000000, 7.071067811865476, 0.000000000000000, 0.000000000000000, 0.000000000000000},
3328
{0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000}};
3329
3330
static const double dmats1[6][6] = \
3331
{{0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
3332
{2.449489742783177, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
3333
{4.242640687119285, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
3334
{2.581988897471611, 4.743416490252570, -0.912870929175278, 0.000000000000000, 0.000000000000000, 0.000000000000000},
3335
{1.999999999999999, 6.123724356957944, 3.535533905932737, 0.000000000000000, 0.000000000000000, 0.000000000000000},
3336
{-2.309401076758502, 0.000000000000000, 8.164965809277259, 0.000000000000000, 0.000000000000000, 0.000000000000000}};
3337
3338
// Compute reference derivatives.
3339
// Declare pointer to array of derivatives on FIAT element.
3340
double *derivatives = new double[num_derivatives];
3341
for (unsigned int r = 0; r < num_derivatives; r++)
3342
{
3343
derivatives[r] = 0.000000000000000;
3344
}// end loop over 'r'
3345
3346
// Declare derivative matrix (of polynomial basis).
3347
double dmats[6][6] = \
3348
{{1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
3349
{0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
3350
{0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
3351
{0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000},
3352
{0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000},
3353
{0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000}};
3354
3355
// Declare (auxiliary) derivative matrix (of polynomial basis).
3356
double dmats_old[6][6] = \
3357
{{1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
3358
{0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
3359
{0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
3360
{0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000},
3361
{0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000},
3362
{0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000}};
3363
3364
// Loop possible derivatives.
3365
for (unsigned int r = 0; r < num_derivatives; r++)
3366
{
3367
// Resetting dmats values to compute next derivative.
3368
for (unsigned int t = 0; t < 6; t++)
3369
{
3370
for (unsigned int u = 0; u < 6; u++)
3371
{
3372
dmats[t][u] = 0.000000000000000;
3373
if (t == u)
3374
{
3375
dmats[t][u] = 1.000000000000000;
3376
}
3377
3378
}// end loop over 'u'
3379
}// end loop over 't'
3380
3381
// Looping derivative order to generate dmats.
3382
for (unsigned int s = 0; s < n; s++)
3383
{
3384
// Updating dmats_old with new values and resetting dmats.
3385
for (unsigned int t = 0; t < 6; t++)
3386
{
3387
for (unsigned int u = 0; u < 6; u++)
3388
{
3389
dmats_old[t][u] = dmats[t][u];
3390
dmats[t][u] = 0.000000000000000;
3391
}// end loop over 'u'
3392
}// end loop over 't'
3393
3394
// Update dmats using an inner product.
3395
if (combinations[r][s] == 0)
3396
{
3397
for (unsigned int t = 0; t < 6; t++)
3398
{
3399
for (unsigned int u = 0; u < 6; u++)
3400
{
3401
for (unsigned int tu = 0; tu < 6; tu++)
3402
{
3403
dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
3404
}// end loop over 'tu'
3405
}// end loop over 'u'
3406
}// end loop over 't'
3407
}
3408
3409
if (combinations[r][s] == 1)
3410
{
3411
for (unsigned int t = 0; t < 6; t++)
3412
{
3413
for (unsigned int u = 0; u < 6; u++)
3414
{
3415
for (unsigned int tu = 0; tu < 6; tu++)
3416
{
3417
dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
3418
}// end loop over 'tu'
3419
}// end loop over 'u'
3420
}// end loop over 't'
3421
}
3422
3423
}// end loop over 's'
3424
for (unsigned int s = 0; s < 6; s++)
3425
{
3426
for (unsigned int t = 0; t < 6; t++)
3427
{
3428
derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
3429
}// end loop over 't'
3430
}// end loop over 's'
3431
}// end loop over 'r'
3432
3433
// Transform derivatives back to physical element
3434
for (unsigned int r = 0; r < num_derivatives; r++)
3435
{
3436
for (unsigned int s = 0; s < num_derivatives; s++)
3437
{
3438
values[r] += transform[r][s]*derivatives[s];
3439
}// end loop over 's'
3440
}// end loop over 'r'
3441
3442
// Delete pointer to array of derivatives on FIAT element
3443
delete [] derivatives;
3444
3445
// Delete pointer to array of combinations of derivatives and transform
3446
for (unsigned int r = 0; r < num_derivatives; r++)
3447
{
3448
delete [] combinations[r];
3449
}// end loop over 'r'
3450
delete [] combinations;
3451
for (unsigned int r = 0; r < num_derivatives; r++)
3452
{
3453
delete [] transform[r];
3454
}// end loop over 'r'
3455
delete [] transform;
3456
break;
3457
}
3458
case 2:
3459
{
3460
3461
// Array of basisvalues.
3462
double basisvalues[6] = {0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000};
3463
3464
// Declare helper variables.
3465
unsigned int rr = 0;
3466
unsigned int ss = 0;
3467
unsigned int tt = 0;
3468
double tmp5 = 0.000000000000000;
3469
double tmp6 = 0.000000000000000;
3470
double tmp7 = 0.000000000000000;
3471
double tmp0 = (1.000000000000000 + Y + 2.000000000000000*X)/2.000000000000000;
3472
double tmp1 = (1.000000000000000 - Y)/2.000000000000000;
3473
double tmp2 = tmp1*tmp1;
3474
3475
// Compute basisvalues.
3476
basisvalues[0] = 1.000000000000000;
3477
basisvalues[1] = tmp0;
3478
for (unsigned int r = 1; r < 2; r++)
3479
{
3480
rr = (r + 1)*((r + 1) + 1)/2;
3481
ss = r*(r + 1)/2;
3482
tt = (r - 1)*((r - 1) + 1)/2;
3483
tmp5 = (1.000000000000000 + 2.000000000000000*r)/(1.000000000000000 + r);
3484
basisvalues[rr] = (basisvalues[ss]*tmp0*tmp5 - basisvalues[tt]*tmp2*r/(1.000000000000000 + r));
3485
}// end loop over 'r'
3486
for (unsigned int r = 0; r < 2; r++)
3487
{
3488
rr = (r + 1)*(r + 1 + 1)/2 + 1;
3489
ss = r*(r + 1)/2;
3490
basisvalues[rr] = basisvalues[ss]*(0.500000000000000 + r + Y*(1.500000000000000 + r));
3491
}// end loop over 'r'
3492
for (unsigned int r = 0; r < 1; r++)
3493
{
3494
for (unsigned int s = 1; s < 2 - r; s++)
3495
{
3496
rr = (r + s + 1)*(r + s + 1 + 1)/2 + s + 1;
3497
ss = (r + s)*(r + s + 1)/2 + s;
3498
tt = (r + s - 1)*(r + s - 1 + 1)/2 + s - 1;
3499
tmp5 = (2.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)*(3.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)/(2.000000000000000*(1.000000000000000 + s)*(2.000000000000000 + s + 2.000000000000000*r));
3500
tmp6 = (1.000000000000000 + 4.000000000000000*r*r + 4.000000000000000*r)*(2.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)/(2.000000000000000*(1.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)*(1.000000000000000 + s)*(2.000000000000000 + s + 2.000000000000000*r));
3501
tmp7 = (1.000000000000000 + s + 2.000000000000000*r)*(3.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)*s/((1.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)*(1.000000000000000 + s)*(2.000000000000000 + s + 2.000000000000000*r));
3502
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Y*tmp5) - basisvalues[tt]*tmp7);
3503
}// end loop over 's'
3504
}// end loop over 'r'
3505
for (unsigned int r = 0; r < 3; r++)
3506
{
3507
for (unsigned int s = 0; s < 3 - r; s++)
3508
{
3509
rr = (r + s)*(r + s + 1)/2 + s;
3510
basisvalues[rr] *= std::sqrt((0.500000000000000 + r)*(1.000000000000000 + r + s));
3511
}// end loop over 's'
3512
}// end loop over 'r'
3513
3514
// Table(s) of coefficients.
3515
static const double coefficients0[6] = \
3516
{0.000000000000000, 0.000000000000000, 0.200000000000000, 0.000000000000000, 0.000000000000000, 0.163299316185545};
3517
3518
// Tables of derivatives of the polynomial base (transpose).
3519
static const double dmats0[6][6] = \
3520
{{0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
3521
{4.898979485566355, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
3522
{0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
3523
{0.000000000000000, 9.486832980505138, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
3524
{3.999999999999999, 0.000000000000000, 7.071067811865476, 0.000000000000000, 0.000000000000000, 0.000000000000000},
3525
{0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000}};
3526
3527
static const double dmats1[6][6] = \
3528
{{0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
3529
{2.449489742783177, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
3530
{4.242640687119285, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
3531
{2.581988897471611, 4.743416490252570, -0.912870929175278, 0.000000000000000, 0.000000000000000, 0.000000000000000},
3532
{1.999999999999999, 6.123724356957944, 3.535533905932737, 0.000000000000000, 0.000000000000000, 0.000000000000000},
3533
{-2.309401076758502, 0.000000000000000, 8.164965809277259, 0.000000000000000, 0.000000000000000, 0.000000000000000}};
3534
3535
// Compute reference derivatives.
3536
// Declare pointer to array of derivatives on FIAT element.
3537
double *derivatives = new double[num_derivatives];
3538
for (unsigned int r = 0; r < num_derivatives; r++)
3539
{
3540
derivatives[r] = 0.000000000000000;
3541
}// end loop over 'r'
3542
3543
// Declare derivative matrix (of polynomial basis).
3544
double dmats[6][6] = \
3545
{{1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
3546
{0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
3547
{0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
3548
{0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000},
3549
{0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000},
3550
{0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000}};
3551
3552
// Declare (auxiliary) derivative matrix (of polynomial basis).
3553
double dmats_old[6][6] = \
3554
{{1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
3555
{0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
3556
{0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
3557
{0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000},
3558
{0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000},
3559
{0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000}};
3560
3561
// Loop possible derivatives.
3562
for (unsigned int r = 0; r < num_derivatives; r++)
3563
{
3564
// Resetting dmats values to compute next derivative.
3565
for (unsigned int t = 0; t < 6; t++)
3566
{
3567
for (unsigned int u = 0; u < 6; u++)
3568
{
3569
dmats[t][u] = 0.000000000000000;
3570
if (t == u)
3571
{
3572
dmats[t][u] = 1.000000000000000;
3573
}
3574
3575
}// end loop over 'u'
3576
}// end loop over 't'
3577
3578
// Looping derivative order to generate dmats.
3579
for (unsigned int s = 0; s < n; s++)
3580
{
3581
// Updating dmats_old with new values and resetting dmats.
3582
for (unsigned int t = 0; t < 6; t++)
3583
{
3584
for (unsigned int u = 0; u < 6; u++)
3585
{
3586
dmats_old[t][u] = dmats[t][u];
3587
dmats[t][u] = 0.000000000000000;
3588
}// end loop over 'u'
3589
}// end loop over 't'
3590
3591
// Update dmats using an inner product.
3592
if (combinations[r][s] == 0)
3593
{
3594
for (unsigned int t = 0; t < 6; t++)
3595
{
3596
for (unsigned int u = 0; u < 6; u++)
3597
{
3598
for (unsigned int tu = 0; tu < 6; tu++)
3599
{
3600
dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
3601
}// end loop over 'tu'
3602
}// end loop over 'u'
3603
}// end loop over 't'
3604
}
3605
3606
if (combinations[r][s] == 1)
3607
{
3608
for (unsigned int t = 0; t < 6; t++)
3609
{
3610
for (unsigned int u = 0; u < 6; u++)
3611
{
3612
for (unsigned int tu = 0; tu < 6; tu++)
3613
{
3614
dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
3615
}// end loop over 'tu'
3616
}// end loop over 'u'
3617
}// end loop over 't'
3618
}
3619
3620
}// end loop over 's'
3621
for (unsigned int s = 0; s < 6; s++)
3622
{
3623
for (unsigned int t = 0; t < 6; t++)
3624
{
3625
derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
3626
}// end loop over 't'
3627
}// end loop over 's'
3628
}// end loop over 'r'
3629
3630
// Transform derivatives back to physical element
3631
for (unsigned int r = 0; r < num_derivatives; r++)
3632
{
3633
for (unsigned int s = 0; s < num_derivatives; s++)
3634
{
3635
values[r] += transform[r][s]*derivatives[s];
3636
}// end loop over 's'
3637
}// end loop over 'r'
3638
3639
// Delete pointer to array of derivatives on FIAT element
3640
delete [] derivatives;
3641
3642
// Delete pointer to array of combinations of derivatives and transform
3643
for (unsigned int r = 0; r < num_derivatives; r++)
3644
{
3645
delete [] combinations[r];
3646
}// end loop over 'r'
3647
delete [] combinations;
3648
for (unsigned int r = 0; r < num_derivatives; r++)
3649
{
3650
delete [] transform[r];
3651
}// end loop over 'r'
3652
delete [] transform;
3653
break;
3654
}
3655
case 3:
3656
{
3657
3658
// Array of basisvalues.
3659
double basisvalues[6] = {0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000};
3660
3661
// Declare helper variables.
3662
unsigned int rr = 0;
3663
unsigned int ss = 0;
3664
unsigned int tt = 0;
3665
double tmp5 = 0.000000000000000;
3666
double tmp6 = 0.000000000000000;
3667
double tmp7 = 0.000000000000000;
3668
double tmp0 = (1.000000000000000 + Y + 2.000000000000000*X)/2.000000000000000;
3669
double tmp1 = (1.000000000000000 - Y)/2.000000000000000;
3670
double tmp2 = tmp1*tmp1;
3671
3672
// Compute basisvalues.
3673
basisvalues[0] = 1.000000000000000;
3674
basisvalues[1] = tmp0;
3675
for (unsigned int r = 1; r < 2; r++)
3676
{
3677
rr = (r + 1)*((r + 1) + 1)/2;
3678
ss = r*(r + 1)/2;
3679
tt = (r - 1)*((r - 1) + 1)/2;
3680
tmp5 = (1.000000000000000 + 2.000000000000000*r)/(1.000000000000000 + r);
3681
basisvalues[rr] = (basisvalues[ss]*tmp0*tmp5 - basisvalues[tt]*tmp2*r/(1.000000000000000 + r));
3682
}// end loop over 'r'
3683
for (unsigned int r = 0; r < 2; r++)
3684
{
3685
rr = (r + 1)*(r + 1 + 1)/2 + 1;
3686
ss = r*(r + 1)/2;
3687
basisvalues[rr] = basisvalues[ss]*(0.500000000000000 + r + Y*(1.500000000000000 + r));
3688
}// end loop over 'r'
3689
for (unsigned int r = 0; r < 1; r++)
3690
{
3691
for (unsigned int s = 1; s < 2 - r; s++)
3692
{
3693
rr = (r + s + 1)*(r + s + 1 + 1)/2 + s + 1;
3694
ss = (r + s)*(r + s + 1)/2 + s;
3695
tt = (r + s - 1)*(r + s - 1 + 1)/2 + s - 1;
3696
tmp5 = (2.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)*(3.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)/(2.000000000000000*(1.000000000000000 + s)*(2.000000000000000 + s + 2.000000000000000*r));
3697
tmp6 = (1.000000000000000 + 4.000000000000000*r*r + 4.000000000000000*r)*(2.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)/(2.000000000000000*(1.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)*(1.000000000000000 + s)*(2.000000000000000 + s + 2.000000000000000*r));
3698
tmp7 = (1.000000000000000 + s + 2.000000000000000*r)*(3.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)*s/((1.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)*(1.000000000000000 + s)*(2.000000000000000 + s + 2.000000000000000*r));
3699
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Y*tmp5) - basisvalues[tt]*tmp7);
3700
}// end loop over 's'
3701
}// end loop over 'r'
3702
for (unsigned int r = 0; r < 3; r++)
3703
{
3704
for (unsigned int s = 0; s < 3 - r; s++)
3705
{
3706
rr = (r + s)*(r + s + 1)/2 + s;
3707
basisvalues[rr] *= std::sqrt((0.500000000000000 + r)*(1.000000000000000 + r + s));
3708
}// end loop over 's'
3709
}// end loop over 'r'
3710
3711
// Table(s) of coefficients.
3712
static const double coefficients0[6] = \
3713
{0.471404520791032, 0.230940107675850, 0.133333333333333, 0.000000000000000, 0.188561808316413, -0.163299316185545};
3714
3715
// Tables of derivatives of the polynomial base (transpose).
3716
static const double dmats0[6][6] = \
3717
{{0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
3718
{4.898979485566355, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
3719
{0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
3720
{0.000000000000000, 9.486832980505138, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
3721
{3.999999999999999, 0.000000000000000, 7.071067811865476, 0.000000000000000, 0.000000000000000, 0.000000000000000},
3722
{0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000}};
3723
3724
static const double dmats1[6][6] = \
3725
{{0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
3726
{2.449489742783177, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
3727
{4.242640687119285, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
3728
{2.581988897471611, 4.743416490252570, -0.912870929175278, 0.000000000000000, 0.000000000000000, 0.000000000000000},
3729
{1.999999999999999, 6.123724356957944, 3.535533905932737, 0.000000000000000, 0.000000000000000, 0.000000000000000},
3730
{-2.309401076758502, 0.000000000000000, 8.164965809277259, 0.000000000000000, 0.000000000000000, 0.000000000000000}};
3731
3732
// Compute reference derivatives.
3733
// Declare pointer to array of derivatives on FIAT element.
3734
double *derivatives = new double[num_derivatives];
3735
for (unsigned int r = 0; r < num_derivatives; r++)
3736
{
3737
derivatives[r] = 0.000000000000000;
3738
}// end loop over 'r'
3739
3740
// Declare derivative matrix (of polynomial basis).
3741
double dmats[6][6] = \
3742
{{1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
3743
{0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
3744
{0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
3745
{0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000},
3746
{0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000},
3747
{0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000}};
3748
3749
// Declare (auxiliary) derivative matrix (of polynomial basis).
3750
double dmats_old[6][6] = \
3751
{{1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
3752
{0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
3753
{0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
3754
{0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000},
3755
{0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000},
3756
{0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000}};
3757
3758
// Loop possible derivatives.
3759
for (unsigned int r = 0; r < num_derivatives; r++)
3760
{
3761
// Resetting dmats values to compute next derivative.
3762
for (unsigned int t = 0; t < 6; t++)
3763
{
3764
for (unsigned int u = 0; u < 6; u++)
3765
{
3766
dmats[t][u] = 0.000000000000000;
3767
if (t == u)
3768
{
3769
dmats[t][u] = 1.000000000000000;
3770
}
3771
3772
}// end loop over 'u'
3773
}// end loop over 't'
3774
3775
// Looping derivative order to generate dmats.
3776
for (unsigned int s = 0; s < n; s++)
3777
{
3778
// Updating dmats_old with new values and resetting dmats.
3779
for (unsigned int t = 0; t < 6; t++)
3780
{
3781
for (unsigned int u = 0; u < 6; u++)
3782
{
3783
dmats_old[t][u] = dmats[t][u];
3784
dmats[t][u] = 0.000000000000000;
3785
}// end loop over 'u'
3786
}// end loop over 't'
3787
3788
// Update dmats using an inner product.
3789
if (combinations[r][s] == 0)
3790
{
3791
for (unsigned int t = 0; t < 6; t++)
3792
{
3793
for (unsigned int u = 0; u < 6; u++)
3794
{
3795
for (unsigned int tu = 0; tu < 6; tu++)
3796
{
3797
dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
3798
}// end loop over 'tu'
3799
}// end loop over 'u'
3800
}// end loop over 't'
3801
}
3802
3803
if (combinations[r][s] == 1)
3804
{
3805
for (unsigned int t = 0; t < 6; t++)
3806
{
3807
for (unsigned int u = 0; u < 6; u++)
3808
{
3809
for (unsigned int tu = 0; tu < 6; tu++)
3810
{
3811
dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
3812
}// end loop over 'tu'
3813
}// end loop over 'u'
3814
}// end loop over 't'
3815
}
3816
3817
}// end loop over 's'
3818
for (unsigned int s = 0; s < 6; s++)
3819
{
3820
for (unsigned int t = 0; t < 6; t++)
3821
{
3822
derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
3823
}// end loop over 't'
3824
}// end loop over 's'
3825
}// end loop over 'r'
3826
3827
// Transform derivatives back to physical element
3828
for (unsigned int r = 0; r < num_derivatives; r++)
3829
{
3830
for (unsigned int s = 0; s < num_derivatives; s++)
3831
{
3832
values[r] += transform[r][s]*derivatives[s];
3833
}// end loop over 's'
3834
}// end loop over 'r'
3835
3836
// Delete pointer to array of derivatives on FIAT element
3837
delete [] derivatives;
3838
3839
// Delete pointer to array of combinations of derivatives and transform
3840
for (unsigned int r = 0; r < num_derivatives; r++)
3841
{
3842
delete [] combinations[r];
3843
}// end loop over 'r'
3844
delete [] combinations;
3845
for (unsigned int r = 0; r < num_derivatives; r++)
3846
{
3847
delete [] transform[r];
3848
}// end loop over 'r'
3849
delete [] transform;
3850
break;
3851
}
3852
case 4:
3853
{
3854
3855
// Array of basisvalues.
3856
double basisvalues[6] = {0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000};
3857
3858
// Declare helper variables.
3859
unsigned int rr = 0;
3860
unsigned int ss = 0;
3861
unsigned int tt = 0;
3862
double tmp5 = 0.000000000000000;
3863
double tmp6 = 0.000000000000000;
3864
double tmp7 = 0.000000000000000;
3865
double tmp0 = (1.000000000000000 + Y + 2.000000000000000*X)/2.000000000000000;
3866
double tmp1 = (1.000000000000000 - Y)/2.000000000000000;
3867
double tmp2 = tmp1*tmp1;
3868
3869
// Compute basisvalues.
3870
basisvalues[0] = 1.000000000000000;
3871
basisvalues[1] = tmp0;
3872
for (unsigned int r = 1; r < 2; r++)
3873
{
3874
rr = (r + 1)*((r + 1) + 1)/2;
3875
ss = r*(r + 1)/2;
3876
tt = (r - 1)*((r - 1) + 1)/2;
3877
tmp5 = (1.000000000000000 + 2.000000000000000*r)/(1.000000000000000 + r);
3878
basisvalues[rr] = (basisvalues[ss]*tmp0*tmp5 - basisvalues[tt]*tmp2*r/(1.000000000000000 + r));
3879
}// end loop over 'r'
3880
for (unsigned int r = 0; r < 2; r++)
3881
{
3882
rr = (r + 1)*(r + 1 + 1)/2 + 1;
3883
ss = r*(r + 1)/2;
3884
basisvalues[rr] = basisvalues[ss]*(0.500000000000000 + r + Y*(1.500000000000000 + r));
3885
}// end loop over 'r'
3886
for (unsigned int r = 0; r < 1; r++)
3887
{
3888
for (unsigned int s = 1; s < 2 - r; s++)
3889
{
3890
rr = (r + s + 1)*(r + s + 1 + 1)/2 + s + 1;
3891
ss = (r + s)*(r + s + 1)/2 + s;
3892
tt = (r + s - 1)*(r + s - 1 + 1)/2 + s - 1;
3893
tmp5 = (2.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)*(3.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)/(2.000000000000000*(1.000000000000000 + s)*(2.000000000000000 + s + 2.000000000000000*r));
3894
tmp6 = (1.000000000000000 + 4.000000000000000*r*r + 4.000000000000000*r)*(2.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)/(2.000000000000000*(1.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)*(1.000000000000000 + s)*(2.000000000000000 + s + 2.000000000000000*r));
3895
tmp7 = (1.000000000000000 + s + 2.000000000000000*r)*(3.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)*s/((1.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)*(1.000000000000000 + s)*(2.000000000000000 + s + 2.000000000000000*r));
3896
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Y*tmp5) - basisvalues[tt]*tmp7);
3897
}// end loop over 's'
3898
}// end loop over 'r'
3899
for (unsigned int r = 0; r < 3; r++)
3900
{
3901
for (unsigned int s = 0; s < 3 - r; s++)
3902
{
3903
rr = (r + s)*(r + s + 1)/2 + s;
3904
basisvalues[rr] *= std::sqrt((0.500000000000000 + r)*(1.000000000000000 + r + s));
3905
}// end loop over 's'
3906
}// end loop over 'r'
3907
3908
// Table(s) of coefficients.
3909
static const double coefficients0[6] = \
3910
{0.471404520791032, -0.230940107675850, 0.133333333333333, 0.000000000000000, -0.188561808316413, -0.163299316185545};
3911
3912
// Tables of derivatives of the polynomial base (transpose).
3913
static const double dmats0[6][6] = \
3914
{{0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
3915
{4.898979485566355, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
3916
{0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
3917
{0.000000000000000, 9.486832980505138, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
3918
{3.999999999999999, 0.000000000000000, 7.071067811865476, 0.000000000000000, 0.000000000000000, 0.000000000000000},
3919
{0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000}};
3920
3921
static const double dmats1[6][6] = \
3922
{{0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
3923
{2.449489742783177, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
3924
{4.242640687119285, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
3925
{2.581988897471611, 4.743416490252570, -0.912870929175278, 0.000000000000000, 0.000000000000000, 0.000000000000000},
3926
{1.999999999999999, 6.123724356957944, 3.535533905932737, 0.000000000000000, 0.000000000000000, 0.000000000000000},
3927
{-2.309401076758502, 0.000000000000000, 8.164965809277259, 0.000000000000000, 0.000000000000000, 0.000000000000000}};
3928
3929
// Compute reference derivatives.
3930
// Declare pointer to array of derivatives on FIAT element.
3931
double *derivatives = new double[num_derivatives];
3932
for (unsigned int r = 0; r < num_derivatives; r++)
3933
{
3934
derivatives[r] = 0.000000000000000;
3935
}// end loop over 'r'
3936
3937
// Declare derivative matrix (of polynomial basis).
3938
double dmats[6][6] = \
3939
{{1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
3940
{0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
3941
{0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
3942
{0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000},
3943
{0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000},
3944
{0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000}};
3945
3946
// Declare (auxiliary) derivative matrix (of polynomial basis).
3947
double dmats_old[6][6] = \
3948
{{1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
3949
{0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
3950
{0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
3951
{0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000},
3952
{0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000},
3953
{0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000}};
3954
3955
// Loop possible derivatives.
3956
for (unsigned int r = 0; r < num_derivatives; r++)
3957
{
3958
// Resetting dmats values to compute next derivative.
3959
for (unsigned int t = 0; t < 6; t++)
3960
{
3961
for (unsigned int u = 0; u < 6; u++)
3962
{
3963
dmats[t][u] = 0.000000000000000;
3964
if (t == u)
3965
{
3966
dmats[t][u] = 1.000000000000000;
3967
}
3968
3969
}// end loop over 'u'
3970
}// end loop over 't'
3971
3972
// Looping derivative order to generate dmats.
3973
for (unsigned int s = 0; s < n; s++)
3974
{
3975
// Updating dmats_old with new values and resetting dmats.
3976
for (unsigned int t = 0; t < 6; t++)
3977
{
3978
for (unsigned int u = 0; u < 6; u++)
3979
{
3980
dmats_old[t][u] = dmats[t][u];
3981
dmats[t][u] = 0.000000000000000;
3982
}// end loop over 'u'
3983
}// end loop over 't'
3984
3985
// Update dmats using an inner product.
3986
if (combinations[r][s] == 0)
3987
{
3988
for (unsigned int t = 0; t < 6; t++)
3989
{
3990
for (unsigned int u = 0; u < 6; u++)
3991
{
3992
for (unsigned int tu = 0; tu < 6; tu++)
3993
{
3994
dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
3995
}// end loop over 'tu'
3996
}// end loop over 'u'
3997
}// end loop over 't'
3998
}
3999
4000
if (combinations[r][s] == 1)
4001
{
4002
for (unsigned int t = 0; t < 6; t++)
4003
{
4004
for (unsigned int u = 0; u < 6; u++)
4005
{
4006
for (unsigned int tu = 0; tu < 6; tu++)
4007
{
4008
dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
4009
}// end loop over 'tu'
4010
}// end loop over 'u'
4011
}// end loop over 't'
4012
}
4013
4014
}// end loop over 's'
4015
for (unsigned int s = 0; s < 6; s++)
4016
{
4017
for (unsigned int t = 0; t < 6; t++)
4018
{
4019
derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
4020
}// end loop over 't'
4021
}// end loop over 's'
4022
}// end loop over 'r'
4023
4024
// Transform derivatives back to physical element
4025
for (unsigned int r = 0; r < num_derivatives; r++)
4026
{
4027
for (unsigned int s = 0; s < num_derivatives; s++)
4028
{
4029
values[r] += transform[r][s]*derivatives[s];
4030
}// end loop over 's'
4031
}// end loop over 'r'
4032
4033
// Delete pointer to array of derivatives on FIAT element
4034
delete [] derivatives;
4035
4036
// Delete pointer to array of combinations of derivatives and transform
4037
for (unsigned int r = 0; r < num_derivatives; r++)
4038
{
4039
delete [] combinations[r];
4040
}// end loop over 'r'
4041
delete [] combinations;
4042
for (unsigned int r = 0; r < num_derivatives; r++)
4043
{
4044
delete [] transform[r];
4045
}// end loop over 'r'
4046
delete [] transform;
4047
break;
4048
}
4049
case 5:
4050
{
4051
4052
// Array of basisvalues.
4053
double basisvalues[6] = {0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000};
4054
4055
// Declare helper variables.
4056
unsigned int rr = 0;
4057
unsigned int ss = 0;
4058
unsigned int tt = 0;
4059
double tmp5 = 0.000000000000000;
4060
double tmp6 = 0.000000000000000;
4061
double tmp7 = 0.000000000000000;
4062
double tmp0 = (1.000000000000000 + Y + 2.000000000000000*X)/2.000000000000000;
4063
double tmp1 = (1.000000000000000 - Y)/2.000000000000000;
4064
double tmp2 = tmp1*tmp1;
4065
4066
// Compute basisvalues.
4067
basisvalues[0] = 1.000000000000000;
4068
basisvalues[1] = tmp0;
4069
for (unsigned int r = 1; r < 2; r++)
4070
{
4071
rr = (r + 1)*((r + 1) + 1)/2;
4072
ss = r*(r + 1)/2;
4073
tt = (r - 1)*((r - 1) + 1)/2;
4074
tmp5 = (1.000000000000000 + 2.000000000000000*r)/(1.000000000000000 + r);
4075
basisvalues[rr] = (basisvalues[ss]*tmp0*tmp5 - basisvalues[tt]*tmp2*r/(1.000000000000000 + r));
4076
}// end loop over 'r'
4077
for (unsigned int r = 0; r < 2; r++)
4078
{
4079
rr = (r + 1)*(r + 1 + 1)/2 + 1;
4080
ss = r*(r + 1)/2;
4081
basisvalues[rr] = basisvalues[ss]*(0.500000000000000 + r + Y*(1.500000000000000 + r));
4082
}// end loop over 'r'
4083
for (unsigned int r = 0; r < 1; r++)
4084
{
4085
for (unsigned int s = 1; s < 2 - r; s++)
4086
{
4087
rr = (r + s + 1)*(r + s + 1 + 1)/2 + s + 1;
4088
ss = (r + s)*(r + s + 1)/2 + s;
4089
tt = (r + s - 1)*(r + s - 1 + 1)/2 + s - 1;
4090
tmp5 = (2.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)*(3.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)/(2.000000000000000*(1.000000000000000 + s)*(2.000000000000000 + s + 2.000000000000000*r));
4091
tmp6 = (1.000000000000000 + 4.000000000000000*r*r + 4.000000000000000*r)*(2.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)/(2.000000000000000*(1.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)*(1.000000000000000 + s)*(2.000000000000000 + s + 2.000000000000000*r));
4092
tmp7 = (1.000000000000000 + s + 2.000000000000000*r)*(3.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)*s/((1.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)*(1.000000000000000 + s)*(2.000000000000000 + s + 2.000000000000000*r));
4093
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Y*tmp5) - basisvalues[tt]*tmp7);
4094
}// end loop over 's'
4095
}// end loop over 'r'
4096
for (unsigned int r = 0; r < 3; r++)
4097
{
4098
for (unsigned int s = 0; s < 3 - r; s++)
4099
{
4100
rr = (r + s)*(r + s + 1)/2 + s;
4101
basisvalues[rr] *= std::sqrt((0.500000000000000 + r)*(1.000000000000000 + r + s));
4102
}// end loop over 's'
4103
}// end loop over 'r'
4104
4105
// Table(s) of coefficients.
4106
static const double coefficients0[6] = \
4107
{0.471404520791032, 0.000000000000000, -0.266666666666667, -0.243432247780074, 0.000000000000000, 0.054433105395182};
4108
4109
// Tables of derivatives of the polynomial base (transpose).
4110
static const double dmats0[6][6] = \
4111
{{0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
4112
{4.898979485566355, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
4113
{0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
4114
{0.000000000000000, 9.486832980505138, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
4115
{3.999999999999999, 0.000000000000000, 7.071067811865476, 0.000000000000000, 0.000000000000000, 0.000000000000000},
4116
{0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000}};
4117
4118
static const double dmats1[6][6] = \
4119
{{0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
4120
{2.449489742783177, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
4121
{4.242640687119285, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
4122
{2.581988897471611, 4.743416490252570, -0.912870929175278, 0.000000000000000, 0.000000000000000, 0.000000000000000},
4123
{1.999999999999999, 6.123724356957944, 3.535533905932737, 0.000000000000000, 0.000000000000000, 0.000000000000000},
4124
{-2.309401076758502, 0.000000000000000, 8.164965809277259, 0.000000000000000, 0.000000000000000, 0.000000000000000}};
4125
4126
// Compute reference derivatives.
4127
// Declare pointer to array of derivatives on FIAT element.
4128
double *derivatives = new double[num_derivatives];
4129
for (unsigned int r = 0; r < num_derivatives; r++)
4130
{
4131
derivatives[r] = 0.000000000000000;
4132
}// end loop over 'r'
4133
4134
// Declare derivative matrix (of polynomial basis).
4135
double dmats[6][6] = \
4136
{{1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
4137
{0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
4138
{0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
4139
{0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000},
4140
{0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000},
4141
{0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000}};
4142
4143
// Declare (auxiliary) derivative matrix (of polynomial basis).
4144
double dmats_old[6][6] = \
4145
{{1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
4146
{0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
4147
{0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
4148
{0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000},
4149
{0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000},
4150
{0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000}};
4151
4152
// Loop possible derivatives.
4153
for (unsigned int r = 0; r < num_derivatives; r++)
4154
{
4155
// Resetting dmats values to compute next derivative.
4156
for (unsigned int t = 0; t < 6; t++)
4157
{
4158
for (unsigned int u = 0; u < 6; u++)
4159
{
4160
dmats[t][u] = 0.000000000000000;
4161
if (t == u)
4162
{
4163
dmats[t][u] = 1.000000000000000;
4164
}
4165
4166
}// end loop over 'u'
4167
}// end loop over 't'
4168
4169
// Looping derivative order to generate dmats.
4170
for (unsigned int s = 0; s < n; s++)
4171
{
4172
// Updating dmats_old with new values and resetting dmats.
4173
for (unsigned int t = 0; t < 6; t++)
4174
{
4175
for (unsigned int u = 0; u < 6; u++)
4176
{
4177
dmats_old[t][u] = dmats[t][u];
4178
dmats[t][u] = 0.000000000000000;
4179
}// end loop over 'u'
4180
}// end loop over 't'
4181
4182
// Update dmats using an inner product.
4183
if (combinations[r][s] == 0)
4184
{
4185
for (unsigned int t = 0; t < 6; t++)
4186
{
4187
for (unsigned int u = 0; u < 6; u++)
4188
{
4189
for (unsigned int tu = 0; tu < 6; tu++)
4190
{
4191
dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
4192
}// end loop over 'tu'
4193
}// end loop over 'u'
4194
}// end loop over 't'
4195
}
4196
4197
if (combinations[r][s] == 1)
4198
{
4199
for (unsigned int t = 0; t < 6; t++)
4200
{
4201
for (unsigned int u = 0; u < 6; u++)
4202
{
4203
for (unsigned int tu = 0; tu < 6; tu++)
4204
{
4205
dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
4206
}// end loop over 'tu'
4207
}// end loop over 'u'
4208
}// end loop over 't'
4209
}
4210
4211
}// end loop over 's'
4212
for (unsigned int s = 0; s < 6; s++)
4213
{
4214
for (unsigned int t = 0; t < 6; t++)
4215
{
4216
derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
4217
}// end loop over 't'
4218
}// end loop over 's'
4219
}// end loop over 'r'
4220
4221
// Transform derivatives back to physical element
4222
for (unsigned int r = 0; r < num_derivatives; r++)
4223
{
4224
for (unsigned int s = 0; s < num_derivatives; s++)
4225
{
4226
values[r] += transform[r][s]*derivatives[s];
4227
}// end loop over 's'
4228
}// end loop over 'r'
4229
4230
// Delete pointer to array of derivatives on FIAT element
4231
delete [] derivatives;
4232
4233
// Delete pointer to array of combinations of derivatives and transform
4234
for (unsigned int r = 0; r < num_derivatives; r++)
4235
{
4236
delete [] combinations[r];
4237
}// end loop over 'r'
4238
delete [] combinations;
4239
for (unsigned int r = 0; r < num_derivatives; r++)
4240
{
4241
delete [] transform[r];
4242
}// end loop over 'r'
4243
delete [] transform;
4244
break;
4245
}
4246
}
4247
4248
}
4249
4250
/// Evaluate order n derivatives of all basis functions at given point in cell
4251
virtual void evaluate_basis_derivatives_all(unsigned int n,
4252
double* values,
4253
const double* coordinates,
4254
const ufc::cell& c) const
4255
{
4256
// Compute number of derivatives.
4257
unsigned int num_derivatives = 1;
4258
for (unsigned int r = 0; r < n; r++)
4259
{
4260
num_derivatives *= 2;
4261
}// end loop over 'r'
4262
4263
// Helper variable to hold values of a single dof.
4264
double *dof_values = new double[num_derivatives];
4265
for (unsigned int r = 0; r < num_derivatives; r++)
4266
{
4267
dof_values[r] = 0.000000000000000;
4268
}// end loop over 'r'
4269
4270
// Loop dofs and call evaluate_basis_derivatives.
4271
for (unsigned int r = 0; r < 6; r++)
4272
{
4273
evaluate_basis_derivatives(r, n, dof_values, coordinates, c);
4274
for (unsigned int s = 0; s < num_derivatives; s++)
4275
{
4276
values[r*num_derivatives + s] = dof_values[s];
4277
}// end loop over 's'
4278
}// end loop over 'r'
4279
4280
// Delete pointer.
4281
delete [] dof_values;
4282
}
4283
4284
/// Evaluate linear functional for dof i on the function f
4285
virtual double evaluate_dof(unsigned int i,
4286
const ufc::function& f,
4287
const ufc::cell& c) const
4288
{
4289
// Declare variables for result of evaluation.
4290
double vals[1];
4291
4292
// Declare variable for physical coordinates.
4293
double y[2];
4294
const double * const * x = c.coordinates;
4295
switch (i)
4296
{
4297
case 0:
4298
{
4299
y[0] = x[0][0];
4300
y[1] = x[0][1];
4301
f.evaluate(vals, y, c);
4302
return vals[0];
4303
break;
4304
}
4305
case 1:
4306
{
4307
y[0] = x[1][0];
4308
y[1] = x[1][1];
4309
f.evaluate(vals, y, c);
4310
return vals[0];
4311
break;
4312
}
4313
case 2:
4314
{
4315
y[0] = x[2][0];
4316
y[1] = x[2][1];
4317
f.evaluate(vals, y, c);
4318
return vals[0];
4319
break;
4320
}
4321
case 3:
4322
{
4323
y[0] = 0.500000000000000*x[1][0] + 0.500000000000000*x[2][0];
4324
y[1] = 0.500000000000000*x[1][1] + 0.500000000000000*x[2][1];
4325
f.evaluate(vals, y, c);
4326
return vals[0];
4327
break;
4328
}
4329
case 4:
4330
{
4331
y[0] = 0.500000000000000*x[0][0] + 0.500000000000000*x[2][0];
4332
y[1] = 0.500000000000000*x[0][1] + 0.500000000000000*x[2][1];
4333
f.evaluate(vals, y, c);
4334
return vals[0];
4335
break;
4336
}
4337
case 5:
4338
{
4339
y[0] = 0.500000000000000*x[0][0] + 0.500000000000000*x[1][0];
4340
y[1] = 0.500000000000000*x[0][1] + 0.500000000000000*x[1][1];
4341
f.evaluate(vals, y, c);
4342
return vals[0];
4343
break;
4344
}
4345
}
4346
4347
return 0.000000000000000;
4348
}
4349
4350
/// Evaluate linear functionals for all dofs on the function f
4351
virtual void evaluate_dofs(double* values,
4352
const ufc::function& f,
4353
const ufc::cell& c) const
4354
{
4355
// Declare variables for result of evaluation.
4356
double vals[1];
4357
4358
// Declare variable for physical coordinates.
4359
double y[2];
4360
const double * const * x = c.coordinates;
4361
y[0] = x[0][0];
4362
y[1] = x[0][1];
4363
f.evaluate(vals, y, c);
4364
values[0] = vals[0];
4365
y[0] = x[1][0];
4366
y[1] = x[1][1];
4367
f.evaluate(vals, y, c);
4368
values[1] = vals[0];
4369
y[0] = x[2][0];
4370
y[1] = x[2][1];
4371
f.evaluate(vals, y, c);
4372
values[2] = vals[0];
4373
y[0] = 0.500000000000000*x[1][0] + 0.500000000000000*x[2][0];
4374
y[1] = 0.500000000000000*x[1][1] + 0.500000000000000*x[2][1];
4375
f.evaluate(vals, y, c);
4376
values[3] = vals[0];
4377
y[0] = 0.500000000000000*x[0][0] + 0.500000000000000*x[2][0];
4378
y[1] = 0.500000000000000*x[0][1] + 0.500000000000000*x[2][1];
4379
f.evaluate(vals, y, c);
4380
values[4] = vals[0];
4381
y[0] = 0.500000000000000*x[0][0] + 0.500000000000000*x[1][0];
4382
y[1] = 0.500000000000000*x[0][1] + 0.500000000000000*x[1][1];
4383
f.evaluate(vals, y, c);
4384
values[5] = vals[0];
4385
}
4386
4387
/// Interpolate vertex values from dof values
4388
virtual void interpolate_vertex_values(double* vertex_values,
4389
const double* dof_values,
4390
const ufc::cell& c) const
4391
{
4392
// Evaluate function and change variables
4393
vertex_values[0] = dof_values[0];
4394
vertex_values[1] = dof_values[1];
4395
vertex_values[2] = dof_values[2];
4396
}
4397
4398
/// Map coordinate xhat from reference cell to coordinate x in cell
4399
virtual void map_from_reference_cell(double* x,
4400
const double* xhat,
4401
const ufc::cell& c)
4402
{
4403
throw std::runtime_error("map_from_reference_cell not yet implemented (introduced in UFC 2.0).");
4404
}
4405
4406
/// Map from coordinate x in cell to coordinate xhat in reference cell
4407
virtual void map_to_reference_cell(double* xhat,
4408
const double* x,
4409
const ufc::cell& c)
4410
{
4411
throw std::runtime_error("map_to_reference_cell not yet implemented (introduced in UFC 2.0).");
4412
}
4413
4414
/// Return the number of sub elements (for a mixed element)
4415
virtual unsigned int num_sub_elements() const
4416
{
4417
return 0;
4418
}
4419
4420
/// Create a new finite element for sub element i (for a mixed element)
4421
virtual ufc::finite_element* create_sub_element(unsigned int i) const
4422
{
4423
return 0;
4424
}
4425
4426
/// Create a new class instance
4427
virtual ufc::finite_element* create() const
4428
{
4429
return new adaptivepoisson_finite_element_2();
4430
}
4431
4432
};
4433
4434
/// This class defines the interface for a finite element.
4435
4436
class adaptivepoisson_finite_element_3: public ufc::finite_element
4437
{
4438
public:
4439
4440
/// Constructor
4441
adaptivepoisson_finite_element_3() : ufc::finite_element()
4442
{
4443
// Do nothing
4444
}
4445
4446
/// Destructor
4447
virtual ~adaptivepoisson_finite_element_3()
4448
{
4449
// Do nothing
4450
}
4451
4452
/// Return a string identifying the finite element
4453
virtual const char* signature() const
4454
{
4455
return "FiniteElement('Bubble', Cell('triangle', 1, Space(2)), 3)";
4456
}
4457
4458
/// Return the cell shape
4459
virtual ufc::shape cell_shape() const
4460
{
4461
return ufc::triangle;
4462
}
4463
4464
/// Return the topological dimension of the cell shape
4465
virtual unsigned int topological_dimension() const
4466
{
4467
return 2;
4468
}
4469
4470
/// Return the geometric dimension of the cell shape
4471
virtual unsigned int geometric_dimension() const
4472
{
4473
return 2;
4474
}
4475
4476
/// Return the dimension of the finite element function space
4477
virtual unsigned int space_dimension() const
4478
{
4479
return 1;
4480
}
4481
4482
/// Return the rank of the value space
4483
virtual unsigned int value_rank() const
4484
{
4485
return 0;
4486
}
4487
4488
/// Return the dimension of the value space for axis i
4489
virtual unsigned int value_dimension(unsigned int i) const
4490
{
4491
return 1;
4492
}
4493
4494
/// Evaluate basis function i at given point in cell
4495
virtual void evaluate_basis(unsigned int i,
4496
double* values,
4497
const double* coordinates,
4498
const ufc::cell& c) const
4499
{
4500
// Extract vertex coordinates
4501
const double * const * x = c.coordinates;
4502
4503
// Compute Jacobian of affine map from reference cell
4504
const double J_00 = x[1][0] - x[0][0];
4505
const double J_01 = x[2][0] - x[0][0];
4506
const double J_10 = x[1][1] - x[0][1];
4507
const double J_11 = x[2][1] - x[0][1];
4508
4509
// Compute determinant of Jacobian
4510
double detJ = J_00*J_11 - J_01*J_10;
4511
4512
// Compute inverse of Jacobian
4513
4514
// Compute constants
4515
const double C0 = x[1][0] + x[2][0];
4516
const double C1 = x[1][1] + x[2][1];
4517
4518
// Get coordinates and map to the reference (FIAT) element
4519
double X = (J_01*(C1 - 2.0*coordinates[1]) + J_11*(2.0*coordinates[0] - C0)) / detJ;
4520
double Y = (J_00*(2.0*coordinates[1] - C1) + J_10*(C0 - 2.0*coordinates[0])) / detJ;
4521
4522
// Reset values.
4523
*values = 0.000000000000000;
4524
4525
// Array of basisvalues.
4526
double basisvalues[10] = {0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000};
4527
4528
// Declare helper variables.
4529
unsigned int rr = 0;
4530
unsigned int ss = 0;
4531
unsigned int tt = 0;
4532
double tmp5 = 0.000000000000000;
4533
double tmp6 = 0.000000000000000;
4534
double tmp7 = 0.000000000000000;
4535
double tmp0 = (1.000000000000000 + Y + 2.000000000000000*X)/2.000000000000000;
4536
double tmp1 = (1.000000000000000 - Y)/2.000000000000000;
4537
double tmp2 = tmp1*tmp1;
4538
4539
// Compute basisvalues.
4540
basisvalues[0] = 1.000000000000000;
4541
basisvalues[1] = tmp0;
4542
for (unsigned int r = 1; r < 3; r++)
4543
{
4544
rr = (r + 1)*((r + 1) + 1)/2;
4545
ss = r*(r + 1)/2;
4546
tt = (r - 1)*((r - 1) + 1)/2;
4547
tmp5 = (1.000000000000000 + 2.000000000000000*r)/(1.000000000000000 + r);
4548
basisvalues[rr] = (basisvalues[ss]*tmp0*tmp5 - basisvalues[tt]*tmp2*r/(1.000000000000000 + r));
4549
}// end loop over 'r'
4550
for (unsigned int r = 0; r < 3; r++)
4551
{
4552
rr = (r + 1)*(r + 1 + 1)/2 + 1;
4553
ss = r*(r + 1)/2;
4554
basisvalues[rr] = basisvalues[ss]*(0.500000000000000 + r + Y*(1.500000000000000 + r));
4555
}// end loop over 'r'
4556
for (unsigned int r = 0; r < 2; r++)
4557
{
4558
for (unsigned int s = 1; s < 3 - r; s++)
4559
{
4560
rr = (r + s + 1)*(r + s + 1 + 1)/2 + s + 1;
4561
ss = (r + s)*(r + s + 1)/2 + s;
4562
tt = (r + s - 1)*(r + s - 1 + 1)/2 + s - 1;
4563
tmp5 = (2.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)*(3.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)/(2.000000000000000*(1.000000000000000 + s)*(2.000000000000000 + s + 2.000000000000000*r));
4564
tmp6 = (1.000000000000000 + 4.000000000000000*r*r + 4.000000000000000*r)*(2.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)/(2.000000000000000*(1.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)*(1.000000000000000 + s)*(2.000000000000000 + s + 2.000000000000000*r));
4565
tmp7 = (1.000000000000000 + s + 2.000000000000000*r)*(3.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)*s/((1.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)*(1.000000000000000 + s)*(2.000000000000000 + s + 2.000000000000000*r));
4566
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Y*tmp5) - basisvalues[tt]*tmp7);
4567
}// end loop over 's'
4568
}// end loop over 'r'
4569
for (unsigned int r = 0; r < 4; r++)
4570
{
4571
for (unsigned int s = 0; s < 4 - r; s++)
4572
{
4573
rr = (r + s)*(r + s + 1)/2 + s;
4574
basisvalues[rr] *= std::sqrt((0.500000000000000 + r)*(1.000000000000000 + r + s));
4575
}// end loop over 's'
4576
}// end loop over 'r'
4577
4578
// Table(s) of coefficients.
4579
static const double coefficients0[10] = \
4580
{0.636396103067893, 0.000000000000000, 0.000000000000000, -0.234738238930786, 0.000000000000000, -0.262445329583912, 0.000000000000000, -0.203289278153682, 0.000000000000000, 0.090913729009699};
4581
4582
// Compute value(s).
4583
for (unsigned int r = 0; r < 10; r++)
4584
{
4585
*values += coefficients0[r]*basisvalues[r];
4586
}// end loop over 'r'
4587
}
4588
4589
/// Evaluate all basis functions at given point in cell
4590
virtual void evaluate_basis_all(double* values,
4591
const double* coordinates,
4592
const ufc::cell& c) const
4593
{
4594
// Element is constant, calling evaluate_basis.
4595
evaluate_basis(0, values, coordinates, c);
4596
}
4597
4598
/// Evaluate order n derivatives of basis function i at given point in cell
4599
virtual void evaluate_basis_derivatives(unsigned int i,
4600
unsigned int n,
4601
double* values,
4602
const double* coordinates,
4603
const ufc::cell& c) const
4604
{
4605
// Extract vertex coordinates
4606
const double * const * x = c.coordinates;
4607
4608
// Compute Jacobian of affine map from reference cell
4609
const double J_00 = x[1][0] - x[0][0];
4610
const double J_01 = x[2][0] - x[0][0];
4611
const double J_10 = x[1][1] - x[0][1];
4612
const double J_11 = x[2][1] - x[0][1];
4613
4614
// Compute determinant of Jacobian
4615
double detJ = J_00*J_11 - J_01*J_10;
4616
4617
// Compute inverse of Jacobian
4618
const double K_00 = J_11 / detJ;
4619
const double K_01 = -J_01 / detJ;
4620
const double K_10 = -J_10 / detJ;
4621
const double K_11 = J_00 / detJ;
4622
4623
// Compute constants
4624
const double C0 = x[1][0] + x[2][0];
4625
const double C1 = x[1][1] + x[2][1];
4626
4627
// Get coordinates and map to the reference (FIAT) element
4628
double X = (J_01*(C1 - 2.0*coordinates[1]) + J_11*(2.0*coordinates[0] - C0)) / detJ;
4629
double Y = (J_00*(2.0*coordinates[1] - C1) + J_10*(C0 - 2.0*coordinates[0])) / detJ;
4630
4631
// Compute number of derivatives.
4632
unsigned int num_derivatives = 1;
4633
for (unsigned int r = 0; r < n; r++)
4634
{
4635
num_derivatives *= 2;
4636
}// end loop over 'r'
4637
4638
// Declare pointer to two dimensional array that holds combinations of derivatives and initialise
4639
unsigned int **combinations = new unsigned int *[num_derivatives];
4640
for (unsigned int row = 0; row < num_derivatives; row++)
4641
{
4642
combinations[row] = new unsigned int [n];
4643
for (unsigned int col = 0; col < n; col++)
4644
combinations[row][col] = 0;
4645
}
4646
4647
// Generate combinations of derivatives
4648
for (unsigned int row = 1; row < num_derivatives; row++)
4649
{
4650
for (unsigned int num = 0; num < row; num++)
4651
{
4652
for (unsigned int col = n-1; col+1 > 0; col--)
4653
{
4654
if (combinations[row][col] + 1 > 1)
4655
combinations[row][col] = 0;
4656
else
4657
{
4658
combinations[row][col] += 1;
4659
break;
4660
}
4661
}
4662
}
4663
}
4664
4665
// Compute inverse of Jacobian
4666
const double Jinv[2][2] = {{K_00, K_01}, {K_10, K_11}};
4667
4668
// Declare transformation matrix
4669
// Declare pointer to two dimensional array and initialise
4670
double **transform = new double *[num_derivatives];
4671
4672
for (unsigned int j = 0; j < num_derivatives; j++)
4673
{
4674
transform[j] = new double [num_derivatives];
4675
for (unsigned int k = 0; k < num_derivatives; k++)
4676
transform[j][k] = 1;
4677
}
4678
4679
// Construct transformation matrix
4680
for (unsigned int row = 0; row < num_derivatives; row++)
4681
{
4682
for (unsigned int col = 0; col < num_derivatives; col++)
4683
{
4684
for (unsigned int k = 0; k < n; k++)
4685
transform[row][col] *= Jinv[combinations[col][k]][combinations[row][k]];
4686
}
4687
}
4688
4689
// Reset values. Assuming that values is always an array.
4690
for (unsigned int r = 0; r < num_derivatives; r++)
4691
{
4692
values[r] = 0.000000000000000;
4693
}// end loop over 'r'
4694
4695
4696
// Array of basisvalues.
4697
double basisvalues[10] = {0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000};
4698
4699
// Declare helper variables.
4700
unsigned int rr = 0;
4701
unsigned int ss = 0;
4702
unsigned int tt = 0;
4703
double tmp5 = 0.000000000000000;
4704
double tmp6 = 0.000000000000000;
4705
double tmp7 = 0.000000000000000;
4706
double tmp0 = (1.000000000000000 + Y + 2.000000000000000*X)/2.000000000000000;
4707
double tmp1 = (1.000000000000000 - Y)/2.000000000000000;
4708
double tmp2 = tmp1*tmp1;
4709
4710
// Compute basisvalues.
4711
basisvalues[0] = 1.000000000000000;
4712
basisvalues[1] = tmp0;
4713
for (unsigned int r = 1; r < 3; r++)
4714
{
4715
rr = (r + 1)*((r + 1) + 1)/2;
4716
ss = r*(r + 1)/2;
4717
tt = (r - 1)*((r - 1) + 1)/2;
4718
tmp5 = (1.000000000000000 + 2.000000000000000*r)/(1.000000000000000 + r);
4719
basisvalues[rr] = (basisvalues[ss]*tmp0*tmp5 - basisvalues[tt]*tmp2*r/(1.000000000000000 + r));
4720
}// end loop over 'r'
4721
for (unsigned int r = 0; r < 3; r++)
4722
{
4723
rr = (r + 1)*(r + 1 + 1)/2 + 1;
4724
ss = r*(r + 1)/2;
4725
basisvalues[rr] = basisvalues[ss]*(0.500000000000000 + r + Y*(1.500000000000000 + r));
4726
}// end loop over 'r'
4727
for (unsigned int r = 0; r < 2; r++)
4728
{
4729
for (unsigned int s = 1; s < 3 - r; s++)
4730
{
4731
rr = (r + s + 1)*(r + s + 1 + 1)/2 + s + 1;
4732
ss = (r + s)*(r + s + 1)/2 + s;
4733
tt = (r + s - 1)*(r + s - 1 + 1)/2 + s - 1;
4734
tmp5 = (2.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)*(3.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)/(2.000000000000000*(1.000000000000000 + s)*(2.000000000000000 + s + 2.000000000000000*r));
4735
tmp6 = (1.000000000000000 + 4.000000000000000*r*r + 4.000000000000000*r)*(2.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)/(2.000000000000000*(1.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)*(1.000000000000000 + s)*(2.000000000000000 + s + 2.000000000000000*r));
4736
tmp7 = (1.000000000000000 + s + 2.000000000000000*r)*(3.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)*s/((1.000000000000000 + 2.000000000000000*r + 2.000000000000000*s)*(1.000000000000000 + s)*(2.000000000000000 + s + 2.000000000000000*r));
4737
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Y*tmp5) - basisvalues[tt]*tmp7);
4738
}// end loop over 's'
4739
}// end loop over 'r'
4740
for (unsigned int r = 0; r < 4; r++)
4741
{
4742
for (unsigned int s = 0; s < 4 - r; s++)
4743
{
4744
rr = (r + s)*(r + s + 1)/2 + s;
4745
basisvalues[rr] *= std::sqrt((0.500000000000000 + r)*(1.000000000000000 + r + s));
4746
}// end loop over 's'
4747
}// end loop over 'r'
4748
4749
// Table(s) of coefficients.
4750
static const double coefficients0[10] = \
4751
{0.636396103067893, 0.000000000000000, 0.000000000000000, -0.234738238930786, 0.000000000000000, -0.262445329583912, 0.000000000000000, -0.203289278153682, 0.000000000000000, 0.090913729009699};
4752
4753
// Tables of derivatives of the polynomial base (transpose).
4754
static const double dmats0[10][10] = \
4755
{{0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
4756
{4.898979485566356, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
4757
{0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
4758
{0.000000000000000, 9.486832980505140, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
4759
{3.999999999999998, 0.000000000000000, 7.071067811865476, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
4760
{0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
4761
{5.291502622129178, 0.000000000000000, -2.993325909419151, 13.662601021279462, 0.000000000000000, 0.611010092660779, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
4762
{0.000000000000000, 4.381780460041330, 0.000000000000000, 0.000000000000000, 12.521980673998824, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
4763
{3.464101615137755, 0.000000000000000, 7.838367176906168, 0.000000000000000, 0.000000000000000, 8.400000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
4764
{0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000}};
4765
4766
static const double dmats1[10][10] = \
4767
{{0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
4768
{2.449489742783178, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
4769
{4.242640687119285, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
4770
{2.581988897471611, 4.743416490252570, -0.912870929175277, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
4771
{1.999999999999999, 6.123724356957946, 3.535533905932738, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
4772
{-2.309401076758503, 0.000000000000000, 8.164965809277261, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
4773
{2.645751311064590, 5.184592558726288, -1.496662954709576, 6.831300510639732, -1.058300524425836, 0.305505046330390, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
4774
{2.236067977499788, 2.190890230020664, 2.529822128134706, 8.082903768654761, 6.260990336999411, -1.807392228230128, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
4775
{1.732050807568876, -5.091168824543143, 3.919183588453085, 0.000000000000000, 9.699484522385713, 4.200000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
4776
{5.000000000000002, 0.000000000000000, -2.828427124746193, 0.000000000000000, 0.000000000000000, 12.124355652982144, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000}};
4777
4778
// Compute reference derivatives.
4779
// Declare pointer to array of derivatives on FIAT element.
4780
double *derivatives = new double[num_derivatives];
4781
for (unsigned int r = 0; r < num_derivatives; r++)
4782
{
4783
derivatives[r] = 0.000000000000000;
4784
}// end loop over 'r'
4785
4786
// Declare derivative matrix (of polynomial basis).
4787
double dmats[10][10] = \
4788
{{1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
4789
{0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
4790
{0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
4791
{0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
4792
{0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
4793
{0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
4794
{0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
4795
{0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000},
4796
{0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000},
4797
{0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000}};
4798
4799
// Declare (auxiliary) derivative matrix (of polynomial basis).
4800
double dmats_old[10][10] = \
4801
{{1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
4802
{0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
4803
{0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
4804
{0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
4805
{0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
4806
{0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
4807
{0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000},
4808
{0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000},
4809
{0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000},
4810
{0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000}};
4811
4812
// Loop possible derivatives.
4813
for (unsigned int r = 0; r < num_derivatives; r++)
4814
{
4815
// Resetting dmats values to compute next derivative.
4816
for (unsigned int t = 0; t < 10; t++)
4817
{
4818
for (unsigned int u = 0; u < 10; u++)
4819
{
4820
dmats[t][u] = 0.000000000000000;
4821
if (t == u)
4822
{
4823
dmats[t][u] = 1.000000000000000;
4824
}
4825
4826
}// end loop over 'u'
4827
}// end loop over 't'
4828
4829
// Looping derivative order to generate dmats.
4830
for (unsigned int s = 0; s < n; s++)
4831
{
4832
// Updating dmats_old with new values and resetting dmats.
4833
for (unsigned int t = 0; t < 10; t++)
4834
{
4835
for (unsigned int u = 0; u < 10; u++)
4836
{
4837
dmats_old[t][u] = dmats[t][u];
4838
dmats[t][u] = 0.000000000000000;
4839
}// end loop over 'u'
4840
}// end loop over 't'
4841
4842
// Update dmats using an inner product.
4843
if (combinations[r][s] == 0)
4844
{
4845
for (unsigned int t = 0; t < 10; t++)
4846
{
4847
for (unsigned int u = 0; u < 10; u++)
4848
{
4849
for (unsigned int tu = 0; tu < 10; tu++)
4850
{
4851
dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
4852
}// end loop over 'tu'
4853
}// end loop over 'u'
4854
}// end loop over 't'
4855
}
4856
4857
if (combinations[r][s] == 1)
4858
{
4859
for (unsigned int t = 0; t < 10; t++)
4860
{
4861
for (unsigned int u = 0; u < 10; u++)
4862
{
4863
for (unsigned int tu = 0; tu < 10; tu++)
4864
{
4865
dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
4866
}// end loop over 'tu'
4867
}// end loop over 'u'
4868
}// end loop over 't'
4869
}
4870
4871
}// end loop over 's'
4872
for (unsigned int s = 0; s < 10; s++)
4873
{
4874
for (unsigned int t = 0; t < 10; t++)
4875
{
4876
derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
4877
}// end loop over 't'
4878
}// end loop over 's'
4879
}// end loop over 'r'
4880
4881
// Transform derivatives back to physical element
4882
for (unsigned int r = 0; r < num_derivatives; r++)
4883
{
4884
for (unsigned int s = 0; s < num_derivatives; s++)
4885
{
4886
values[r] += transform[r][s]*derivatives[s];
4887
}// end loop over 's'
4888
}// end loop over 'r'
4889
4890
// Delete pointer to array of derivatives on FIAT element
4891
delete [] derivatives;
4892
4893
// Delete pointer to array of combinations of derivatives and transform
4894
for (unsigned int r = 0; r < num_derivatives; r++)
4895
{
4896
delete [] combinations[r];
4897
}// end loop over 'r'
4898
delete [] combinations;
4899
for (unsigned int r = 0; r < num_derivatives; r++)
4900
{
4901
delete [] transform[r];
4902
}// end loop over 'r'
4903
delete [] transform;
4904
}
4905
4906
/// Evaluate order n derivatives of all basis functions at given point in cell
4907
virtual void evaluate_basis_derivatives_all(unsigned int n,
4908
double* values,
4909
const double* coordinates,
4910
const ufc::cell& c) const
4911
{
4912
// Element is constant, calling evaluate_basis_derivatives.
4913
evaluate_basis_derivatives(0, n, values, coordinates, c);
4914
}
4915
4916
/// Evaluate linear functional for dof i on the function f
4917
virtual double evaluate_dof(unsigned int i,
4918
const ufc::function& f,
4919
const ufc::cell& c) const
4920
{
4921
// Declare variables for result of evaluation.
4922
double vals[1];
4923
4924
// Declare variable for physical coordinates.
4925
double y[2];
4926
const double * const * x = c.coordinates;
4927
switch (i)
4928
{
4929
case 0:
4930
{
4931
y[0] = 0.333333333333333*x[0][0] + 0.333333333333333*x[1][0] + 0.333333333333333*x[2][0];
4932
y[1] = 0.333333333333333*x[0][1] + 0.333333333333333*x[1][1] + 0.333333333333333*x[2][1];
4933
f.evaluate(vals, y, c);
4934
return vals[0];
4935
break;
4936
}
4937
}
4938
4939
return 0.000000000000000;
4940
}
4941
4942
/// Evaluate linear functionals for all dofs on the function f
4943
virtual void evaluate_dofs(double* values,
4944
const ufc::function& f,
4945
const ufc::cell& c) const
4946
{
4947
// Declare variables for result of evaluation.
4948
double vals[1];
4949
4950
// Declare variable for physical coordinates.
4951
double y[2];
4952
const double * const * x = c.coordinates;
4953
y[0] = 0.333333333333333*x[0][0] + 0.333333333333333*x[1][0] + 0.333333333333333*x[2][0];
4954
y[1] = 0.333333333333333*x[0][1] + 0.333333333333333*x[1][1] + 0.333333333333333*x[2][1];
4955
f.evaluate(vals, y, c);
4956
values[0] = vals[0];
4957
}
4958
4959
/// Interpolate vertex values from dof values
4960
virtual void interpolate_vertex_values(double* vertex_values,
4961
const double* dof_values,
4962
const ufc::cell& c) const
4963
{
4964
// Evaluate function and change variables
4965
vertex_values[0] = 0;
4966
vertex_values[1] = 0;
4967
vertex_values[2] = 0;
4968
}
4969
4970
/// Map coordinate xhat from reference cell to coordinate x in cell
4971
virtual void map_from_reference_cell(double* x,
4972
const double* xhat,
4973
const ufc::cell& c)
4974
{
4975
throw std::runtime_error("map_from_reference_cell not yet implemented (introduced in UFC 2.0).");
4976
}
4977
4978
/// Map from coordinate x in cell to coordinate xhat in reference cell
4979
virtual void map_to_reference_cell(double* xhat,
4980
const double* x,
4981
const ufc::cell& c)
4982
{
4983
throw std::runtime_error("map_to_reference_cell not yet implemented (introduced in UFC 2.0).");
4984
}
4985
4986
/// Return the number of sub elements (for a mixed element)
4987
virtual unsigned int num_sub_elements() const
4988
{
4989
return 0;
4990
}
4991
4992
/// Create a new finite element for sub element i (for a mixed element)
4993
virtual ufc::finite_element* create_sub_element(unsigned int i) const
4994
{
4995
return 0;
4996
}
4997
4998
/// Create a new class instance
4999
virtual ufc::finite_element* create() const
5000
{
5001
return new adaptivepoisson_finite_element_3();
5002
}
5003
5004
};
5005
5006
/// This class defines the interface for a finite element.
5007
5008
class adaptivepoisson_finite_element_4: public ufc::finite_element
5009
{
5010
public:
5011
5012
/// Constructor
5013
adaptivepoisson_finite_element_4() : ufc::finite_element()
5014
{
5015
// Do nothing
5016
}
5017
5018
/// Destructor
5019
virtual ~adaptivepoisson_finite_element_4()
5020
{
5021
// Do nothing
5022
}
5023
5024
/// Return a string identifying the finite element
5025
virtual const char* signature() const
5026
{
5027
return "FiniteElement('Discontinuous Lagrange', Cell('triangle', 1, Space(2)), 1)";
5028
}
5029
5030
/// Return the cell shape
5031
virtual ufc::shape cell_shape() const
5032
{
5033
return ufc::triangle;
5034
}
5035
5036
/// Return the topological dimension of the cell shape
5037
virtual unsigned int topological_dimension() const
5038
{
5039
return 2;
5040
}
5041
5042
/// Return the geometric dimension of the cell shape
5043
virtual unsigned int geometric_dimension() const
5044
{
5045
return 2;
5046
}
5047
5048
/// Return the dimension of the finite element function space
5049
virtual unsigned int space_dimension() const
5050
{
5051
return 3;
5052
}
5053
5054
/// Return the rank of the value space
5055
virtual unsigned int value_rank() const
5056
{
5057
return 0;
5058
}
5059
5060
/// Return the dimension of the value space for axis i
5061
virtual unsigned int value_dimension(unsigned int i) const
5062
{
5063
return 1;
5064
}
5065
5066
/// Evaluate basis function i at given point in cell
5067
virtual void evaluate_basis(unsigned int i,
5068
double* values,
5069
const double* coordinates,
5070
const ufc::cell& c) const
5071
{
5072
// Extract vertex coordinates
5073
const double * const * x = c.coordinates;
5074
5075
// Compute Jacobian of affine map from reference cell
5076
const double J_00 = x[1][0] - x[0][0];
5077
const double J_01 = x[2][0] - x[0][0];
5078
const double J_10 = x[1][1] - x[0][1];
5079
const double J_11 = x[2][1] - x[0][1];
5080
5081
// Compute determinant of Jacobian
5082
double detJ = J_00*J_11 - J_01*J_10;
5083
5084
// Compute inverse of Jacobian
5085
5086
// Compute constants
5087
const double C0 = x[1][0] + x[2][0];
5088
const double C1 = x[1][1] + x[2][1];
5089
5090
// Get coordinates and map to the reference (FIAT) element
5091
double X = (J_01*(C1 - 2.0*coordinates[1]) + J_11*(2.0*coordinates[0] - C0)) / detJ;
5092
double Y = (J_00*(2.0*coordinates[1] - C1) + J_10*(C0 - 2.0*coordinates[0])) / detJ;
5093
5094
// Reset values.
5095
*values = 0.000000000000000;
5096
switch (i)
5097
{
5098
case 0:
5099
{
5100
5101
// Array of basisvalues.
5102
double basisvalues[3] = {0.000000000000000, 0.000000000000000, 0.000000000000000};
5103
5104
// Declare helper variables.
5105
unsigned int rr = 0;
5106
unsigned int ss = 0;
5107
double tmp0 = (1.000000000000000 + Y + 2.000000000000000*X)/2.000000000000000;
5108
5109
// Compute basisvalues.
5110
basisvalues[0] = 1.000000000000000;
5111
basisvalues[1] = tmp0;
5112
for (unsigned int r = 0; r < 1; r++)
5113
{
5114
rr = (r + 1)*(r + 1 + 1)/2 + 1;
5115
ss = r*(r + 1)/2;
5116
basisvalues[rr] = basisvalues[ss]*(0.500000000000000 + r + Y*(1.500000000000000 + r));
5117
}// end loop over 'r'
5118
for (unsigned int r = 0; r < 2; r++)
5119
{
5120
for (unsigned int s = 0; s < 2 - r; s++)
5121
{
5122
rr = (r + s)*(r + s + 1)/2 + s;
5123
basisvalues[rr] *= std::sqrt((0.500000000000000 + r)*(1.000000000000000 + r + s));
5124
}// end loop over 's'
5125
}// end loop over 'r'
5126
5127
// Table(s) of coefficients.
5128
static const double coefficients0[3] = \
5129
{0.471404520791032, -0.288675134594813, -0.166666666666667};
5130
5131
// Compute value(s).
5132
for (unsigned int r = 0; r < 3; r++)
5133
{
5134
*values += coefficients0[r]*basisvalues[r];
5135
}// end loop over 'r'
5136
break;
5137
}
5138
case 1:
5139
{
5140
5141
// Array of basisvalues.
5142
double basisvalues[3] = {0.000000000000000, 0.000000000000000, 0.000000000000000};
5143
5144
// Declare helper variables.
5145
unsigned int rr = 0;
5146
unsigned int ss = 0;
5147
double tmp0 = (1.000000000000000 + Y + 2.000000000000000*X)/2.000000000000000;
5148
5149
// Compute basisvalues.
5150
basisvalues[0] = 1.000000000000000;
5151
basisvalues[1] = tmp0;
5152
for (unsigned int r = 0; r < 1; r++)
5153
{
5154
rr = (r + 1)*(r + 1 + 1)/2 + 1;
5155
ss = r*(r + 1)/2;
5156
basisvalues[rr] = basisvalues[ss]*(0.500000000000000 + r + Y*(1.500000000000000 + r));
5157
}// end loop over 'r'
5158
for (unsigned int r = 0; r < 2; r++)
5159
{
5160
for (unsigned int s = 0; s < 2 - r; s++)
5161
{
5162
rr = (r + s)*(r + s + 1)/2 + s;
5163
basisvalues[rr] *= std::sqrt((0.500000000000000 + r)*(1.000000000000000 + r + s));
5164
}// end loop over 's'
5165
}// end loop over 'r'
5166
5167
// Table(s) of coefficients.
5168
static const double coefficients0[3] = \
5169
{0.471404520791032, 0.288675134594813, -0.166666666666667};
5170
5171
// Compute value(s).
5172
for (unsigned int r = 0; r < 3; r++)
5173
{
5174
*values += coefficients0[r]*basisvalues[r];
5175
}// end loop over 'r'
5176
break;
5177
}
5178
case 2:
5179
{
5180
5181
// Array of basisvalues.
5182
double basisvalues[3] = {0.000000000000000, 0.000000000000000, 0.000000000000000};
5183
5184
// Declare helper variables.
5185
unsigned int rr = 0;
5186
unsigned int ss = 0;
5187
double tmp0 = (1.000000000000000 + Y + 2.000000000000000*X)/2.000000000000000;
5188
5189
// Compute basisvalues.
5190
basisvalues[0] = 1.000000000000000;
5191
basisvalues[1] = tmp0;
5192
for (unsigned int r = 0; r < 1; r++)
5193
{
5194
rr = (r + 1)*(r + 1 + 1)/2 + 1;
5195
ss = r*(r + 1)/2;
5196
basisvalues[rr] = basisvalues[ss]*(0.500000000000000 + r + Y*(1.500000000000000 + r));
5197
}// end loop over 'r'
5198
for (unsigned int r = 0; r < 2; r++)
5199
{
5200
for (unsigned int s = 0; s < 2 - r; s++)
5201
{
5202
rr = (r + s)*(r + s + 1)/2 + s;
5203
basisvalues[rr] *= std::sqrt((0.500000000000000 + r)*(1.000000000000000 + r + s));
5204
}// end loop over 's'
5205
}// end loop over 'r'
5206
5207
// Table(s) of coefficients.
5208
static const double coefficients0[3] = \
5209
{0.471404520791032, 0.000000000000000, 0.333333333333333};
5210
5211
// Compute value(s).
5212
for (unsigned int r = 0; r < 3; r++)
5213
{
5214
*values += coefficients0[r]*basisvalues[r];
5215
}// end loop over 'r'
5216
break;
5217
}
5218
}
5219
5220
}
5221
5222
/// Evaluate all basis functions at given point in cell
5223
virtual void evaluate_basis_all(double* values,
5224
const double* coordinates,
5225
const ufc::cell& c) const
5226
{
5227
// Helper variable to hold values of a single dof.
5228
double dof_values = 0.000000000000000;
5229
5230
// Loop dofs and call evaluate_basis.
5231
for (unsigned int r = 0; r < 3; r++)
5232
{
5233
evaluate_basis(r, &dof_values, coordinates, c);
5234
values[r] = dof_values;
5235
}// end loop over 'r'
5236
}
5237
5238
/// Evaluate order n derivatives of basis function i at given point in cell
5239
virtual void evaluate_basis_derivatives(unsigned int i,
5240
unsigned int n,
5241
double* values,
5242
const double* coordinates,
5243
const ufc::cell& c) const
5244
{
5245
// Extract vertex coordinates
5246
const double * const * x = c.coordinates;
5247
5248
// Compute Jacobian of affine map from reference cell
5249
const double J_00 = x[1][0] - x[0][0];
5250
const double J_01 = x[2][0] - x[0][0];
5251
const double J_10 = x[1][1] - x[0][1];
5252
const double J_11 = x[2][1] - x[0][1];
5253
5254
// Compute determinant of Jacobian
5255
double detJ = J_00*J_11 - J_01*J_10;
5256
5257
// Compute inverse of Jacobian
5258
const double K_00 = J_11 / detJ;
5259
const double K_01 = -J_01 / detJ;
5260
const double K_10 = -J_10 / detJ;
5261
const double K_11 = J_00 / detJ;
5262
5263
// Compute constants
5264
const double C0 = x[1][0] + x[2][0];
5265
const double C1 = x[1][1] + x[2][1];
5266
5267
// Get coordinates and map to the reference (FIAT) element
5268
double X = (J_01*(C1 - 2.0*coordinates[1]) + J_11*(2.0*coordinates[0] - C0)) / detJ;
5269
double Y = (J_00*(2.0*coordinates[1] - C1) + J_10*(C0 - 2.0*coordinates[0])) / detJ;
5270
5271
// Compute number of derivatives.
5272
unsigned int num_derivatives = 1;
5273
for (unsigned int r = 0; r < n; r++)
5274
{
5275
num_derivatives *= 2;
5276
}// end loop over 'r'
5277
5278
// Declare pointer to two dimensional array that holds combinations of derivatives and initialise
5279
unsigned int **combinations = new unsigned int *[num_derivatives];
5280
for (unsigned int row = 0; row < num_derivatives; row++)
5281
{
5282
combinations[row] = new unsigned int [n];
5283
for (unsigned int col = 0; col < n; col++)
5284
combinations[row][col] = 0;
5285
}
5286
5287
// Generate combinations of derivatives
5288
for (unsigned int row = 1; row < num_derivatives; row++)
5289
{
5290
for (unsigned int num = 0; num < row; num++)
5291
{
5292
for (unsigned int col = n-1; col+1 > 0; col--)
5293
{
5294
if (combinations[row][col] + 1 > 1)
5295
combinations[row][col] = 0;
5296
else
5297
{
5298
combinations[row][col] += 1;
5299
break;
5300
}
5301
}
5302
}
5303
}
5304
5305
// Compute inverse of Jacobian
5306
const double Jinv[2][2] = {{K_00, K_01}, {K_10, K_11}};
5307
5308
// Declare transformation matrix
5309
// Declare pointer to two dimensional array and initialise
5310
double **transform = new double *[num_derivatives];
5311
5312
for (unsigned int j = 0; j < num_derivatives; j++)
5313
{
5314
transform[j] = new double [num_derivatives];
5315
for (unsigned int k = 0; k < num_derivatives; k++)
5316
transform[j][k] = 1;
5317
}
5318
5319
// Construct transformation matrix
5320
for (unsigned int row = 0; row < num_derivatives; row++)
5321
{
5322
for (unsigned int col = 0; col < num_derivatives; col++)
5323
{
5324
for (unsigned int k = 0; k < n; k++)
5325
transform[row][col] *= Jinv[combinations[col][k]][combinations[row][k]];
5326
}
5327
}
5328
5329
// Reset values. Assuming that values is always an array.
5330
for (unsigned int r = 0; r < num_derivatives; r++)
5331
{
5332
values[r] = 0.000000000000000;
5333
}// end loop over 'r'
5334
5335
switch (i)
5336
{
5337
case 0:
5338
{
5339
5340
// Array of basisvalues.
5341
double basisvalues[3] = {0.000000000000000, 0.000000000000000, 0.000000000000000};
5342
5343
// Declare helper variables.
5344
unsigned int rr = 0;
5345
unsigned int ss = 0;
5346
double tmp0 = (1.000000000000000 + Y + 2.000000000000000*X)/2.000000000000000;
5347
5348
// Compute basisvalues.
5349
basisvalues[0] = 1.000000000000000;
5350
basisvalues[1] = tmp0;
5351
for (unsigned int r = 0; r < 1; r++)
5352
{
5353
rr = (r + 1)*(r + 1 + 1)/2 + 1;
5354
ss = r*(r + 1)/2;
5355
basisvalues[rr] = basisvalues[ss]*(0.500000000000000 + r + Y*(1.500000000000000 + r));
5356
}// end loop over 'r'
5357
for (unsigned int r = 0; r < 2; r++)
5358
{
5359
for (unsigned int s = 0; s < 2 - r; s++)
5360
{
5361
rr = (r + s)*(r + s + 1)/2 + s;
5362
basisvalues[rr] *= std::sqrt((0.500000000000000 + r)*(1.000000000000000 + r + s));
5363
}// end loop over 's'
5364
}// end loop over 'r'
5365
5366
// Table(s) of coefficients.
5367
static const double coefficients0[3] = \
5368
{0.471404520791032, -0.288675134594813, -0.166666666666667};
5369
5370
// Tables of derivatives of the polynomial base (transpose).
5371
static const double dmats0[3][3] = \
5372
{{0.000000000000000, 0.000000000000000, 0.000000000000000},
5373
{4.898979485566356, 0.000000000000000, 0.000000000000000},
5374
{0.000000000000000, 0.000000000000000, 0.000000000000000}};
5375
5376
static const double dmats1[3][3] = \
5377
{{0.000000000000000, 0.000000000000000, 0.000000000000000},
5378
{2.449489742783178, 0.000000000000000, 0.000000000000000},
5379
{4.242640687119285, 0.000000000000000, 0.000000000000000}};
5380
5381
// Compute reference derivatives.
5382
// Declare pointer to array of derivatives on FIAT element.
5383
double *derivatives = new double[num_derivatives];
5384
for (unsigned int r = 0; r < num_derivatives; r++)
5385
{
5386
derivatives[r] = 0.000000000000000;
5387
}// end loop over 'r'
5388
5389
// Declare derivative matrix (of polynomial basis).
5390
double dmats[3][3] = \
5391
{{1.000000000000000, 0.000000000000000, 0.000000000000000},
5392
{0.000000000000000, 1.000000000000000, 0.000000000000000},
5393
{0.000000000000000, 0.000000000000000, 1.000000000000000}};
5394
5395
// Declare (auxiliary) derivative matrix (of polynomial basis).
5396
double dmats_old[3][3] = \
5397
{{1.000000000000000, 0.000000000000000, 0.000000000000000},
5398
{0.000000000000000, 1.000000000000000, 0.000000000000000},
5399
{0.000000000000000, 0.000000000000000, 1.000000000000000}};
5400
5401
// Loop possible derivatives.
5402
for (unsigned int r = 0; r < num_derivatives; r++)
5403
{
5404
// Resetting dmats values to compute next derivative.
5405
for (unsigned int t = 0; t < 3; t++)
5406
{
5407
for (unsigned int u = 0; u < 3; u++)
5408
{
5409
dmats[t][u] = 0.000000000000000;
5410
if (t == u)
5411
{
5412
dmats[t][u] = 1.000000000000000;
5413
}
5414
5415
}// end loop over 'u'
5416
}// end loop over 't'
5417
5418
// Looping derivative order to generate dmats.
5419
for (unsigned int s = 0; s < n; s++)
5420
{
5421
// Updating dmats_old with new values and resetting dmats.
5422
for (unsigned int t = 0; t < 3; t++)
5423
{
5424
for (unsigned int u = 0; u < 3; u++)
5425
{
5426
dmats_old[t][u] = dmats[t][u];
5427
dmats[t][u] = 0.000000000000000;
5428
}// end loop over 'u'
5429
}// end loop over 't'
5430
5431
// Update dmats using an inner product.
5432
if (combinations[r][s] == 0)
5433
{
5434
for (unsigned int t = 0; t < 3; t++)
5435
{
5436
for (unsigned int u = 0; u < 3; u++)
5437
{
5438
for (unsigned int tu = 0; tu < 3; tu++)
5439
{
5440
dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
5441
}// end loop over 'tu'
5442
}// end loop over 'u'
5443
}// end loop over 't'
5444
}
5445
5446
if (combinations[r][s] == 1)
5447
{
5448
for (unsigned int t = 0; t < 3; t++)
5449
{
5450
for (unsigned int u = 0; u < 3; u++)
5451
{
5452
for (unsigned int tu = 0; tu < 3; tu++)
5453
{
5454
dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
5455
}// end loop over 'tu'
5456
}// end loop over 'u'
5457
}// end loop over 't'
5458
}
5459
5460
}// end loop over 's'
5461
for (unsigned int s = 0; s < 3; s++)
5462
{
5463
for (unsigned int t = 0; t < 3; t++)
5464
{
5465
derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
5466
}// end loop over 't'
5467
}// end loop over 's'
5468
}// end loop over 'r'
5469
5470
// Transform derivatives back to physical element
5471
for (unsigned int r = 0; r < num_derivatives; r++)
5472
{
5473
for (unsigned int s = 0; s < num_derivatives; s++)
5474
{
5475
values[r] += transform[r][s]*derivatives[s];
5476
}// end loop over 's'
5477
}// end loop over 'r'
5478
5479
// Delete pointer to array of derivatives on FIAT element
5480
delete [] derivatives;
5481
5482
// Delete pointer to array of combinations of derivatives and transform
5483
for (unsigned int r = 0; r < num_derivatives; r++)
5484
{
5485
delete [] combinations[r];
5486
}// end loop over 'r'
5487
delete [] combinations;
5488
for (unsigned int r = 0; r < num_derivatives; r++)
5489
{
5490
delete [] transform[r];
5491
}// end loop over 'r'
5492
delete [] transform;
5493
break;
5494
}
5495
case 1:
5496
{
5497
5498
// Array of basisvalues.
5499
double basisvalues[3] = {0.000000000000000, 0.000000000000000, 0.000000000000000};
5500
5501
// Declare helper variables.
5502
unsigned int rr = 0;
5503
unsigned int ss = 0;
5504
double tmp0 = (1.000000000000000 + Y + 2.000000000000000*X)/2.000000000000000;
5505
5506
// Compute basisvalues.
5507
basisvalues[0] = 1.000000000000000;
5508
basisvalues[1] = tmp0;
5509
for (unsigned int r = 0; r < 1; r++)
5510
{
5511
rr = (r + 1)*(r + 1 + 1)/2 + 1;
5512
ss = r*(r + 1)/2;
5513
basisvalues[rr] = basisvalues[ss]*(0.500000000000000 + r + Y*(1.500000000000000 + r));
5514
}// end loop over 'r'
5515
for (unsigned int r = 0; r < 2; r++)
5516
{
5517
for (unsigned int s = 0; s < 2 - r; s++)
5518
{
5519
rr = (r + s)*(r + s + 1)/2 + s;
5520
basisvalues[rr] *= std::sqrt((0.500000000000000 + r)*(1.000000000000000 + r + s));
5521
}// end loop over 's'
5522
}// end loop over 'r'
5523
5524
// Table(s) of coefficients.
5525
static const double coefficients0[3] = \
5526
{0.471404520791032, 0.288675134594813, -0.166666666666667};
5527
5528
// Tables of derivatives of the polynomial base (transpose).
5529
static const double dmats0[3][3] = \
5530
{{0.000000000000000, 0.000000000000000, 0.000000000000000},
5531
{4.898979485566356, 0.000000000000000, 0.000000000000000},
5532
{0.000000000000000, 0.000000000000000, 0.000000000000000}};
5533
5534
static const double dmats1[3][3] = \
5535
{{0.000000000000000, 0.000000000000000, 0.000000000000000},
5536
{2.449489742783178, 0.000000000000000, 0.000000000000000},
5537
{4.242640687119285, 0.000000000000000, 0.000000000000000}};
5538
5539
// Compute reference derivatives.
5540
// Declare pointer to array of derivatives on FIAT element.
5541
double *derivatives = new double[num_derivatives];
5542
for (unsigned int r = 0; r < num_derivatives; r++)
5543
{
5544
derivatives[r] = 0.000000000000000;
5545
}// end loop over 'r'
5546
5547
// Declare derivative matrix (of polynomial basis).
5548
double dmats[3][3] = \
5549
{{1.000000000000000, 0.000000000000000, 0.000000000000000},
5550
{0.000000000000000, 1.000000000000000, 0.000000000000000},
5551
{0.000000000000000, 0.000000000000000, 1.000000000000000}};
5552
5553
// Declare (auxiliary) derivative matrix (of polynomial basis).
5554
double dmats_old[3][3] = \
5555
{{1.000000000000000, 0.000000000000000, 0.000000000000000},
5556
{0.000000000000000, 1.000000000000000, 0.000000000000000},
5557
{0.000000000000000, 0.000000000000000, 1.000000000000000}};
5558
5559
// Loop possible derivatives.
5560
for (unsigned int r = 0; r < num_derivatives; r++)
5561
{
5562
// Resetting dmats values to compute next derivative.
5563
for (unsigned int t = 0; t < 3; t++)
5564
{
5565
for (unsigned int u = 0; u < 3; u++)
5566
{
5567
dmats[t][u] = 0.000000000000000;
5568
if (t == u)
5569
{
5570
dmats[t][u] = 1.000000000000000;
5571
}
5572
5573
}// end loop over 'u'
5574
}// end loop over 't'
5575
5576
// Looping derivative order to generate dmats.
5577
for (unsigned int s = 0; s < n; s++)
5578
{
5579
// Updating dmats_old with new values and resetting dmats.
5580
for (unsigned int t = 0; t < 3; t++)
5581
{
5582
for (unsigned int u = 0; u < 3; u++)
5583
{
5584
dmats_old[t][u] = dmats[t][u];
5585
dmats[t][u] = 0.000000000000000;
5586
}// end loop over 'u'
5587
}// end loop over 't'
5588
5589
// Update dmats using an inner product.
5590
if (combinations[r][s] == 0)
5591
{
5592
for (unsigned int t = 0; t < 3; t++)
5593
{
5594
for (unsigned int u = 0; u < 3; u++)
5595
{
5596
for (unsigned int tu = 0; tu < 3; tu++)
5597
{
5598
dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
5599
}// end loop over 'tu'
5600
}// end loop over 'u'
5601
}// end loop over 't'
5602
}
5603
5604
if (combinations[r][s] == 1)
5605
{
5606
for (unsigned int t = 0; t < 3; t++)
5607
{
5608
for (unsigned int u = 0; u < 3; u++)
5609
{
5610
for (unsigned int tu = 0; tu < 3; tu++)
5611
{
5612
dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
5613
}// end loop over 'tu'
5614
}// end loop over 'u'
5615
}// end loop over 't'
5616
}
5617
5618
}// end loop over 's'
5619
for (unsigned int s = 0; s < 3; s++)
5620
{
5621
for (unsigned int t = 0; t < 3; t++)
5622
{
5623
derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
5624
}// end loop over 't'
5625
}// end loop over 's'
5626
}// end loop over 'r'
5627
5628
// Transform derivatives back to physical element
5629
for (unsigned int r = 0; r < num_derivatives; r++)
5630
{
5631
for (unsigned int s = 0; s < num_derivatives; s++)
5632
{
5633
values[r] += transform[r][s]*derivatives[s];
5634
}// end loop over 's'
5635
}// end loop over 'r'
5636
5637
// Delete pointer to array of derivatives on FIAT element
5638
delete [] derivatives;
5639
5640
// Delete pointer to array of combinations of derivatives and transform
5641
for (unsigned int r = 0; r < num_derivatives; r++)
5642
{
5643
delete [] combinations[r];
5644
}// end loop over 'r'
5645
delete [] combinations;
5646
for (unsigned int r = 0; r < num_derivatives; r++)
5647
{
5648
delete [] transform[r];
5649
}// end loop over 'r'
5650
delete [] transform;
5651
break;
5652
}
5653
case 2:
5654
{
5655
5656
// Array of basisvalues.
5657
double basisvalues[3] = {0.000000000000000, 0.000000000000000, 0.000000000000000};
5658
5659
// Declare helper variables.
5660
unsigned int rr = 0;
5661
unsigned int ss = 0;
5662
double tmp0 = (1.000000000000000 + Y + 2.000000000000000*X)/2.000000000000000;
5663
5664
// Compute basisvalues.
5665
basisvalues[0] = 1.000000000000000;
5666
basisvalues[1] = tmp0;
5667
for (unsigned int r = 0; r < 1; r++)
5668
{
5669
rr = (r + 1)*(r + 1 + 1)/2 + 1;
5670
ss = r*(r + 1)/2;
5671
basisvalues[rr] = basisvalues[ss]*(0.500000000000000 + r + Y*(1.500000000000000 + r));
5672
}// end loop over 'r'
5673
for (unsigned int r = 0; r < 2; r++)
5674
{
5675
for (unsigned int s = 0; s < 2 - r; s++)
5676
{
5677
rr = (r + s)*(r + s + 1)/2 + s;
5678
basisvalues[rr] *= std::sqrt((0.500000000000000 + r)*(1.000000000000000 + r + s));
5679
}// end loop over 's'
5680
}// end loop over 'r'
5681
5682
// Table(s) of coefficients.
5683
static const double coefficients0[3] = \
5684
{0.471404520791032, 0.000000000000000, 0.333333333333333};
5685
5686
// Tables of derivatives of the polynomial base (transpose).
5687
static const double dmats0[3][3] = \
5688
{{0.000000000000000, 0.000000000000000, 0.000000000000000},
5689
{4.898979485566356, 0.000000000000000, 0.000000000000000},
5690
{0.000000000000000, 0.000000000000000, 0.000000000000000}};
5691
5692
static const double dmats1[3][3] = \
5693
{{0.000000000000000, 0.000000000000000, 0.000000000000000},
5694
{2.449489742783178, 0.000000000000000, 0.000000000000000},
5695
{4.242640687119285, 0.000000000000000, 0.000000000000000}};
5696
5697
// Compute reference derivatives.
5698
// Declare pointer to array of derivatives on FIAT element.
5699
double *derivatives = new double[num_derivatives];
5700
for (unsigned int r = 0; r < num_derivatives; r++)
5701
{
5702
derivatives[r] = 0.000000000000000;
5703
}// end loop over 'r'
5704
5705
// Declare derivative matrix (of polynomial basis).
5706
double dmats[3][3] = \
5707
{{1.000000000000000, 0.000000000000000, 0.000000000000000},
5708
{0.000000000000000, 1.000000000000000, 0.000000000000000},
5709
{0.000000000000000, 0.000000000000000, 1.000000000000000}};
5710
5711
// Declare (auxiliary) derivative matrix (of polynomial basis).
5712
double dmats_old[3][3] = \
5713
{{1.000000000000000, 0.000000000000000, 0.000000000000000},
5714
{0.000000000000000, 1.000000000000000, 0.000000000000000},
5715
{0.000000000000000, 0.000000000000000, 1.000000000000000}};
5716
5717
// Loop possible derivatives.
5718
for (unsigned int r = 0; r < num_derivatives; r++)
5719
{
5720
// Resetting dmats values to compute next derivative.
5721
for (unsigned int t = 0; t < 3; t++)
5722
{
5723
for (unsigned int u = 0; u < 3; u++)
5724
{
5725
dmats[t][u] = 0.000000000000000;
5726
if (t == u)
5727
{
5728
dmats[t][u] = 1.000000000000000;
5729
}
5730
5731
}// end loop over 'u'
5732
}// end loop over 't'
5733
5734
// Looping derivative order to generate dmats.
5735
for (unsigned int s = 0; s < n; s++)
5736
{
5737
// Updating dmats_old with new values and resetting dmats.
5738
for (unsigned int t = 0; t < 3; t++)
5739
{
5740
for (unsigned int u = 0; u < 3; u++)
5741
{
5742
dmats_old[t][u] = dmats[t][u];
5743
dmats[t][u] = 0.000000000000000;
5744
}// end loop over 'u'
5745
}// end loop over 't'
5746
5747
// Update dmats using an inner product.
5748
if (combinations[r][s] == 0)
5749
{
5750
for (unsigned int t = 0; t < 3; t++)
5751
{
5752
for (unsigned int u = 0; u < 3; u++)
5753
{
5754
for (unsigned int tu = 0; tu < 3; tu++)
5755
{
5756
dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
5757
}// end loop over 'tu'
5758
}// end loop over 'u'
5759
}// end loop over 't'
5760
}
5761
5762
if (combinations[r][s] == 1)
5763
{
5764
for (unsigned int t = 0; t < 3; t++)
5765
{
5766
for (unsigned int u = 0; u < 3; u++)
5767
{
5768
for (unsigned int tu = 0; tu < 3; tu++)
5769
{
5770
dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
5771
}// end loop over 'tu'
5772
}// end loop over 'u'
5773
}// end loop over 't'
5774
}
5775
5776
}// end loop over 's'
5777
for (unsigned int s = 0; s < 3; s++)
5778
{
5779
for (unsigned int t = 0; t < 3; t++)
5780
{
5781
derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
5782
}// end loop over 't'
5783
}// end loop over 's'
5784
}// end loop over 'r'
5785
5786
// Transform derivatives back to physical element
5787
for (unsigned int r = 0; r < num_derivatives; r++)
5788
{
5789
for (unsigned int s = 0; s < num_derivatives; s++)
5790
{
5791
values[r] += transform[r][s]*derivatives[s];
5792
}// end loop over 's'
5793
}// end loop over 'r'
5794
5795
// Delete pointer to array of derivatives on FIAT element
5796
delete [] derivatives;
5797
5798
// Delete pointer to array of combinations of derivatives and transform
5799
for (unsigned int r = 0; r < num_derivatives; r++)
5800
{
5801
delete [] combinations[r];
5802
}// end loop over 'r'
5803
delete [] combinations;
5804
for (unsigned int r = 0; r < num_derivatives; r++)
5805
{
5806
delete [] transform[r];
5807
}// end loop over 'r'
5808
delete [] transform;
5809
break;
5810
}
5811
}
5812
5813
}
5814
5815
/// Evaluate order n derivatives of all basis functions at given point in cell
5816
virtual void evaluate_basis_derivatives_all(unsigned int n,
5817
double* values,
5818
const double* coordinates,
5819
const ufc::cell& c) const
5820
{
5821
// Compute number of derivatives.
5822
unsigned int num_derivatives = 1;
5823
for (unsigned int r = 0; r < n; r++)
5824
{
5825
num_derivatives *= 2;
5826
}// end loop over 'r'
5827
5828
// Helper variable to hold values of a single dof.
5829
double *dof_values = new double[num_derivatives];
5830
for (unsigned int r = 0; r < num_derivatives; r++)
5831
{
5832
dof_values[r] = 0.000000000000000;
5833
}// end loop over 'r'
5834
5835
// Loop dofs and call evaluate_basis_derivatives.
5836
for (unsigned int r = 0; r < 3; r++)
5837
{
5838
evaluate_basis_derivatives(r, n, dof_values, coordinates, c);
5839
for (unsigned int s = 0; s < num_derivatives; s++)
5840
{
5841
values[r*num_derivatives + s] = dof_values[s];
5842
}// end loop over 's'
5843
}// end loop over 'r'
5844
5845
// Delete pointer.
5846
delete [] dof_values;
5847
}
5848
5849
/// Evaluate linear functional for dof i on the function f
5850
virtual double evaluate_dof(unsigned int i,
5851
const ufc::function& f,
5852
const ufc::cell& c) const
5853
{
5854
// Declare variables for result of evaluation.
5855
double vals[1];
5856
5857
// Declare variable for physical coordinates.
5858
double y[2];
5859
const double * const * x = c.coordinates;
5860
switch (i)
5861
{
5862
case 0:
5863
{
5864
y[0] = x[0][0];
5865
y[1] = x[0][1];
5866
f.evaluate(vals, y, c);
5867
return vals[0];
5868
break;
5869
}
5870
case 1:
5871
{
5872
y[0] = x[1][0];
5873
y[1] = x[1][1];
5874
f.evaluate(vals, y, c);
5875
return vals[0];
5876
break;
5877
}
5878
case 2:
5879
{
5880
y[0] = x[2][0];
5881
y[1] = x[2][1];
5882
f.evaluate(vals, y, c);
5883
return vals[0];
5884
break;
5885
}
5886
}
5887
5888
return 0.000000000000000;
5889
}
5890
5891
/// Evaluate linear functionals for all dofs on the function f
5892
virtual void evaluate_dofs(double* values,
5893
const ufc::function& f,
5894
const ufc::cell& c) const
5895
{
5896
// Declare variables for result of evaluation.
5897
double vals[1];
5898
5899
// Declare variable for physical coordinates.
5900
double y[2];
5901
const double * const * x = c.coordinates;
5902
y[0] = x[0][0];
5903
y[1] = x[0][1];
5904
f.evaluate(vals, y, c);
5905
values[0] = vals[0];
5906
y[0] = x[1][0];
5907
y[1] = x[1][1];
5908
f.evaluate(vals, y, c);
5909
values[1] = vals[0];
5910
y[0] = x[2][0];
5911
y[1] = x[2][1];
5912
f.evaluate(vals, y, c);
5913
values[2] = vals[0];
5914
}
5915
5916
/// Interpolate vertex values from dof values
5917
virtual void interpolate_vertex_values(double* vertex_values,
5918
const double* dof_values,
5919
const ufc::cell& c) const
5920
{
5921
// Evaluate function and change variables
5922
vertex_values[0] = dof_values[0];
5923
vertex_values[1] = dof_values[1];
5924
vertex_values[2] = dof_values[2];
5925
}
5926
5927
/// Map coordinate xhat from reference cell to coordinate x in cell
5928
virtual void map_from_reference_cell(double* x,
5929
const double* xhat,
5930
const ufc::cell& c)
5931
{
5932
throw std::runtime_error("map_from_reference_cell not yet implemented (introduced in UFC 2.0).");
5933
}
5934
5935
/// Map from coordinate x in cell to coordinate xhat in reference cell
5936
virtual void map_to_reference_cell(double* xhat,
5937
const double* x,
5938
const ufc::cell& c)
5939
{
5940
throw std::runtime_error("map_to_reference_cell not yet implemented (introduced in UFC 2.0).");
5941
}
5942
5943
/// Return the number of sub elements (for a mixed element)
5944
virtual unsigned int num_sub_elements() const
5945
{
5946
return 0;
5947
}
5948
5949
/// Create a new finite element for sub element i (for a mixed element)
5950
virtual ufc::finite_element* create_sub_element(unsigned int i) const
5951
{
5952
return 0;
5953
}
5954
5955
/// Create a new class instance
5956
virtual ufc::finite_element* create() const
5957
{
5958
return new adaptivepoisson_finite_element_4();
5959
}
5960
5961
};
5962
5963
/// This class defines the interface for a finite element.
5964
5965
class adaptivepoisson_finite_element_5: public ufc::finite_element
5966
{
5967
public:
5968
5969
/// Constructor
5970
adaptivepoisson_finite_element_5() : ufc::finite_element()
5971
{
5972
// Do nothing
5973
}
5974
5975
/// Destructor
5976
virtual ~adaptivepoisson_finite_element_5()
5977
{
5978
// Do nothing
5979
}
5980
5981
/// Return a string identifying the finite element
5982
virtual const char* signature() const
5983
{
5984
return "FiniteElement('Lagrange', Cell('triangle', 1, Space(2)), 1)";
5985
}
5986
5987
/// Return the cell shape
5988
virtual ufc::shape cell_shape() const
5989
{
5990
return ufc::triangle;
5991
}
5992
5993
/// Return the topological dimension of the cell shape
5994
virtual unsigned int topological_dimension() const
5995
{
5996
return 2;
5997
}
5998
5999
/// Return the geometric dimension of the cell shape
6000
virtual unsigned int geometric_dimension() const
6001
{
6002
return 2;
6003
}
6004
6005
/// Return the dimension of the finite element function space
6006
virtual unsigned int space_dimension() const
6007
{
6008
return 3;
6009
}
6010
6011
/// Return the rank of the value space
6012
virtual unsigned int value_rank() const
6013
{
6014
return 0;
6015
}
6016
6017
/// Return the dimension of the value space for axis i
6018
virtual unsigned int value_dimension(unsigned int i) const
6019
{
6020
return 1;
6021
}
6022
6023
/// Evaluate basis function i at given point in cell
6024
virtual void evaluate_basis(unsigned int i,
6025
double* values,
6026
const double* coordinates,
6027
const ufc::cell& c) const
6028
{
6029
// Extract vertex coordinates
6030
const double * const * x = c.coordinates;
6031
6032
// Compute Jacobian of affine map from reference cell
6033
const double J_00 = x[1][0] - x[0][0];
6034
const double J_01 = x[2][0] - x[0][0];
6035
const double J_10 = x[1][1] - x[0][1];
6036
const double J_11 = x[2][1] - x[0][1];
6037
6038
// Compute determinant of Jacobian
6039
double detJ = J_00*J_11 - J_01*J_10;
6040
6041
// Compute inverse of Jacobian
6042
6043
// Compute constants
6044
const double C0 = x[1][0] + x[2][0];
6045
const double C1 = x[1][1] + x[2][1];
6046
6047
// Get coordinates and map to the reference (FIAT) element
6048
double X = (J_01*(C1 - 2.0*coordinates[1]) + J_11*(2.0*coordinates[0] - C0)) / detJ;
6049
double Y = (J_00*(2.0*coordinates[1] - C1) + J_10*(C0 - 2.0*coordinates[0])) / detJ;
6050
6051
// Reset values.
6052
*values = 0.000000000000000;
6053
switch (i)
6054
{
6055
case 0:
6056
{
6057
6058
// Array of basisvalues.
6059
double basisvalues[3] = {0.000000000000000, 0.000000000000000, 0.000000000000000};
6060
6061
// Declare helper variables.
6062
unsigned int rr = 0;
6063
unsigned int ss = 0;
6064
double tmp0 = (1.000000000000000 + Y + 2.000000000000000*X)/2.000000000000000;
6065
6066
// Compute basisvalues.
6067
basisvalues[0] = 1.000000000000000;
6068
basisvalues[1] = tmp0;
6069
for (unsigned int r = 0; r < 1; r++)
6070
{
6071
rr = (r + 1)*(r + 1 + 1)/2 + 1;
6072
ss = r*(r + 1)/2;
6073
basisvalues[rr] = basisvalues[ss]*(0.500000000000000 + r + Y*(1.500000000000000 + r));
6074
}// end loop over 'r'
6075
for (unsigned int r = 0; r < 2; r++)
6076
{
6077
for (unsigned int s = 0; s < 2 - r; s++)
6078
{
6079
rr = (r + s)*(r + s + 1)/2 + s;
6080
basisvalues[rr] *= std::sqrt((0.500000000000000 + r)*(1.000000000000000 + r + s));
6081
}// end loop over 's'
6082
}// end loop over 'r'
6083
6084
// Table(s) of coefficients.
6085
static const double coefficients0[3] = \
6086
{0.471404520791032, -0.288675134594813, -0.166666666666667};
6087
6088
// Compute value(s).
6089
for (unsigned int r = 0; r < 3; r++)
6090
{
6091
*values += coefficients0[r]*basisvalues[r];
6092
}// end loop over 'r'
6093
break;
6094
}
6095
case 1:
6096
{
6097
6098
// Array of basisvalues.
6099
double basisvalues[3] = {0.000000000000000, 0.000000000000000, 0.000000000000000};
6100
6101
// Declare helper variables.
6102
unsigned int rr = 0;
6103
unsigned int ss = 0;
6104
double tmp0 = (1.000000000000000 + Y + 2.000000000000000*X)/2.000000000000000;
6105
6106
// Compute basisvalues.
6107
basisvalues[0] = 1.000000000000000;
6108
basisvalues[1] = tmp0;
6109
for (unsigned int r = 0; r < 1; r++)
6110
{
6111
rr = (r + 1)*(r + 1 + 1)/2 + 1;
6112
ss = r*(r + 1)/2;
6113
basisvalues[rr] = basisvalues[ss]*(0.500000000000000 + r + Y*(1.500000000000000 + r));
6114
}// end loop over 'r'
6115
for (unsigned int r = 0; r < 2; r++)
6116
{
6117
for (unsigned int s = 0; s < 2 - r; s++)
6118
{
6119
rr = (r + s)*(r + s + 1)/2 + s;
6120
basisvalues[rr] *= std::sqrt((0.500000000000000 + r)*(1.000000000000000 + r + s));
6121
}// end loop over 's'
6122
}// end loop over 'r'
6123
6124
// Table(s) of coefficients.
6125
static const double coefficients0[3] = \
6126
{0.471404520791032, 0.288675134594813, -0.166666666666667};
6127
6128
// Compute value(s).
6129
for (unsigned int r = 0; r < 3; r++)
6130
{
6131
*values += coefficients0[r]*basisvalues[r];
6132
}// end loop over 'r'
6133
break;
6134
}
6135
case 2:
6136
{
6137
6138
// Array of basisvalues.
6139
double basisvalues[3] = {0.000000000000000, 0.000000000000000, 0.000000000000000};
6140
6141
// Declare helper variables.
6142
unsigned int rr = 0;
6143
unsigned int ss = 0;
6144
double tmp0 = (1.000000000000000 + Y + 2.000000000000000*X)/2.000000000000000;
6145
6146
// Compute basisvalues.
6147
basisvalues[0] = 1.000000000000000;
6148
basisvalues[1] = tmp0;
6149
for (unsigned int r = 0; r < 1; r++)
6150
{
6151
rr = (r + 1)*(r + 1 + 1)/2 + 1;
6152
ss = r*(r + 1)/2;
6153
basisvalues[rr] = basisvalues[ss]*(0.500000000000000 + r + Y*(1.500000000000000 + r));
6154
}// end loop over 'r'
6155
for (unsigned int r = 0; r < 2; r++)
6156
{
6157
for (unsigned int s = 0; s < 2 - r; s++)
6158
{
6159
rr = (r + s)*(r + s + 1)/2 + s;
6160
basisvalues[rr] *= std::sqrt((0.500000000000000 + r)*(1.000000000000000 + r + s));
6161
}// end loop over 's'
6162
}// end loop over 'r'
6163
6164
// Table(s) of coefficients.
6165
static const double coefficients0[3] = \
6166
{0.471404520791032, 0.000000000000000, 0.333333333333333};
6167
6168
// Compute value(s).
6169
for (unsigned int r = 0; r < 3; r++)
6170
{
6171
*values += coefficients0[r]*basisvalues[r];
6172
}// end loop over 'r'
6173
break;
6174
}
6175
}
6176
6177
}
6178
6179
/// Evaluate all basis functions at given point in cell
6180
virtual void evaluate_basis_all(double* values,
6181
const double* coordinates,
6182
const ufc::cell& c) const
6183
{
6184
// Helper variable to hold values of a single dof.
6185
double dof_values = 0.000000000000000;
6186
6187
// Loop dofs and call evaluate_basis.
6188
for (unsigned int r = 0; r < 3; r++)
6189
{
6190
evaluate_basis(r, &dof_values, coordinates, c);
6191
values[r] = dof_values;
6192
}// end loop over 'r'
6193
}
6194
6195
/// Evaluate order n derivatives of basis function i at given point in cell
6196
virtual void evaluate_basis_derivatives(unsigned int i,
6197
unsigned int n,
6198
double* values,
6199
const double* coordinates,
6200
const ufc::cell& c) const
6201
{
6202
// Extract vertex coordinates
6203
const double * const * x = c.coordinates;
6204
6205
// Compute Jacobian of affine map from reference cell
6206
const double J_00 = x[1][0] - x[0][0];
6207
const double J_01 = x[2][0] - x[0][0];
6208
const double J_10 = x[1][1] - x[0][1];
6209
const double J_11 = x[2][1] - x[0][1];
6210
6211
// Compute determinant of Jacobian
6212
double detJ = J_00*J_11 - J_01*J_10;
6213
6214
// Compute inverse of Jacobian
6215
const double K_00 = J_11 / detJ;
6216
const double K_01 = -J_01 / detJ;
6217
const double K_10 = -J_10 / detJ;
6218
const double K_11 = J_00 / detJ;
6219
6220
// Compute constants
6221
const double C0 = x[1][0] + x[2][0];
6222
const double C1 = x[1][1] + x[2][1];
6223
6224
// Get coordinates and map to the reference (FIAT) element
6225
double X = (J_01*(C1 - 2.0*coordinates[1]) + J_11*(2.0*coordinates[0] - C0)) / detJ;
6226
double Y = (J_00*(2.0*coordinates[1] - C1) + J_10*(C0 - 2.0*coordinates[0])) / detJ;
6227
6228
// Compute number of derivatives.
6229
unsigned int num_derivatives = 1;
6230
for (unsigned int r = 0; r < n; r++)
6231
{
6232
num_derivatives *= 2;
6233
}// end loop over 'r'
6234
6235
// Declare pointer to two dimensional array that holds combinations of derivatives and initialise
6236
unsigned int **combinations = new unsigned int *[num_derivatives];
6237
for (unsigned int row = 0; row < num_derivatives; row++)
6238
{
6239
combinations[row] = new unsigned int [n];
6240
for (unsigned int col = 0; col < n; col++)
6241
combinations[row][col] = 0;
6242
}
6243
6244
// Generate combinations of derivatives
6245
for (unsigned int row = 1; row < num_derivatives; row++)
6246
{
6247
for (unsigned int num = 0; num < row; num++)
6248
{
6249
for (unsigned int col = n-1; col+1 > 0; col--)
6250
{
6251
if (combinations[row][col] + 1 > 1)
6252
combinations[row][col] = 0;
6253
else
6254
{
6255
combinations[row][col] += 1;
6256
break;
6257
}
6258
}
6259
}
6260
}
6261
6262
// Compute inverse of Jacobian
6263
const double Jinv[2][2] = {{K_00, K_01}, {K_10, K_11}};
6264
6265
// Declare transformation matrix
6266
// Declare pointer to two dimensional array and initialise
6267
double **transform = new double *[num_derivatives];
6268
6269
for (unsigned int j = 0; j < num_derivatives; j++)
6270
{
6271
transform[j] = new double [num_derivatives];
6272
for (unsigned int k = 0; k < num_derivatives; k++)
6273
transform[j][k] = 1;
6274
}
6275
6276
// Construct transformation matrix
6277
for (unsigned int row = 0; row < num_derivatives; row++)
6278
{
6279
for (unsigned int col = 0; col < num_derivatives; col++)
6280
{
6281
for (unsigned int k = 0; k < n; k++)
6282
transform[row][col] *= Jinv[combinations[col][k]][combinations[row][k]];
6283
}
6284
}
6285
6286
// Reset values. Assuming that values is always an array.
6287
for (unsigned int r = 0; r < num_derivatives; r++)
6288
{
6289
values[r] = 0.000000000000000;
6290
}// end loop over 'r'
6291
6292
switch (i)
6293
{
6294
case 0:
6295
{
6296
6297
// Array of basisvalues.
6298
double basisvalues[3] = {0.000000000000000, 0.000000000000000, 0.000000000000000};
6299
6300
// Declare helper variables.
6301
unsigned int rr = 0;
6302
unsigned int ss = 0;
6303
double tmp0 = (1.000000000000000 + Y + 2.000000000000000*X)/2.000000000000000;
6304
6305
// Compute basisvalues.
6306
basisvalues[0] = 1.000000000000000;
6307
basisvalues[1] = tmp0;
6308
for (unsigned int r = 0; r < 1; r++)
6309
{
6310
rr = (r + 1)*(r + 1 + 1)/2 + 1;
6311
ss = r*(r + 1)/2;
6312
basisvalues[rr] = basisvalues[ss]*(0.500000000000000 + r + Y*(1.500000000000000 + r));
6313
}// end loop over 'r'
6314
for (unsigned int r = 0; r < 2; r++)
6315
{
6316
for (unsigned int s = 0; s < 2 - r; s++)
6317
{
6318
rr = (r + s)*(r + s + 1)/2 + s;
6319
basisvalues[rr] *= std::sqrt((0.500000000000000 + r)*(1.000000000000000 + r + s));
6320
}// end loop over 's'
6321
}// end loop over 'r'
6322
6323
// Table(s) of coefficients.
6324
static const double coefficients0[3] = \
6325
{0.471404520791032, -0.288675134594813, -0.166666666666667};
6326
6327
// Tables of derivatives of the polynomial base (transpose).
6328
static const double dmats0[3][3] = \
6329
{{0.000000000000000, 0.000000000000000, 0.000000000000000},
6330
{4.898979485566356, 0.000000000000000, 0.000000000000000},
6331
{0.000000000000000, 0.000000000000000, 0.000000000000000}};
6332
6333
static const double dmats1[3][3] = \
6334
{{0.000000000000000, 0.000000000000000, 0.000000000000000},
6335
{2.449489742783178, 0.000000000000000, 0.000000000000000},
6336
{4.242640687119285, 0.000000000000000, 0.000000000000000}};
6337
6338
// Compute reference derivatives.
6339
// Declare pointer to array of derivatives on FIAT element.
6340
double *derivatives = new double[num_derivatives];
6341
for (unsigned int r = 0; r < num_derivatives; r++)
6342
{
6343
derivatives[r] = 0.000000000000000;
6344
}// end loop over 'r'
6345
6346
// Declare derivative matrix (of polynomial basis).
6347
double dmats[3][3] = \
6348
{{1.000000000000000, 0.000000000000000, 0.000000000000000},
6349
{0.000000000000000, 1.000000000000000, 0.000000000000000},
6350
{0.000000000000000, 0.000000000000000, 1.000000000000000}};
6351
6352
// Declare (auxiliary) derivative matrix (of polynomial basis).
6353
double dmats_old[3][3] = \
6354
{{1.000000000000000, 0.000000000000000, 0.000000000000000},
6355
{0.000000000000000, 1.000000000000000, 0.000000000000000},
6356
{0.000000000000000, 0.000000000000000, 1.000000000000000}};
6357
6358
// Loop possible derivatives.
6359
for (unsigned int r = 0; r < num_derivatives; r++)
6360
{
6361
// Resetting dmats values to compute next derivative.
6362
for (unsigned int t = 0; t < 3; t++)
6363
{
6364
for (unsigned int u = 0; u < 3; u++)
6365
{
6366
dmats[t][u] = 0.000000000000000;
6367
if (t == u)
6368
{
6369
dmats[t][u] = 1.000000000000000;
6370
}
6371
6372
}// end loop over 'u'
6373
}// end loop over 't'
6374
6375
// Looping derivative order to generate dmats.
6376
for (unsigned int s = 0; s < n; s++)
6377
{
6378
// Updating dmats_old with new values and resetting dmats.
6379
for (unsigned int t = 0; t < 3; t++)
6380
{
6381
for (unsigned int u = 0; u < 3; u++)
6382
{
6383
dmats_old[t][u] = dmats[t][u];
6384
dmats[t][u] = 0.000000000000000;
6385
}// end loop over 'u'
6386
}// end loop over 't'
6387
6388
// Update dmats using an inner product.
6389
if (combinations[r][s] == 0)
6390
{
6391
for (unsigned int t = 0; t < 3; t++)
6392
{
6393
for (unsigned int u = 0; u < 3; u++)
6394
{
6395
for (unsigned int tu = 0; tu < 3; tu++)
6396
{
6397
dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
6398
}// end loop over 'tu'
6399
}// end loop over 'u'
6400
}// end loop over 't'
6401
}
6402
6403
if (combinations[r][s] == 1)
6404
{
6405
for (unsigned int t = 0; t < 3; t++)
6406
{
6407
for (unsigned int u = 0; u < 3; u++)
6408
{
6409
for (unsigned int tu = 0; tu < 3; tu++)
6410
{
6411
dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
6412
}// end loop over 'tu'
6413
}// end loop over 'u'
6414
}// end loop over 't'
6415
}
6416
6417
}// end loop over 's'
6418
for (unsigned int s = 0; s < 3; s++)
6419
{
6420
for (unsigned int t = 0; t < 3; t++)
6421
{
6422
derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
6423
}// end loop over 't'
6424
}// end loop over 's'
6425
}// end loop over 'r'
6426
6427
// Transform derivatives back to physical element
6428
for (unsigned int r = 0; r < num_derivatives; r++)
6429
{
6430
for (unsigned int s = 0; s < num_derivatives; s++)
6431
{
6432
values[r] += transform[r][s]*derivatives[s];
6433
}// end loop over 's'
6434
}// end loop over 'r'
6435
6436
// Delete pointer to array of derivatives on FIAT element
6437
delete [] derivatives;
6438
6439
// Delete pointer to array of combinations of derivatives and transform
6440
for (unsigned int r = 0; r < num_derivatives; r++)
6441
{
6442
delete [] combinations[r];
6443
}// end loop over 'r'
6444
delete [] combinations;
6445
for (unsigned int r = 0; r < num_derivatives; r++)
6446
{
6447
delete [] transform[r];
6448
}// end loop over 'r'
6449
delete [] transform;
6450
break;
6451
}
6452
case 1:
6453
{
6454
6455
// Array of basisvalues.
6456
double basisvalues[3] = {0.000000000000000, 0.000000000000000, 0.000000000000000};
6457
6458
// Declare helper variables.
6459
unsigned int rr = 0;
6460
unsigned int ss = 0;
6461
double tmp0 = (1.000000000000000 + Y + 2.000000000000000*X)/2.000000000000000;
6462
6463
// Compute basisvalues.
6464
basisvalues[0] = 1.000000000000000;
6465
basisvalues[1] = tmp0;
6466
for (unsigned int r = 0; r < 1; r++)
6467
{
6468
rr = (r + 1)*(r + 1 + 1)/2 + 1;
6469
ss = r*(r + 1)/2;
6470
basisvalues[rr] = basisvalues[ss]*(0.500000000000000 + r + Y*(1.500000000000000 + r));
6471
}// end loop over 'r'
6472
for (unsigned int r = 0; r < 2; r++)
6473
{
6474
for (unsigned int s = 0; s < 2 - r; s++)
6475
{
6476
rr = (r + s)*(r + s + 1)/2 + s;
6477
basisvalues[rr] *= std::sqrt((0.500000000000000 + r)*(1.000000000000000 + r + s));
6478
}// end loop over 's'
6479
}// end loop over 'r'
6480
6481
// Table(s) of coefficients.
6482
static const double coefficients0[3] = \
6483
{0.471404520791032, 0.288675134594813, -0.166666666666667};
6484
6485
// Tables of derivatives of the polynomial base (transpose).
6486
static const double dmats0[3][3] = \
6487
{{0.000000000000000, 0.000000000000000, 0.000000000000000},
6488
{4.898979485566356, 0.000000000000000, 0.000000000000000},
6489
{0.000000000000000, 0.000000000000000, 0.000000000000000}};
6490
6491
static const double dmats1[3][3] = \
6492
{{0.000000000000000, 0.000000000000000, 0.000000000000000},
6493
{2.449489742783178, 0.000000000000000, 0.000000000000000},
6494
{4.242640687119285, 0.000000000000000, 0.000000000000000}};
6495
6496
// Compute reference derivatives.
6497
// Declare pointer to array of derivatives on FIAT element.
6498
double *derivatives = new double[num_derivatives];
6499
for (unsigned int r = 0; r < num_derivatives; r++)
6500
{
6501
derivatives[r] = 0.000000000000000;
6502
}// end loop over 'r'
6503
6504
// Declare derivative matrix (of polynomial basis).
6505
double dmats[3][3] = \
6506
{{1.000000000000000, 0.000000000000000, 0.000000000000000},
6507
{0.000000000000000, 1.000000000000000, 0.000000000000000},
6508
{0.000000000000000, 0.000000000000000, 1.000000000000000}};
6509
6510
// Declare (auxiliary) derivative matrix (of polynomial basis).
6511
double dmats_old[3][3] = \
6512
{{1.000000000000000, 0.000000000000000, 0.000000000000000},
6513
{0.000000000000000, 1.000000000000000, 0.000000000000000},
6514
{0.000000000000000, 0.000000000000000, 1.000000000000000}};
6515
6516
// Loop possible derivatives.
6517
for (unsigned int r = 0; r < num_derivatives; r++)
6518
{
6519
// Resetting dmats values to compute next derivative.
6520
for (unsigned int t = 0; t < 3; t++)
6521
{
6522
for (unsigned int u = 0; u < 3; u++)
6523
{
6524
dmats[t][u] = 0.000000000000000;
6525
if (t == u)
6526
{
6527
dmats[t][u] = 1.000000000000000;
6528
}
6529
6530
}// end loop over 'u'
6531
}// end loop over 't'
6532
6533
// Looping derivative order to generate dmats.
6534
for (unsigned int s = 0; s < n; s++)
6535
{
6536
// Updating dmats_old with new values and resetting dmats.
6537
for (unsigned int t = 0; t < 3; t++)
6538
{
6539
for (unsigned int u = 0; u < 3; u++)
6540
{
6541
dmats_old[t][u] = dmats[t][u];
6542
dmats[t][u] = 0.000000000000000;
6543
}// end loop over 'u'
6544
}// end loop over 't'
6545
6546
// Update dmats using an inner product.
6547
if (combinations[r][s] == 0)
6548
{
6549
for (unsigned int t = 0; t < 3; t++)
6550
{
6551
for (unsigned int u = 0; u < 3; u++)
6552
{
6553
for (unsigned int tu = 0; tu < 3; tu++)
6554
{
6555
dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
6556
}// end loop over 'tu'
6557
}// end loop over 'u'
6558
}// end loop over 't'
6559
}
6560
6561
if (combinations[r][s] == 1)
6562
{
6563
for (unsigned int t = 0; t < 3; t++)
6564
{
6565
for (unsigned int u = 0; u < 3; u++)
6566
{
6567
for (unsigned int tu = 0; tu < 3; tu++)
6568
{
6569
dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
6570
}// end loop over 'tu'
6571
}// end loop over 'u'
6572
}// end loop over 't'
6573
}
6574
6575
}// end loop over 's'
6576
for (unsigned int s = 0; s < 3; s++)
6577
{
6578
for (unsigned int t = 0; t < 3; t++)
6579
{
6580
derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
6581
}// end loop over 't'
6582
}// end loop over 's'
6583
}// end loop over 'r'
6584
6585
// Transform derivatives back to physical element
6586
for (unsigned int r = 0; r < num_derivatives; r++)
6587
{
6588
for (unsigned int s = 0; s < num_derivatives; s++)
6589
{
6590
values[r] += transform[r][s]*derivatives[s];
6591
}// end loop over 's'
6592
}// end loop over 'r'
6593
6594
// Delete pointer to array of derivatives on FIAT element
6595
delete [] derivatives;
6596
6597
// Delete pointer to array of combinations of derivatives and transform
6598
for (unsigned int r = 0; r < num_derivatives; r++)
6599
{
6600
delete [] combinations[r];
6601
}// end loop over 'r'
6602
delete [] combinations;
6603
for (unsigned int r = 0; r < num_derivatives; r++)
6604
{
6605
delete [] transform[r];
6606
}// end loop over 'r'
6607
delete [] transform;
6608
break;
6609
}
6610
case 2:
6611
{
6612
6613
// Array of basisvalues.
6614
double basisvalues[3] = {0.000000000000000, 0.000000000000000, 0.000000000000000};
6615
6616
// Declare helper variables.
6617
unsigned int rr = 0;
6618
unsigned int ss = 0;
6619
double tmp0 = (1.000000000000000 + Y + 2.000000000000000*X)/2.000000000000000;
6620
6621
// Compute basisvalues.
6622
basisvalues[0] = 1.000000000000000;
6623
basisvalues[1] = tmp0;
6624
for (unsigned int r = 0; r < 1; r++)
6625
{
6626
rr = (r + 1)*(r + 1 + 1)/2 + 1;
6627
ss = r*(r + 1)/2;
6628
basisvalues[rr] = basisvalues[ss]*(0.500000000000000 + r + Y*(1.500000000000000 + r));
6629
}// end loop over 'r'
6630
for (unsigned int r = 0; r < 2; r++)
6631
{
6632
for (unsigned int s = 0; s < 2 - r; s++)
6633
{
6634
rr = (r + s)*(r + s + 1)/2 + s;
6635
basisvalues[rr] *= std::sqrt((0.500000000000000 + r)*(1.000000000000000 + r + s));
6636
}// end loop over 's'
6637
}// end loop over 'r'
6638
6639
// Table(s) of coefficients.
6640
static const double coefficients0[3] = \
6641
{0.471404520791032, 0.000000000000000, 0.333333333333333};
6642
6643
// Tables of derivatives of the polynomial base (transpose).
6644
static const double dmats0[3][3] = \
6645
{{0.000000000000000, 0.000000000000000, 0.000000000000000},
6646
{4.898979485566356, 0.000000000000000, 0.000000000000000},
6647
{0.000000000000000, 0.000000000000000, 0.000000000000000}};
6648
6649
static const double dmats1[3][3] = \
6650
{{0.000000000000000, 0.000000000000000, 0.000000000000000},
6651
{2.449489742783178, 0.000000000000000, 0.000000000000000},
6652
{4.242640687119285, 0.000000000000000, 0.000000000000000}};
6653
6654
// Compute reference derivatives.
6655
// Declare pointer to array of derivatives on FIAT element.
6656
double *derivatives = new double[num_derivatives];
6657
for (unsigned int r = 0; r < num_derivatives; r++)
6658
{
6659
derivatives[r] = 0.000000000000000;
6660
}// end loop over 'r'
6661
6662
// Declare derivative matrix (of polynomial basis).
6663
double dmats[3][3] = \
6664
{{1.000000000000000, 0.000000000000000, 0.000000000000000},
6665
{0.000000000000000, 1.000000000000000, 0.000000000000000},
6666
{0.000000000000000, 0.000000000000000, 1.000000000000000}};
6667
6668
// Declare (auxiliary) derivative matrix (of polynomial basis).
6669
double dmats_old[3][3] = \
6670
{{1.000000000000000, 0.000000000000000, 0.000000000000000},
6671
{0.000000000000000, 1.000000000000000, 0.000000000000000},
6672
{0.000000000000000, 0.000000000000000, 1.000000000000000}};
6673
6674
// Loop possible derivatives.
6675
for (unsigned int r = 0; r < num_derivatives; r++)
6676
{
6677
// Resetting dmats values to compute next derivative.
6678
for (unsigned int t = 0; t < 3; t++)
6679
{
6680
for (unsigned int u = 0; u < 3; u++)
6681
{
6682
dmats[t][u] = 0.000000000000000;
6683
if (t == u)
6684
{
6685
dmats[t][u] = 1.000000000000000;
6686
}
6687
6688
}// end loop over 'u'
6689
}// end loop over 't'
6690
6691
// Looping derivative order to generate dmats.
6692
for (unsigned int s = 0; s < n; s++)
6693
{
6694
// Updating dmats_old with new values and resetting dmats.
6695
for (unsigned int t = 0; t < 3; t++)
6696
{
6697
for (unsigned int u = 0; u < 3; u++)
6698
{
6699
dmats_old[t][u] = dmats[t][u];
6700
dmats[t][u] = 0.000000000000000;
6701
}// end loop over 'u'
6702
}// end loop over 't'
6703
6704
// Update dmats using an inner product.
6705
if (combinations[r][s] == 0)
6706
{
6707
for (unsigned int t = 0; t < 3; t++)
6708
{
6709
for (unsigned int u = 0; u < 3; u++)
6710
{
6711
for (unsigned int tu = 0; tu < 3; tu++)
6712
{
6713
dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
6714
}// end loop over 'tu'
6715
}// end loop over 'u'
6716
}// end loop over 't'
6717
}
6718
6719
if (combinations[r][s] == 1)
6720
{
6721
for (unsigned int t = 0; t < 3; t++)
6722
{
6723
for (unsigned int u = 0; u < 3; u++)
6724
{
6725
for (unsigned int tu = 0; tu < 3; tu++)
6726
{
6727
dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
6728
}// end loop over 'tu'
6729
}// end loop over 'u'
6730
}// end loop over 't'
6731
}
6732
6733
}// end loop over 's'
6734
for (unsigned int s = 0; s < 3; s++)
6735
{
6736
for (unsigned int t = 0; t < 3; t++)
6737
{
6738
derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
6739
}// end loop over 't'
6740
}// end loop over 's'
6741
}// end loop over 'r'
6742
6743
// Transform derivatives back to physical element
6744
for (unsigned int r = 0; r < num_derivatives; r++)
6745
{
6746
for (unsigned int s = 0; s < num_derivatives; s++)
6747
{
6748
values[r] += transform[r][s]*derivatives[s];
6749
}// end loop over 's'
6750
}// end loop over 'r'
6751
6752
// Delete pointer to array of derivatives on FIAT element
6753
delete [] derivatives;
6754
6755
// Delete pointer to array of combinations of derivatives and transform
6756
for (unsigned int r = 0; r < num_derivatives; r++)
6757
{
6758
delete [] combinations[r];
6759
}// end loop over 'r'
6760
delete [] combinations;
6761
for (unsigned int r = 0; r < num_derivatives; r++)
6762
{
6763
delete [] transform[r];
6764
}// end loop over 'r'
6765
delete [] transform;
6766
break;
6767
}
6768
}
6769
6770
}
6771
6772
/// Evaluate order n derivatives of all basis functions at given point in cell
6773
virtual void evaluate_basis_derivatives_all(unsigned int n,
6774
double* values,
6775
const double* coordinates,
6776
const ufc::cell& c) const
6777
{
6778
// Compute number of derivatives.
6779
unsigned int num_derivatives = 1;
6780
for (unsigned int r = 0; r < n; r++)
6781
{
6782
num_derivatives *= 2;
6783
}// end loop over 'r'
6784
6785
// Helper variable to hold values of a single dof.
6786
double *dof_values = new double[num_derivatives];
6787
for (unsigned int r = 0; r < num_derivatives; r++)
6788
{
6789
dof_values[r] = 0.000000000000000;
6790
}// end loop over 'r'
6791
6792
// Loop dofs and call evaluate_basis_derivatives.
6793
for (unsigned int r = 0; r < 3; r++)
6794
{
6795
evaluate_basis_derivatives(r, n, dof_values, coordinates, c);
6796
for (unsigned int s = 0; s < num_derivatives; s++)
6797
{
6798
values[r*num_derivatives + s] = dof_values[s];
6799
}// end loop over 's'
6800
}// end loop over 'r'
6801
6802
// Delete pointer.
6803
delete [] dof_values;
6804
}
6805
6806
/// Evaluate linear functional for dof i on the function f
6807
virtual double evaluate_dof(unsigned int i,
6808
const ufc::function& f,
6809
const ufc::cell& c) const
6810
{
6811
// Declare variables for result of evaluation.
6812
double vals[1];
6813
6814
// Declare variable for physical coordinates.
6815
double y[2];
6816
const double * const * x = c.coordinates;
6817
switch (i)
6818
{
6819
case 0:
6820
{
6821
y[0] = x[0][0];
6822
y[1] = x[0][1];
6823
f.evaluate(vals, y, c);
6824
return vals[0];
6825
break;
6826
}
6827
case 1:
6828
{
6829
y[0] = x[1][0];
6830
y[1] = x[1][1];
6831
f.evaluate(vals, y, c);
6832
return vals[0];
6833
break;
6834
}
6835
case 2:
6836
{
6837
y[0] = x[2][0];
6838
y[1] = x[2][1];
6839
f.evaluate(vals, y, c);
6840
return vals[0];
6841
break;
6842
}
6843
}
6844
6845
return 0.000000000000000;
6846
}
6847
6848
/// Evaluate linear functionals for all dofs on the function f
6849
virtual void evaluate_dofs(double* values,
6850
const ufc::function& f,
6851
const ufc::cell& c) const
6852
{
6853
// Declare variables for result of evaluation.
6854
double vals[1];
6855
6856
// Declare variable for physical coordinates.
6857
double y[2];
6858
const double * const * x = c.coordinates;
6859
y[0] = x[0][0];
6860
y[1] = x[0][1];
6861
f.evaluate(vals, y, c);
6862
values[0] = vals[0];
6863
y[0] = x[1][0];
6864
y[1] = x[1][1];
6865
f.evaluate(vals, y, c);
6866
values[1] = vals[0];
6867
y[0] = x[2][0];
6868
y[1] = x[2][1];
6869
f.evaluate(vals, y, c);
6870
values[2] = vals[0];
6871
}
6872
6873
/// Interpolate vertex values from dof values
6874
virtual void interpolate_vertex_values(double* vertex_values,
6875
const double* dof_values,
6876
const ufc::cell& c) const
6877
{
6878
// Evaluate function and change variables
6879
vertex_values[0] = dof_values[0];
6880
vertex_values[1] = dof_values[1];
6881
vertex_values[2] = dof_values[2];
6882
}
6883
6884
/// Map coordinate xhat from reference cell to coordinate x in cell
6885
virtual void map_from_reference_cell(double* x,
6886
const double* xhat,
6887
const ufc::cell& c)
6888
{
6889
throw std::runtime_error("map_from_reference_cell not yet implemented (introduced in UFC 2.0).");
6890
}
6891
6892
/// Map from coordinate x in cell to coordinate xhat in reference cell
6893
virtual void map_to_reference_cell(double* xhat,
6894
const double* x,
6895
const ufc::cell& c)
6896
{
6897
throw std::runtime_error("map_to_reference_cell not yet implemented (introduced in UFC 2.0).");
6898
}
6899
6900
/// Return the number of sub elements (for a mixed element)
6901
virtual unsigned int num_sub_elements() const
6902
{
6903
return 0;
6904
}
6905
6906
/// Create a new finite element for sub element i (for a mixed element)
6907
virtual ufc::finite_element* create_sub_element(unsigned int i) const
6908
{
6909
return 0;
6910
}
6911
6912
/// Create a new class instance
6913
virtual ufc::finite_element* create() const
6914
{
6915
return new adaptivepoisson_finite_element_5();
6916
}
6917
6918
};
6919
6920
/// This class defines the interface for a local-to-global mapping of
6921
/// degrees of freedom (dofs).
6922
6923
class adaptivepoisson_dofmap_0: public ufc::dofmap
6924
{
6925
private:
6926
6927
unsigned int _global_dimension;
6928
public:
6929
6930
/// Constructor
6931
adaptivepoisson_dofmap_0() : ufc::dofmap()
6932
{
6933
_global_dimension = 0;
6934
}
6935
6936
/// Destructor
6937
virtual ~adaptivepoisson_dofmap_0()
6938
{
6939
// Do nothing
6940
}
6941
6942
/// Return a string identifying the dofmap
6943
virtual const char* signature() const
6944
{
6945
return "FFC dofmap for FiniteElement('Discontinuous Lagrange', Cell('triangle', 1, Space(2)), 0)";
6946
}
6947
6948
/// Return true iff mesh entities of topological dimension d are needed
6949
virtual bool needs_mesh_entities(unsigned int d) const
6950
{
6951
switch (d)
6952
{
6953
case 0:
6954
{
6955
return false;
6956
break;
6957
}
6958
case 1:
6959
{
6960
return false;
6961
break;
6962
}
6963
case 2:
6964
{
6965
return true;
6966
break;
6967
}
6968
}
6969
6970
return false;
6971
}
6972
6973
/// Initialize dofmap for mesh (return true iff init_cell() is needed)
6974
virtual bool init_mesh(const ufc::mesh& m)
6975
{
6976
_global_dimension = m.num_entities[2];
6977
return false;
6978
}
6979
6980
/// Initialize dofmap for given cell
6981
virtual void init_cell(const ufc::mesh& m,
6982
const ufc::cell& c)
6983
{
6984
// Do nothing
6985
}
6986
6987
/// Finish initialization of dofmap for cells
6988
virtual void init_cell_finalize()
6989
{
6990
// Do nothing
6991
}
6992
6993
/// Return the topological dimension of the associated cell shape
6994
virtual unsigned int topological_dimension() const
6995
{
6996
return 2;
6997
}
6998
6999
/// Return the geometric dimension of the associated cell shape
7000
virtual unsigned int geometric_dimension() const
7001
{
7002
return 2;
7003
}
7004
7005
/// Return the dimension of the global finite element function space
7006
virtual unsigned int global_dimension() const
7007
{
7008
return _global_dimension;
7009
}
7010
7011
/// Return the dimension of the local finite element function space for a cell
7012
virtual unsigned int local_dimension(const ufc::cell& c) const
7013
{
7014
return 1;
7015
}
7016
7017
/// Return the maximum dimension of the local finite element function space
7018
virtual unsigned int max_local_dimension() const
7019
{
7020
return 1;
7021
}
7022
7023
/// Return the number of dofs on each cell facet
7024
virtual unsigned int num_facet_dofs() const
7025
{
7026
return 0;
7027
}
7028
7029
/// Return the number of dofs associated with each cell entity of dimension d
7030
virtual unsigned int num_entity_dofs(unsigned int d) const
7031
{
7032
switch (d)
7033
{
7034
case 0:
7035
{
7036
return 0;
7037
break;
7038
}
7039
case 1:
7040
{
7041
return 0;
7042
break;
7043
}
7044
case 2:
7045
{
7046
return 1;
7047
break;
7048
}
7049
}
7050
7051
return 0;
7052
}
7053
7054
/// Tabulate the local-to-global mapping of dofs on a cell
7055
virtual void tabulate_dofs(unsigned int* dofs,
7056
const ufc::mesh& m,
7057
const ufc::cell& c) const
7058
{
7059
dofs[0] = c.entity_indices[2][0];
7060
}
7061
7062
/// Tabulate the local-to-local mapping from facet dofs to cell dofs
7063
virtual void tabulate_facet_dofs(unsigned int* dofs,
7064
unsigned int facet) const
7065
{
7066
switch (facet)
7067
{
7068
case 0:
7069
{
7070
7071
break;
7072
}
7073
case 1:
7074
{
7075
7076
break;
7077
}
7078
case 2:
7079
{
7080
7081
break;
7082
}
7083
}
7084
7085
}
7086
7087
/// Tabulate the local-to-local mapping of dofs on entity (d, i)
7088
virtual void tabulate_entity_dofs(unsigned int* dofs,
7089
unsigned int d, unsigned int i) const
7090
{
7091
if (d > 2)
7092
{
7093
throw std::runtime_error("d is larger than dimension (2)");
7094
}
7095
7096
switch (d)
7097
{
7098
case 0:
7099
{
7100
7101
break;
7102
}
7103
case 1:
7104
{
7105
7106
break;
7107
}
7108
case 2:
7109
{
7110
if (i > 0)
7111
{
7112
throw std::runtime_error("i is larger than number of entities (0)");
7113
}
7114
7115
dofs[0] = 0;
7116
break;
7117
}
7118
}
7119
7120
}
7121
7122
/// Tabulate the coordinates of all dofs on a cell
7123
virtual void tabulate_coordinates(double** coordinates,
7124
const ufc::cell& c) const
7125
{
7126
const double * const * x = c.coordinates;
7127
7128
coordinates[0][0] = 0.333333333333333*x[0][0] + 0.333333333333333*x[1][0] + 0.333333333333333*x[2][0];
7129
coordinates[0][1] = 0.333333333333333*x[0][1] + 0.333333333333333*x[1][1] + 0.333333333333333*x[2][1];
7130
}
7131
7132
/// Return the number of sub dofmaps (for a mixed element)
7133
virtual unsigned int num_sub_dofmaps() const
7134
{
7135
return 0;
7136
}
7137
7138
/// Create a new dofmap for sub dofmap i (for a mixed element)
7139
virtual ufc::dofmap* create_sub_dofmap(unsigned int i) const
7140
{
7141
return 0;
7142
}
7143
7144
/// Create a new class instance
7145
virtual ufc::dofmap* create() const
7146
{
7147
return new adaptivepoisson_dofmap_0();
7148
}
7149
7150
};
7151
7152
/// This class defines the interface for a local-to-global mapping of
7153
/// degrees of freedom (dofs).
7154
7155
class adaptivepoisson_dofmap_1: public ufc::dofmap
7156
{
7157
private:
7158
7159
unsigned int _global_dimension;
7160
public:
7161
7162
/// Constructor
7163
adaptivepoisson_dofmap_1() : ufc::dofmap()
7164
{
7165
_global_dimension = 0;
7166
}
7167
7168
/// Destructor
7169
virtual ~adaptivepoisson_dofmap_1()
7170
{
7171
// Do nothing
7172
}
7173
7174
/// Return a string identifying the dofmap
7175
virtual const char* signature() const
7176
{
7177
return "FFC dofmap for FiniteElement('Lagrange', Cell('triangle', 1, Space(2)), 2)";
7178
}
7179
7180
/// Return true iff mesh entities of topological dimension d are needed
7181
virtual bool needs_mesh_entities(unsigned int d) const
7182
{
7183
switch (d)
7184
{
7185
case 0:
7186
{
7187
return true;
7188
break;
7189
}
7190
case 1:
7191
{
7192
return true;
7193
break;
7194
}
7195
case 2:
7196
{
7197
return false;
7198
break;
7199
}
7200
}
7201
7202
return false;
7203
}
7204
7205
/// Initialize dofmap for mesh (return true iff init_cell() is needed)
7206
virtual bool init_mesh(const ufc::mesh& m)
7207
{
7208
_global_dimension = m.num_entities[0] + m.num_entities[1];
7209
return false;
7210
}
7211
7212
/// Initialize dofmap for given cell
7213
virtual void init_cell(const ufc::mesh& m,
7214
const ufc::cell& c)
7215
{
7216
// Do nothing
7217
}
7218
7219
/// Finish initialization of dofmap for cells
7220
virtual void init_cell_finalize()
7221
{
7222
// Do nothing
7223
}
7224
7225
/// Return the topological dimension of the associated cell shape
7226
virtual unsigned int topological_dimension() const
7227
{
7228
return 2;
7229
}
7230
7231
/// Return the geometric dimension of the associated cell shape
7232
virtual unsigned int geometric_dimension() const
7233
{
7234
return 2;
7235
}
7236
7237
/// Return the dimension of the global finite element function space
7238
virtual unsigned int global_dimension() const
7239
{
7240
return _global_dimension;
7241
}
7242
7243
/// Return the dimension of the local finite element function space for a cell
7244
virtual unsigned int local_dimension(const ufc::cell& c) const
7245
{
7246
return 6;
7247
}
7248
7249
/// Return the maximum dimension of the local finite element function space
7250
virtual unsigned int max_local_dimension() const
7251
{
7252
return 6;
7253
}
7254
7255
/// Return the number of dofs on each cell facet
7256
virtual unsigned int num_facet_dofs() const
7257
{
7258
return 3;
7259
}
7260
7261
/// Return the number of dofs associated with each cell entity of dimension d
7262
virtual unsigned int num_entity_dofs(unsigned int d) const
7263
{
7264
switch (d)
7265
{
7266
case 0:
7267
{
7268
return 1;
7269
break;
7270
}
7271
case 1:
7272
{
7273
return 1;
7274
break;
7275
}
7276
case 2:
7277
{
7278
return 0;
7279
break;
7280
}
7281
}
7282
7283
return 0;
7284
}
7285
7286
/// Tabulate the local-to-global mapping of dofs on a cell
7287
virtual void tabulate_dofs(unsigned int* dofs,
7288
const ufc::mesh& m,
7289
const ufc::cell& c) const
7290
{
7291
unsigned int offset = 0;
7292
dofs[0] = offset + c.entity_indices[0][0];
7293
dofs[1] = offset + c.entity_indices[0][1];
7294
dofs[2] = offset + c.entity_indices[0][2];
7295
offset += m.num_entities[0];
7296
dofs[3] = offset + c.entity_indices[1][0];
7297
dofs[4] = offset + c.entity_indices[1][1];
7298
dofs[5] = offset + c.entity_indices[1][2];
7299
offset += m.num_entities[1];
7300
}
7301
7302
/// Tabulate the local-to-local mapping from facet dofs to cell dofs
7303
virtual void tabulate_facet_dofs(unsigned int* dofs,
7304
unsigned int facet) const
7305
{
7306
switch (facet)
7307
{
7308
case 0:
7309
{
7310
dofs[0] = 1;
7311
dofs[1] = 2;
7312
dofs[2] = 3;
7313
break;
7314
}
7315
case 1:
7316
{
7317
dofs[0] = 0;
7318
dofs[1] = 2;
7319
dofs[2] = 4;
7320
break;
7321
}
7322
case 2:
7323
{
7324
dofs[0] = 0;
7325
dofs[1] = 1;
7326
dofs[2] = 5;
7327
break;
7328
}
7329
}
7330
7331
}
7332
7333
/// Tabulate the local-to-local mapping of dofs on entity (d, i)
7334
virtual void tabulate_entity_dofs(unsigned int* dofs,
7335
unsigned int d, unsigned int i) const
7336
{
7337
if (d > 2)
7338
{
7339
throw std::runtime_error("d is larger than dimension (2)");
7340
}
7341
7342
switch (d)
7343
{
7344
case 0:
7345
{
7346
if (i > 2)
7347
{
7348
throw std::runtime_error("i is larger than number of entities (2)");
7349
}
7350
7351
switch (i)
7352
{
7353
case 0:
7354
{
7355
dofs[0] = 0;
7356
break;
7357
}
7358
case 1:
7359
{
7360
dofs[0] = 1;
7361
break;
7362
}
7363
case 2:
7364
{
7365
dofs[0] = 2;
7366
break;
7367
}
7368
}
7369
7370
break;
7371
}
7372
case 1:
7373
{
7374
if (i > 2)
7375
{
7376
throw std::runtime_error("i is larger than number of entities (2)");
7377
}
7378
7379
switch (i)
7380
{
7381
case 0:
7382
{
7383
dofs[0] = 3;
7384
break;
7385
}
7386
case 1:
7387
{
7388
dofs[0] = 4;
7389
break;
7390
}
7391
case 2:
7392
{
7393
dofs[0] = 5;
7394
break;
7395
}
7396
}
7397
7398
break;
7399
}
7400
case 2:
7401
{
7402
7403
break;
7404
}
7405
}
7406
7407
}
7408
7409
/// Tabulate the coordinates of all dofs on a cell
7410
virtual void tabulate_coordinates(double** coordinates,
7411
const ufc::cell& c) const
7412
{
7413
const double * const * x = c.coordinates;
7414
7415
coordinates[0][0] = x[0][0];
7416
coordinates[0][1] = x[0][1];
7417
coordinates[1][0] = x[1][0];
7418
coordinates[1][1] = x[1][1];
7419
coordinates[2][0] = x[2][0];
7420
coordinates[2][1] = x[2][1];
7421
coordinates[3][0] = 0.500000000000000*x[1][0] + 0.500000000000000*x[2][0];
7422
coordinates[3][1] = 0.500000000000000*x[1][1] + 0.500000000000000*x[2][1];
7423
coordinates[4][0] = 0.500000000000000*x[0][0] + 0.500000000000000*x[2][0];
7424
coordinates[4][1] = 0.500000000000000*x[0][1] + 0.500000000000000*x[2][1];
7425
coordinates[5][0] = 0.500000000000000*x[0][0] + 0.500000000000000*x[1][0];
7426
coordinates[5][1] = 0.500000000000000*x[0][1] + 0.500000000000000*x[1][1];
7427
}
7428
7429
/// Return the number of sub dofmaps (for a mixed element)
7430
virtual unsigned int num_sub_dofmaps() const
7431
{
7432
return 0;
7433
}
7434
7435
/// Create a new dofmap for sub dofmap i (for a mixed element)
7436
virtual ufc::dofmap* create_sub_dofmap(unsigned int i) const
7437
{
7438
return 0;
7439
}
7440
7441
/// Create a new class instance
7442
virtual ufc::dofmap* create() const
7443
{
7444
return new adaptivepoisson_dofmap_1();
7445
}
7446
7447
};
7448
7449
/// This class defines the interface for a local-to-global mapping of
7450
/// degrees of freedom (dofs).
7451
7452
class adaptivepoisson_dofmap_2: public ufc::dofmap
7453
{
7454
private:
7455
7456
unsigned int _global_dimension;
7457
public:
7458
7459
/// Constructor
7460
adaptivepoisson_dofmap_2() : ufc::dofmap()
7461
{
7462
_global_dimension = 0;
7463
}
7464
7465
/// Destructor
7466
virtual ~adaptivepoisson_dofmap_2()
7467
{
7468
// Do nothing
7469
}
7470
7471
/// Return a string identifying the dofmap
7472
virtual const char* signature() const
7473
{
7474
return "FFC dofmap for FiniteElement('Discontinuous Lagrange', Cell('triangle', 1, Space(2)), 2)";
7475
}
7476
7477
/// Return true iff mesh entities of topological dimension d are needed
7478
virtual bool needs_mesh_entities(unsigned int d) const
7479
{
7480
switch (d)
7481
{
7482
case 0:
7483
{
7484
return false;
7485
break;
7486
}
7487
case 1:
7488
{
7489
return false;
7490
break;
7491
}
7492
case 2:
7493
{
7494
return true;
7495
break;
7496
}
7497
}
7498
7499
return false;
7500
}
7501
7502
/// Initialize dofmap for mesh (return true iff init_cell() is needed)
7503
virtual bool init_mesh(const ufc::mesh& m)
7504
{
7505
_global_dimension = 6.000000000000000*m.num_entities[2];
7506
return false;
7507
}
7508
7509
/// Initialize dofmap for given cell
7510
virtual void init_cell(const ufc::mesh& m,
7511
const ufc::cell& c)
7512
{
7513
// Do nothing
7514
}
7515
7516
/// Finish initialization of dofmap for cells
7517
virtual void init_cell_finalize()
7518
{
7519
// Do nothing
7520
}
7521
7522
/// Return the topological dimension of the associated cell shape
7523
virtual unsigned int topological_dimension() const
7524
{
7525
return 2;
7526
}
7527
7528
/// Return the geometric dimension of the associated cell shape
7529
virtual unsigned int geometric_dimension() const
7530
{
7531
return 2;
7532
}
7533
7534
/// Return the dimension of the global finite element function space
7535
virtual unsigned int global_dimension() const
7536
{
7537
return _global_dimension;
7538
}
7539
7540
/// Return the dimension of the local finite element function space for a cell
7541
virtual unsigned int local_dimension(const ufc::cell& c) const
7542
{
7543
return 6;
7544
}
7545
7546
/// Return the maximum dimension of the local finite element function space
7547
virtual unsigned int max_local_dimension() const
7548
{
7549
return 6;
7550
}
7551
7552
/// Return the number of dofs on each cell facet
7553
virtual unsigned int num_facet_dofs() const
7554
{
7555
return 0;
7556
}
7557
7558
/// Return the number of dofs associated with each cell entity of dimension d
7559
virtual unsigned int num_entity_dofs(unsigned int d) const
7560
{
7561
switch (d)
7562
{
7563
case 0:
7564
{
7565
return 0;
7566
break;
7567
}
7568
case 1:
7569
{
7570
return 0;
7571
break;
7572
}
7573
case 2:
7574
{
7575
return 6;
7576
break;
7577
}
7578
}
7579
7580
return 0;
7581
}
7582
7583
/// Tabulate the local-to-global mapping of dofs on a cell
7584
virtual void tabulate_dofs(unsigned int* dofs,
7585
const ufc::mesh& m,
7586
const ufc::cell& c) const
7587
{
7588
dofs[0] = 6*c.entity_indices[2][0];
7589
dofs[1] = 6*c.entity_indices[2][0] + 1;
7590
dofs[2] = 6*c.entity_indices[2][0] + 2;
7591
dofs[3] = 6*c.entity_indices[2][0] + 3;
7592
dofs[4] = 6*c.entity_indices[2][0] + 4;
7593
dofs[5] = 6*c.entity_indices[2][0] + 5;
7594
}
7595
7596
/// Tabulate the local-to-local mapping from facet dofs to cell dofs
7597
virtual void tabulate_facet_dofs(unsigned int* dofs,
7598
unsigned int facet) const
7599
{
7600
switch (facet)
7601
{
7602
case 0:
7603
{
7604
7605
break;
7606
}
7607
case 1:
7608
{
7609
7610
break;
7611
}
7612
case 2:
7613
{
7614
7615
break;
7616
}
7617
}
7618
7619
}
7620
7621
/// Tabulate the local-to-local mapping of dofs on entity (d, i)
7622
virtual void tabulate_entity_dofs(unsigned int* dofs,
7623
unsigned int d, unsigned int i) const
7624
{
7625
if (d > 2)
7626
{
7627
throw std::runtime_error("d is larger than dimension (2)");
7628
}
7629
7630
switch (d)
7631
{
7632
case 0:
7633
{
7634
7635
break;
7636
}
7637
case 1:
7638
{
7639
7640
break;
7641
}
7642
case 2:
7643
{
7644
if (i > 0)
7645
{
7646
throw std::runtime_error("i is larger than number of entities (0)");
7647
}
7648
7649
dofs[0] = 0;
7650
dofs[1] = 1;
7651
dofs[2] = 2;
7652
dofs[3] = 3;
7653
dofs[4] = 4;
7654
dofs[5] = 5;
7655
break;
7656
}
7657
}
7658
7659
}
7660
7661
/// Tabulate the coordinates of all dofs on a cell
7662
virtual void tabulate_coordinates(double** coordinates,
7663
const ufc::cell& c) const
7664
{
7665
const double * const * x = c.coordinates;
7666
7667
coordinates[0][0] = x[0][0];
7668
coordinates[0][1] = x[0][1];
7669
coordinates[1][0] = x[1][0];
7670
coordinates[1][1] = x[1][1];
7671
coordinates[2][0] = x[2][0];
7672
coordinates[2][1] = x[2][1];
7673
coordinates[3][0] = 0.500000000000000*x[1][0] + 0.500000000000000*x[2][0];
7674
coordinates[3][1] = 0.500000000000000*x[1][1] + 0.500000000000000*x[2][1];
7675
coordinates[4][0] = 0.500000000000000*x[0][0] + 0.500000000000000*x[2][0];
7676
coordinates[4][1] = 0.500000000000000*x[0][1] + 0.500000000000000*x[2][1];
7677
coordinates[5][0] = 0.500000000000000*x[0][0] + 0.500000000000000*x[1][0];
7678
coordinates[5][1] = 0.500000000000000*x[0][1] + 0.500000000000000*x[1][1];
7679
}
7680
7681
/// Return the number of sub dofmaps (for a mixed element)
7682
virtual unsigned int num_sub_dofmaps() const
7683
{
7684
return 0;
7685
}
7686
7687
/// Create a new dofmap for sub dofmap i (for a mixed element)
7688
virtual ufc::dofmap* create_sub_dofmap(unsigned int i) const
7689
{
7690
return 0;
7691
}
7692
7693
/// Create a new class instance
7694
virtual ufc::dofmap* create() const
7695
{
7696
return new adaptivepoisson_dofmap_2();
7697
}
7698
7699
};
7700
7701
/// This class defines the interface for a local-to-global mapping of
7702
/// degrees of freedom (dofs).
7703
7704
class adaptivepoisson_dofmap_3: public ufc::dofmap
7705
{
7706
private:
7707
7708
unsigned int _global_dimension;
7709
public:
7710
7711
/// Constructor
7712
adaptivepoisson_dofmap_3() : ufc::dofmap()
7713
{
7714
_global_dimension = 0;
7715
}
7716
7717
/// Destructor
7718
virtual ~adaptivepoisson_dofmap_3()
7719
{
7720
// Do nothing
7721
}
7722
7723
/// Return a string identifying the dofmap
7724
virtual const char* signature() const
7725
{
7726
return "FFC dofmap for FiniteElement('Bubble', Cell('triangle', 1, Space(2)), 3)";
7727
}
7728
7729
/// Return true iff mesh entities of topological dimension d are needed
7730
virtual bool needs_mesh_entities(unsigned int d) const
7731
{
7732
switch (d)
7733
{
7734
case 0:
7735
{
7736
return false;
7737
break;
7738
}
7739
case 1:
7740
{
7741
return false;
7742
break;
7743
}
7744
case 2:
7745
{
7746
return true;
7747
break;
7748
}
7749
}
7750
7751
return false;
7752
}
7753
7754
/// Initialize dofmap for mesh (return true iff init_cell() is needed)
7755
virtual bool init_mesh(const ufc::mesh& m)
7756
{
7757
_global_dimension = m.num_entities[2];
7758
return false;
7759
}
7760
7761
/// Initialize dofmap for given cell
7762
virtual void init_cell(const ufc::mesh& m,
7763
const ufc::cell& c)
7764
{
7765
// Do nothing
7766
}
7767
7768
/// Finish initialization of dofmap for cells
7769
virtual void init_cell_finalize()
7770
{
7771
// Do nothing
7772
}
7773
7774
/// Return the topological dimension of the associated cell shape
7775
virtual unsigned int topological_dimension() const
7776
{
7777
return 2;
7778
}
7779
7780
/// Return the geometric dimension of the associated cell shape
7781
virtual unsigned int geometric_dimension() const
7782
{
7783
return 2;
7784
}
7785
7786
/// Return the dimension of the global finite element function space
7787
virtual unsigned int global_dimension() const
7788
{
7789
return _global_dimension;
7790
}
7791
7792
/// Return the dimension of the local finite element function space for a cell
7793
virtual unsigned int local_dimension(const ufc::cell& c) const
7794
{
7795
return 1;
7796
}
7797
7798
/// Return the maximum dimension of the local finite element function space
7799
virtual unsigned int max_local_dimension() const
7800
{
7801
return 1;
7802
}
7803
7804
/// Return the number of dofs on each cell facet
7805
virtual unsigned int num_facet_dofs() const
7806
{
7807
return 0;
7808
}
7809
7810
/// Return the number of dofs associated with each cell entity of dimension d
7811
virtual unsigned int num_entity_dofs(unsigned int d) const
7812
{
7813
switch (d)
7814
{
7815
case 0:
7816
{
7817
return 0;
7818
break;
7819
}
7820
case 1:
7821
{
7822
return 0;
7823
break;
7824
}
7825
case 2:
7826
{
7827
return 1;
7828
break;
7829
}
7830
}
7831
7832
return 0;
7833
}
7834
7835
/// Tabulate the local-to-global mapping of dofs on a cell
7836
virtual void tabulate_dofs(unsigned int* dofs,
7837
const ufc::mesh& m,
7838
const ufc::cell& c) const
7839
{
7840
dofs[0] = c.entity_indices[2][0];
7841
}
7842
7843
/// Tabulate the local-to-local mapping from facet dofs to cell dofs
7844
virtual void tabulate_facet_dofs(unsigned int* dofs,
7845
unsigned int facet) const
7846
{
7847
switch (facet)
7848
{
7849
case 0:
7850
{
7851
7852
break;
7853
}
7854
case 1:
7855
{
7856
7857
break;
7858
}
7859
case 2:
7860
{
7861
7862
break;
7863
}
7864
}
7865
7866
}
7867
7868
/// Tabulate the local-to-local mapping of dofs on entity (d, i)
7869
virtual void tabulate_entity_dofs(unsigned int* dofs,
7870
unsigned int d, unsigned int i) const
7871
{
7872
if (d > 2)
7873
{
7874
throw std::runtime_error("d is larger than dimension (2)");
7875
}
7876
7877
switch (d)
7878
{
7879
case 0:
7880
{
7881
7882
break;
7883
}
7884
case 1:
7885
{
7886
7887
break;
7888
}
7889
case 2:
7890
{
7891
if (i > 0)
7892
{
7893
throw std::runtime_error("i is larger than number of entities (0)");
7894
}
7895
7896
dofs[0] = 0;
7897
break;
7898
}
7899
}
7900
7901
}
7902
7903
/// Tabulate the coordinates of all dofs on a cell
7904
virtual void tabulate_coordinates(double** coordinates,
7905
const ufc::cell& c) const
7906
{
7907
const double * const * x = c.coordinates;
7908
7909
coordinates[0][0] = 0.333333333333333*x[0][0] + 0.333333333333333*x[1][0] + 0.333333333333333*x[2][0];
7910
coordinates[0][1] = 0.333333333333333*x[0][1] + 0.333333333333333*x[1][1] + 0.333333333333333*x[2][1];
7911
}
7912
7913
/// Return the number of sub dofmaps (for a mixed element)
7914
virtual unsigned int num_sub_dofmaps() const
7915
{
7916
return 0;
7917
}
7918
7919
/// Create a new dofmap for sub dofmap i (for a mixed element)
7920
virtual ufc::dofmap* create_sub_dofmap(unsigned int i) const
7921
{
7922
return 0;
7923
}
7924
7925
/// Create a new class instance
7926
virtual ufc::dofmap* create() const
7927
{
7928
return new adaptivepoisson_dofmap_3();
7929
}
7930
7931
};
7932
7933
/// This class defines the interface for a local-to-global mapping of
7934
/// degrees of freedom (dofs).
7935
7936
class adaptivepoisson_dofmap_4: public ufc::dofmap
7937
{
7938
private:
7939
7940
unsigned int _global_dimension;
7941
public:
7942
7943
/// Constructor
7944
adaptivepoisson_dofmap_4() : ufc::dofmap()
7945
{
7946
_global_dimension = 0;
7947
}
7948
7949
/// Destructor
7950
virtual ~adaptivepoisson_dofmap_4()
7951
{
7952
// Do nothing
7953
}
7954
7955
/// Return a string identifying the dofmap
7956
virtual const char* signature() const
7957
{
7958
return "FFC dofmap for FiniteElement('Discontinuous Lagrange', Cell('triangle', 1, Space(2)), 1)";
7959
}
7960
7961
/// Return true iff mesh entities of topological dimension d are needed
7962
virtual bool needs_mesh_entities(unsigned int d) const
7963
{
7964
switch (d)
7965
{
7966
case 0:
7967
{
7968
return false;
7969
break;
7970
}
7971
case 1:
7972
{
7973
return false;
7974
break;
7975
}
7976
case 2:
7977
{
7978
return true;
7979
break;
7980
}
7981
}
7982
7983
return false;
7984
}
7985
7986
/// Initialize dofmap for mesh (return true iff init_cell() is needed)
7987
virtual bool init_mesh(const ufc::mesh& m)
7988
{
7989
_global_dimension = 3.000000000000000*m.num_entities[2];
7990
return false;
7991
}
7992
7993
/// Initialize dofmap for given cell
7994
virtual void init_cell(const ufc::mesh& m,
7995
const ufc::cell& c)
7996
{
7997
// Do nothing
7998
}
7999
8000
/// Finish initialization of dofmap for cells
8001
virtual void init_cell_finalize()
8002
{
8003
// Do nothing
8004
}
8005
8006
/// Return the topological dimension of the associated cell shape
8007
virtual unsigned int topological_dimension() const
8008
{
8009
return 2;
8010
}
8011
8012
/// Return the geometric dimension of the associated cell shape
8013
virtual unsigned int geometric_dimension() const
8014
{
8015
return 2;
8016
}
8017
8018
/// Return the dimension of the global finite element function space
8019
virtual unsigned int global_dimension() const
8020
{
8021
return _global_dimension;
8022
}
8023
8024
/// Return the dimension of the local finite element function space for a cell
8025
virtual unsigned int local_dimension(const ufc::cell& c) const
8026
{
8027
return 3;
8028
}
8029
8030
/// Return the maximum dimension of the local finite element function space
8031
virtual unsigned int max_local_dimension() const
8032
{
8033
return 3;
8034
}
8035
8036
/// Return the number of dofs on each cell facet
8037
virtual unsigned int num_facet_dofs() const
8038
{
8039
return 0;
8040
}
8041
8042
/// Return the number of dofs associated with each cell entity of dimension d
8043
virtual unsigned int num_entity_dofs(unsigned int d) const
8044
{
8045
switch (d)
8046
{
8047
case 0:
8048
{
8049
return 0;
8050
break;
8051
}
8052
case 1:
8053
{
8054
return 0;
8055
break;
8056
}
8057
case 2:
8058
{
8059
return 3;
8060
break;
8061
}
8062
}
8063
8064
return 0;
8065
}
8066
8067
/// Tabulate the local-to-global mapping of dofs on a cell
8068
virtual void tabulate_dofs(unsigned int* dofs,
8069
const ufc::mesh& m,
8070
const ufc::cell& c) const
8071
{
8072
dofs[0] = 3*c.entity_indices[2][0];
8073
dofs[1] = 3*c.entity_indices[2][0] + 1;
8074
dofs[2] = 3*c.entity_indices[2][0] + 2;
8075
}
8076
8077
/// Tabulate the local-to-local mapping from facet dofs to cell dofs
8078
virtual void tabulate_facet_dofs(unsigned int* dofs,
8079
unsigned int facet) const
8080
{
8081
switch (facet)
8082
{
8083
case 0:
8084
{
8085
8086
break;
8087
}
8088
case 1:
8089
{
8090
8091
break;
8092
}
8093
case 2:
8094
{
8095
8096
break;
8097
}
8098
}
8099
8100
}
8101
8102
/// Tabulate the local-to-local mapping of dofs on entity (d, i)
8103
virtual void tabulate_entity_dofs(unsigned int* dofs,
8104
unsigned int d, unsigned int i) const
8105
{
8106
if (d > 2)
8107
{
8108
throw std::runtime_error("d is larger than dimension (2)");
8109
}
8110
8111
switch (d)
8112
{
8113
case 0:
8114
{
8115
8116
break;
8117
}
8118
case 1:
8119
{
8120
8121
break;
8122
}
8123
case 2:
8124
{
8125
if (i > 0)
8126
{
8127
throw std::runtime_error("i is larger than number of entities (0)");
8128
}
8129
8130
dofs[0] = 0;
8131
dofs[1] = 1;
8132
dofs[2] = 2;
8133
break;
8134
}
8135
}
8136
8137
}
8138
8139
/// Tabulate the coordinates of all dofs on a cell
8140
virtual void tabulate_coordinates(double** coordinates,
8141
const ufc::cell& c) const
8142
{
8143
const double * const * x = c.coordinates;
8144
8145
coordinates[0][0] = x[0][0];
8146
coordinates[0][1] = x[0][1];
8147
coordinates[1][0] = x[1][0];
8148
coordinates[1][1] = x[1][1];
8149
coordinates[2][0] = x[2][0];
8150
coordinates[2][1] = x[2][1];
8151
}
8152
8153
/// Return the number of sub dofmaps (for a mixed element)
8154
virtual unsigned int num_sub_dofmaps() const
8155
{
8156
return 0;
8157
}
8158
8159
/// Create a new dofmap for sub dofmap i (for a mixed element)
8160
virtual ufc::dofmap* create_sub_dofmap(unsigned int i) const
8161
{
8162
return 0;
8163
}
8164
8165
/// Create a new class instance
8166
virtual ufc::dofmap* create() const
8167
{
8168
return new adaptivepoisson_dofmap_4();
8169
}
8170
8171
};
8172
8173
/// This class defines the interface for a local-to-global mapping of
8174
/// degrees of freedom (dofs).
8175
8176
class adaptivepoisson_dofmap_5: public ufc::dofmap
8177
{
8178
private:
8179
8180
unsigned int _global_dimension;
8181
public:
8182
8183
/// Constructor
8184
adaptivepoisson_dofmap_5() : ufc::dofmap()
8185
{
8186
_global_dimension = 0;
8187
}
8188
8189
/// Destructor
8190
virtual ~adaptivepoisson_dofmap_5()
8191
{
8192
// Do nothing
8193
}
8194
8195
/// Return a string identifying the dofmap
8196
virtual const char* signature() const
8197
{
8198
return "FFC dofmap for FiniteElement('Lagrange', Cell('triangle', 1, Space(2)), 1)";
8199
}
8200
8201
/// Return true iff mesh entities of topological dimension d are needed
8202
virtual bool needs_mesh_entities(unsigned int d) const
8203
{
8204
switch (d)
8205
{
8206
case 0:
8207
{
8208
return true;
8209
break;
8210
}
8211
case 1:
8212
{
8213
return false;
8214
break;
8215
}
8216
case 2:
8217
{
8218
return false;
8219
break;
8220
}
8221
}
8222
8223
return false;
8224
}
8225
8226
/// Initialize dofmap for mesh (return true iff init_cell() is needed)
8227
virtual bool init_mesh(const ufc::mesh& m)
8228
{
8229
_global_dimension = m.num_entities[0];
8230
return false;
8231
}
8232
8233
/// Initialize dofmap for given cell
8234
virtual void init_cell(const ufc::mesh& m,
8235
const ufc::cell& c)
8236
{
8237
// Do nothing
8238
}
8239
8240
/// Finish initialization of dofmap for cells
8241
virtual void init_cell_finalize()
8242
{
8243
// Do nothing
8244
}
8245
8246
/// Return the topological dimension of the associated cell shape
8247
virtual unsigned int topological_dimension() const
8248
{
8249
return 2;
8250
}
8251
8252
/// Return the geometric dimension of the associated cell shape
8253
virtual unsigned int geometric_dimension() const
8254
{
8255
return 2;
8256
}
8257
8258
/// Return the dimension of the global finite element function space
8259
virtual unsigned int global_dimension() const
8260
{
8261
return _global_dimension;
8262
}
8263
8264
/// Return the dimension of the local finite element function space for a cell
8265
virtual unsigned int local_dimension(const ufc::cell& c) const
8266
{
8267
return 3;
8268
}
8269
8270
/// Return the maximum dimension of the local finite element function space
8271
virtual unsigned int max_local_dimension() const
8272
{
8273
return 3;
8274
}
8275
8276
/// Return the number of dofs on each cell facet
8277
virtual unsigned int num_facet_dofs() const
8278
{
8279
return 2;
8280
}
8281
8282
/// Return the number of dofs associated with each cell entity of dimension d
8283
virtual unsigned int num_entity_dofs(unsigned int d) const
8284
{
8285
switch (d)
8286
{
8287
case 0:
8288
{
8289
return 1;
8290
break;
8291
}
8292
case 1:
8293
{
8294
return 0;
8295
break;
8296
}
8297
case 2:
8298
{
8299
return 0;
8300
break;
8301
}
8302
}
8303
8304
return 0;
8305
}
8306
8307
/// Tabulate the local-to-global mapping of dofs on a cell
8308
virtual void tabulate_dofs(unsigned int* dofs,
8309
const ufc::mesh& m,
8310
const ufc::cell& c) const
8311
{
8312
dofs[0] = c.entity_indices[0][0];
8313
dofs[1] = c.entity_indices[0][1];
8314
dofs[2] = c.entity_indices[0][2];
8315
}
8316
8317
/// Tabulate the local-to-local mapping from facet dofs to cell dofs
8318
virtual void tabulate_facet_dofs(unsigned int* dofs,
8319
unsigned int facet) const
8320
{
8321
switch (facet)
8322
{
8323
case 0:
8324
{
8325
dofs[0] = 1;
8326
dofs[1] = 2;
8327
break;
8328
}
8329
case 1:
8330
{
8331
dofs[0] = 0;
8332
dofs[1] = 2;
8333
break;
8334
}
8335
case 2:
8336
{
8337
dofs[0] = 0;
8338
dofs[1] = 1;
8339
break;
8340
}
8341
}
8342
8343
}
8344
8345
/// Tabulate the local-to-local mapping of dofs on entity (d, i)
8346
virtual void tabulate_entity_dofs(unsigned int* dofs,
8347
unsigned int d, unsigned int i) const
8348
{
8349
if (d > 2)
8350
{
8351
throw std::runtime_error("d is larger than dimension (2)");
8352
}
8353
8354
switch (d)
8355
{
8356
case 0:
8357
{
8358
if (i > 2)
8359
{
8360
throw std::runtime_error("i is larger than number of entities (2)");
8361
}
8362
8363
switch (i)
8364
{
8365
case 0:
8366
{
8367
dofs[0] = 0;
8368
break;
8369
}
8370
case 1:
8371
{
8372
dofs[0] = 1;
8373
break;
8374
}
8375
case 2:
8376
{
8377
dofs[0] = 2;
8378
break;
8379
}
8380
}
8381
8382
break;
8383
}
8384
case 1:
8385
{
8386
8387
break;
8388
}
8389
case 2:
8390
{
8391
8392
break;
8393
}
8394
}
8395
8396
}
8397
8398
/// Tabulate the coordinates of all dofs on a cell
8399
virtual void tabulate_coordinates(double** coordinates,
8400
const ufc::cell& c) const
8401
{
8402
const double * const * x = c.coordinates;
8403
8404
coordinates[0][0] = x[0][0];
8405
coordinates[0][1] = x[0][1];
8406
coordinates[1][0] = x[1][0];
8407
coordinates[1][1] = x[1][1];
8408
coordinates[2][0] = x[2][0];
8409
coordinates[2][1] = x[2][1];
8410
}
8411
8412
/// Return the number of sub dofmaps (for a mixed element)
8413
virtual unsigned int num_sub_dofmaps() const
8414
{
8415
return 0;
8416
}
8417
8418
/// Create a new dofmap for sub dofmap i (for a mixed element)
8419
virtual ufc::dofmap* create_sub_dofmap(unsigned int i) const
8420
{
8421
return 0;
8422
}
8423
8424
/// Create a new class instance
8425
virtual ufc::dofmap* create() const
8426
{
8427
return new adaptivepoisson_dofmap_5();
8428
}
8429
8430
};
8431
8432
/// This class defines the interface for the tabulation of the cell
8433
/// tensor corresponding to the local contribution to a form from
8434
/// the integral over a cell.
8435
8436
class adaptivepoisson_cell_integral_0_0: public ufc::cell_integral
8437
{
8438
public:
8439
8440
/// Constructor
8441
adaptivepoisson_cell_integral_0_0() : ufc::cell_integral()
8442
{
8443
// Do nothing
8444
}
8445
8446
/// Destructor
8447
virtual ~adaptivepoisson_cell_integral_0_0()
8448
{
8449
// Do nothing
8450
}
8451
8452
/// Tabulate the tensor for the contribution from a local cell
8453
virtual void tabulate_tensor(double* A,
8454
const double * const * w,
8455
const ufc::cell& c) const
8456
{
8457
// Number of operations (multiply-add pairs) for Jacobian data: 11
8458
// Number of operations (multiply-add pairs) for geometry tensor: 8
8459
// Number of operations (multiply-add pairs) for tensor contraction: 11
8460
// Total number of operations (multiply-add pairs): 30
8461
8462
// Extract vertex coordinates
8463
const double * const * x = c.coordinates;
8464
8465
// Compute Jacobian of affine map from reference cell
8466
const double J_00 = x[1][0] - x[0][0];
8467
const double J_01 = x[2][0] - x[0][0];
8468
const double J_10 = x[1][1] - x[0][1];
8469
const double J_11 = x[2][1] - x[0][1];
8470
8471
// Compute determinant of Jacobian
8472
double detJ = J_00*J_11 - J_01*J_10;
8473
8474
// Compute inverse of Jacobian
8475
const double K_00 = J_11 / detJ;
8476
const double K_01 = -J_01 / detJ;
8477
const double K_10 = -J_10 / detJ;
8478
const double K_11 = J_00 / detJ;
8479
8480
// Set scale factor
8481
const double det = std::abs(detJ);
8482
8483
// Compute geometry tensor
8484
const double G0_0_0 = det*(K_00*K_00 + K_01*K_01);
8485
const double G0_0_1 = det*(K_00*K_10 + K_01*K_11);
8486
const double G0_1_0 = det*(K_10*K_00 + K_11*K_01);
8487
const double G0_1_1 = det*(K_10*K_10 + K_11*K_11);
8488
8489
// Compute element tensor
8490
A[0] = 0.500000000000000*G0_0_0 + 0.500000000000000*G0_0_1 + 0.500000000000000*G0_1_0 + 0.500000000000000*G0_1_1;
8491
A[1] = -0.500000000000000*G0_0_0 - 0.500000000000000*G0_1_0;
8492
A[2] = -0.500000000000000*G0_0_1 - 0.500000000000000*G0_1_1;
8493
A[3] = -0.500000000000000*G0_0_0 - 0.500000000000000*G0_0_1;
8494
A[4] = 0.500000000000000*G0_0_0;
8495
A[5] = 0.500000000000000*G0_0_1;
8496
A[6] = -0.500000000000000*G0_1_0 - 0.500000000000000*G0_1_1;
8497
A[7] = 0.500000000000000*G0_1_0;
8498
A[8] = 0.500000000000000*G0_1_1;
8499
}
8500
8501
/// Tabulate the tensor for the contribution from a local cell
8502
/// using the specified reference cell quadrature points/weights
8503
virtual void tabulate_tensor(double* A,
8504
const double * const * w,
8505
const ufc::cell& c,
8506
unsigned int num_quadrature_points,
8507
const double * const * quadrature_points,
8508
const double* quadrature_weights) const
8509
{
8510
throw std::runtime_error("Quadrature version of tabulate_tensor not available when using the FFC tensor representation.");
8511
}
8512
8513
};
8514
8515
/// This class defines the interface for the tabulation of the cell
8516
/// tensor corresponding to the local contribution to a form from
8517
/// the integral over a cell.
8518
8519
class adaptivepoisson_cell_integral_1_0: public ufc::cell_integral
8520
{
8521
public:
8522
8523
/// Constructor
8524
adaptivepoisson_cell_integral_1_0() : ufc::cell_integral()
8525
{
8526
// Do nothing
8527
}
8528
8529
/// Destructor
8530
virtual ~adaptivepoisson_cell_integral_1_0()
8531
{
8532
// Do nothing
8533
}
8534
8535
/// Tabulate the tensor for the contribution from a local cell
8536
virtual void tabulate_tensor(double* A,
8537
const double * const * w,
8538
const ufc::cell& c) const
8539
{
8540
// Number of operations (multiply-add pairs) for Jacobian data: 9
8541
// Number of operations (multiply-add pairs) for geometry tensor: 0
8542
// Number of operations (multiply-add pairs) for tensor contraction: 1
8543
// Total number of operations (multiply-add pairs): 10
8544
8545
// Extract vertex coordinates
8546
const double * const * x = c.coordinates;
8547
8548
// Compute Jacobian of affine map from reference cell
8549
const double J_00 = x[1][0] - x[0][0];
8550
const double J_01 = x[2][0] - x[0][0];
8551
const double J_10 = x[1][1] - x[0][1];
8552
const double J_11 = x[2][1] - x[0][1];
8553
8554
// Compute determinant of Jacobian
8555
double detJ = J_00*J_11 - J_01*J_10;
8556
8557
// Compute inverse of Jacobian
8558
8559
// Set scale factor
8560
const double det = std::abs(detJ);
8561
8562
// Compute geometry tensor
8563
const double G0_ = det;
8564
8565
// Compute element tensor
8566
A[0] = 0.166666666666667*G0_;
8567
A[1] = 0.166666666666667*G0_;
8568
A[2] = 0.166666666666667*G0_;
8569
}
8570
8571
/// Tabulate the tensor for the contribution from a local cell
8572
/// using the specified reference cell quadrature points/weights
8573
virtual void tabulate_tensor(double* A,
8574
const double * const * w,
8575
const ufc::cell& c,
8576
unsigned int num_quadrature_points,
8577
const double * const * quadrature_points,
8578
const double* quadrature_weights) const
8579
{
8580
throw std::runtime_error("Quadrature version of tabulate_tensor not available when using the FFC tensor representation.");
8581
}
8582
8583
};
8584
8585
/// This class defines the interface for the tabulation of the cell
8586
/// tensor corresponding to the local contribution to a form from
8587
/// the integral over a cell.
8588
8589
class adaptivepoisson_cell_integral_2_0: public ufc::cell_integral
8590
{
8591
public:
8592
8593
/// Constructor
8594
adaptivepoisson_cell_integral_2_0() : ufc::cell_integral()
8595
{
8596
// Do nothing
8597
}
8598
8599
/// Destructor
8600
virtual ~adaptivepoisson_cell_integral_2_0()
8601
{
8602
// Do nothing
8603
}
8604
8605
/// Tabulate the tensor for the contribution from a local cell
8606
virtual void tabulate_tensor(double* A,
8607
const double * const * w,
8608
const ufc::cell& c) const
8609
{
8610
// Number of operations (multiply-add pairs) for Jacobian data: 9
8611
// Number of operations (multiply-add pairs) for geometry tensor: 1
8612
// Number of operations (multiply-add pairs) for tensor contraction: 4
8613
// Total number of operations (multiply-add pairs): 14
8614
8615
// Extract vertex coordinates
8616
const double * const * x = c.coordinates;
8617
8618
// Compute Jacobian of affine map from reference cell
8619
const double J_00 = x[1][0] - x[0][0];
8620
const double J_01 = x[2][0] - x[0][0];
8621
const double J_10 = x[1][1] - x[0][1];
8622
const double J_11 = x[2][1] - x[0][1];
8623
8624
// Compute determinant of Jacobian
8625
double detJ = J_00*J_11 - J_01*J_10;
8626
8627
// Compute inverse of Jacobian
8628
8629
// Set scale factor
8630
const double det = std::abs(detJ);
8631
8632
// Compute geometry tensor
8633
const double G0_0 = det*w[0][0]*(1.0);
8634
8635
// Compute element tensor
8636
A[0] = 0.032142857142857*G0_0;
8637
A[1] = 0.021428571428571*G0_0;
8638
A[2] = 0.021428571428571*G0_0;
8639
A[3] = 0.021428571428571*G0_0;
8640
A[4] = 0.032142857142857*G0_0;
8641
A[5] = 0.021428571428571*G0_0;
8642
A[6] = 0.021428571428571*G0_0;
8643
A[7] = 0.021428571428571*G0_0;
8644
A[8] = 0.032142857142857*G0_0;
8645
}
8646
8647
/// Tabulate the tensor for the contribution from a local cell
8648
/// using the specified reference cell quadrature points/weights
8649
virtual void tabulate_tensor(double* A,
8650
const double * const * w,
8651
const ufc::cell& c,
8652
unsigned int num_quadrature_points,
8653
const double * const * quadrature_points,
8654
const double* quadrature_weights) const
8655
{
8656
throw std::runtime_error("Quadrature version of tabulate_tensor not available when using the FFC tensor representation.");
8657
}
8658
8659
};
8660
8661
/// This class defines the interface for the tabulation of the cell
8662
/// tensor corresponding to the local contribution to a form from
8663
/// the integral over a cell.
8664
8665
class adaptivepoisson_cell_integral_3_0: public ufc::cell_integral
8666
{
8667
public:
8668
8669
/// Constructor
8670
adaptivepoisson_cell_integral_3_0() : ufc::cell_integral()
8671
{
8672
// Do nothing
8673
}
8674
8675
/// Destructor
8676
virtual ~adaptivepoisson_cell_integral_3_0()
8677
{
8678
// Do nothing
8679
}
8680
8681
/// Tabulate the tensor for the contribution from a local cell
8682
virtual void tabulate_tensor(double* A,
8683
const double * const * w,
8684
const ufc::cell& c) const
8685
{
8686
// Extract vertex coordinates
8687
const double * const * x = c.coordinates;
8688
8689
// Compute Jacobian of affine map from reference cell
8690
const double J_00 = x[1][0] - x[0][0];
8691
const double J_01 = x[2][0] - x[0][0];
8692
const double J_10 = x[1][1] - x[0][1];
8693
const double J_11 = x[2][1] - x[0][1];
8694
8695
// Compute determinant of Jacobian
8696
double detJ = J_00*J_11 - J_01*J_10;
8697
8698
// Compute inverse of Jacobian
8699
const double K_00 = J_11 / detJ;
8700
const double K_01 = -J_01 / detJ;
8701
const double K_10 = -J_10 / detJ;
8702
const double K_11 = J_00 / detJ;
8703
8704
// Set scale factor
8705
const double det = std::abs(detJ);
8706
8707
// Cell Volume.
8708
8709
// Compute circumradius, assuming triangle is embedded in 2D.
8710
8711
8712
// Array of quadrature weights.
8713
static const double W9[9] = {0.055814420483044, 0.063678085099885, 0.019396383305959, 0.089303072772871, 0.101884936159816, 0.031034213289535, 0.055814420483044, 0.063678085099885, 0.019396383305959};
8714
// Quadrature points on the UFC reference element: (0.102717654809626, 0.088587959512704), (0.066554067839165, 0.409466864440735), (0.023931132287081, 0.787659461760847), (0.455706020243648, 0.088587959512704), (0.295266567779633, 0.409466864440735), (0.106170269119576, 0.787659461760847), (0.808694385677670, 0.088587959512704), (0.523979067720101, 0.409466864440735), (0.188409405952072, 0.787659461760847)
8715
8716
// Value of basis functions at quadrature points.
8717
static const double FE0[9][1] = \
8718
{{0.198686329147682},
8719
{0.385541444206917},
8720
{0.095888844721203},
8721
{0.496715822869205},
8722
{0.963853610517293},
8723
{0.239722111803007},
8724
{0.198686329147682},
8725
{0.385541444206917},
8726
{0.095888844721203}};
8727
8728
static const double FE0_D01[9][1] = \
8729
{{1.997126369343180},
8730
{0.205773829527613},
8731
{-0.387199773682209},
8732
{4.517043581212140},
8733
{-0.910427300132565},
8734
{-1.953555056589780},
8735
{0.308518341964844},
8736
{-4.851336441759750},
8737
{-3.885127223352865}};
8738
8739
static const double FE0_D10[9][1] = \
8740
{{1.688608027378335},
8741
{5.057110271287362},
8742
{3.497927449670658},
8743
{0.000000000000000},
8744
{0.000000000000000},
8745
{0.000000000000000},
8746
{-1.688608027378333},
8747
{-5.057110271287364},
8748
{-3.497927449670658}};
8749
8750
static const double FE1[9][3] = \
8751
{{0.808694385677670, 0.102717654809626, 0.088587959512704},
8752
{0.523979067720101, 0.066554067839165, 0.409466864440735},
8753
{0.188409405952072, 0.023931132287081, 0.787659461760847},
8754
{0.455706020243648, 0.455706020243648, 0.088587959512704},
8755
{0.295266567779633, 0.295266567779633, 0.409466864440735},
8756
{0.106170269119576, 0.106170269119577, 0.787659461760847},
8757
{0.102717654809626, 0.808694385677670, 0.088587959512704},
8758
{0.066554067839164, 0.523979067720101, 0.409466864440735},
8759
{0.023931132287081, 0.188409405952072, 0.787659461760847}};
8760
8761
static const double FE1_D01[9][2] = \
8762
{{-1.000000000000000, 1.000000000000000},
8763
{-1.000000000000000, 1.000000000000000},
8764
{-1.000000000000000, 1.000000000000000},
8765
{-1.000000000000000, 1.000000000000000},
8766
{-1.000000000000000, 1.000000000000000},
8767
{-1.000000000000000, 1.000000000000000},
8768
{-1.000000000000000, 1.000000000000000},
8769
{-1.000000000000000, 1.000000000000000},
8770
{-1.000000000000000, 1.000000000000000}};
8771
8772
// Array of non-zero columns
8773
static const unsigned int nzc0[2] = {0, 2};
8774
8775
// Array of non-zero columns
8776
static const unsigned int nzc1[2] = {0, 1};
8777
8778
// Reset values in the element tensor.
8779
for (unsigned int r = 0; r < 3; r++)
8780
{
8781
A[r] = 0.000000000000000;
8782
}// end loop over 'r'
8783
// Number of operations to compute geometry constants: 12.
8784
double G[3];
8785
G[0] = - det*(K_00*K_00 + K_01*K_01);
8786
G[1] = - det*(K_00*K_10 + K_01*K_11);
8787
G[2] = - det*(K_10*K_10 + K_11*K_11);
8788
8789
// Compute element tensor using UFL quadrature representation
8790
// Optimisations: ('eliminate zeros', True), ('ignore ones', True), ('ignore zero tables', True), ('optimisation', 'simplify_expressions'), ('remove zero terms', True)
8791
8792
// Loop quadrature points for integral.
8793
// Number of operations to compute element tensor for following IP loop = 513
8794
for (unsigned int ip = 0; ip < 9; ip++)
8795
{
8796
8797
// Coefficient declarations.
8798
double F0 = 0.000000000000000;
8799
double F1 = 0.000000000000000;
8800
double F2 = 0.000000000000000;
8801
double F3 = 0.000000000000000;
8802
double F4 = 0.000000000000000;
8803
double F5 = 0.000000000000000;
8804
8805
// Total number of operations to compute function values = 6
8806
for (unsigned int r = 0; r < 1; r++)
8807
{
8808
F1 += FE0[ip][r]*w[3][r];
8809
F4 += FE0_D10[ip][r]*w[3][r];
8810
F5 += FE0_D01[ip][r]*w[3][r];
8811
}// end loop over 'r'
8812
8813
// Total number of operations to compute function values = 8
8814
for (unsigned int r = 0; r < 2; r++)
8815
{
8816
F2 += FE1_D01[ip][r]*w[2][nzc1[r]];
8817
F3 += FE1_D01[ip][r]*w[2][nzc0[r]];
8818
}// end loop over 'r'
8819
8820
// Total number of operations to compute function values = 6
8821
for (unsigned int r = 0; r < 3; r++)
8822
{
8823
F0 += FE1[ip][r]*w[0][r];
8824
}// end loop over 'r'
8825
8826
// Number of operations to compute ip constants: 23
8827
double I[3];
8828
// Number of operations: 13
8829
I[0] = W9[ip]*(F0*F1*det + F2*(F4*G[0] + F5*G[1]) + F3*(F4*G[1] + F5*G[2]));
8830
8831
// Number of operations: 5
8832
I[1] = F1*W9[ip]*(F2*G[0] + F3*G[1]);
8833
8834
// Number of operations: 5
8835
I[2] = F1*W9[ip]*(F2*G[1] + F3*G[2]);
8836
8837
8838
// Number of operations for primary indices: 6
8839
for (unsigned int j = 0; j < 3; j++)
8840
{
8841
// Number of operations to compute entry: 2
8842
A[j] += FE1[ip][j]*I[0];
8843
}// end loop over 'j'
8844
8845
// Number of operations for primary indices: 8
8846
for (unsigned int j = 0; j < 2; j++)
8847
{
8848
// Number of operations to compute entry: 2
8849
A[nzc1[j]] += FE1_D01[ip][j]*I[1];
8850
// Number of operations to compute entry: 2
8851
A[nzc0[j]] += FE1_D01[ip][j]*I[2];
8852
}// end loop over 'j'
8853
}// end loop over 'ip'
8854
}
8855
8856
/// Tabulate the tensor for the contribution from a local cell
8857
/// using the specified reference cell quadrature points/weights
8858
virtual void tabulate_tensor(double* A,
8859
const double * const * w,
8860
const ufc::cell& c,
8861
unsigned int num_quadrature_points,
8862
const double * const * quadrature_points,
8863
const double* quadrature_weights) const
8864
{
8865
throw std::runtime_error("Quadrature version of tabulate_tensor not yet implemented (introduced in UFC 2.0).");
8866
}
8867
8868
};
8869
8870
/// This class defines the interface for the tabulation of the
8871
/// exterior facet tensor corresponding to the local contribution to
8872
/// a form from the integral over an exterior facet.
8873
8874
class adaptivepoisson_exterior_facet_integral_3_0: public ufc::exterior_facet_integral
8875
{
8876
public:
8877
8878
/// Constructor
8879
adaptivepoisson_exterior_facet_integral_3_0() : ufc::exterior_facet_integral()
8880
{
8881
// Do nothing
8882
}
8883
8884
/// Destructor
8885
virtual ~adaptivepoisson_exterior_facet_integral_3_0()
8886
{
8887
// Do nothing
8888
}
8889
8890
/// Tabulate the tensor for the contribution from a local exterior facet
8891
virtual void tabulate_tensor(double* A,
8892
const double * const * w,
8893
const ufc::cell& c,
8894
unsigned int facet) const
8895
{
8896
// Number of operations (multiply-add pairs) for Jacobian data: 6
8897
// Number of operations (multiply-add pairs) for geometry tensor: 0
8898
// Number of operations (multiply-add pairs) for tensor contraction: 0
8899
// Total number of operations (multiply-add pairs): 6
8900
8901
// Extract vertex coordinates
8902
8903
// Compute Jacobian of affine map from reference cell
8904
8905
// Compute determinant of Jacobian
8906
8907
// Compute inverse of Jacobian
8908
8909
// Get vertices on edge
8910
8911
// Compute scale factor (length of edge scaled by length of reference interval)
8912
8913
// Compute geometry tensor
8914
8915
8916
// Compute element tensor
8917
switch (facet)
8918
{
8919
case 0:
8920
{
8921
A[0] = 0.000000000000000;
8922
A[1] = 0.000000000000000;
8923
A[2] = 0.000000000000000;
8924
break;
8925
}
8926
case 1:
8927
{
8928
A[0] = 0.000000000000000;
8929
A[1] = 0.000000000000000;
8930
A[2] = 0.000000000000000;
8931
break;
8932
}
8933
case 2:
8934
{
8935
A[0] = 0.000000000000000;
8936
A[1] = 0.000000000000000;
8937
A[2] = 0.000000000000000;
8938
break;
8939
}
8940
}
8941
8942
}
8943
8944
/// Tabulate the tensor for the contribution from a local exterior facet
8945
/// using the specified reference cell quadrature points/weights
8946
virtual void tabulate_tensor(double* A,
8947
const double * const * w,
8948
const ufc::cell& c,
8949
unsigned int num_quadrature_points,
8950
const double * const * quadrature_points,
8951
const double* quadrature_weights) const
8952
{
8953
throw std::runtime_error("Quadrature version of tabulate_tensor not available when using the FFC tensor representation.");
8954
}
8955
8956
};
8957
8958
/// This class defines the interface for the tabulation of the
8959
/// exterior facet tensor corresponding to the local contribution to
8960
/// a form from the integral over an exterior facet.
8961
8962
class adaptivepoisson_exterior_facet_integral_4_0: public ufc::exterior_facet_integral
8963
{
8964
public:
8965
8966
/// Constructor
8967
adaptivepoisson_exterior_facet_integral_4_0() : ufc::exterior_facet_integral()
8968
{
8969
// Do nothing
8970
}
8971
8972
/// Destructor
8973
virtual ~adaptivepoisson_exterior_facet_integral_4_0()
8974
{
8975
// Do nothing
8976
}
8977
8978
/// Tabulate the tensor for the contribution from a local exterior facet
8979
virtual void tabulate_tensor(double* A,
8980
const double * const * w,
8981
const ufc::cell& c,
8982
unsigned int facet) const
8983
{
8984
// Number of operations (multiply-add pairs) for Jacobian data: 9
8985
// Number of operations (multiply-add pairs) for geometry tensor: 6
8986
// Number of operations (multiply-add pairs) for tensor contraction: 30
8987
// Total number of operations (multiply-add pairs): 45
8988
8989
// Extract vertex coordinates
8990
const double * const * x = c.coordinates;
8991
8992
// Compute Jacobian of affine map from reference cell
8993
8994
// Compute determinant of Jacobian
8995
8996
// Compute inverse of Jacobian
8997
8998
// Get vertices on edge
8999
static unsigned int edge_vertices[3][2] = {{1, 2}, {0, 2}, {0, 1}};
9000
const unsigned int v0 = edge_vertices[facet][0];
9001
const unsigned int v1 = edge_vertices[facet][1];
9002
9003
// Compute scale factor (length of edge scaled by length of reference interval)
9004
const double dx0 = x[v1][0] - x[v0][0];
9005
const double dx1 = x[v1][1] - x[v0][1];
9006
const double det = std::sqrt(dx0*dx0 + dx1*dx1);
9007
9008
// Compute geometry tensor
9009
const double G0_0 = det*w[0][0]*(1.0);
9010
const double G0_1 = det*w[0][1]*(1.0);
9011
const double G0_2 = det*w[0][2]*(1.0);
9012
const double G0_3 = det*w[0][3]*(1.0);
9013
const double G0_4 = det*w[0][4]*(1.0);
9014
const double G0_5 = det*w[0][5]*(1.0);
9015
9016
// Compute element tensor
9017
switch (facet)
9018
{
9019
case 0:
9020
{
9021
A[0] = 0.000000000000000;
9022
A[1] = 0.000000000000000;
9023
A[2] = 0.000000000000000;
9024
A[3] = 0.000000000000000;
9025
A[4] = 0.150000000000000*G0_1 - 0.016666666666667*G0_2 + 0.200000000000000*G0_3;
9026
A[5] = 0.016666666666667*G0_1 + 0.016666666666667*G0_2 + 0.133333333333333*G0_3;
9027
A[6] = 0.000000000000000;
9028
A[7] = 0.016666666666667*G0_1 + 0.016666666666667*G0_2 + 0.133333333333333*G0_3;
9029
A[8] = -0.016666666666667*G0_1 + 0.150000000000000*G0_2 + 0.200000000000000*G0_3;
9030
break;
9031
}
9032
case 1:
9033
{
9034
A[0] = 0.150000000000000*G0_0 - 0.016666666666667*G0_2 + 0.200000000000000*G0_4;
9035
A[1] = 0.000000000000000;
9036
A[2] = 0.016666666666667*G0_0 + 0.016666666666667*G0_2 + 0.133333333333333*G0_4;
9037
A[3] = 0.000000000000000;
9038
A[4] = 0.000000000000000;
9039
A[5] = 0.000000000000000;
9040
A[6] = 0.016666666666667*G0_0 + 0.016666666666667*G0_2 + 0.133333333333333*G0_4;
9041
A[7] = 0.000000000000000;
9042
A[8] = -0.016666666666667*G0_0 + 0.150000000000000*G0_2 + 0.200000000000000*G0_4;
9043
break;
9044
}
9045
case 2:
9046
{
9047
A[0] = 0.150000000000000*G0_0 - 0.016666666666667*G0_1 + 0.200000000000000*G0_5;
9048
A[1] = 0.016666666666667*G0_0 + 0.016666666666667*G0_1 + 0.133333333333333*G0_5;
9049
A[2] = 0.000000000000000;
9050
A[3] = 0.016666666666667*G0_0 + 0.016666666666667*G0_1 + 0.133333333333333*G0_5;
9051
A[4] = -0.016666666666667*G0_0 + 0.150000000000000*G0_1 + 0.200000000000000*G0_5;
9052
A[5] = 0.000000000000000;
9053
A[6] = 0.000000000000000;
9054
A[7] = 0.000000000000000;
9055
A[8] = 0.000000000000000;
9056
break;
9057
}
9058
}
9059
9060
}
9061
9062
/// Tabulate the tensor for the contribution from a local exterior facet
9063
/// using the specified reference cell quadrature points/weights
9064
virtual void tabulate_tensor(double* A,
9065
const double * const * w,
9066
const ufc::cell& c,
9067
unsigned int num_quadrature_points,
9068
const double * const * quadrature_points,
9069
const double* quadrature_weights) const
9070
{
9071
throw std::runtime_error("Quadrature version of tabulate_tensor not available when using the FFC tensor representation.");
9072
}
9073
9074
};
9075
9076
/// This class defines the interface for the tabulation of the
9077
/// interior facet tensor corresponding to the local contribution to
9078
/// a form from the integral over an interior facet.
9079
9080
class adaptivepoisson_interior_facet_integral_4_0: public ufc::interior_facet_integral
9081
{
9082
public:
9083
9084
/// Constructor
9085
adaptivepoisson_interior_facet_integral_4_0() : ufc::interior_facet_integral()
9086
{
9087
// Do nothing
9088
}
9089
9090
/// Destructor
9091
virtual ~adaptivepoisson_interior_facet_integral_4_0()
9092
{
9093
// Do nothing
9094
}
9095
9096
/// Tabulate the tensor for the contribution from a local interior facet
9097
virtual void tabulate_tensor(double* A,
9098
const double * const * w,
9099
const ufc::cell& c0,
9100
const ufc::cell& c1,
9101
unsigned int facet0,
9102
unsigned int facet1) const
9103
{
9104
// Number of operations (multiply-add pairs) for Jacobian data: 12
9105
// Number of operations (multiply-add pairs) for geometry tensor: 12
9106
// Number of operations (multiply-add pairs) for tensor contraction: 180
9107
// Total number of operations (multiply-add pairs): 204
9108
9109
// Extract vertex coordinates
9110
const double * const * x0 = c0.coordinates;
9111
9112
// Compute Jacobian of affine map from reference cell
9113
9114
// Compute determinant of Jacobian
9115
9116
// Compute inverse of Jacobian
9117
9118
// Compute Jacobian of affine map from reference cell
9119
9120
// Compute determinant of Jacobian
9121
9122
// Compute inverse of Jacobian
9123
9124
// Get vertices on edge
9125
static unsigned int edge_vertices[3][2] = {{1, 2}, {0, 2}, {0, 1}};
9126
const unsigned int v0 = edge_vertices[facet0][0];
9127
const unsigned int v1 = edge_vertices[facet0][1];
9128
9129
// Compute scale factor (length of edge scaled by length of reference interval)
9130
const double dx0 = x0[v1][0] - x0[v0][0];
9131
const double dx1 = x0[v1][1] - x0[v0][1];
9132
const double det = std::sqrt(dx0*dx0 + dx1*dx1);
9133
9134
// Compute geometry tensor
9135
const double G0_6 = det*w[0][6]*(1.0);
9136
const double G0_7 = det*w[0][7]*(1.0);
9137
const double G0_8 = det*w[0][8]*(1.0);
9138
const double G0_9 = det*w[0][9]*(1.0);
9139
const double G0_10 = det*w[0][10]*(1.0);
9140
const double G0_11 = det*w[0][11]*(1.0);
9141
const double G1_0 = det*w[0][0]*(1.0);
9142
const double G1_1 = det*w[0][1]*(1.0);
9143
const double G1_2 = det*w[0][2]*(1.0);
9144
const double G1_3 = det*w[0][3]*(1.0);
9145
const double G1_4 = det*w[0][4]*(1.0);
9146
const double G1_5 = det*w[0][5]*(1.0);
9147
9148
// Compute element tensor
9149
switch (facet0)
9150
{
9151
case 0:
9152
{
9153
switch (facet1)
9154
{
9155
case 0:
9156
{
9157
A[0] = 0.000000000000000;
9158
A[1] = 0.000000000000000;
9159
A[2] = 0.000000000000000;
9160
A[3] = 0.000000000000000;
9161
A[4] = 0.000000000000000;
9162
A[5] = 0.000000000000000;
9163
A[6] = 0.000000000000000;
9164
A[7] = 0.150000000000000*G1_1 - 0.016666666666667*G1_2 + 0.200000000000000*G1_3;
9165
A[8] = 0.016666666666667*G1_1 + 0.016666666666667*G1_2 + 0.133333333333333*G1_3;
9166
A[9] = 0.000000000000000;
9167
A[10] = 0.000000000000000;
9168
A[11] = 0.000000000000000;
9169
A[12] = 0.000000000000000;
9170
A[13] = 0.016666666666667*G1_1 + 0.016666666666667*G1_2 + 0.133333333333333*G1_3;
9171
A[14] = -0.016666666666667*G1_1 + 0.150000000000000*G1_2 + 0.200000000000000*G1_3;
9172
A[15] = 0.000000000000000;
9173
A[16] = 0.000000000000000;
9174
A[17] = 0.000000000000000;
9175
A[18] = 0.000000000000000;
9176
A[19] = 0.000000000000000;
9177
A[20] = 0.000000000000000;
9178
A[21] = 0.000000000000000;
9179
A[22] = 0.000000000000000;
9180
A[23] = 0.000000000000000;
9181
A[24] = 0.000000000000000;
9182
A[25] = 0.000000000000000;
9183
A[26] = 0.000000000000000;
9184
A[27] = 0.000000000000000;
9185
A[28] = 0.150000000000000*G0_7 - 0.016666666666667*G0_8 + 0.200000000000000*G0_9;
9186
A[29] = 0.016666666666667*G0_7 + 0.016666666666667*G0_8 + 0.133333333333333*G0_9;
9187
A[30] = 0.000000000000000;
9188
A[31] = 0.000000000000000;
9189
A[32] = 0.000000000000000;
9190
A[33] = 0.000000000000000;
9191
A[34] = 0.016666666666667*G0_7 + 0.016666666666667*G0_8 + 0.133333333333333*G0_9;
9192
A[35] = -0.016666666666667*G0_7 + 0.150000000000000*G0_8 + 0.200000000000000*G0_9;
9193
break;
9194
}
9195
case 1:
9196
{
9197
A[0] = 0.000000000000000;
9198
A[1] = 0.000000000000000;
9199
A[2] = 0.000000000000000;
9200
A[3] = 0.000000000000000;
9201
A[4] = 0.000000000000000;
9202
A[5] = 0.000000000000000;
9203
A[6] = 0.000000000000000;
9204
A[7] = 0.150000000000000*G1_1 - 0.016666666666667*G1_2 + 0.200000000000000*G1_3;
9205
A[8] = 0.016666666666667*G1_1 + 0.016666666666667*G1_2 + 0.133333333333333*G1_3;
9206
A[9] = 0.000000000000000;
9207
A[10] = 0.000000000000000;
9208
A[11] = 0.000000000000000;
9209
A[12] = 0.000000000000000;
9210
A[13] = 0.016666666666667*G1_1 + 0.016666666666667*G1_2 + 0.133333333333333*G1_3;
9211
A[14] = -0.016666666666667*G1_1 + 0.150000000000000*G1_2 + 0.200000000000000*G1_3;
9212
A[15] = 0.000000000000000;
9213
A[16] = 0.000000000000000;
9214
A[17] = 0.000000000000000;
9215
A[18] = 0.000000000000000;
9216
A[19] = 0.000000000000000;
9217
A[20] = 0.000000000000000;
9218
A[21] = 0.150000000000000*G0_6 - 0.016666666666667*G0_8 + 0.200000000000000*G0_10;
9219
A[22] = 0.000000000000000;
9220
A[23] = 0.016666666666667*G0_6 + 0.016666666666667*G0_8 + 0.133333333333333*G0_10;
9221
A[24] = 0.000000000000000;
9222
A[25] = 0.000000000000000;
9223
A[26] = 0.000000000000000;
9224
A[27] = 0.000000000000000;
9225
A[28] = 0.000000000000000;
9226
A[29] = 0.000000000000000;
9227
A[30] = 0.000000000000000;
9228
A[31] = 0.000000000000000;
9229
A[32] = 0.000000000000000;
9230
A[33] = 0.016666666666667*G0_6 + 0.016666666666667*G0_8 + 0.133333333333333*G0_10;
9231
A[34] = 0.000000000000000;
9232
A[35] = -0.016666666666667*G0_6 + 0.150000000000000*G0_8 + 0.200000000000000*G0_10;
9233
break;
9234
}
9235
case 2:
9236
{
9237
A[0] = 0.000000000000000;
9238
A[1] = 0.000000000000000;
9239
A[2] = 0.000000000000000;
9240
A[3] = 0.000000000000000;
9241
A[4] = 0.000000000000000;
9242
A[5] = 0.000000000000000;
9243
A[6] = 0.000000000000000;
9244
A[7] = 0.150000000000000*G1_1 - 0.016666666666667*G1_2 + 0.200000000000000*G1_3;
9245
A[8] = 0.016666666666667*G1_1 + 0.016666666666667*G1_2 + 0.133333333333333*G1_3;
9246
A[9] = 0.000000000000000;
9247
A[10] = 0.000000000000000;
9248
A[11] = 0.000000000000000;
9249
A[12] = 0.000000000000000;
9250
A[13] = 0.016666666666667*G1_1 + 0.016666666666667*G1_2 + 0.133333333333333*G1_3;
9251
A[14] = -0.016666666666667*G1_1 + 0.150000000000000*G1_2 + 0.200000000000000*G1_3;
9252
A[15] = 0.000000000000000;
9253
A[16] = 0.000000000000000;
9254
A[17] = 0.000000000000000;
9255
A[18] = 0.000000000000000;
9256
A[19] = 0.000000000000000;
9257
A[20] = 0.000000000000000;
9258
A[21] = 0.150000000000000*G0_6 - 0.016666666666667*G0_7 + 0.200000000000000*G0_11;
9259
A[22] = 0.016666666666667*G0_6 + 0.016666666666667*G0_7 + 0.133333333333333*G0_11;
9260
A[23] = 0.000000000000000;
9261
A[24] = 0.000000000000000;
9262
A[25] = 0.000000000000000;
9263
A[26] = 0.000000000000000;
9264
A[27] = 0.016666666666667*G0_6 + 0.016666666666667*G0_7 + 0.133333333333333*G0_11;
9265
A[28] = -0.016666666666667*G0_6 + 0.150000000000000*G0_7 + 0.200000000000000*G0_11;
9266
A[29] = 0.000000000000000;
9267
A[30] = 0.000000000000000;
9268
A[31] = 0.000000000000000;
9269
A[32] = 0.000000000000000;
9270
A[33] = 0.000000000000000;
9271
A[34] = 0.000000000000000;
9272
A[35] = 0.000000000000000;
9273
break;
9274
}
9275
}
9276
9277
break;
9278
}
9279
case 1:
9280
{
9281
switch (facet1)
9282
{
9283
case 0:
9284
{
9285
A[0] = 0.150000000000000*G1_0 - 0.016666666666667*G1_2 + 0.200000000000000*G1_4;
9286
A[1] = 0.000000000000000;
9287
A[2] = 0.016666666666667*G1_0 + 0.016666666666667*G1_2 + 0.133333333333333*G1_4;
9288
A[3] = 0.000000000000000;
9289
A[4] = 0.000000000000000;
9290
A[5] = 0.000000000000000;
9291
A[6] = 0.000000000000000;
9292
A[7] = 0.000000000000000;
9293
A[8] = 0.000000000000000;
9294
A[9] = 0.000000000000000;
9295
A[10] = 0.000000000000000;
9296
A[11] = 0.000000000000000;
9297
A[12] = 0.016666666666667*G1_0 + 0.016666666666667*G1_2 + 0.133333333333333*G1_4;
9298
A[13] = 0.000000000000000;
9299
A[14] = -0.016666666666667*G1_0 + 0.150000000000000*G1_2 + 0.200000000000000*G1_4;
9300
A[15] = 0.000000000000000;
9301
A[16] = 0.000000000000000;
9302
A[17] = 0.000000000000000;
9303
A[18] = 0.000000000000000;
9304
A[19] = 0.000000000000000;
9305
A[20] = 0.000000000000000;
9306
A[21] = 0.000000000000000;
9307
A[22] = 0.000000000000000;
9308
A[23] = 0.000000000000000;
9309
A[24] = 0.000000000000000;
9310
A[25] = 0.000000000000000;
9311
A[26] = 0.000000000000000;
9312
A[27] = 0.000000000000000;
9313
A[28] = 0.150000000000000*G0_7 - 0.016666666666667*G0_8 + 0.200000000000000*G0_9;
9314
A[29] = 0.016666666666667*G0_7 + 0.016666666666667*G0_8 + 0.133333333333333*G0_9;
9315
A[30] = 0.000000000000000;
9316
A[31] = 0.000000000000000;
9317
A[32] = 0.000000000000000;
9318
A[33] = 0.000000000000000;
9319
A[34] = 0.016666666666667*G0_7 + 0.016666666666667*G0_8 + 0.133333333333333*G0_9;
9320
A[35] = -0.016666666666667*G0_7 + 0.150000000000000*G0_8 + 0.200000000000000*G0_9;
9321
break;
9322
}
9323
case 1:
9324
{
9325
A[0] = 0.150000000000000*G1_0 - 0.016666666666667*G1_2 + 0.200000000000000*G1_4;
9326
A[1] = 0.000000000000000;
9327
A[2] = 0.016666666666667*G1_0 + 0.016666666666667*G1_2 + 0.133333333333333*G1_4;
9328
A[3] = 0.000000000000000;
9329
A[4] = 0.000000000000000;
9330
A[5] = 0.000000000000000;
9331
A[6] = 0.000000000000000;
9332
A[7] = 0.000000000000000;
9333
A[8] = 0.000000000000000;
9334
A[9] = 0.000000000000000;
9335
A[10] = 0.000000000000000;
9336
A[11] = 0.000000000000000;
9337
A[12] = 0.016666666666667*G1_0 + 0.016666666666667*G1_2 + 0.133333333333333*G1_4;
9338
A[13] = 0.000000000000000;
9339
A[14] = -0.016666666666667*G1_0 + 0.150000000000000*G1_2 + 0.200000000000000*G1_4;
9340
A[15] = 0.000000000000000;
9341
A[16] = 0.000000000000000;
9342
A[17] = 0.000000000000000;
9343
A[18] = 0.000000000000000;
9344
A[19] = 0.000000000000000;
9345
A[20] = 0.000000000000000;
9346
A[21] = 0.150000000000000*G0_6 - 0.016666666666667*G0_8 + 0.200000000000000*G0_10;
9347
A[22] = 0.000000000000000;
9348
A[23] = 0.016666666666667*G0_6 + 0.016666666666667*G0_8 + 0.133333333333333*G0_10;
9349
A[24] = 0.000000000000000;
9350
A[25] = 0.000000000000000;
9351
A[26] = 0.000000000000000;
9352
A[27] = 0.000000000000000;
9353
A[28] = 0.000000000000000;
9354
A[29] = 0.000000000000000;
9355
A[30] = 0.000000000000000;
9356
A[31] = 0.000000000000000;
9357
A[32] = 0.000000000000000;
9358
A[33] = 0.016666666666667*G0_6 + 0.016666666666667*G0_8 + 0.133333333333333*G0_10;
9359
A[34] = 0.000000000000000;
9360
A[35] = -0.016666666666667*G0_6 + 0.150000000000000*G0_8 + 0.200000000000000*G0_10;
9361
break;
9362
}
9363
case 2:
9364
{
9365
A[0] = 0.150000000000000*G1_0 - 0.016666666666667*G1_2 + 0.200000000000000*G1_4;
9366
A[1] = 0.000000000000000;
9367
A[2] = 0.016666666666667*G1_0 + 0.016666666666667*G1_2 + 0.133333333333333*G1_4;
9368
A[3] = 0.000000000000000;
9369
A[4] = 0.000000000000000;
9370
A[5] = 0.000000000000000;
9371
A[6] = 0.000000000000000;
9372
A[7] = 0.000000000000000;
9373
A[8] = 0.000000000000000;
9374
A[9] = 0.000000000000000;
9375
A[10] = 0.000000000000000;
9376
A[11] = 0.000000000000000;
9377
A[12] = 0.016666666666667*G1_0 + 0.016666666666667*G1_2 + 0.133333333333333*G1_4;
9378
A[13] = 0.000000000000000;
9379
A[14] = -0.016666666666667*G1_0 + 0.150000000000000*G1_2 + 0.200000000000000*G1_4;
9380
A[15] = 0.000000000000000;
9381
A[16] = 0.000000000000000;
9382
A[17] = 0.000000000000000;
9383
A[18] = 0.000000000000000;
9384
A[19] = 0.000000000000000;
9385
A[20] = 0.000000000000000;
9386
A[21] = 0.150000000000000*G0_6 - 0.016666666666667*G0_7 + 0.200000000000000*G0_11;
9387
A[22] = 0.016666666666667*G0_6 + 0.016666666666667*G0_7 + 0.133333333333333*G0_11;
9388
A[23] = 0.000000000000000;
9389
A[24] = 0.000000000000000;
9390
A[25] = 0.000000000000000;
9391
A[26] = 0.000000000000000;
9392
A[27] = 0.016666666666667*G0_6 + 0.016666666666667*G0_7 + 0.133333333333333*G0_11;
9393
A[28] = -0.016666666666667*G0_6 + 0.150000000000000*G0_7 + 0.200000000000000*G0_11;
9394
A[29] = 0.000000000000000;
9395
A[30] = 0.000000000000000;
9396
A[31] = 0.000000000000000;
9397
A[32] = 0.000000000000000;
9398
A[33] = 0.000000000000000;
9399
A[34] = 0.000000000000000;
9400
A[35] = 0.000000000000000;
9401
break;
9402
}
9403
}
9404
9405
break;
9406
}
9407
case 2:
9408
{
9409
switch (facet1)
9410
{
9411
case 0:
9412
{
9413
A[0] = 0.150000000000000*G1_0 - 0.016666666666667*G1_1 + 0.200000000000000*G1_5;
9414
A[1] = 0.016666666666667*G1_0 + 0.016666666666667*G1_1 + 0.133333333333333*G1_5;
9415
A[2] = 0.000000000000000;
9416
A[3] = 0.000000000000000;
9417
A[4] = 0.000000000000000;
9418
A[5] = 0.000000000000000;
9419
A[6] = 0.016666666666667*G1_0 + 0.016666666666667*G1_1 + 0.133333333333333*G1_5;
9420
A[7] = -0.016666666666667*G1_0 + 0.150000000000000*G1_1 + 0.200000000000000*G1_5;
9421
A[8] = 0.000000000000000;
9422
A[9] = 0.000000000000000;
9423
A[10] = 0.000000000000000;
9424
A[11] = 0.000000000000000;
9425
A[12] = 0.000000000000000;
9426
A[13] = 0.000000000000000;
9427
A[14] = 0.000000000000000;
9428
A[15] = 0.000000000000000;
9429
A[16] = 0.000000000000000;
9430
A[17] = 0.000000000000000;
9431
A[18] = 0.000000000000000;
9432
A[19] = 0.000000000000000;
9433
A[20] = 0.000000000000000;
9434
A[21] = 0.000000000000000;
9435
A[22] = 0.000000000000000;
9436
A[23] = 0.000000000000000;
9437
A[24] = 0.000000000000000;
9438
A[25] = 0.000000000000000;
9439
A[26] = 0.000000000000000;
9440
A[27] = 0.000000000000000;
9441
A[28] = 0.150000000000000*G0_7 - 0.016666666666667*G0_8 + 0.200000000000000*G0_9;
9442
A[29] = 0.016666666666667*G0_7 + 0.016666666666667*G0_8 + 0.133333333333333*G0_9;
9443
A[30] = 0.000000000000000;
9444
A[31] = 0.000000000000000;
9445
A[32] = 0.000000000000000;
9446
A[33] = 0.000000000000000;
9447
A[34] = 0.016666666666667*G0_7 + 0.016666666666667*G0_8 + 0.133333333333333*G0_9;
9448
A[35] = -0.016666666666667*G0_7 + 0.150000000000000*G0_8 + 0.200000000000000*G0_9;
9449
break;
9450
}
9451
case 1:
9452
{
9453
A[0] = 0.150000000000000*G1_0 - 0.016666666666667*G1_1 + 0.200000000000000*G1_5;
9454
A[1] = 0.016666666666667*G1_0 + 0.016666666666667*G1_1 + 0.133333333333333*G1_5;
9455
A[2] = 0.000000000000000;
9456
A[3] = 0.000000000000000;
9457
A[4] = 0.000000000000000;
9458
A[5] = 0.000000000000000;
9459
A[6] = 0.016666666666667*G1_0 + 0.016666666666667*G1_1 + 0.133333333333333*G1_5;
9460
A[7] = -0.016666666666667*G1_0 + 0.150000000000000*G1_1 + 0.200000000000000*G1_5;
9461
A[8] = 0.000000000000000;
9462
A[9] = 0.000000000000000;
9463
A[10] = 0.000000000000000;
9464
A[11] = 0.000000000000000;
9465
A[12] = 0.000000000000000;
9466
A[13] = 0.000000000000000;
9467
A[14] = 0.000000000000000;
9468
A[15] = 0.000000000000000;
9469
A[16] = 0.000000000000000;
9470
A[17] = 0.000000000000000;
9471
A[18] = 0.000000000000000;
9472
A[19] = 0.000000000000000;
9473
A[20] = 0.000000000000000;
9474
A[21] = 0.150000000000000*G0_6 - 0.016666666666667*G0_8 + 0.200000000000000*G0_10;
9475
A[22] = 0.000000000000000;
9476
A[23] = 0.016666666666667*G0_6 + 0.016666666666667*G0_8 + 0.133333333333333*G0_10;
9477
A[24] = 0.000000000000000;
9478
A[25] = 0.000000000000000;
9479
A[26] = 0.000000000000000;
9480
A[27] = 0.000000000000000;
9481
A[28] = 0.000000000000000;
9482
A[29] = 0.000000000000000;
9483
A[30] = 0.000000000000000;
9484
A[31] = 0.000000000000000;
9485
A[32] = 0.000000000000000;
9486
A[33] = 0.016666666666667*G0_6 + 0.016666666666667*G0_8 + 0.133333333333333*G0_10;
9487
A[34] = 0.000000000000000;
9488
A[35] = -0.016666666666667*G0_6 + 0.150000000000000*G0_8 + 0.200000000000000*G0_10;
9489
break;
9490
}
9491
case 2:
9492
{
9493
A[0] = 0.150000000000000*G1_0 - 0.016666666666667*G1_1 + 0.200000000000000*G1_5;
9494
A[1] = 0.016666666666667*G1_0 + 0.016666666666667*G1_1 + 0.133333333333333*G1_5;
9495
A[2] = 0.000000000000000;
9496
A[3] = 0.000000000000000;
9497
A[4] = 0.000000000000000;
9498
A[5] = 0.000000000000000;
9499
A[6] = 0.016666666666667*G1_0 + 0.016666666666667*G1_1 + 0.133333333333333*G1_5;
9500
A[7] = -0.016666666666667*G1_0 + 0.150000000000000*G1_1 + 0.200000000000000*G1_5;
9501
A[8] = 0.000000000000000;
9502
A[9] = 0.000000000000000;
9503
A[10] = 0.000000000000000;
9504
A[11] = 0.000000000000000;
9505
A[12] = 0.000000000000000;
9506
A[13] = 0.000000000000000;
9507
A[14] = 0.000000000000000;
9508
A[15] = 0.000000000000000;
9509
A[16] = 0.000000000000000;
9510
A[17] = 0.000000000000000;
9511
A[18] = 0.000000000000000;
9512
A[19] = 0.000000000000000;
9513
A[20] = 0.000000000000000;
9514
A[21] = 0.150000000000000*G0_6 - 0.016666666666667*G0_7 + 0.200000000000000*G0_11;
9515
A[22] = 0.016666666666667*G0_6 + 0.016666666666667*G0_7 + 0.133333333333333*G0_11;
9516
A[23] = 0.000000000000000;
9517
A[24] = 0.000000000000000;
9518
A[25] = 0.000000000000000;
9519
A[26] = 0.000000000000000;
9520
A[27] = 0.016666666666667*G0_6 + 0.016666666666667*G0_7 + 0.133333333333333*G0_11;
9521
A[28] = -0.016666666666667*G0_6 + 0.150000000000000*G0_7 + 0.200000000000000*G0_11;
9522
A[29] = 0.000000000000000;
9523
A[30] = 0.000000000000000;
9524
A[31] = 0.000000000000000;
9525
A[32] = 0.000000000000000;
9526
A[33] = 0.000000000000000;
9527
A[34] = 0.000000000000000;
9528
A[35] = 0.000000000000000;
9529
break;
9530
}
9531
}
9532
9533
break;
9534
}
9535
}
9536
9537
}
9538
9539
/// Tabulate the tensor for the contribution from a local interior facet
9540
/// using the specified reference cell quadrature points/weights
9541
virtual void tabulate_tensor(double* A,
9542
const double * const * w,
9543
const ufc::cell& c,
9544
unsigned int num_quadrature_points,
9545
const double * const * quadrature_points,
9546
const double* quadrature_weights) const
9547
{
9548
throw std::runtime_error("Quadrature version of tabulate_tensor not available when using the FFC tensor representation.");
9549
}
9550
9551
};
9552
9553
/// This class defines the interface for the tabulation of the cell
9554
/// tensor corresponding to the local contribution to a form from
9555
/// the integral over a cell.
9556
9557
class adaptivepoisson_cell_integral_5_0: public ufc::cell_integral
9558
{
9559
public:
9560
9561
/// Constructor
9562
adaptivepoisson_cell_integral_5_0() : ufc::cell_integral()
9563
{
9564
// Do nothing
9565
}
9566
9567
/// Destructor
9568
virtual ~adaptivepoisson_cell_integral_5_0()
9569
{
9570
// Do nothing
9571
}
9572
9573
/// Tabulate the tensor for the contribution from a local cell
9574
virtual void tabulate_tensor(double* A,
9575
const double * const * w,
9576
const ufc::cell& c) const
9577
{
9578
// Extract vertex coordinates
9579
const double * const * x = c.coordinates;
9580
9581
// Compute Jacobian of affine map from reference cell
9582
const double J_00 = x[1][0] - x[0][0];
9583
const double J_01 = x[2][0] - x[0][0];
9584
const double J_10 = x[1][1] - x[0][1];
9585
const double J_11 = x[2][1] - x[0][1];
9586
9587
// Compute determinant of Jacobian
9588
double detJ = J_00*J_11 - J_01*J_10;
9589
9590
// Compute inverse of Jacobian
9591
const double K_00 = J_11 / detJ;
9592
const double K_01 = -J_01 / detJ;
9593
const double K_10 = -J_10 / detJ;
9594
const double K_11 = J_00 / detJ;
9595
9596
// Set scale factor
9597
const double det = std::abs(detJ);
9598
9599
// Cell Volume.
9600
9601
// Compute circumradius, assuming triangle is embedded in 2D.
9602
9603
9604
// Array of quadrature weights.
9605
static const double W9[9] = {0.055814420483044, 0.063678085099885, 0.019396383305959, 0.089303072772871, 0.101884936159816, 0.031034213289535, 0.055814420483044, 0.063678085099885, 0.019396383305959};
9606
// Quadrature points on the UFC reference element: (0.102717654809626, 0.088587959512704), (0.066554067839165, 0.409466864440735), (0.023931132287081, 0.787659461760847), (0.455706020243648, 0.088587959512704), (0.295266567779633, 0.409466864440735), (0.106170269119576, 0.787659461760847), (0.808694385677670, 0.088587959512704), (0.523979067720101, 0.409466864440735), (0.188409405952072, 0.787659461760847)
9607
9608
// Value of basis functions at quadrature points.
9609
static const double FE0[9][3] = \
9610
{{0.808694385677670, 0.102717654809626, 0.088587959512704},
9611
{0.523979067720101, 0.066554067839165, 0.409466864440735},
9612
{0.188409405952072, 0.023931132287081, 0.787659461760847},
9613
{0.455706020243648, 0.455706020243648, 0.088587959512704},
9614
{0.295266567779633, 0.295266567779633, 0.409466864440735},
9615
{0.106170269119576, 0.106170269119577, 0.787659461760847},
9616
{0.102717654809626, 0.808694385677670, 0.088587959512704},
9617
{0.066554067839164, 0.523979067720101, 0.409466864440735},
9618
{0.023931132287081, 0.188409405952072, 0.787659461760847}};
9619
9620
static const double FE0_D01[9][2] = \
9621
{{-1.000000000000000, 1.000000000000000},
9622
{-1.000000000000000, 1.000000000000000},
9623
{-1.000000000000000, 1.000000000000000},
9624
{-1.000000000000000, 1.000000000000000},
9625
{-1.000000000000000, 1.000000000000000},
9626
{-1.000000000000000, 1.000000000000000},
9627
{-1.000000000000000, 1.000000000000000},
9628
{-1.000000000000000, 1.000000000000000},
9629
{-1.000000000000000, 1.000000000000000}};
9630
9631
// Array of non-zero columns
9632
static const unsigned int nzc1[2] = {0, 1};
9633
9634
// Array of non-zero columns
9635
static const unsigned int nzc0[2] = {0, 2};
9636
9637
static const double FE2[9][6] = \
9638
{{0.499278833175498, -0.081615821590447, -0.072892306371455, 0.036398189782060, 0.286562341986258, 0.332268763018087},
9639
{0.025129059097551, -0.057695179947284, -0.074140638290881, 0.109006741895515, 0.858208263567716, 0.139491753677383},
9640
{-0.117413197449647, -0.022785734101997, 0.453155393641927, 0.075398331106278, 0.593609805131561, 0.018035401671877},
9641
{-0.040370066471040, -0.040370066471040, -0.072892306371455, 0.161480265884159, 0.161480265884159, 0.830671907545217},
9642
{-0.120901875682904, -0.120901875682904, -0.074140638290881, 0.483607502731615, 0.483607502731615, 0.348729384193458},
9643
{-0.083626017029730, -0.083626017029730, 0.453155393641927, 0.334504068118920, 0.334504068118920, 0.045088504179693},
9644
{-0.081615821590447, 0.499278833175498, -0.072892306371455, 0.286562341986258, 0.036398189782060, 0.332268763018087},
9645
{-0.057695179947284, 0.025129059097551, -0.074140638290881, 0.858208263567716, 0.109006741895515, 0.139491753677383},
9646
{-0.022785734101997, -0.117413197449647, 0.453155393641927, 0.593609805131561, 0.075398331106278, 0.018035401671877}};
9647
9648
static const double FE2_D01[9][5] = \
9649
{{-2.234777542710679, -0.645648161949184, 0.410870619238505, 2.880425704659863, -0.410870619238505},
9650
{-1.095916270880403, 0.637867457762939, 0.266216271356658, 0.458048813117464, -0.266216271356658},
9651
{0.246362376191710, 2.150637847043388, 0.095724529148321, -2.397000223235098, -0.095724529148322},
9652
{-0.822824080974592, -0.645648161949184, 1.822824080974592, 1.468472242923776, -1.822824080974592},
9653
{-0.181066271118530, 0.637867457762939, 1.181066271118531, -0.456801186644409, -1.181066271118531},
9654
{0.575318923521694, 2.150637847043388, 0.424681076478305, -2.725956770565081, -0.424681076478306},
9655
{0.589129380761495, -0.645648161949184, 3.234777542710678, 0.056518781187689, -3.234777542710679},
9656
{0.733783728643342, 0.637867457762939, 2.095916270880403, -1.371651186406281, -2.095916270880403},
9657
{0.904275470851677, 2.150637847043388, 0.753637623808288, -3.054913317895065, -0.753637623808289}};
9658
9659
// Array of non-zero columns
9660
static const unsigned int nzc2[5] = {0, 2, 3, 4, 5};
9661
9662
static const double FE2_D10[9][5] = \
9663
{{-2.234777542710679, -0.589129380761495, 0.354351838050815, -0.354351838050816, 2.823906923472175},
9664
{-1.095916270880403, -0.733783728643342, 1.637867457762939, -1.637867457762940, 1.829699999523745},
9665
{0.246362376191711, -0.904275470851678, 3.150637847043387, -3.150637847043388, 0.657913094659968},
9666
{-0.822824080974592, 0.822824080974592, 0.354351838050816, -0.354351838050816, 0.000000000000000},
9667
{-0.181066271118530, 0.181066271118531, 1.637867457762939, -1.637867457762940, 0.000000000000000},
9668
{0.575318923521694, -0.575318923521695, 3.150637847043387, -3.150637847043388, 0.000000000000000},
9669
{0.589129380761495, 2.234777542710679, 0.354351838050815, -0.354351838050816, -2.823906923472174},
9670
{0.733783728643342, 1.095916270880403, 1.637867457762939, -1.637867457762940, -1.829699999523746},
9671
{0.904275470851678, -0.246362376191711, 3.150637847043387, -3.150637847043388, -0.657913094659966}};
9672
9673
// Array of non-zero columns
9674
static const unsigned int nzc3[5] = {0, 1, 3, 4, 5};
9675
9676
// Reset values in the element tensor.
9677
for (unsigned int r = 0; r < 3; r++)
9678
{
9679
A[r] = 0.000000000000000;
9680
}// end loop over 'r'
9681
// Number of operations to compute geometry constants: 12.
9682
double G[3];
9683
G[0] = - det*(K_00*K_00 + K_01*K_01);
9684
G[1] = - det*(K_00*K_10 + K_01*K_11);
9685
G[2] = - det*(K_10*K_10 + K_11*K_11);
9686
9687
// Compute element tensor using UFL quadrature representation
9688
// Optimisations: ('eliminate zeros', True), ('ignore ones', True), ('ignore zero tables', True), ('optimisation', 'simplify_expressions'), ('remove zero terms', True)
9689
9690
// Loop quadrature points for integral.
9691
// Number of operations to compute element tensor for following IP loop = 810
9692
for (unsigned int ip = 0; ip < 9; ip++)
9693
{
9694
9695
// Coefficient declarations.
9696
double F0 = 0.000000000000000;
9697
double F1 = 0.000000000000000;
9698
double F2 = 0.000000000000000;
9699
double F3 = 0.000000000000000;
9700
double F4 = 0.000000000000000;
9701
double F5 = 0.000000000000000;
9702
double F6 = 0.000000000000000;
9703
9704
// Total number of operations to compute function values = 8
9705
for (unsigned int r = 0; r < 2; r++)
9706
{
9707
F3 += FE0_D01[ip][r]*w[2][nzc1[r]];
9708
F4 += FE0_D01[ip][r]*w[2][nzc0[r]];
9709
}// end loop over 'r'
9710
9711
// Total number of operations to compute function values = 12
9712
for (unsigned int r = 0; r < 3; r++)
9713
{
9714
F0 += FE0[ip][r]*w[3][r];
9715
F2 += FE0[ip][r]*w[0][r];
9716
}// end loop over 'r'
9717
9718
// Total number of operations to compute function values = 20
9719
for (unsigned int r = 0; r < 5; r++)
9720
{
9721
F5 += FE2_D10[ip][r]*w[4][nzc3[r]];
9722
F6 += FE2_D01[ip][r]*w[4][nzc2[r]];
9723
}// end loop over 'r'
9724
9725
// Total number of operations to compute function values = 12
9726
for (unsigned int r = 0; r < 6; r++)
9727
{
9728
F1 += FE2[ip][r]*w[4][r];
9729
}// end loop over 'r'
9730
9731
// Number of operations to compute ip constants: 24
9732
double I[3];
9733
// Number of operations: 14
9734
I[0] = W9[ip]*(F1*det*(F2 - F0) + F5*(F3*G[0] + F4*G[1]) + F6*(F3*G[1] + F4*G[2]));
9735
9736
// Number of operations: 5
9737
I[1] = F1*W9[ip]*(F3*G[0] + F4*G[1]);
9738
9739
// Number of operations: 5
9740
I[2] = F1*W9[ip]*(F3*G[1] + F4*G[2]);
9741
9742
9743
// Number of operations for primary indices: 6
9744
for (unsigned int j = 0; j < 3; j++)
9745
{
9746
// Number of operations to compute entry: 2
9747
A[j] += FE0[ip][j]*I[0];
9748
}// end loop over 'j'
9749
9750
// Number of operations for primary indices: 8
9751
for (unsigned int j = 0; j < 2; j++)
9752
{
9753
// Number of operations to compute entry: 2
9754
A[nzc1[j]] += FE0_D01[ip][j]*I[1];
9755
// Number of operations to compute entry: 2
9756
A[nzc0[j]] += FE0_D01[ip][j]*I[2];
9757
}// end loop over 'j'
9758
}// end loop over 'ip'
9759
}
9760
9761
/// Tabulate the tensor for the contribution from a local cell
9762
/// using the specified reference cell quadrature points/weights
9763
virtual void tabulate_tensor(double* A,
9764
const double * const * w,
9765
const ufc::cell& c,
9766
unsigned int num_quadrature_points,
9767
const double * const * quadrature_points,
9768
const double* quadrature_weights) const
9769
{
9770
throw std::runtime_error("Quadrature version of tabulate_tensor not yet implemented (introduced in UFC 2.0).");
9771
}
9772
9773
};
9774
9775
/// This class defines the interface for the tabulation of the
9776
/// exterior facet tensor corresponding to the local contribution to
9777
/// a form from the integral over an exterior facet.
9778
9779
class adaptivepoisson_exterior_facet_integral_5_0: public ufc::exterior_facet_integral
9780
{
9781
public:
9782
9783
/// Constructor
9784
adaptivepoisson_exterior_facet_integral_5_0() : ufc::exterior_facet_integral()
9785
{
9786
// Do nothing
9787
}
9788
9789
/// Destructor
9790
virtual ~adaptivepoisson_exterior_facet_integral_5_0()
9791
{
9792
// Do nothing
9793
}
9794
9795
/// Tabulate the tensor for the contribution from a local exterior facet
9796
virtual void tabulate_tensor(double* A,
9797
const double * const * w,
9798
const ufc::cell& c,
9799
unsigned int facet) const
9800
{
9801
// Number of operations (multiply-add pairs) for Jacobian data: 9
9802
// Number of operations (multiply-add pairs) for geometry tensor: 22
9803
// Number of operations (multiply-add pairs) for tensor contraction: 33
9804
// Total number of operations (multiply-add pairs): 64
9805
9806
// Extract vertex coordinates
9807
const double * const * x = c.coordinates;
9808
9809
// Compute Jacobian of affine map from reference cell
9810
9811
// Compute determinant of Jacobian
9812
9813
// Compute inverse of Jacobian
9814
9815
// Get vertices on edge
9816
static unsigned int edge_vertices[3][2] = {{1, 2}, {0, 2}, {0, 1}};
9817
const unsigned int v0 = edge_vertices[facet][0];
9818
const unsigned int v1 = edge_vertices[facet][1];
9819
9820
// Compute scale factor (length of edge scaled by length of reference interval)
9821
const double dx0 = x[v1][0] - x[v0][0];
9822
const double dx1 = x[v1][1] - x[v0][1];
9823
const double det = std::sqrt(dx0*dx0 + dx1*dx1);
9824
9825
// Compute geometry tensor
9826
const double G0_0_0 = det*w[1][0]*w[4][0]*(1.0);
9827
const double G0_0_1 = det*w[1][0]*w[4][1]*(1.0);
9828
const double G0_0_2 = det*w[1][0]*w[4][2]*(1.0);
9829
const double G0_0_4 = det*w[1][0]*w[4][4]*(1.0);
9830
const double G0_0_5 = det*w[1][0]*w[4][5]*(1.0);
9831
const double G0_1_0 = det*w[1][1]*w[4][0]*(1.0);
9832
const double G0_1_1 = det*w[1][1]*w[4][1]*(1.0);
9833
const double G0_1_2 = det*w[1][1]*w[4][2]*(1.0);
9834
const double G0_1_3 = det*w[1][1]*w[4][3]*(1.0);
9835
const double G0_1_5 = det*w[1][1]*w[4][5]*(1.0);
9836
const double G0_2_0 = det*w[1][2]*w[4][0]*(1.0);
9837
const double G0_2_1 = det*w[1][2]*w[4][1]*(1.0);
9838
const double G0_2_2 = det*w[1][2]*w[4][2]*(1.0);
9839
const double G0_2_3 = det*w[1][2]*w[4][3]*(1.0);
9840
const double G0_2_4 = det*w[1][2]*w[4][4]*(1.0);
9841
9842
// Compute element tensor
9843
switch (facet)
9844
{
9845
case 0:
9846
{
9847
A[0] = 0.000000000000000;
9848
A[1] = 0.150000000000000*G0_1_1 - 0.016666666666667*G0_1_2 + 0.200000000000000*G0_1_3 + 0.016666666666667*G0_2_1 + 0.016666666666667*G0_2_2 + 0.133333333333333*G0_2_3;
9849
A[2] = 0.016666666666667*G0_1_1 + 0.016666666666667*G0_1_2 + 0.133333333333333*G0_1_3 - 0.016666666666667*G0_2_1 + 0.150000000000000*G0_2_2 + 0.200000000000000*G0_2_3;
9850
break;
9851
}
9852
case 1:
9853
{
9854
A[0] = 0.150000000000000*G0_0_0 - 0.016666666666667*G0_0_2 + 0.200000000000000*G0_0_4 + 0.016666666666667*G0_2_0 + 0.016666666666667*G0_2_2 + 0.133333333333333*G0_2_4;
9855
A[1] = 0.000000000000000;
9856
A[2] = 0.016666666666667*G0_0_0 + 0.016666666666667*G0_0_2 + 0.133333333333333*G0_0_4 - 0.016666666666667*G0_2_0 + 0.150000000000000*G0_2_2 + 0.200000000000000*G0_2_4;
9857
break;
9858
}
9859
case 2:
9860
{
9861
A[0] = 0.150000000000000*G0_0_0 - 0.016666666666667*G0_0_1 + 0.200000000000000*G0_0_5 + 0.016666666666667*G0_1_0 + 0.016666666666667*G0_1_1 + 0.133333333333333*G0_1_5;
9862
A[1] = 0.016666666666667*G0_0_0 + 0.016666666666667*G0_0_1 + 0.133333333333333*G0_0_5 - 0.016666666666667*G0_1_0 + 0.150000000000000*G0_1_1 + 0.200000000000000*G0_1_5;
9863
A[2] = 0.000000000000000;
9864
break;
9865
}
9866
}
9867
9868
}
9869
9870
/// Tabulate the tensor for the contribution from a local exterior facet
9871
/// using the specified reference cell quadrature points/weights
9872
virtual void tabulate_tensor(double* A,
9873
const double * const * w,
9874
const ufc::cell& c,
9875
unsigned int num_quadrature_points,
9876
const double * const * quadrature_points,
9877
const double* quadrature_weights) const
9878
{
9879
throw std::runtime_error("Quadrature version of tabulate_tensor not available when using the FFC tensor representation.");
9880
}
9881
9882
};
9883
9884
/// This class defines the interface for the tabulation of the cell
9885
/// tensor corresponding to the local contribution to a form from
9886
/// the integral over a cell.
9887
9888
class adaptivepoisson_cell_integral_6_0: public ufc::cell_integral
9889
{
9890
public:
9891
9892
/// Constructor
9893
adaptivepoisson_cell_integral_6_0() : ufc::cell_integral()
9894
{
9895
// Do nothing
9896
}
9897
9898
/// Destructor
9899
virtual ~adaptivepoisson_cell_integral_6_0()
9900
{
9901
// Do nothing
9902
}
9903
9904
/// Tabulate the tensor for the contribution from a local cell
9905
virtual void tabulate_tensor(double* A,
9906
const double * const * w,
9907
const ufc::cell& c) const
9908
{
9909
// Extract vertex coordinates
9910
const double * const * x = c.coordinates;
9911
9912
// Compute Jacobian of affine map from reference cell
9913
const double J_00 = x[1][0] - x[0][0];
9914
const double J_01 = x[2][0] - x[0][0];
9915
const double J_10 = x[1][1] - x[0][1];
9916
const double J_11 = x[2][1] - x[0][1];
9917
9918
// Compute determinant of Jacobian
9919
double detJ = J_00*J_11 - J_01*J_10;
9920
9921
// Compute inverse of Jacobian
9922
const double K_00 = J_11 / detJ;
9923
const double K_01 = -J_01 / detJ;
9924
const double K_10 = -J_10 / detJ;
9925
const double K_11 = J_00 / detJ;
9926
9927
// Set scale factor
9928
const double det = std::abs(detJ);
9929
9930
// Cell Volume.
9931
9932
// Compute circumradius, assuming triangle is embedded in 2D.
9933
9934
9935
// Array of quadrature weights.
9936
static const double W4[4] = {0.159020690871988, 0.090979309128011, 0.159020690871988, 0.090979309128011};
9937
// Quadrature points on the UFC reference element: (0.178558728263616, 0.155051025721682), (0.075031110222608, 0.644948974278318), (0.666390246014701, 0.155051025721682), (0.280019915499074, 0.644948974278318)
9938
9939
// Value of basis functions at quadrature points.
9940
static const double FE0[4][3] = \
9941
{{0.666390246014701, 0.178558728263616, 0.155051025721682},
9942
{0.280019915499074, 0.075031110222608, 0.644948974278318},
9943
{0.178558728263616, 0.666390246014701, 0.155051025721682},
9944
{0.075031110222608, 0.280019915499074, 0.644948974278318}};
9945
9946
static const double FE0_D01[4][2] = \
9947
{{-1.000000000000000, 1.000000000000000},
9948
{-1.000000000000000, 1.000000000000000},
9949
{-1.000000000000000, 1.000000000000000},
9950
{-1.000000000000000, 1.000000000000000}};
9951
9952
// Array of non-zero columns
9953
static const unsigned int nzc1[2] = {0, 1};
9954
9955
// Array of non-zero columns
9956
static const unsigned int nzc0[2] = {0, 2};
9957
9958
static const double FE1[4][6] = \
9959
{{0.221761673952367, -0.114792289385376, -0.106969384566991, 0.110742855875331, 0.413297964702014, 0.475959179422654},
9960
{-0.123197609346857, -0.063771775220134, 0.186969384566991, 0.193564950308138, 0.722394229114516, 0.084040820577346},
9961
{-0.114792289385376, 0.221761673952367, -0.106969384566991, 0.413297964702014, 0.110742855875331, 0.475959179422654},
9962
{-0.063771775220134, -0.123197609346857, 0.186969384566991, 0.722394229114516, 0.193564950308138, 0.084040820577346}};
9963
9964
static const double FE1_D01[4][5] = \
9965
{{-1.665560984058806, -0.379795897113271, 0.714234913054465, 2.045356881172077, -0.714234913054465},
9966
{-0.120079661996297, 1.579795897113271, 0.300124440890432, -1.459716235116974, -0.300124440890432},
9967
{0.285765086945535, -0.379795897113271, 2.665560984058804, 0.094030810167737, -2.665560984058805},
9968
{0.699875559109568, 1.579795897113271, 1.120079661996296, -2.279671456222839, -1.120079661996296}};
9969
9970
// Array of non-zero columns
9971
static const unsigned int nzc2[5] = {0, 2, 3, 4, 5};
9972
9973
static const double FE1_D10[4][5] = \
9974
{{-1.665560984058806, -0.285765086945535, 0.620204102886728, -0.620204102886729, 1.951326071004340},
9975
{-0.120079661996296, -0.699875559109568, 2.579795897113270, -2.579795897113271, 0.819955221105864},
9976
{0.285765086945534, 1.665560984058805, 0.620204102886728, -0.620204102886729, -1.951326071004339},
9977
{0.699875559109568, 0.120079661996296, 2.579795897113271, -2.579795897113272, -0.819955221105864}};
9978
9979
// Array of non-zero columns
9980
static const unsigned int nzc3[5] = {0, 1, 3, 4, 5};
9981
9982
// Reset values in the element tensor.
9983
A[0] = 0.000000000000000;
9984
// Number of operations to compute geometry constants: 12.
9985
double G[3];
9986
G[0] = - det*(K_00*K_00 + K_01*K_01);
9987
G[1] = - det*(K_00*K_10 + K_01*K_11);
9988
G[2] = - det*(K_10*K_10 + K_11*K_11);
9989
9990
// Compute element tensor using UFL quadrature representation
9991
// Optimisations: ('eliminate zeros', True), ('ignore ones', True), ('ignore zero tables', True), ('optimisation', 'simplify_expressions'), ('remove zero terms', True)
9992
9993
// Loop quadrature points for integral.
9994
// Number of operations to compute element tensor for following IP loop = 240
9995
for (unsigned int ip = 0; ip < 4; ip++)
9996
{
9997
9998
// Coefficient declarations.
9999
double F0 = 0.000000000000000;
10000
double F1 = 0.000000000000000;
10001
double F2 = 0.000000000000000;
10002
double F3 = 0.000000000000000;
10003
double F4 = 0.000000000000000;
10004
double F5 = 0.000000000000000;
10005
10006
// Total number of operations to compute function values = 8
10007
for (unsigned int r = 0; r < 2; r++)
10008
{
10009
F2 += FE0_D01[ip][r]*w[2][nzc1[r]];
10010
F3 += FE0_D01[ip][r]*w[2][nzc0[r]];
10011
}// end loop over 'r'
10012
10013
// Total number of operations to compute function values = 6
10014
for (unsigned int r = 0; r < 3; r++)
10015
{
10016
F0 += FE0[ip][r]*w[0][r];
10017
}// end loop over 'r'
10018
10019
// Total number of operations to compute function values = 20
10020
for (unsigned int r = 0; r < 5; r++)
10021
{
10022
F4 += FE1_D10[ip][r]*w[3][nzc3[r]];
10023
F5 += FE1_D01[ip][r]*w[3][nzc2[r]];
10024
}// end loop over 'r'
10025
10026
// Total number of operations to compute function values = 12
10027
for (unsigned int r = 0; r < 6; r++)
10028
{
10029
F1 += FE1[ip][r]*w[3][r];
10030
}// end loop over 'r'
10031
10032
// Number of operations to compute ip constants: 13
10033
double I[1];
10034
// Number of operations: 13
10035
I[0] = W4[ip]*(F0*F1*det + F2*(F4*G[0] + F5*G[1]) + F3*(F4*G[1] + F5*G[2]));
10036
10037
10038
// Number of operations for primary indices: 1
10039
// Number of operations to compute entry: 1
10040
A[0] += I[0];
10041
}// end loop over 'ip'
10042
}
10043
10044
/// Tabulate the tensor for the contribution from a local cell
10045
/// using the specified reference cell quadrature points/weights
10046
virtual void tabulate_tensor(double* A,
10047
const double * const * w,
10048
const ufc::cell& c,
10049
unsigned int num_quadrature_points,
10050
const double * const * quadrature_points,
10051
const double* quadrature_weights) const
10052
{
10053
throw std::runtime_error("Quadrature version of tabulate_tensor not yet implemented (introduced in UFC 2.0).");
10054
}
10055
10056
};
10057
10058
/// This class defines the interface for the tabulation of the
10059
/// exterior facet tensor corresponding to the local contribution to
10060
/// a form from the integral over an exterior facet.
10061
10062
class adaptivepoisson_exterior_facet_integral_6_0: public ufc::exterior_facet_integral
10063
{
10064
public:
10065
10066
/// Constructor
10067
adaptivepoisson_exterior_facet_integral_6_0() : ufc::exterior_facet_integral()
10068
{
10069
// Do nothing
10070
}
10071
10072
/// Destructor
10073
virtual ~adaptivepoisson_exterior_facet_integral_6_0()
10074
{
10075
// Do nothing
10076
}
10077
10078
/// Tabulate the tensor for the contribution from a local exterior facet
10079
virtual void tabulate_tensor(double* A,
10080
const double * const * w,
10081
const ufc::cell& c,
10082
unsigned int facet) const
10083
{
10084
// Number of operations (multiply-add pairs) for Jacobian data: 9
10085
// Number of operations (multiply-add pairs) for geometry tensor: 13
10086
// Number of operations (multiply-add pairs) for tensor contraction: 10
10087
// Total number of operations (multiply-add pairs): 32
10088
10089
// Extract vertex coordinates
10090
const double * const * x = c.coordinates;
10091
10092
// Compute Jacobian of affine map from reference cell
10093
10094
// Compute determinant of Jacobian
10095
10096
// Compute inverse of Jacobian
10097
10098
// Get vertices on edge
10099
static unsigned int edge_vertices[3][2] = {{1, 2}, {0, 2}, {0, 1}};
10100
const unsigned int v0 = edge_vertices[facet][0];
10101
const unsigned int v1 = edge_vertices[facet][1];
10102
10103
// Compute scale factor (length of edge scaled by length of reference interval)
10104
const double dx0 = x[v1][0] - x[v0][0];
10105
const double dx1 = x[v1][1] - x[v0][1];
10106
const double det = std::sqrt(dx0*dx0 + dx1*dx1);
10107
10108
// Compute geometry tensor
10109
const double G0_0_0 = det*w[1][0]*w[3][0]*(1.0);
10110
const double G0_0_4 = det*w[1][0]*w[3][4]*(1.0);
10111
const double G0_0_5 = det*w[1][0]*w[3][5]*(1.0);
10112
const double G0_1_1 = det*w[1][1]*w[3][1]*(1.0);
10113
const double G0_1_3 = det*w[1][1]*w[3][3]*(1.0);
10114
const double G0_1_5 = det*w[1][1]*w[3][5]*(1.0);
10115
const double G0_2_2 = det*w[1][2]*w[3][2]*(1.0);
10116
const double G0_2_3 = det*w[1][2]*w[3][3]*(1.0);
10117
const double G0_2_4 = det*w[1][2]*w[3][4]*(1.0);
10118
10119
// Compute element tensor
10120
switch (facet)
10121
{
10122
case 0:
10123
{
10124
A[0] = 0.166666666666666*G0_1_1 + 0.333333333333333*G0_1_3 + 0.166666666666666*G0_2_2 + 0.333333333333333*G0_2_3;
10125
break;
10126
}
10127
case 1:
10128
{
10129
A[0] = 0.166666666666667*G0_0_0 + 0.333333333333333*G0_0_4 + 0.166666666666666*G0_2_2 + 0.333333333333333*G0_2_4;
10130
break;
10131
}
10132
case 2:
10133
{
10134
A[0] = 0.166666666666666*G0_0_0 + 0.333333333333333*G0_0_5 + 0.166666666666667*G0_1_1 + 0.333333333333333*G0_1_5;
10135
break;
10136
}
10137
}
10138
10139
}
10140
10141
/// Tabulate the tensor for the contribution from a local exterior facet
10142
/// using the specified reference cell quadrature points/weights
10143
virtual void tabulate_tensor(double* A,
10144
const double * const * w,
10145
const ufc::cell& c,
10146
unsigned int num_quadrature_points,
10147
const double * const * quadrature_points,
10148
const double* quadrature_weights) const
10149
{
10150
throw std::runtime_error("Quadrature version of tabulate_tensor not available when using the FFC tensor representation.");
10151
}
10152
10153
};
10154
10155
/// This class defines the interface for the tabulation of the cell
10156
/// tensor corresponding to the local contribution to a form from
10157
/// the integral over a cell.
10158
10159
class adaptivepoisson_cell_integral_7_0: public ufc::cell_integral
10160
{
10161
public:
10162
10163
/// Constructor
10164
adaptivepoisson_cell_integral_7_0() : ufc::cell_integral()
10165
{
10166
// Do nothing
10167
}
10168
10169
/// Destructor
10170
virtual ~adaptivepoisson_cell_integral_7_0()
10171
{
10172
// Do nothing
10173
}
10174
10175
/// Tabulate the tensor for the contribution from a local cell
10176
virtual void tabulate_tensor(double* A,
10177
const double * const * w,
10178
const ufc::cell& c) const
10179
{
10180
// Number of operations (multiply-add pairs) for Jacobian data: 9
10181
// Number of operations (multiply-add pairs) for geometry tensor: 40
10182
// Number of operations (multiply-add pairs) for tensor contraction: 26
10183
// Total number of operations (multiply-add pairs): 75
10184
10185
// Extract vertex coordinates
10186
const double * const * x = c.coordinates;
10187
10188
// Compute Jacobian of affine map from reference cell
10189
const double J_00 = x[1][0] - x[0][0];
10190
const double J_01 = x[2][0] - x[0][0];
10191
const double J_10 = x[1][1] - x[0][1];
10192
const double J_11 = x[2][1] - x[0][1];
10193
10194
// Compute determinant of Jacobian
10195
double detJ = J_00*J_11 - J_01*J_10;
10196
10197
// Compute inverse of Jacobian
10198
10199
// Set scale factor
10200
const double det = std::abs(detJ);
10201
10202
// Compute geometry tensor
10203
const double G0_0_0 = det*w[1][0]*w[0][0]*(1.0);
10204
const double G0_0_1 = det*w[1][0]*w[0][1]*(1.0);
10205
const double G0_0_2 = det*w[1][0]*w[0][2]*(1.0);
10206
const double G0_0_3 = det*w[1][0]*w[0][3]*(1.0);
10207
const double G0_0_4 = det*w[1][0]*w[0][4]*(1.0);
10208
const double G0_0_5 = det*w[1][0]*w[0][5]*(1.0);
10209
const double G0_1_0 = det*w[1][1]*w[0][0]*(1.0);
10210
const double G0_1_1 = det*w[1][1]*w[0][1]*(1.0);
10211
const double G0_1_2 = det*w[1][1]*w[0][2]*(1.0);
10212
const double G0_1_3 = det*w[1][1]*w[0][3]*(1.0);
10213
const double G0_1_4 = det*w[1][1]*w[0][4]*(1.0);
10214
const double G0_1_5 = det*w[1][1]*w[0][5]*(1.0);
10215
const double G0_2_0 = det*w[1][2]*w[0][0]*(1.0);
10216
const double G0_2_1 = det*w[1][2]*w[0][1]*(1.0);
10217
const double G0_2_2 = det*w[1][2]*w[0][2]*(1.0);
10218
const double G0_2_3 = det*w[1][2]*w[0][3]*(1.0);
10219
const double G0_2_4 = det*w[1][2]*w[0][4]*(1.0);
10220
const double G0_2_5 = det*w[1][2]*w[0][5]*(1.0);
10221
const double G1_0_0 = det*w[1][0]*w[3][0]*(1.0);
10222
const double G1_0_1 = det*w[1][0]*w[3][1]*(1.0);
10223
const double G1_0_2 = det*w[1][0]*w[3][2]*(1.0);
10224
const double G1_1_0 = det*w[1][1]*w[3][0]*(1.0);
10225
const double G1_1_1 = det*w[1][1]*w[3][1]*(1.0);
10226
const double G1_1_2 = det*w[1][1]*w[3][2]*(1.0);
10227
const double G1_2_0 = det*w[1][2]*w[3][0]*(1.0);
10228
const double G1_2_1 = det*w[1][2]*w[3][1]*(1.0);
10229
const double G1_2_2 = det*w[1][2]*w[3][2]*(1.0);
10230
10231
// Compute element tensor
10232
A[0] = 0.016666666666667*G0_0_0 - 0.008333333333333*G0_0_1 - 0.008333333333333*G0_0_2 + 0.033333333333333*G0_0_3 + 0.066666666666667*G0_0_4 + 0.066666666666666*G0_0_5 - 0.008333333333333*G0_1_0 + 0.016666666666667*G0_1_1 - 0.008333333333333*G0_1_2 + 0.066666666666667*G0_1_3 + 0.033333333333333*G0_1_4 + 0.066666666666666*G0_1_5 - 0.008333333333333*G0_2_0 - 0.008333333333333*G0_2_1 + 0.016666666666667*G0_2_2 + 0.066666666666667*G0_2_3 + 0.066666666666667*G0_2_4 + 0.033333333333333*G0_2_5 - 0.083333333333333*G1_0_0 - 0.041666666666667*G1_0_1 - 0.041666666666667*G1_0_2 - 0.041666666666667*G1_1_0 - 0.083333333333333*G1_1_1 - 0.041666666666667*G1_1_2 - 0.041666666666667*G1_2_0 - 0.041666666666667*G1_2_1 - 0.083333333333333*G1_2_2;
10233
}
10234
10235
/// Tabulate the tensor for the contribution from a local cell
10236
/// using the specified reference cell quadrature points/weights
10237
virtual void tabulate_tensor(double* A,
10238
const double * const * w,
10239
const ufc::cell& c,
10240
unsigned int num_quadrature_points,
10241
const double * const * quadrature_points,
10242
const double* quadrature_weights) const
10243
{
10244
throw std::runtime_error("Quadrature version of tabulate_tensor not available when using the FFC tensor representation.");
10245
}
10246
10247
};
10248
10249
/// This class defines the interface for the tabulation of the
10250
/// exterior facet tensor corresponding to the local contribution to
10251
/// a form from the integral over an exterior facet.
10252
10253
class adaptivepoisson_exterior_facet_integral_7_0: public ufc::exterior_facet_integral
10254
{
10255
public:
10256
10257
/// Constructor
10258
adaptivepoisson_exterior_facet_integral_7_0() : ufc::exterior_facet_integral()
10259
{
10260
// Do nothing
10261
}
10262
10263
/// Destructor
10264
virtual ~adaptivepoisson_exterior_facet_integral_7_0()
10265
{
10266
// Do nothing
10267
}
10268
10269
/// Tabulate the tensor for the contribution from a local exterior facet
10270
virtual void tabulate_tensor(double* A,
10271
const double * const * w,
10272
const ufc::cell& c,
10273
unsigned int facet) const
10274
{
10275
// Number of operations (multiply-add pairs) for Jacobian data: 9
10276
// Number of operations (multiply-add pairs) for geometry tensor: 27
10277
// Number of operations (multiply-add pairs) for tensor contraction: 22
10278
// Total number of operations (multiply-add pairs): 58
10279
10280
// Extract vertex coordinates
10281
const double * const * x = c.coordinates;
10282
10283
// Compute Jacobian of affine map from reference cell
10284
10285
// Compute determinant of Jacobian
10286
10287
// Compute inverse of Jacobian
10288
10289
// Get vertices on edge
10290
static unsigned int edge_vertices[3][2] = {{1, 2}, {0, 2}, {0, 1}};
10291
const unsigned int v0 = edge_vertices[facet][0];
10292
const unsigned int v1 = edge_vertices[facet][1];
10293
10294
// Compute scale factor (length of edge scaled by length of reference interval)
10295
const double dx0 = x[v1][0] - x[v0][0];
10296
const double dx1 = x[v1][1] - x[v0][1];
10297
const double det = std::sqrt(dx0*dx0 + dx1*dx1);
10298
10299
// Compute geometry tensor
10300
const double G0_0_0 = det*w[2][0]*w[0][0]*(1.0);
10301
const double G0_0_4 = det*w[2][0]*w[0][4]*(1.0);
10302
const double G0_0_5 = det*w[2][0]*w[0][5]*(1.0);
10303
const double G0_1_1 = det*w[2][1]*w[0][1]*(1.0);
10304
const double G0_1_3 = det*w[2][1]*w[0][3]*(1.0);
10305
const double G0_1_5 = det*w[2][1]*w[0][5]*(1.0);
10306
const double G0_2_2 = det*w[2][2]*w[0][2]*(1.0);
10307
const double G0_2_3 = det*w[2][2]*w[0][3]*(1.0);
10308
const double G0_2_4 = det*w[2][2]*w[0][4]*(1.0);
10309
const double G1_0_0 = det*w[2][0]*w[3][0]*(1.0);
10310
const double G1_0_1 = det*w[2][0]*w[3][1]*(1.0);
10311
const double G1_0_2 = det*w[2][0]*w[3][2]*(1.0);
10312
const double G1_1_0 = det*w[2][1]*w[3][0]*(1.0);
10313
const double G1_1_1 = det*w[2][1]*w[3][1]*(1.0);
10314
const double G1_1_2 = det*w[2][1]*w[3][2]*(1.0);
10315
const double G1_2_0 = det*w[2][2]*w[3][0]*(1.0);
10316
const double G1_2_1 = det*w[2][2]*w[3][1]*(1.0);
10317
const double G1_2_2 = det*w[2][2]*w[3][2]*(1.0);
10318
10319
// Compute element tensor
10320
switch (facet)
10321
{
10322
case 0:
10323
{
10324
A[0] = 0.166666666666666*G0_1_1 + 0.333333333333333*G0_1_3 + 0.166666666666666*G0_2_2 + 0.333333333333333*G0_2_3 - 0.333333333333333*G1_1_1 - 0.166666666666667*G1_1_2 - 0.166666666666667*G1_2_1 - 0.333333333333333*G1_2_2;
10325
break;
10326
}
10327
case 1:
10328
{
10329
A[0] = 0.166666666666667*G0_0_0 + 0.333333333333333*G0_0_4 + 0.166666666666666*G0_2_2 + 0.333333333333333*G0_2_4 - 0.333333333333333*G1_0_0 - 0.166666666666667*G1_0_2 - 0.166666666666667*G1_2_0 - 0.333333333333333*G1_2_2;
10330
break;
10331
}
10332
case 2:
10333
{
10334
A[0] = 0.166666666666666*G0_0_0 + 0.333333333333333*G0_0_5 + 0.166666666666667*G0_1_1 + 0.333333333333333*G0_1_5 - 0.333333333333333*G1_0_0 - 0.166666666666667*G1_0_1 - 0.166666666666667*G1_1_0 - 0.333333333333333*G1_1_1;
10335
break;
10336
}
10337
}
10338
10339
}
10340
10341
/// Tabulate the tensor for the contribution from a local exterior facet
10342
/// using the specified reference cell quadrature points/weights
10343
virtual void tabulate_tensor(double* A,
10344
const double * const * w,
10345
const ufc::cell& c,
10346
unsigned int num_quadrature_points,
10347
const double * const * quadrature_points,
10348
const double* quadrature_weights) const
10349
{
10350
throw std::runtime_error("Quadrature version of tabulate_tensor not available when using the FFC tensor representation.");
10351
}
10352
10353
};
10354
10355
/// This class defines the interface for the tabulation of the
10356
/// interior facet tensor corresponding to the local contribution to
10357
/// a form from the integral over an interior facet.
10358
10359
class adaptivepoisson_interior_facet_integral_7_0: public ufc::interior_facet_integral
10360
{
10361
public:
10362
10363
/// Constructor
10364
adaptivepoisson_interior_facet_integral_7_0() : ufc::interior_facet_integral()
10365
{
10366
// Do nothing
10367
}
10368
10369
/// Destructor
10370
virtual ~adaptivepoisson_interior_facet_integral_7_0()
10371
{
10372
// Do nothing
10373
}
10374
10375
/// Tabulate the tensor for the contribution from a local interior facet
10376
virtual void tabulate_tensor(double* A,
10377
const double * const * w,
10378
const ufc::cell& c0,
10379
const ufc::cell& c1,
10380
unsigned int facet0,
10381
unsigned int facet1) const
10382
{
10383
// Number of operations (multiply-add pairs) for Jacobian data: 12
10384
// Number of operations (multiply-add pairs) for geometry tensor: 108
10385
// Number of operations (multiply-add pairs) for tensor contraction: 279
10386
// Total number of operations (multiply-add pairs): 399
10387
10388
// Extract vertex coordinates
10389
const double * const * x0 = c0.coordinates;
10390
10391
// Compute Jacobian of affine map from reference cell
10392
10393
// Compute determinant of Jacobian
10394
10395
// Compute inverse of Jacobian
10396
10397
// Compute Jacobian of affine map from reference cell
10398
10399
// Compute determinant of Jacobian
10400
10401
// Compute inverse of Jacobian
10402
10403
// Get vertices on edge
10404
static unsigned int edge_vertices[3][2] = {{1, 2}, {0, 2}, {0, 1}};
10405
const unsigned int v0 = edge_vertices[facet0][0];
10406
const unsigned int v1 = edge_vertices[facet0][1];
10407
10408
// Compute scale factor (length of edge scaled by length of reference interval)
10409
const double dx0 = x0[v1][0] - x0[v0][0];
10410
const double dx1 = x0[v1][1] - x0[v0][1];
10411
const double det = std::sqrt(dx0*dx0 + dx1*dx1);
10412
10413
// Compute geometry tensor
10414
const double G0_3_6 = det*w[2][3]*w[0][6]*(1.0);
10415
const double G0_3_10 = det*w[2][3]*w[0][10]*(1.0);
10416
const double G0_3_11 = det*w[2][3]*w[0][11]*(1.0);
10417
const double G0_4_7 = det*w[2][4]*w[0][7]*(1.0);
10418
const double G0_4_9 = det*w[2][4]*w[0][9]*(1.0);
10419
const double G0_4_11 = det*w[2][4]*w[0][11]*(1.0);
10420
const double G0_5_8 = det*w[2][5]*w[0][8]*(1.0);
10421
const double G0_5_9 = det*w[2][5]*w[0][9]*(1.0);
10422
const double G0_5_10 = det*w[2][5]*w[0][10]*(1.0);
10423
const double G1_3_3 = det*w[2][3]*w[3][3]*(1.0);
10424
const double G1_3_4 = det*w[2][3]*w[3][4]*(1.0);
10425
const double G1_3_5 = det*w[2][3]*w[3][5]*(1.0);
10426
const double G1_4_3 = det*w[2][4]*w[3][3]*(1.0);
10427
const double G1_4_4 = det*w[2][4]*w[3][4]*(1.0);
10428
const double G1_4_5 = det*w[2][4]*w[3][5]*(1.0);
10429
const double G1_5_3 = det*w[2][5]*w[3][3]*(1.0);
10430
const double G1_5_4 = det*w[2][5]*w[3][4]*(1.0);
10431
const double G1_5_5 = det*w[2][5]*w[3][5]*(1.0);
10432
const double G2_0_0 = det*w[2][0]*w[0][0]*(1.0);
10433
const double G2_0_4 = det*w[2][0]*w[0][4]*(1.0);
10434
const double G2_0_5 = det*w[2][0]*w[0][5]*(1.0);
10435
const double G2_1_1 = det*w[2][1]*w[0][1]*(1.0);
10436
const double G2_1_3 = det*w[2][1]*w[0][3]*(1.0);
10437
const double G2_1_5 = det*w[2][1]*w[0][5]*(1.0);
10438
const double G2_2_2 = det*w[2][2]*w[0][2]*(1.0);
10439
const double G2_2_3 = det*w[2][2]*w[0][3]*(1.0);
10440
const double G2_2_4 = det*w[2][2]*w[0][4]*(1.0);
10441
const double G3_0_0 = det*w[2][0]*w[3][0]*(1.0);
10442
const double G3_0_1 = det*w[2][0]*w[3][1]*(1.0);
10443
const double G3_0_2 = det*w[2][0]*w[3][2]*(1.0);
10444
const double G3_1_0 = det*w[2][1]*w[3][0]*(1.0);
10445
const double G3_1_1 = det*w[2][1]*w[3][1]*(1.0);
10446
const double G3_1_2 = det*w[2][1]*w[3][2]*(1.0);
10447
const double G3_2_0 = det*w[2][2]*w[3][0]*(1.0);
10448
const double G3_2_1 = det*w[2][2]*w[3][1]*(1.0);
10449
const double G3_2_2 = det*w[2][2]*w[3][2]*(1.0);
10450
const double G4_3_6 = det*w[2][3]*w[0][6]*(1.0);
10451
const double G4_3_10 = det*w[2][3]*w[0][10]*(1.0);
10452
const double G4_3_11 = det*w[2][3]*w[0][11]*(1.0);
10453
const double G4_4_7 = det*w[2][4]*w[0][7]*(1.0);
10454
const double G4_4_9 = det*w[2][4]*w[0][9]*(1.0);
10455
const double G4_4_11 = det*w[2][4]*w[0][11]*(1.0);
10456
const double G4_5_8 = det*w[2][5]*w[0][8]*(1.0);
10457
const double G4_5_9 = det*w[2][5]*w[0][9]*(1.0);
10458
const double G4_5_10 = det*w[2][5]*w[0][10]*(1.0);
10459
const double G5_3_3 = det*w[2][3]*w[3][3]*(1.0);
10460
const double G5_3_4 = det*w[2][3]*w[3][4]*(1.0);
10461
const double G5_3_5 = det*w[2][3]*w[3][5]*(1.0);
10462
const double G5_4_3 = det*w[2][4]*w[3][3]*(1.0);
10463
const double G5_4_4 = det*w[2][4]*w[3][4]*(1.0);
10464
const double G5_4_5 = det*w[2][4]*w[3][5]*(1.0);
10465
const double G5_5_3 = det*w[2][5]*w[3][3]*(1.0);
10466
const double G5_5_4 = det*w[2][5]*w[3][4]*(1.0);
10467
const double G5_5_5 = det*w[2][5]*w[3][5]*(1.0);
10468
const double G6_0_0 = det*w[2][0]*w[0][0]*(1.0);
10469
const double G6_0_4 = det*w[2][0]*w[0][4]*(1.0);
10470
const double G6_0_5 = det*w[2][0]*w[0][5]*(1.0);
10471
const double G6_1_1 = det*w[2][1]*w[0][1]*(1.0);
10472
const double G6_1_3 = det*w[2][1]*w[0][3]*(1.0);
10473
const double G6_1_5 = det*w[2][1]*w[0][5]*(1.0);
10474
const double G6_2_2 = det*w[2][2]*w[0][2]*(1.0);
10475
const double G6_2_3 = det*w[2][2]*w[0][3]*(1.0);
10476
const double G6_2_4 = det*w[2][2]*w[0][4]*(1.0);
10477
const double G7_0_0 = det*w[2][0]*w[3][0]*(1.0);
10478
const double G7_0_1 = det*w[2][0]*w[3][1]*(1.0);
10479
const double G7_0_2 = det*w[2][0]*w[3][2]*(1.0);
10480
const double G7_1_0 = det*w[2][1]*w[3][0]*(1.0);
10481
const double G7_1_1 = det*w[2][1]*w[3][1]*(1.0);
10482
const double G7_1_2 = det*w[2][1]*w[3][2]*(1.0);
10483
const double G7_2_0 = det*w[2][2]*w[3][0]*(1.0);
10484
const double G7_2_1 = det*w[2][2]*w[3][1]*(1.0);
10485
const double G7_2_2 = det*w[2][2]*w[3][2]*(1.0);
10486
10487
// Compute element tensor
10488
switch (facet0)
10489
{
10490
case 0:
10491
{
10492
switch (facet1)
10493
{
10494
case 0:
10495
{
10496
A[0] = 0.083333333333333*G4_4_7 + 0.166666666666667*G4_4_9 + 0.083333333333333*G4_5_8 + 0.166666666666667*G4_5_9 - 0.166666666666667*G5_4_4 - 0.083333333333333*G5_4_5 - 0.083333333333333*G5_5_4 - 0.166666666666667*G5_5_5 + 0.083333333333333*G6_1_1 + 0.166666666666667*G6_1_3 + 0.083333333333333*G6_2_2 + 0.166666666666667*G6_2_3 - 0.166666666666667*G7_1_1 - 0.083333333333333*G7_1_2 - 0.083333333333333*G7_2_1 - 0.166666666666667*G7_2_2;
10497
A[1] = 0.083333333333333*G0_4_7 + 0.166666666666667*G0_4_9 + 0.083333333333333*G0_5_8 + 0.166666666666667*G0_5_9 - 0.166666666666667*G1_4_4 - 0.083333333333333*G1_4_5 - 0.083333333333333*G1_5_4 - 0.166666666666667*G1_5_5 + 0.083333333333333*G2_1_1 + 0.166666666666667*G2_1_3 + 0.083333333333333*G2_2_2 + 0.166666666666667*G2_2_3 - 0.166666666666667*G3_1_1 - 0.083333333333333*G3_1_2 - 0.083333333333333*G3_2_1 - 0.166666666666667*G3_2_2;
10498
break;
10499
}
10500
case 1:
10501
{
10502
A[0] = 0.083333333333333*G4_3_6 + 0.166666666666667*G4_3_10 + 0.083333333333333*G4_5_8 + 0.166666666666667*G4_5_10 - 0.166666666666667*G5_3_3 - 0.083333333333333*G5_3_5 - 0.083333333333333*G5_5_3 - 0.166666666666667*G5_5_5 + 0.083333333333333*G6_1_1 + 0.166666666666667*G6_1_3 + 0.083333333333333*G6_2_2 + 0.166666666666667*G6_2_3 - 0.166666666666667*G7_1_1 - 0.083333333333333*G7_1_2 - 0.083333333333333*G7_2_1 - 0.166666666666667*G7_2_2;
10503
A[1] = 0.083333333333333*G0_3_6 + 0.166666666666667*G0_3_10 + 0.083333333333333*G0_5_8 + 0.166666666666667*G0_5_10 - 0.166666666666667*G1_3_3 - 0.083333333333333*G1_3_5 - 0.083333333333333*G1_5_3 - 0.166666666666667*G1_5_5 + 0.083333333333333*G2_1_1 + 0.166666666666667*G2_1_3 + 0.083333333333333*G2_2_2 + 0.166666666666667*G2_2_3 - 0.166666666666667*G3_1_1 - 0.083333333333333*G3_1_2 - 0.083333333333333*G3_2_1 - 0.166666666666667*G3_2_2;
10504
break;
10505
}
10506
case 2:
10507
{
10508
A[0] = 0.083333333333333*G4_3_6 + 0.166666666666667*G4_3_11 + 0.083333333333333*G4_4_7 + 0.166666666666667*G4_4_11 - 0.166666666666666*G5_3_3 - 0.083333333333333*G5_3_4 - 0.083333333333333*G5_4_3 - 0.166666666666667*G5_4_4 + 0.083333333333333*G6_1_1 + 0.166666666666667*G6_1_3 + 0.083333333333333*G6_2_2 + 0.166666666666667*G6_2_3 - 0.166666666666667*G7_1_1 - 0.083333333333333*G7_1_2 - 0.083333333333333*G7_2_1 - 0.166666666666667*G7_2_2;
10509
A[1] = 0.083333333333333*G0_3_6 + 0.166666666666667*G0_3_11 + 0.083333333333333*G0_4_7 + 0.166666666666667*G0_4_11 - 0.166666666666666*G1_3_3 - 0.083333333333333*G1_3_4 - 0.083333333333333*G1_4_3 - 0.166666666666667*G1_4_4 + 0.083333333333333*G2_1_1 + 0.166666666666667*G2_1_3 + 0.083333333333333*G2_2_2 + 0.166666666666667*G2_2_3 - 0.166666666666667*G3_1_1 - 0.083333333333333*G3_1_2 - 0.083333333333333*G3_2_1 - 0.166666666666667*G3_2_2;
10510
break;
10511
}
10512
}
10513
10514
break;
10515
}
10516
case 1:
10517
{
10518
switch (facet1)
10519
{
10520
case 0:
10521
{
10522
A[0] = 0.083333333333333*G4_4_7 + 0.166666666666667*G4_4_9 + 0.083333333333333*G4_5_8 + 0.166666666666667*G4_5_9 - 0.166666666666667*G5_4_4 - 0.083333333333333*G5_4_5 - 0.083333333333333*G5_5_4 - 0.166666666666667*G5_5_5 + 0.083333333333333*G6_0_0 + 0.166666666666667*G6_0_4 + 0.083333333333333*G6_2_2 + 0.166666666666667*G6_2_4 - 0.166666666666667*G7_0_0 - 0.083333333333333*G7_0_2 - 0.083333333333333*G7_2_0 - 0.166666666666667*G7_2_2;
10523
A[1] = 0.083333333333333*G0_4_7 + 0.166666666666667*G0_4_9 + 0.083333333333333*G0_5_8 + 0.166666666666667*G0_5_9 - 0.166666666666667*G1_4_4 - 0.083333333333333*G1_4_5 - 0.083333333333333*G1_5_4 - 0.166666666666667*G1_5_5 + 0.083333333333333*G2_0_0 + 0.166666666666667*G2_0_4 + 0.083333333333333*G2_2_2 + 0.166666666666667*G2_2_4 - 0.166666666666667*G3_0_0 - 0.083333333333333*G3_0_2 - 0.083333333333333*G3_2_0 - 0.166666666666667*G3_2_2;
10524
break;
10525
}
10526
case 1:
10527
{
10528
A[0] = 0.083333333333333*G4_3_6 + 0.166666666666667*G4_3_10 + 0.083333333333333*G4_5_8 + 0.166666666666667*G4_5_10 - 0.166666666666667*G5_3_3 - 0.083333333333333*G5_3_5 - 0.083333333333333*G5_5_3 - 0.166666666666667*G5_5_5 + 0.083333333333333*G6_0_0 + 0.166666666666667*G6_0_4 + 0.083333333333333*G6_2_2 + 0.166666666666667*G6_2_4 - 0.166666666666667*G7_0_0 - 0.083333333333333*G7_0_2 - 0.083333333333333*G7_2_0 - 0.166666666666667*G7_2_2;
10529
A[1] = 0.083333333333333*G0_3_6 + 0.166666666666667*G0_3_10 + 0.083333333333333*G0_5_8 + 0.166666666666667*G0_5_10 - 0.166666666666667*G1_3_3 - 0.083333333333333*G1_3_5 - 0.083333333333333*G1_5_3 - 0.166666666666667*G1_5_5 + 0.083333333333333*G2_0_0 + 0.166666666666667*G2_0_4 + 0.083333333333333*G2_2_2 + 0.166666666666667*G2_2_4 - 0.166666666666667*G3_0_0 - 0.083333333333333*G3_0_2 - 0.083333333333333*G3_2_0 - 0.166666666666667*G3_2_2;
10530
break;
10531
}
10532
case 2:
10533
{
10534
A[0] = 0.083333333333333*G4_3_6 + 0.166666666666667*G4_3_11 + 0.083333333333333*G4_4_7 + 0.166666666666667*G4_4_11 - 0.166666666666666*G5_3_3 - 0.083333333333333*G5_3_4 - 0.083333333333333*G5_4_3 - 0.166666666666667*G5_4_4 + 0.083333333333333*G6_0_0 + 0.166666666666667*G6_0_4 + 0.083333333333333*G6_2_2 + 0.166666666666667*G6_2_4 - 0.166666666666667*G7_0_0 - 0.083333333333333*G7_0_2 - 0.083333333333333*G7_2_0 - 0.166666666666667*G7_2_2;
10535
A[1] = 0.083333333333333*G0_3_6 + 0.166666666666667*G0_3_11 + 0.083333333333333*G0_4_7 + 0.166666666666667*G0_4_11 - 0.166666666666666*G1_3_3 - 0.083333333333333*G1_3_4 - 0.083333333333333*G1_4_3 - 0.166666666666667*G1_4_4 + 0.083333333333333*G2_0_0 + 0.166666666666667*G2_0_4 + 0.083333333333333*G2_2_2 + 0.166666666666667*G2_2_4 - 0.166666666666667*G3_0_0 - 0.083333333333333*G3_0_2 - 0.083333333333333*G3_2_0 - 0.166666666666667*G3_2_2;
10536
break;
10537
}
10538
}
10539
10540
break;
10541
}
10542
case 2:
10543
{
10544
switch (facet1)
10545
{
10546
case 0:
10547
{
10548
A[0] = 0.083333333333333*G4_4_7 + 0.166666666666667*G4_4_9 + 0.083333333333333*G4_5_8 + 0.166666666666667*G4_5_9 - 0.166666666666667*G5_4_4 - 0.083333333333333*G5_4_5 - 0.083333333333333*G5_5_4 - 0.166666666666667*G5_5_5 + 0.083333333333333*G6_0_0 + 0.166666666666667*G6_0_5 + 0.083333333333333*G6_1_1 + 0.166666666666667*G6_1_5 - 0.166666666666666*G7_0_0 - 0.083333333333333*G7_0_1 - 0.083333333333333*G7_1_0 - 0.166666666666667*G7_1_1;
10549
A[1] = 0.083333333333333*G0_4_7 + 0.166666666666667*G0_4_9 + 0.083333333333333*G0_5_8 + 0.166666666666667*G0_5_9 - 0.166666666666667*G1_4_4 - 0.083333333333333*G1_4_5 - 0.083333333333333*G1_5_4 - 0.166666666666667*G1_5_5 + 0.083333333333333*G2_0_0 + 0.166666666666667*G2_0_5 + 0.083333333333333*G2_1_1 + 0.166666666666667*G2_1_5 - 0.166666666666666*G3_0_0 - 0.083333333333333*G3_0_1 - 0.083333333333333*G3_1_0 - 0.166666666666667*G3_1_1;
10550
break;
10551
}
10552
case 1:
10553
{
10554
A[0] = 0.083333333333333*G4_3_6 + 0.166666666666667*G4_3_10 + 0.083333333333333*G4_5_8 + 0.166666666666667*G4_5_10 - 0.166666666666667*G5_3_3 - 0.083333333333333*G5_3_5 - 0.083333333333333*G5_5_3 - 0.166666666666667*G5_5_5 + 0.083333333333333*G6_0_0 + 0.166666666666667*G6_0_5 + 0.083333333333333*G6_1_1 + 0.166666666666667*G6_1_5 - 0.166666666666666*G7_0_0 - 0.083333333333333*G7_0_1 - 0.083333333333333*G7_1_0 - 0.166666666666667*G7_1_1;
10555
A[1] = 0.083333333333333*G0_3_6 + 0.166666666666667*G0_3_10 + 0.083333333333333*G0_5_8 + 0.166666666666667*G0_5_10 - 0.166666666666667*G1_3_3 - 0.083333333333333*G1_3_5 - 0.083333333333333*G1_5_3 - 0.166666666666667*G1_5_5 + 0.083333333333333*G2_0_0 + 0.166666666666667*G2_0_5 + 0.083333333333333*G2_1_1 + 0.166666666666667*G2_1_5 - 0.166666666666666*G3_0_0 - 0.083333333333333*G3_0_1 - 0.083333333333333*G3_1_0 - 0.166666666666667*G3_1_1;
10556
break;
10557
}
10558
case 2:
10559
{
10560
A[0] = 0.083333333333333*G4_3_6 + 0.166666666666667*G4_3_11 + 0.083333333333333*G4_4_7 + 0.166666666666667*G4_4_11 - 0.166666666666666*G5_3_3 - 0.083333333333333*G5_3_4 - 0.083333333333333*G5_4_3 - 0.166666666666667*G5_4_4 + 0.083333333333333*G6_0_0 + 0.166666666666667*G6_0_5 + 0.083333333333333*G6_1_1 + 0.166666666666667*G6_1_5 - 0.166666666666666*G7_0_0 - 0.083333333333333*G7_0_1 - 0.083333333333333*G7_1_0 - 0.166666666666667*G7_1_1;
10561
A[1] = 0.083333333333333*G0_3_6 + 0.166666666666667*G0_3_11 + 0.083333333333333*G0_4_7 + 0.166666666666667*G0_4_11 - 0.166666666666666*G1_3_3 - 0.083333333333333*G1_3_4 - 0.083333333333333*G1_4_3 - 0.166666666666667*G1_4_4 + 0.083333333333333*G2_0_0 + 0.166666666666667*G2_0_5 + 0.083333333333333*G2_1_1 + 0.166666666666667*G2_1_5 - 0.166666666666666*G3_0_0 - 0.083333333333333*G3_0_1 - 0.083333333333333*G3_1_0 - 0.166666666666667*G3_1_1;
10562
break;
10563
}
10564
}
10565
10566
break;
10567
}
10568
}
10569
10570
}
10571
10572
/// Tabulate the tensor for the contribution from a local interior facet
10573
/// using the specified reference cell quadrature points/weights
10574
virtual void tabulate_tensor(double* A,
10575
const double * const * w,
10576
const ufc::cell& c,
10577
unsigned int num_quadrature_points,
10578
const double * const * quadrature_points,
10579
const double* quadrature_weights) const
10580
{
10581
throw std::runtime_error("Quadrature version of tabulate_tensor not available when using the FFC tensor representation.");
10582
}
10583
10584
};
10585
10586
/// This class defines the interface for the tabulation of the cell
10587
/// tensor corresponding to the local contribution to a form from
10588
/// the integral over a cell.
10589
10590
class adaptivepoisson_cell_integral_8_0: public ufc::cell_integral
10591
{
10592
public:
10593
10594
/// Constructor
10595
adaptivepoisson_cell_integral_8_0() : ufc::cell_integral()
10596
{
10597
// Do nothing
10598
}
10599
10600
/// Destructor
10601
virtual ~adaptivepoisson_cell_integral_8_0()
10602
{
10603
// Do nothing
10604
}
10605
10606
/// Tabulate the tensor for the contribution from a local cell
10607
virtual void tabulate_tensor(double* A,
10608
const double * const * w,
10609
const ufc::cell& c) const
10610
{
10611
// Number of operations (multiply-add pairs) for Jacobian data: 11
10612
// Number of operations (multiply-add pairs) for geometry tensor: 8
10613
// Number of operations (multiply-add pairs) for tensor contraction: 11
10614
// Total number of operations (multiply-add pairs): 30
10615
10616
// Extract vertex coordinates
10617
const double * const * x = c.coordinates;
10618
10619
// Compute Jacobian of affine map from reference cell
10620
const double J_00 = x[1][0] - x[0][0];
10621
const double J_01 = x[2][0] - x[0][0];
10622
const double J_10 = x[1][1] - x[0][1];
10623
const double J_11 = x[2][1] - x[0][1];
10624
10625
// Compute determinant of Jacobian
10626
double detJ = J_00*J_11 - J_01*J_10;
10627
10628
// Compute inverse of Jacobian
10629
const double K_00 = J_11 / detJ;
10630
const double K_01 = -J_01 / detJ;
10631
const double K_10 = -J_10 / detJ;
10632
const double K_11 = J_00 / detJ;
10633
10634
// Set scale factor
10635
const double det = std::abs(detJ);
10636
10637
// Compute geometry tensor
10638
const double G0_0_0 = det*(K_00*K_00 + K_01*K_01);
10639
const double G0_0_1 = det*(K_00*K_10 + K_01*K_11);
10640
const double G0_1_0 = det*(K_10*K_00 + K_11*K_01);
10641
const double G0_1_1 = det*(K_10*K_10 + K_11*K_11);
10642
10643
// Compute element tensor
10644
A[0] = 0.500000000000000*G0_0_0 + 0.500000000000000*G0_0_1 + 0.500000000000000*G0_1_0 + 0.500000000000000*G0_1_1;
10645
A[1] = -0.500000000000000*G0_0_0 - 0.500000000000000*G0_1_0;
10646
A[2] = -0.500000000000000*G0_0_1 - 0.500000000000000*G0_1_1;
10647
A[3] = -0.500000000000000*G0_0_0 - 0.500000000000000*G0_0_1;
10648
A[4] = 0.500000000000000*G0_0_0;
10649
A[5] = 0.500000000000000*G0_0_1;
10650
A[6] = -0.500000000000000*G0_1_0 - 0.500000000000000*G0_1_1;
10651
A[7] = 0.500000000000000*G0_1_0;
10652
A[8] = 0.500000000000000*G0_1_1;
10653
}
10654
10655
/// Tabulate the tensor for the contribution from a local cell
10656
/// using the specified reference cell quadrature points/weights
10657
virtual void tabulate_tensor(double* A,
10658
const double * const * w,
10659
const ufc::cell& c,
10660
unsigned int num_quadrature_points,
10661
const double * const * quadrature_points,
10662
const double* quadrature_weights) const
10663
{
10664
throw std::runtime_error("Quadrature version of tabulate_tensor not available when using the FFC tensor representation.");
10665
}
10666
10667
};
10668
10669
/// This class defines the interface for the tabulation of the cell
10670
/// tensor corresponding to the local contribution to a form from
10671
/// the integral over a cell.
10672
10673
class adaptivepoisson_cell_integral_9_0: public ufc::cell_integral
10674
{
10675
public:
10676
10677
/// Constructor
10678
adaptivepoisson_cell_integral_9_0() : ufc::cell_integral()
10679
{
10680
// Do nothing
10681
}
10682
10683
/// Destructor
10684
virtual ~adaptivepoisson_cell_integral_9_0()
10685
{
10686
// Do nothing
10687
}
10688
10689
/// Tabulate the tensor for the contribution from a local cell
10690
virtual void tabulate_tensor(double* A,
10691
const double * const * w,
10692
const ufc::cell& c) const
10693
{
10694
// Number of operations (multiply-add pairs) for Jacobian data: 9
10695
// Number of operations (multiply-add pairs) for geometry tensor: 3
10696
// Number of operations (multiply-add pairs) for tensor contraction: 7
10697
// Total number of operations (multiply-add pairs): 19
10698
10699
// Extract vertex coordinates
10700
const double * const * x = c.coordinates;
10701
10702
// Compute Jacobian of affine map from reference cell
10703
const double J_00 = x[1][0] - x[0][0];
10704
const double J_01 = x[2][0] - x[0][0];
10705
const double J_10 = x[1][1] - x[0][1];
10706
const double J_11 = x[2][1] - x[0][1];
10707
10708
// Compute determinant of Jacobian
10709
double detJ = J_00*J_11 - J_01*J_10;
10710
10711
// Compute inverse of Jacobian
10712
10713
// Set scale factor
10714
const double det = std::abs(detJ);
10715
10716
// Compute geometry tensor
10717
const double G0_0 = det*w[0][0]*(1.0);
10718
const double G0_1 = det*w[0][1]*(1.0);
10719
const double G0_2 = det*w[0][2]*(1.0);
10720
10721
// Compute element tensor
10722
A[0] = 0.083333333333333*G0_0 + 0.041666666666667*G0_1 + 0.041666666666667*G0_2;
10723
A[1] = 0.041666666666667*G0_0 + 0.083333333333333*G0_1 + 0.041666666666667*G0_2;
10724
A[2] = 0.041666666666667*G0_0 + 0.041666666666667*G0_1 + 0.083333333333333*G0_2;
10725
}
10726
10727
/// Tabulate the tensor for the contribution from a local cell
10728
/// using the specified reference cell quadrature points/weights
10729
virtual void tabulate_tensor(double* A,
10730
const double * const * w,
10731
const ufc::cell& c,
10732
unsigned int num_quadrature_points,
10733
const double * const * quadrature_points,
10734
const double* quadrature_weights) const
10735
{
10736
throw std::runtime_error("Quadrature version of tabulate_tensor not available when using the FFC tensor representation.");
10737
}
10738
10739
};
10740
10741
/// This class defines the interface for the tabulation of the
10742
/// exterior facet tensor corresponding to the local contribution to
10743
/// a form from the integral over an exterior facet.
10744
10745
class adaptivepoisson_exterior_facet_integral_9_0: public ufc::exterior_facet_integral
10746
{
10747
public:
10748
10749
/// Constructor
10750
adaptivepoisson_exterior_facet_integral_9_0() : ufc::exterior_facet_integral()
10751
{
10752
// Do nothing
10753
}
10754
10755
/// Destructor
10756
virtual ~adaptivepoisson_exterior_facet_integral_9_0()
10757
{
10758
// Do nothing
10759
}
10760
10761
/// Tabulate the tensor for the contribution from a local exterior facet
10762
virtual void tabulate_tensor(double* A,
10763
const double * const * w,
10764
const ufc::cell& c,
10765
unsigned int facet) const
10766
{
10767
// Number of operations (multiply-add pairs) for Jacobian data: 9
10768
// Number of operations (multiply-add pairs) for geometry tensor: 3
10769
// Number of operations (multiply-add pairs) for tensor contraction: 9
10770
// Total number of operations (multiply-add pairs): 21
10771
10772
// Extract vertex coordinates
10773
const double * const * x = c.coordinates;
10774
10775
// Compute Jacobian of affine map from reference cell
10776
10777
// Compute determinant of Jacobian
10778
10779
// Compute inverse of Jacobian
10780
10781
// Get vertices on edge
10782
static unsigned int edge_vertices[3][2] = {{1, 2}, {0, 2}, {0, 1}};
10783
const unsigned int v0 = edge_vertices[facet][0];
10784
const unsigned int v1 = edge_vertices[facet][1];
10785
10786
// Compute scale factor (length of edge scaled by length of reference interval)
10787
const double dx0 = x[v1][0] - x[v0][0];
10788
const double dx1 = x[v1][1] - x[v0][1];
10789
const double det = std::sqrt(dx0*dx0 + dx1*dx1);
10790
10791
// Compute geometry tensor
10792
const double G0_0 = det*w[1][0]*(1.0);
10793
const double G0_1 = det*w[1][1]*(1.0);
10794
const double G0_2 = det*w[1][2]*(1.0);
10795
10796
// Compute element tensor
10797
switch (facet)
10798
{
10799
case 0:
10800
{
10801
A[0] = 0.000000000000000;
10802
A[1] = 0.333333333333333*G0_1 + 0.166666666666667*G0_2;
10803
A[2] = 0.166666666666667*G0_1 + 0.333333333333333*G0_2;
10804
break;
10805
}
10806
case 1:
10807
{
10808
A[0] = 0.333333333333333*G0_0 + 0.166666666666667*G0_2;
10809
A[1] = 0.000000000000000;
10810
A[2] = 0.166666666666667*G0_0 + 0.333333333333333*G0_2;
10811
break;
10812
}
10813
case 2:
10814
{
10815
A[0] = 0.333333333333333*G0_0 + 0.166666666666667*G0_1;
10816
A[1] = 0.166666666666667*G0_0 + 0.333333333333333*G0_1;
10817
A[2] = 0.000000000000000;
10818
break;
10819
}
10820
}
10821
10822
}
10823
10824
/// Tabulate the tensor for the contribution from a local exterior facet
10825
/// using the specified reference cell quadrature points/weights
10826
virtual void tabulate_tensor(double* A,
10827
const double * const * w,
10828
const ufc::cell& c,
10829
unsigned int num_quadrature_points,
10830
const double * const * quadrature_points,
10831
const double* quadrature_weights) const
10832
{
10833
throw std::runtime_error("Quadrature version of tabulate_tensor not available when using the FFC tensor representation.");
10834
}
10835
10836
};
10837
10838
/// This class defines the interface for the tabulation of the cell
10839
/// tensor corresponding to the local contribution to a form from
10840
/// the integral over a cell.
10841
10842
class adaptivepoisson_cell_integral_10_0: public ufc::cell_integral
10843
{
10844
public:
10845
10846
/// Constructor
10847
adaptivepoisson_cell_integral_10_0() : ufc::cell_integral()
10848
{
10849
// Do nothing
10850
}
10851
10852
/// Destructor
10853
virtual ~adaptivepoisson_cell_integral_10_0()
10854
{
10855
// Do nothing
10856
}
10857
10858
/// Tabulate the tensor for the contribution from a local cell
10859
virtual void tabulate_tensor(double* A,
10860
const double * const * w,
10861
const ufc::cell& c) const
10862
{
10863
// Number of operations (multiply-add pairs) for Jacobian data: 9
10864
// Number of operations (multiply-add pairs) for geometry tensor: 3
10865
// Number of operations (multiply-add pairs) for tensor contraction: 2
10866
// Total number of operations (multiply-add pairs): 14
10867
10868
// Extract vertex coordinates
10869
const double * const * x = c.coordinates;
10870
10871
// Compute Jacobian of affine map from reference cell
10872
const double J_00 = x[1][0] - x[0][0];
10873
const double J_01 = x[2][0] - x[0][0];
10874
const double J_10 = x[1][1] - x[0][1];
10875
const double J_11 = x[2][1] - x[0][1];
10876
10877
// Compute determinant of Jacobian
10878
double detJ = J_00*J_11 - J_01*J_10;
10879
10880
// Compute inverse of Jacobian
10881
10882
// Set scale factor
10883
const double det = std::abs(detJ);
10884
10885
// Compute geometry tensor
10886
const double G0_0 = det*w[0][0]*(1.0);
10887
const double G0_1 = det*w[0][1]*(1.0);
10888
const double G0_2 = det*w[0][2]*(1.0);
10889
10890
// Compute element tensor
10891
A[0] = 0.166666666666667*G0_0 + 0.166666666666667*G0_1 + 0.166666666666667*G0_2;
10892
}
10893
10894
/// Tabulate the tensor for the contribution from a local cell
10895
/// using the specified reference cell quadrature points/weights
10896
virtual void tabulate_tensor(double* A,
10897
const double * const * w,
10898
const ufc::cell& c,
10899
unsigned int num_quadrature_points,
10900
const double * const * quadrature_points,
10901
const double* quadrature_weights) const
10902
{
10903
throw std::runtime_error("Quadrature version of tabulate_tensor not available when using the FFC tensor representation.");
10904
}
10905
10906
};
10907
10908
/// This class defines the interface for the assembly of the global
10909
/// tensor corresponding to a form with r + n arguments, that is, a
10910
/// mapping
10911
///
10912
/// a : V1 x V2 x ... Vr x W1 x W2 x ... x Wn -> R
10913
///
10914
/// with arguments v1, v2, ..., vr, w1, w2, ..., wn. The rank r
10915
/// global tensor A is defined by
10916
///
10917
/// A = a(V1, V2, ..., Vr, w1, w2, ..., wn),
10918
///
10919
/// where each argument Vj represents the application to the
10920
/// sequence of basis functions of Vj and w1, w2, ..., wn are given
10921
/// fixed functions (coefficients).
10922
10923
class adaptivepoisson_form_0: public ufc::form
10924
{
10925
public:
10926
10927
/// Constructor
10928
adaptivepoisson_form_0() : ufc::form()
10929
{
10930
// Do nothing
10931
}
10932
10933
/// Destructor
10934
virtual ~adaptivepoisson_form_0()
10935
{
10936
// Do nothing
10937
}
10938
10939
/// Return a string identifying the form
10940
virtual const char* signature() const
10941
{
10942
return "Form([Integral(IndexSum(Product(Indexed(ComponentTensor(SpatialDerivative(Argument(FiniteElement('Lagrange', Cell('triangle', 1, Space(2)), 1), 0), MultiIndex((Index(0),), {Index(0): 2})), MultiIndex((Index(0),), {Index(0): 2})), MultiIndex((Index(1),), {Index(1): 2})), Indexed(ComponentTensor(SpatialDerivative(Argument(FiniteElement('Lagrange', Cell('triangle', 1, Space(2)), 1), 1), MultiIndex((Index(2),), {Index(2): 2})), MultiIndex((Index(2),), {Index(2): 2})), MultiIndex((Index(1),), {Index(1): 2}))), MultiIndex((Index(1),), {Index(1): 2})), Measure('cell', 0, None))])";
10943
}
10944
10945
/// Return the rank of the global tensor (r)
10946
virtual unsigned int rank() const
10947
{
10948
return 2;
10949
}
10950
10951
/// Return the number of coefficients (n)
10952
virtual unsigned int num_coefficients() const
10953
{
10954
return 0;
10955
}
10956
10957
/// Return the number of cell domains
10958
virtual unsigned int num_cell_domains() const
10959
{
10960
return 1;
10961
}
10962
10963
/// Return the number of exterior facet domains
10964
virtual unsigned int num_exterior_facet_domains() const
10965
{
10966
return 0;
10967
}
10968
10969
/// Return the number of interior facet domains
10970
virtual unsigned int num_interior_facet_domains() const
10971
{
10972
return 0;
10973
}
10974
10975
/// Create a new finite element for argument function i
10976
virtual ufc::finite_element* create_finite_element(unsigned int i) const
10977
{
10978
switch (i)
10979
{
10980
case 0:
10981
{
10982
return new adaptivepoisson_finite_element_5();
10983
break;
10984
}
10985
case 1:
10986
{
10987
return new adaptivepoisson_finite_element_5();
10988
break;
10989
}
10990
}
10991
10992
return 0;
10993
}
10994
10995
/// Create a new dofmap for argument function i
10996
virtual ufc::dofmap* create_dofmap(unsigned int i) const
10997
{
10998
switch (i)
10999
{
11000
case 0:
11001
{
11002
return new adaptivepoisson_dofmap_5();
11003
break;
11004
}
11005
case 1:
11006
{
11007
return new adaptivepoisson_dofmap_5();
11008
break;
11009
}
11010
}
11011
11012
return 0;
11013
}
11014
11015
/// Create a new cell integral on sub domain i
11016
virtual ufc::cell_integral* create_cell_integral(unsigned int i) const
11017
{
11018
switch (i)
11019
{
11020
case 0:
11021
{
11022
return new adaptivepoisson_cell_integral_0_0();
11023
break;
11024
}
11025
}
11026
11027
return 0;
11028
}
11029
11030
/// Create a new exterior facet integral on sub domain i
11031
virtual ufc::exterior_facet_integral* create_exterior_facet_integral(unsigned int i) const
11032
{
11033
return 0;
11034
}
11035
11036
/// Create a new interior facet integral on sub domain i
11037
virtual ufc::interior_facet_integral* create_interior_facet_integral(unsigned int i) const
11038
{
11039
return 0;
11040
}
11041
11042
};
11043
11044
/// This class defines the interface for the assembly of the global
11045
/// tensor corresponding to a form with r + n arguments, that is, a
11046
/// mapping
11047
///
11048
/// a : V1 x V2 x ... Vr x W1 x W2 x ... x Wn -> R
11049
///
11050
/// with arguments v1, v2, ..., vr, w1, w2, ..., wn. The rank r
11051
/// global tensor A is defined by
11052
///
11053
/// A = a(V1, V2, ..., Vr, w1, w2, ..., wn),
11054
///
11055
/// where each argument Vj represents the application to the
11056
/// sequence of basis functions of Vj and w1, w2, ..., wn are given
11057
/// fixed functions (coefficients).
11058
11059
class adaptivepoisson_form_1: public ufc::form
11060
{
11061
public:
11062
11063
/// Constructor
11064
adaptivepoisson_form_1() : ufc::form()
11065
{
11066
// Do nothing
11067
}
11068
11069
/// Destructor
11070
virtual ~adaptivepoisson_form_1()
11071
{
11072
// Do nothing
11073
}
11074
11075
/// Return a string identifying the form
11076
virtual const char* signature() const
11077
{
11078
return "Form([Integral(Argument(FiniteElement('Lagrange', Cell('triangle', 1, Space(2)), 1), 0), Measure('cell', 0, None))])";
11079
}
11080
11081
/// Return the rank of the global tensor (r)
11082
virtual unsigned int rank() const
11083
{
11084
return 1;
11085
}
11086
11087
/// Return the number of coefficients (n)
11088
virtual unsigned int num_coefficients() const
11089
{
11090
return 0;
11091
}
11092
11093
/// Return the number of cell domains
11094
virtual unsigned int num_cell_domains() const
11095
{
11096
return 1;
11097
}
11098
11099
/// Return the number of exterior facet domains
11100
virtual unsigned int num_exterior_facet_domains() const
11101
{
11102
return 0;
11103
}
11104
11105
/// Return the number of interior facet domains
11106
virtual unsigned int num_interior_facet_domains() const
11107
{
11108
return 0;
11109
}
11110
11111
/// Create a new finite element for argument function i
11112
virtual ufc::finite_element* create_finite_element(unsigned int i) const
11113
{
11114
switch (i)
11115
{
11116
case 0:
11117
{
11118
return new adaptivepoisson_finite_element_5();
11119
break;
11120
}
11121
}
11122
11123
return 0;
11124
}
11125
11126
/// Create a new dofmap for argument function i
11127
virtual ufc::dofmap* create_dofmap(unsigned int i) const
11128
{
11129
switch (i)
11130
{
11131
case 0:
11132
{
11133
return new adaptivepoisson_dofmap_5();
11134
break;
11135
}
11136
}
11137
11138
return 0;
11139
}
11140
11141
/// Create a new cell integral on sub domain i
11142
virtual ufc::cell_integral* create_cell_integral(unsigned int i) const
11143
{
11144
switch (i)
11145
{
11146
case 0:
11147
{
11148
return new adaptivepoisson_cell_integral_1_0();
11149
break;
11150
}
11151
}
11152
11153
return 0;
11154
}
11155
11156
/// Create a new exterior facet integral on sub domain i
11157
virtual ufc::exterior_facet_integral* create_exterior_facet_integral(unsigned int i) const
11158
{
11159
return 0;
11160
}
11161
11162
/// Create a new interior facet integral on sub domain i
11163
virtual ufc::interior_facet_integral* create_interior_facet_integral(unsigned int i) const
11164
{
11165
return 0;
11166
}
11167
11168
};
11169
11170
/// This class defines the interface for the assembly of the global
11171
/// tensor corresponding to a form with r + n arguments, that is, a
11172
/// mapping
11173
///
11174
/// a : V1 x V2 x ... Vr x W1 x W2 x ... x Wn -> R
11175
///
11176
/// with arguments v1, v2, ..., vr, w1, w2, ..., wn. The rank r
11177
/// global tensor A is defined by
11178
///
11179
/// A = a(V1, V2, ..., Vr, w1, w2, ..., wn),
11180
///
11181
/// where each argument Vj represents the application to the
11182
/// sequence of basis functions of Vj and w1, w2, ..., wn are given
11183
/// fixed functions (coefficients).
11184
11185
class adaptivepoisson_form_2: public ufc::form
11186
{
11187
public:
11188
11189
/// Constructor
11190
adaptivepoisson_form_2() : ufc::form()
11191
{
11192
// Do nothing
11193
}
11194
11195
/// Destructor
11196
virtual ~adaptivepoisson_form_2()
11197
{
11198
// Do nothing
11199
}
11200
11201
/// Return a string identifying the form
11202
virtual const char* signature() const
11203
{
11204
return "Form([Integral(Product(Argument(FiniteElement('Discontinuous Lagrange', Cell('triangle', 1, Space(2)), 1), 1), Product(Argument(FiniteElement('Discontinuous Lagrange', Cell('triangle', 1, Space(2)), 1), 0), Coefficient(FiniteElement('Bubble', Cell('triangle', 1, Space(2)), 3), 0))), Measure('cell', 0, None))])";
11205
}
11206
11207
/// Return the rank of the global tensor (r)
11208
virtual unsigned int rank() const
11209
{
11210
return 2;
11211
}
11212
11213
/// Return the number of coefficients (n)
11214
virtual unsigned int num_coefficients() const
11215
{
11216
return 1;
11217
}
11218
11219
/// Return the number of cell domains
11220
virtual unsigned int num_cell_domains() const
11221
{
11222
return 1;
11223
}
11224
11225
/// Return the number of exterior facet domains
11226
virtual unsigned int num_exterior_facet_domains() const
11227
{
11228
return 0;
11229
}
11230
11231
/// Return the number of interior facet domains
11232
virtual unsigned int num_interior_facet_domains() const
11233
{
11234
return 0;
11235
}
11236
11237
/// Create a new finite element for argument function i
11238
virtual ufc::finite_element* create_finite_element(unsigned int i) const
11239
{
11240
switch (i)
11241
{
11242
case 0:
11243
{
11244
return new adaptivepoisson_finite_element_4();
11245
break;
11246
}
11247
case 1:
11248
{
11249
return new adaptivepoisson_finite_element_4();
11250
break;
11251
}
11252
case 2:
11253
{
11254
return new adaptivepoisson_finite_element_3();
11255
break;
11256
}
11257
}
11258
11259
return 0;
11260
}
11261
11262
/// Create a new dofmap for argument function i
11263
virtual ufc::dofmap* create_dofmap(unsigned int i) const
11264
{
11265
switch (i)
11266
{
11267
case 0:
11268
{
11269
return new adaptivepoisson_dofmap_4();
11270
break;
11271
}
11272
case 1:
11273
{
11274
return new adaptivepoisson_dofmap_4();
11275
break;
11276
}
11277
case 2:
11278
{
11279
return new adaptivepoisson_dofmap_3();
11280
break;
11281
}
11282
}
11283
11284
return 0;
11285
}
11286
11287
/// Create a new cell integral on sub domain i
11288
virtual ufc::cell_integral* create_cell_integral(unsigned int i) const
11289
{
11290
switch (i)
11291
{
11292
case 0:
11293
{
11294
return new adaptivepoisson_cell_integral_2_0();
11295
break;
11296
}
11297
}
11298
11299
return 0;
11300
}
11301
11302
/// Create a new exterior facet integral on sub domain i
11303
virtual ufc::exterior_facet_integral* create_exterior_facet_integral(unsigned int i) const
11304
{
11305
return 0;
11306
}
11307
11308
/// Create a new interior facet integral on sub domain i
11309
virtual ufc::interior_facet_integral* create_interior_facet_integral(unsigned int i) const
11310
{
11311
return 0;
11312
}
11313
11314
};
11315
11316
/// This class defines the interface for the assembly of the global
11317
/// tensor corresponding to a form with r + n arguments, that is, a
11318
/// mapping
11319
///
11320
/// a : V1 x V2 x ... Vr x W1 x W2 x ... x Wn -> R
11321
///
11322
/// with arguments v1, v2, ..., vr, w1, w2, ..., wn. The rank r
11323
/// global tensor A is defined by
11324
///
11325
/// A = a(V1, V2, ..., Vr, w1, w2, ..., wn),
11326
///
11327
/// where each argument Vj represents the application to the
11328
/// sequence of basis functions of Vj and w1, w2, ..., wn are given
11329
/// fixed functions (coefficients).
11330
11331
class adaptivepoisson_form_3: public ufc::form
11332
{
11333
public:
11334
11335
/// Constructor
11336
adaptivepoisson_form_3() : ufc::form()
11337
{
11338
// Do nothing
11339
}
11340
11341
/// Destructor
11342
virtual ~adaptivepoisson_form_3()
11343
{
11344
// Do nothing
11345
}
11346
11347
/// Return a string identifying the form
11348
virtual const char* signature() const
11349
{
11350
return "Form([Integral(Sum(Product(Coefficient(FiniteElement('Lagrange', Cell('triangle', 1, Space(2)), 1), 0), Product(Argument(FiniteElement('Discontinuous Lagrange', Cell('triangle', 1, Space(2)), 1), 0), Coefficient(FiniteElement('Bubble', Cell('triangle', 1, Space(2)), 3), 3))), Product(IntValue(-1, (), (), {}), IndexSum(Product(Indexed(ComponentTensor(SpatialDerivative(Coefficient(FiniteElement('Lagrange', Cell('triangle', 1, Space(2)), 1), 2), MultiIndex((Index(0),), {Index(0): 2})), MultiIndex((Index(0),), {Index(0): 2})), MultiIndex((Index(1),), {Index(1): 2})), Indexed(ComponentTensor(Sum(Product(Argument(FiniteElement('Discontinuous Lagrange', Cell('triangle', 1, Space(2)), 1), 0), SpatialDerivative(Coefficient(FiniteElement('Bubble', Cell('triangle', 1, Space(2)), 3), 3), MultiIndex((Index(2),), {Index(2): 2}))), Product(Coefficient(FiniteElement('Bubble', Cell('triangle', 1, Space(2)), 3), 3), SpatialDerivative(Argument(FiniteElement('Discontinuous Lagrange', Cell('triangle', 1, Space(2)), 1), 0), MultiIndex((Index(2),), {Index(2): 2})))), MultiIndex((Index(2),), {Index(2): 2})), MultiIndex((Index(1),), {Index(1): 2}))), MultiIndex((Index(1),), {Index(1): 2})))), Measure('cell', 0, None)), Integral(Product(Coefficient(FiniteElement('Lagrange', Cell('triangle', 1, Space(2)), 1), 1), Product(Argument(FiniteElement('Discontinuous Lagrange', Cell('triangle', 1, Space(2)), 1), 0), Coefficient(FiniteElement('Bubble', Cell('triangle', 1, Space(2)), 3), 3))), Measure('exterior_facet', 0, None))])";
11351
}
11352
11353
/// Return the rank of the global tensor (r)
11354
virtual unsigned int rank() const
11355
{
11356
return 1;
11357
}
11358
11359
/// Return the number of coefficients (n)
11360
virtual unsigned int num_coefficients() const
11361
{
11362
return 4;
11363
}
11364
11365
/// Return the number of cell domains
11366
virtual unsigned int num_cell_domains() const
11367
{
11368
return 1;
11369
}
11370
11371
/// Return the number of exterior facet domains
11372
virtual unsigned int num_exterior_facet_domains() const
11373
{
11374
return 1;
11375
}
11376
11377
/// Return the number of interior facet domains
11378
virtual unsigned int num_interior_facet_domains() const
11379
{
11380
return 0;
11381
}
11382
11383
/// Create a new finite element for argument function i
11384
virtual ufc::finite_element* create_finite_element(unsigned int i) const
11385
{
11386
switch (i)
11387
{
11388
case 0:
11389
{
11390
return new adaptivepoisson_finite_element_4();
11391
break;
11392
}
11393
case 1:
11394
{
11395
return new adaptivepoisson_finite_element_5();
11396
break;
11397
}
11398
case 2:
11399
{
11400
return new adaptivepoisson_finite_element_5();
11401
break;
11402
}
11403
case 3:
11404
{
11405
return new adaptivepoisson_finite_element_5();
11406
break;
11407
}
11408
case 4:
11409
{
11410
return new adaptivepoisson_finite_element_3();
11411
break;
11412
}
11413
}
11414
11415
return 0;
11416
}
11417
11418
/// Create a new dofmap for argument function i
11419
virtual ufc::dofmap* create_dofmap(unsigned int i) const
11420
{
11421
switch (i)
11422
{
11423
case 0:
11424
{
11425
return new adaptivepoisson_dofmap_4();
11426
break;
11427
}
11428
case 1:
11429
{
11430
return new adaptivepoisson_dofmap_5();
11431
break;
11432
}
11433
case 2:
11434
{
11435
return new adaptivepoisson_dofmap_5();
11436
break;
11437
}
11438
case 3:
11439
{
11440
return new adaptivepoisson_dofmap_5();
11441
break;
11442
}
11443
case 4:
11444
{
11445
return new adaptivepoisson_dofmap_3();
11446
break;
11447
}
11448
}
11449
11450
return 0;
11451
}
11452
11453
/// Create a new cell integral on sub domain i
11454
virtual ufc::cell_integral* create_cell_integral(unsigned int i) const
11455
{
11456
switch (i)
11457
{
11458
case 0:
11459
{
11460
return new adaptivepoisson_cell_integral_3_0();
11461
break;
11462
}
11463
}
11464
11465
return 0;
11466
}
11467
11468
/// Create a new exterior facet integral on sub domain i
11469
virtual ufc::exterior_facet_integral* create_exterior_facet_integral(unsigned int i) const
11470
{
11471
switch (i)
11472
{
11473
case 0:
11474
{
11475
return new adaptivepoisson_exterior_facet_integral_3_0();
11476
break;
11477
}
11478
}
11479
11480
return 0;
11481
}
11482
11483
/// Create a new interior facet integral on sub domain i
11484
virtual ufc::interior_facet_integral* create_interior_facet_integral(unsigned int i) const
11485
{
11486
return 0;
11487
}
11488
11489
};
11490
11491
/// This class defines the interface for the assembly of the global
11492
/// tensor corresponding to a form with r + n arguments, that is, a
11493
/// mapping
11494
///
11495
/// a : V1 x V2 x ... Vr x W1 x W2 x ... x Wn -> R
11496
///
11497
/// with arguments v1, v2, ..., vr, w1, w2, ..., wn. The rank r
11498
/// global tensor A is defined by
11499
///
11500
/// A = a(V1, V2, ..., Vr, w1, w2, ..., wn),
11501
///
11502
/// where each argument Vj represents the application to the
11503
/// sequence of basis functions of Vj and w1, w2, ..., wn are given
11504
/// fixed functions (coefficients).
11505
11506
class adaptivepoisson_form_4: public ufc::form
11507
{
11508
public:
11509
11510
/// Constructor
11511
adaptivepoisson_form_4() : ufc::form()
11512
{
11513
// Do nothing
11514
}
11515
11516
/// Destructor
11517
virtual ~adaptivepoisson_form_4()
11518
{
11519
// Do nothing
11520
}
11521
11522
/// Return a string identifying the form
11523
virtual const char* signature() const
11524
{
11525
return "Form([Integral(Sum(Product(NegativeRestricted(Argument(FiniteElement('Discontinuous Lagrange', Cell('triangle', 1, Space(2)), 1), 1)), NegativeRestricted(Product(Argument(FiniteElement('Discontinuous Lagrange', Cell('triangle', 1, Space(2)), 1), 0), Coefficient(FiniteElement('Discontinuous Lagrange', Cell('triangle', 1, Space(2)), 2), 0)))), Product(PositiveRestricted(Argument(FiniteElement('Discontinuous Lagrange', Cell('triangle', 1, Space(2)), 1), 1)), PositiveRestricted(Product(Argument(FiniteElement('Discontinuous Lagrange', Cell('triangle', 1, Space(2)), 1), 0), Coefficient(FiniteElement('Discontinuous Lagrange', Cell('triangle', 1, Space(2)), 2), 0))))), Measure('interior_facet', 0, None)), Integral(Product(Argument(FiniteElement('Discontinuous Lagrange', Cell('triangle', 1, Space(2)), 1), 1), Product(Argument(FiniteElement('Discontinuous Lagrange', Cell('triangle', 1, Space(2)), 1), 0), Coefficient(FiniteElement('Discontinuous Lagrange', Cell('triangle', 1, Space(2)), 2), 0))), Measure('exterior_facet', 0, None))])";
11526
}
11527
11528
/// Return the rank of the global tensor (r)
11529
virtual unsigned int rank() const
11530
{
11531
return 2;
11532
}
11533
11534
/// Return the number of coefficients (n)
11535
virtual unsigned int num_coefficients() const
11536
{
11537
return 1;
11538
}
11539
11540
/// Return the number of cell domains
11541
virtual unsigned int num_cell_domains() const
11542
{
11543
return 0;
11544
}
11545
11546
/// Return the number of exterior facet domains
11547
virtual unsigned int num_exterior_facet_domains() const
11548
{
11549
return 1;
11550
}
11551
11552
/// Return the number of interior facet domains
11553
virtual unsigned int num_interior_facet_domains() const
11554
{
11555
return 1;
11556
}
11557
11558
/// Create a new finite element for argument function i
11559
virtual ufc::finite_element* create_finite_element(unsigned int i) const
11560
{
11561
switch (i)
11562
{
11563
case 0:
11564
{
11565
return new adaptivepoisson_finite_element_4();
11566
break;
11567
}
11568
case 1:
11569
{
11570
return new adaptivepoisson_finite_element_4();
11571
break;
11572
}
11573
case 2:
11574
{
11575
return new adaptivepoisson_finite_element_2();
11576
break;
11577
}
11578
}
11579
11580
return 0;
11581
}
11582
11583
/// Create a new dofmap for argument function i
11584
virtual ufc::dofmap* create_dofmap(unsigned int i) const
11585
{
11586
switch (i)
11587
{
11588
case 0:
11589
{
11590
return new adaptivepoisson_dofmap_4();
11591
break;
11592
}
11593
case 1:
11594
{
11595
return new adaptivepoisson_dofmap_4();
11596
break;
11597
}
11598
case 2:
11599
{
11600
return new adaptivepoisson_dofmap_2();
11601
break;
11602
}
11603
}
11604
11605
return 0;
11606
}
11607
11608
/// Create a new cell integral on sub domain i
11609
virtual ufc::cell_integral* create_cell_integral(unsigned int i) const
11610
{
11611
return 0;
11612
}
11613
11614
/// Create a new exterior facet integral on sub domain i
11615
virtual ufc::exterior_facet_integral* create_exterior_facet_integral(unsigned int i) const
11616
{
11617
switch (i)
11618
{
11619
case 0:
11620
{
11621
return new adaptivepoisson_exterior_facet_integral_4_0();
11622
break;
11623
}
11624
}
11625
11626
return 0;
11627
}
11628
11629
/// Create a new interior facet integral on sub domain i
11630
virtual ufc::interior_facet_integral* create_interior_facet_integral(unsigned int i) const
11631
{
11632
switch (i)
11633
{
11634
case 0:
11635
{
11636
return new adaptivepoisson_interior_facet_integral_4_0();
11637
break;
11638
}
11639
}
11640
11641
return 0;
11642
}
11643
11644
};
11645
11646
/// This class defines the interface for the assembly of the global
11647
/// tensor corresponding to a form with r + n arguments, that is, a
11648
/// mapping
11649
///
11650
/// a : V1 x V2 x ... Vr x W1 x W2 x ... x Wn -> R
11651
///
11652
/// with arguments v1, v2, ..., vr, w1, w2, ..., wn. The rank r
11653
/// global tensor A is defined by
11654
///
11655
/// A = a(V1, V2, ..., Vr, w1, w2, ..., wn),
11656
///
11657
/// where each argument Vj represents the application to the
11658
/// sequence of basis functions of Vj and w1, w2, ..., wn are given
11659
/// fixed functions (coefficients).
11660
11661
class adaptivepoisson_form_5: public ufc::form
11662
{
11663
public:
11664
11665
/// Constructor
11666
adaptivepoisson_form_5() : ufc::form()
11667
{
11668
// Do nothing
11669
}
11670
11671
/// Destructor
11672
virtual ~adaptivepoisson_form_5()
11673
{
11674
// Do nothing
11675
}
11676
11677
/// Return a string identifying the form
11678
virtual const char* signature() const
11679
{
11680
return "Form([Integral(Sum(Product(IntValue(-1, (), (), {}), Product(Coefficient(FiniteElement('Discontinuous Lagrange', Cell('triangle', 1, Space(2)), 1), 3), Product(Argument(FiniteElement('Discontinuous Lagrange', Cell('triangle', 1, Space(2)), 1), 0), Coefficient(FiniteElement('Discontinuous Lagrange', Cell('triangle', 1, Space(2)), 2), 4)))), Sum(Product(Coefficient(FiniteElement('Lagrange', Cell('triangle', 1, Space(2)), 1), 0), Product(Argument(FiniteElement('Discontinuous Lagrange', Cell('triangle', 1, Space(2)), 1), 0), Coefficient(FiniteElement('Discontinuous Lagrange', Cell('triangle', 1, Space(2)), 2), 4))), Product(IntValue(-1, (), (), {}), IndexSum(Product(Indexed(ComponentTensor(SpatialDerivative(Coefficient(FiniteElement('Lagrange', Cell('triangle', 1, Space(2)), 1), 2), MultiIndex((Index(0),), {Index(0): 2})), MultiIndex((Index(0),), {Index(0): 2})), MultiIndex((Index(1),), {Index(1): 2})), Indexed(ComponentTensor(Sum(Product(Argument(FiniteElement('Discontinuous Lagrange', Cell('triangle', 1, Space(2)), 1), 0), SpatialDerivative(Coefficient(FiniteElement('Discontinuous Lagrange', Cell('triangle', 1, Space(2)), 2), 4), MultiIndex((Index(2),), {Index(2): 2}))), Product(Coefficient(FiniteElement('Discontinuous Lagrange', Cell('triangle', 1, Space(2)), 2), 4), SpatialDerivative(Argument(FiniteElement('Discontinuous Lagrange', Cell('triangle', 1, Space(2)), 1), 0), MultiIndex((Index(2),), {Index(2): 2})))), MultiIndex((Index(2),), {Index(2): 2})), MultiIndex((Index(1),), {Index(1): 2}))), MultiIndex((Index(1),), {Index(1): 2}))))), Measure('cell', 0, None)), Integral(Product(Coefficient(FiniteElement('Lagrange', Cell('triangle', 1, Space(2)), 1), 1), Product(Argument(FiniteElement('Discontinuous Lagrange', Cell('triangle', 1, Space(2)), 1), 0), Coefficient(FiniteElement('Discontinuous Lagrange', Cell('triangle', 1, Space(2)), 2), 4))), Measure('exterior_facet', 0, None))])";
11681
}
11682
11683
/// Return the rank of the global tensor (r)
11684
virtual unsigned int rank() const
11685
{
11686
return 1;
11687
}
11688
11689
/// Return the number of coefficients (n)
11690
virtual unsigned int num_coefficients() const
11691
{
11692
return 5;
11693
}
11694
11695
/// Return the number of cell domains
11696
virtual unsigned int num_cell_domains() const
11697
{
11698
return 1;
11699
}
11700
11701
/// Return the number of exterior facet domains
11702
virtual unsigned int num_exterior_facet_domains() const
11703
{
11704
return 1;
11705
}
11706
11707
/// Return the number of interior facet domains
11708
virtual unsigned int num_interior_facet_domains() const
11709
{
11710
return 0;
11711
}
11712
11713
/// Create a new finite element for argument function i
11714
virtual ufc::finite_element* create_finite_element(unsigned int i) const
11715
{
11716
switch (i)
11717
{
11718
case 0:
11719
{
11720
return new adaptivepoisson_finite_element_4();
11721
break;
11722
}
11723
case 1:
11724
{
11725
return new adaptivepoisson_finite_element_5();
11726
break;
11727
}
11728
case 2:
11729
{
11730
return new adaptivepoisson_finite_element_5();
11731
break;
11732
}
11733
case 3:
11734
{
11735
return new adaptivepoisson_finite_element_5();
11736
break;
11737
}
11738
case 4:
11739
{
11740
return new adaptivepoisson_finite_element_4();
11741
break;
11742
}
11743
case 5:
11744
{
11745
return new adaptivepoisson_finite_element_2();
11746
break;
11747
}
11748
}
11749
11750
return 0;
11751
}
11752
11753
/// Create a new dofmap for argument function i
11754
virtual ufc::dofmap* create_dofmap(unsigned int i) const
11755
{
11756
switch (i)
11757
{
11758
case 0:
11759
{
11760
return new adaptivepoisson_dofmap_4();
11761
break;
11762
}
11763
case 1:
11764
{
11765
return new adaptivepoisson_dofmap_5();
11766
break;
11767
}
11768
case 2:
11769
{
11770
return new adaptivepoisson_dofmap_5();
11771
break;
11772
}
11773
case 3:
11774
{
11775
return new adaptivepoisson_dofmap_5();
11776
break;
11777
}
11778
case 4:
11779
{
11780
return new adaptivepoisson_dofmap_4();
11781
break;
11782
}
11783
case 5:
11784
{
11785
return new adaptivepoisson_dofmap_2();
11786
break;
11787
}
11788
}
11789
11790
return 0;
11791
}
11792
11793
/// Create a new cell integral on sub domain i
11794
virtual ufc::cell_integral* create_cell_integral(unsigned int i) const
11795
{
11796
switch (i)
11797
{
11798
case 0:
11799
{
11800
return new adaptivepoisson_cell_integral_5_0();
11801
break;
11802
}
11803
}
11804
11805
return 0;
11806
}
11807
11808
/// Create a new exterior facet integral on sub domain i
11809
virtual ufc::exterior_facet_integral* create_exterior_facet_integral(unsigned int i) const
11810
{
11811
switch (i)
11812
{
11813
case 0:
11814
{
11815
return new adaptivepoisson_exterior_facet_integral_5_0();
11816
break;
11817
}
11818
}
11819
11820
return 0;
11821
}
11822
11823
/// Create a new interior facet integral on sub domain i
11824
virtual ufc::interior_facet_integral* create_interior_facet_integral(unsigned int i) const
11825
{
11826
return 0;
11827
}
11828
11829
};
11830
11831
/// This class defines the interface for the assembly of the global
11832
/// tensor corresponding to a form with r + n arguments, that is, a
11833
/// mapping
11834
///
11835
/// a : V1 x V2 x ... Vr x W1 x W2 x ... x Wn -> R
11836
///
11837
/// with arguments v1, v2, ..., vr, w1, w2, ..., wn. The rank r
11838
/// global tensor A is defined by
11839
///
11840
/// A = a(V1, V2, ..., Vr, w1, w2, ..., wn),
11841
///
11842
/// where each argument Vj represents the application to the
11843
/// sequence of basis functions of Vj and w1, w2, ..., wn are given
11844
/// fixed functions (coefficients).
11845
11846
class adaptivepoisson_form_6: public ufc::form
11847
{
11848
public:
11849
11850
/// Constructor
11851
adaptivepoisson_form_6() : ufc::form()
11852
{
11853
// Do nothing
11854
}
11855
11856
/// Destructor
11857
virtual ~adaptivepoisson_form_6()
11858
{
11859
// Do nothing
11860
}
11861
11862
/// Return a string identifying the form
11863
virtual const char* signature() const
11864
{
11865
return "Form([Integral(Sum(Product(Coefficient(FiniteElement('Lagrange', Cell('triangle', 1, Space(2)), 1), 0), Coefficient(FiniteElement('Lagrange', Cell('triangle', 1, Space(2)), 2), 3)), Product(IntValue(-1, (), (), {}), IndexSum(Product(Indexed(ComponentTensor(SpatialDerivative(Coefficient(FiniteElement('Lagrange', Cell('triangle', 1, Space(2)), 1), 2), MultiIndex((Index(0),), {Index(0): 2})), MultiIndex((Index(0),), {Index(0): 2})), MultiIndex((Index(1),), {Index(1): 2})), Indexed(ComponentTensor(SpatialDerivative(Coefficient(FiniteElement('Lagrange', Cell('triangle', 1, Space(2)), 2), 3), MultiIndex((Index(2),), {Index(2): 2})), MultiIndex((Index(2),), {Index(2): 2})), MultiIndex((Index(1),), {Index(1): 2}))), MultiIndex((Index(1),), {Index(1): 2})))), Measure('cell', 0, None)), Integral(Product(Coefficient(FiniteElement('Lagrange', Cell('triangle', 1, Space(2)), 1), 1), Coefficient(FiniteElement('Lagrange', Cell('triangle', 1, Space(2)), 2), 3)), Measure('exterior_facet', 0, None))])";
11866
}
11867
11868
/// Return the rank of the global tensor (r)
11869
virtual unsigned int rank() const
11870
{
11871
return 0;
11872
}
11873
11874
/// Return the number of coefficients (n)
11875
virtual unsigned int num_coefficients() const
11876
{
11877
return 4;
11878
}
11879
11880
/// Return the number of cell domains
11881
virtual unsigned int num_cell_domains() const
11882
{
11883
return 1;
11884
}
11885
11886
/// Return the number of exterior facet domains
11887
virtual unsigned int num_exterior_facet_domains() const
11888
{
11889
return 1;
11890
}
11891
11892
/// Return the number of interior facet domains
11893
virtual unsigned int num_interior_facet_domains() const
11894
{
11895
return 0;
11896
}
11897
11898
/// Create a new finite element for argument function i
11899
virtual ufc::finite_element* create_finite_element(unsigned int i) const
11900
{
11901
switch (i)
11902
{
11903
case 0:
11904
{
11905
return new adaptivepoisson_finite_element_5();
11906
break;
11907
}
11908
case 1:
11909
{
11910
return new adaptivepoisson_finite_element_5();
11911
break;
11912
}
11913
case 2:
11914
{
11915
return new adaptivepoisson_finite_element_5();
11916
break;
11917
}
11918
case 3:
11919
{
11920
return new adaptivepoisson_finite_element_1();
11921
break;
11922
}
11923
}
11924
11925
return 0;
11926
}
11927
11928
/// Create a new dofmap for argument function i
11929
virtual ufc::dofmap* create_dofmap(unsigned int i) const
11930
{
11931
switch (i)
11932
{
11933
case 0:
11934
{
11935
return new adaptivepoisson_dofmap_5();
11936
break;
11937
}
11938
case 1:
11939
{
11940
return new adaptivepoisson_dofmap_5();
11941
break;
11942
}
11943
case 2:
11944
{
11945
return new adaptivepoisson_dofmap_5();
11946
break;
11947
}
11948
case 3:
11949
{
11950
return new adaptivepoisson_dofmap_1();
11951
break;
11952
}
11953
}
11954
11955
return 0;
11956
}
11957
11958
/// Create a new cell integral on sub domain i
11959
virtual ufc::cell_integral* create_cell_integral(unsigned int i) const
11960
{
11961
switch (i)
11962
{
11963
case 0:
11964
{
11965
return new adaptivepoisson_cell_integral_6_0();
11966
break;
11967
}
11968
}
11969
11970
return 0;
11971
}
11972
11973
/// Create a new exterior facet integral on sub domain i
11974
virtual ufc::exterior_facet_integral* create_exterior_facet_integral(unsigned int i) const
11975
{
11976
switch (i)
11977
{
11978
case 0:
11979
{
11980
return new adaptivepoisson_exterior_facet_integral_6_0();
11981
break;
11982
}
11983
}
11984
11985
return 0;
11986
}
11987
11988
/// Create a new interior facet integral on sub domain i
11989
virtual ufc::interior_facet_integral* create_interior_facet_integral(unsigned int i) const
11990
{
11991
return 0;
11992
}
11993
11994
};
11995
11996
/// This class defines the interface for the assembly of the global
11997
/// tensor corresponding to a form with r + n arguments, that is, a
11998
/// mapping
11999
///
12000
/// a : V1 x V2 x ... Vr x W1 x W2 x ... x Wn -> R
12001
///
12002
/// with arguments v1, v2, ..., vr, w1, w2, ..., wn. The rank r
12003
/// global tensor A is defined by
12004
///
12005
/// A = a(V1, V2, ..., Vr, w1, w2, ..., wn),
12006
///
12007
/// where each argument Vj represents the application to the
12008
/// sequence of basis functions of Vj and w1, w2, ..., wn are given
12009
/// fixed functions (coefficients).
12010
12011
class adaptivepoisson_form_7: public ufc::form
12012
{
12013
public:
12014
12015
/// Constructor
12016
adaptivepoisson_form_7() : ufc::form()
12017
{
12018
// Do nothing
12019
}
12020
12021
/// Destructor
12022
virtual ~adaptivepoisson_form_7()
12023
{
12024
// Do nothing
12025
}
12026
12027
/// Return a string identifying the form
12028
virtual const char* signature() const
12029
{
12030
return "Form([Integral(Product(Argument(FiniteElement('Discontinuous Lagrange', Cell('triangle', 1, Space(2)), 0), 0), Product(Coefficient(FiniteElement('Discontinuous Lagrange', Cell('triangle', 1, Space(2)), 1), 1), Sum(Coefficient(FiniteElement('Lagrange', Cell('triangle', 1, Space(2)), 2), 0), Product(IntValue(-1, (), (), {}), Coefficient(FiniteElement('Lagrange', Cell('triangle', 1, Space(2)), 1), 3))))), Measure('cell', 0, None)), Integral(Product(Product(FloatValue(0.5, (), (), {}), Sum(NegativeRestricted(Argument(FiniteElement('Discontinuous Lagrange', Cell('triangle', 1, Space(2)), 0), 0)), PositiveRestricted(Argument(FiniteElement('Discontinuous Lagrange', Cell('triangle', 1, Space(2)), 0), 0)))), Sum(Product(NegativeRestricted(Coefficient(FiniteElement('Discontinuous Lagrange', Cell('triangle', 1, Space(2)), 1), 2)), NegativeRestricted(Sum(Coefficient(FiniteElement('Lagrange', Cell('triangle', 1, Space(2)), 2), 0), Product(IntValue(-1, (), (), {}), Coefficient(FiniteElement('Lagrange', Cell('triangle', 1, Space(2)), 1), 3))))), Product(PositiveRestricted(Coefficient(FiniteElement('Discontinuous Lagrange', Cell('triangle', 1, Space(2)), 1), 2)), PositiveRestricted(Sum(Coefficient(FiniteElement('Lagrange', Cell('triangle', 1, Space(2)), 2), 0), Product(IntValue(-1, (), (), {}), Coefficient(FiniteElement('Lagrange', Cell('triangle', 1, Space(2)), 1), 3))))))), Measure('interior_facet', 0, None)), Integral(Product(Argument(FiniteElement('Discontinuous Lagrange', Cell('triangle', 1, Space(2)), 0), 0), Product(Coefficient(FiniteElement('Discontinuous Lagrange', Cell('triangle', 1, Space(2)), 1), 2), Sum(Coefficient(FiniteElement('Lagrange', Cell('triangle', 1, Space(2)), 2), 0), Product(IntValue(-1, (), (), {}), Coefficient(FiniteElement('Lagrange', Cell('triangle', 1, Space(2)), 1), 3))))), Measure('exterior_facet', 0, None))])";
12031
}
12032
12033
/// Return the rank of the global tensor (r)
12034
virtual unsigned int rank() const
12035
{
12036
return 1;
12037
}
12038
12039
/// Return the number of coefficients (n)
12040
virtual unsigned int num_coefficients() const
12041
{
12042
return 4;
12043
}
12044
12045
/// Return the number of cell domains
12046
virtual unsigned int num_cell_domains() const
12047
{
12048
return 1;
12049
}
12050
12051
/// Return the number of exterior facet domains
12052
virtual unsigned int num_exterior_facet_domains() const
12053
{
12054
return 1;
12055
}
12056
12057
/// Return the number of interior facet domains
12058
virtual unsigned int num_interior_facet_domains() const
12059
{
12060
return 1;
12061
}
12062
12063
/// Create a new finite element for argument function i
12064
virtual ufc::finite_element* create_finite_element(unsigned int i) const
12065
{
12066
switch (i)
12067
{
12068
case 0:
12069
{
12070
return new adaptivepoisson_finite_element_0();
12071
break;
12072
}
12073
case 1:
12074
{
12075
return new adaptivepoisson_finite_element_1();
12076
break;
12077
}
12078
case 2:
12079
{
12080
return new adaptivepoisson_finite_element_4();
12081
break;
12082
}
12083
case 3:
12084
{
12085
return new adaptivepoisson_finite_element_4();
12086
break;
12087
}
12088
case 4:
12089
{
12090
return new adaptivepoisson_finite_element_5();
12091
break;
12092
}
12093
}
12094
12095
return 0;
12096
}
12097
12098
/// Create a new dofmap for argument function i
12099
virtual ufc::dofmap* create_dofmap(unsigned int i) const
12100
{
12101
switch (i)
12102
{
12103
case 0:
12104
{
12105
return new adaptivepoisson_dofmap_0();
12106
break;
12107
}
12108
case 1:
12109
{
12110
return new adaptivepoisson_dofmap_1();
12111
break;
12112
}
12113
case 2:
12114
{
12115
return new adaptivepoisson_dofmap_4();
12116
break;
12117
}
12118
case 3:
12119
{
12120
return new adaptivepoisson_dofmap_4();
12121
break;
12122
}
12123
case 4:
12124
{
12125
return new adaptivepoisson_dofmap_5();
12126
break;
12127
}
12128
}
12129
12130
return 0;
12131
}
12132
12133
/// Create a new cell integral on sub domain i
12134
virtual ufc::cell_integral* create_cell_integral(unsigned int i) const
12135
{
12136
switch (i)
12137
{
12138
case 0:
12139
{
12140
return new adaptivepoisson_cell_integral_7_0();
12141
break;
12142
}
12143
}
12144
12145
return 0;
12146
}
12147
12148
/// Create a new exterior facet integral on sub domain i
12149
virtual ufc::exterior_facet_integral* create_exterior_facet_integral(unsigned int i) const
12150
{
12151
switch (i)
12152
{
12153
case 0:
12154
{
12155
return new adaptivepoisson_exterior_facet_integral_7_0();
12156
break;
12157
}
12158
}
12159
12160
return 0;
12161
}
12162
12163
/// Create a new interior facet integral on sub domain i
12164
virtual ufc::interior_facet_integral* create_interior_facet_integral(unsigned int i) const
12165
{
12166
switch (i)
12167
{
12168
case 0:
12169
{
12170
return new adaptivepoisson_interior_facet_integral_7_0();
12171
break;
12172
}
12173
}
12174
12175
return 0;
12176
}
12177
12178
};
12179
12180
/// This class defines the interface for the assembly of the global
12181
/// tensor corresponding to a form with r + n arguments, that is, a
12182
/// mapping
12183
///
12184
/// a : V1 x V2 x ... Vr x W1 x W2 x ... x Wn -> R
12185
///
12186
/// with arguments v1, v2, ..., vr, w1, w2, ..., wn. The rank r
12187
/// global tensor A is defined by
12188
///
12189
/// A = a(V1, V2, ..., Vr, w1, w2, ..., wn),
12190
///
12191
/// where each argument Vj represents the application to the
12192
/// sequence of basis functions of Vj and w1, w2, ..., wn are given
12193
/// fixed functions (coefficients).
12194
12195
class adaptivepoisson_form_8: public ufc::form
12196
{
12197
public:
12198
12199
/// Constructor
12200
adaptivepoisson_form_8() : ufc::form()
12201
{
12202
// Do nothing
12203
}
12204
12205
/// Destructor
12206
virtual ~adaptivepoisson_form_8()
12207
{
12208
// Do nothing
12209
}
12210
12211
/// Return a string identifying the form
12212
virtual const char* signature() const
12213
{
12214
return "Form([Integral(IndexSum(Product(Indexed(ComponentTensor(SpatialDerivative(Argument(FiniteElement('Lagrange', Cell('triangle', 1, Space(2)), 1), 0), MultiIndex((Index(0),), {Index(0): 2})), MultiIndex((Index(0),), {Index(0): 2})), MultiIndex((Index(1),), {Index(1): 2})), Indexed(ComponentTensor(SpatialDerivative(Argument(FiniteElement('Lagrange', Cell('triangle', 1, Space(2)), 1), 1), MultiIndex((Index(2),), {Index(2): 2})), MultiIndex((Index(2),), {Index(2): 2})), MultiIndex((Index(1),), {Index(1): 2}))), MultiIndex((Index(1),), {Index(1): 2})), Measure('cell', 0, None))])";
12215
}
12216
12217
/// Return the rank of the global tensor (r)
12218
virtual unsigned int rank() const
12219
{
12220
return 2;
12221
}
12222
12223
/// Return the number of coefficients (n)
12224
virtual unsigned int num_coefficients() const
12225
{
12226
return 0;
12227
}
12228
12229
/// Return the number of cell domains
12230
virtual unsigned int num_cell_domains() const
12231
{
12232
return 1;
12233
}
12234
12235
/// Return the number of exterior facet domains
12236
virtual unsigned int num_exterior_facet_domains() const
12237
{
12238
return 0;
12239
}
12240
12241
/// Return the number of interior facet domains
12242
virtual unsigned int num_interior_facet_domains() const
12243
{
12244
return 0;
12245
}
12246
12247
/// Create a new finite element for argument function i
12248
virtual ufc::finite_element* create_finite_element(unsigned int i) const
12249
{
12250
switch (i)
12251
{
12252
case 0:
12253
{
12254
return new adaptivepoisson_finite_element_5();
12255
break;
12256
}
12257
case 1:
12258
{
12259
return new adaptivepoisson_finite_element_5();
12260
break;
12261
}
12262
}
12263
12264
return 0;
12265
}
12266
12267
/// Create a new dofmap for argument function i
12268
virtual ufc::dofmap* create_dofmap(unsigned int i) const
12269
{
12270
switch (i)
12271
{
12272
case 0:
12273
{
12274
return new adaptivepoisson_dofmap_5();
12275
break;
12276
}
12277
case 1:
12278
{
12279
return new adaptivepoisson_dofmap_5();
12280
break;
12281
}
12282
}
12283
12284
return 0;
12285
}
12286
12287
/// Create a new cell integral on sub domain i
12288
virtual ufc::cell_integral* create_cell_integral(unsigned int i) const
12289
{
12290
switch (i)
12291
{
12292
case 0:
12293
{
12294
return new adaptivepoisson_cell_integral_8_0();
12295
break;
12296
}
12297
}
12298
12299
return 0;
12300
}
12301
12302
/// Create a new exterior facet integral on sub domain i
12303
virtual ufc::exterior_facet_integral* create_exterior_facet_integral(unsigned int i) const
12304
{
12305
return 0;
12306
}
12307
12308
/// Create a new interior facet integral on sub domain i
12309
virtual ufc::interior_facet_integral* create_interior_facet_integral(unsigned int i) const
12310
{
12311
return 0;
12312
}
12313
12314
};
12315
12316
/// This class defines the interface for the assembly of the global
12317
/// tensor corresponding to a form with r + n arguments, that is, a
12318
/// mapping
12319
///
12320
/// a : V1 x V2 x ... Vr x W1 x W2 x ... x Wn -> R
12321
///
12322
/// with arguments v1, v2, ..., vr, w1, w2, ..., wn. The rank r
12323
/// global tensor A is defined by
12324
///
12325
/// A = a(V1, V2, ..., Vr, w1, w2, ..., wn),
12326
///
12327
/// where each argument Vj represents the application to the
12328
/// sequence of basis functions of Vj and w1, w2, ..., wn are given
12329
/// fixed functions (coefficients).
12330
12331
class adaptivepoisson_form_9: public ufc::form
12332
{
12333
public:
12334
12335
/// Constructor
12336
adaptivepoisson_form_9() : ufc::form()
12337
{
12338
// Do nothing
12339
}
12340
12341
/// Destructor
12342
virtual ~adaptivepoisson_form_9()
12343
{
12344
// Do nothing
12345
}
12346
12347
/// Return a string identifying the form
12348
virtual const char* signature() const
12349
{
12350
return "Form([Integral(Product(Argument(FiniteElement('Lagrange', Cell('triangle', 1, Space(2)), 1), 0), Coefficient(FiniteElement('Lagrange', Cell('triangle', 1, Space(2)), 1), 0)), Measure('cell', 0, None)), Integral(Product(Argument(FiniteElement('Lagrange', Cell('triangle', 1, Space(2)), 1), 0), Coefficient(FiniteElement('Lagrange', Cell('triangle', 1, Space(2)), 1), 1)), Measure('exterior_facet', 0, None))])";
12351
}
12352
12353
/// Return the rank of the global tensor (r)
12354
virtual unsigned int rank() const
12355
{
12356
return 1;
12357
}
12358
12359
/// Return the number of coefficients (n)
12360
virtual unsigned int num_coefficients() const
12361
{
12362
return 2;
12363
}
12364
12365
/// Return the number of cell domains
12366
virtual unsigned int num_cell_domains() const
12367
{
12368
return 1;
12369
}
12370
12371
/// Return the number of exterior facet domains
12372
virtual unsigned int num_exterior_facet_domains() const
12373
{
12374
return 1;
12375
}
12376
12377
/// Return the number of interior facet domains
12378
virtual unsigned int num_interior_facet_domains() const
12379
{
12380
return 0;
12381
}
12382
12383
/// Create a new finite element for argument function i
12384
virtual ufc::finite_element* create_finite_element(unsigned int i) const
12385
{
12386
switch (i)
12387
{
12388
case 0:
12389
{
12390
return new adaptivepoisson_finite_element_5();
12391
break;
12392
}
12393
case 1:
12394
{
12395
return new adaptivepoisson_finite_element_5();
12396
break;
12397
}
12398
case 2:
12399
{
12400
return new adaptivepoisson_finite_element_5();
12401
break;
12402
}
12403
}
12404
12405
return 0;
12406
}
12407
12408
/// Create a new dofmap for argument function i
12409
virtual ufc::dofmap* create_dofmap(unsigned int i) const
12410
{
12411
switch (i)
12412
{
12413
case 0:
12414
{
12415
return new adaptivepoisson_dofmap_5();
12416
break;
12417
}
12418
case 1:
12419
{
12420
return new adaptivepoisson_dofmap_5();
12421
break;
12422
}
12423
case 2:
12424
{
12425
return new adaptivepoisson_dofmap_5();
12426
break;
12427
}
12428
}
12429
12430
return 0;
12431
}
12432
12433
/// Create a new cell integral on sub domain i
12434
virtual ufc::cell_integral* create_cell_integral(unsigned int i) const
12435
{
12436
switch (i)
12437
{
12438
case 0:
12439
{
12440
return new adaptivepoisson_cell_integral_9_0();
12441
break;
12442
}
12443
}
12444
12445
return 0;
12446
}
12447
12448
/// Create a new exterior facet integral on sub domain i
12449
virtual ufc::exterior_facet_integral* create_exterior_facet_integral(unsigned int i) const
12450
{
12451
switch (i)
12452
{
12453
case 0:
12454
{
12455
return new adaptivepoisson_exterior_facet_integral_9_0();
12456
break;
12457
}
12458
}
12459
12460
return 0;
12461
}
12462
12463
/// Create a new interior facet integral on sub domain i
12464
virtual ufc::interior_facet_integral* create_interior_facet_integral(unsigned int i) const
12465
{
12466
return 0;
12467
}
12468
12469
};
12470
12471
/// This class defines the interface for the assembly of the global
12472
/// tensor corresponding to a form with r + n arguments, that is, a
12473
/// mapping
12474
///
12475
/// a : V1 x V2 x ... Vr x W1 x W2 x ... x Wn -> R
12476
///
12477
/// with arguments v1, v2, ..., vr, w1, w2, ..., wn. The rank r
12478
/// global tensor A is defined by
12479
///
12480
/// A = a(V1, V2, ..., Vr, w1, w2, ..., wn),
12481
///
12482
/// where each argument Vj represents the application to the
12483
/// sequence of basis functions of Vj and w1, w2, ..., wn are given
12484
/// fixed functions (coefficients).
12485
12486
class adaptivepoisson_form_10: public ufc::form
12487
{
12488
public:
12489
12490
/// Constructor
12491
adaptivepoisson_form_10() : ufc::form()
12492
{
12493
// Do nothing
12494
}
12495
12496
/// Destructor
12497
virtual ~adaptivepoisson_form_10()
12498
{
12499
// Do nothing
12500
}
12501
12502
/// Return a string identifying the form
12503
virtual const char* signature() const
12504
{
12505
return "Form([Integral(Coefficient(FiniteElement('Lagrange', Cell('triangle', 1, Space(2)), 1), 0), Measure('cell', 0, None))])";
12506
}
12507
12508
/// Return the rank of the global tensor (r)
12509
virtual unsigned int rank() const
12510
{
12511
return 0;
12512
}
12513
12514
/// Return the number of coefficients (n)
12515
virtual unsigned int num_coefficients() const
12516
{
12517
return 1;
12518
}
12519
12520
/// Return the number of cell domains
12521
virtual unsigned int num_cell_domains() const
12522
{
12523
return 1;
12524
}
12525
12526
/// Return the number of exterior facet domains
12527
virtual unsigned int num_exterior_facet_domains() const
12528
{
12529
return 0;
12530
}
12531
12532
/// Return the number of interior facet domains
12533
virtual unsigned int num_interior_facet_domains() const
12534
{
12535
return 0;
12536
}
12537
12538
/// Create a new finite element for argument function i
12539
virtual ufc::finite_element* create_finite_element(unsigned int i) const
12540
{
12541
switch (i)
12542
{
12543
case 0:
12544
{
12545
return new adaptivepoisson_finite_element_5();
12546
break;
12547
}
12548
}
12549
12550
return 0;
12551
}
12552
12553
/// Create a new dofmap for argument function i
12554
virtual ufc::dofmap* create_dofmap(unsigned int i) const
12555
{
12556
switch (i)
12557
{
12558
case 0:
12559
{
12560
return new adaptivepoisson_dofmap_5();
12561
break;
12562
}
12563
}
12564
12565
return 0;
12566
}
12567
12568
/// Create a new cell integral on sub domain i
12569
virtual ufc::cell_integral* create_cell_integral(unsigned int i) const
12570
{
12571
switch (i)
12572
{
12573
case 0:
12574
{
12575
return new adaptivepoisson_cell_integral_10_0();
12576
break;
12577
}
12578
}
12579
12580
return 0;
12581
}
12582
12583
/// Create a new exterior facet integral on sub domain i
12584
virtual ufc::exterior_facet_integral* create_exterior_facet_integral(unsigned int i) const
12585
{
12586
return 0;
12587
}
12588
12589
/// Create a new interior facet integral on sub domain i
12590
virtual ufc::interior_facet_integral* create_interior_facet_integral(unsigned int i) const
12591
{
12592
return 0;
12593
}
12594
12595
};
12596
12597
// DOLFIN wrappers
12598
12599
// Standard library includes
12600
#include <string>
12601
12602
// DOLFIN includes
12603
#include <dolfin/common/NoDeleter.h>
12604
#include <dolfin/fem/FiniteElement.h>
12605
#include <dolfin/fem/DofMap.h>
12606
#include <dolfin/fem/Form.h>
12607
#include <dolfin/function/FunctionSpace.h>
12608
#include <dolfin/function/GenericFunction.h>
12609
#include <dolfin/function/CoefficientAssigner.h>
12610
#include <dolfin/adaptivity/ErrorControl.h>
12611
#include <dolfin/adaptivity/GoalFunctional.h>
12612
12613
namespace AdaptivePoisson
12614
{
12615
12616
class CoefficientSpace___cell_bubble: public dolfin::FunctionSpace
12617
{
12618
public:
12619
12620
CoefficientSpace___cell_bubble(const dolfin::Mesh& mesh):
12621
dolfin::FunctionSpace(dolfin::reference_to_no_delete_pointer(mesh),
12622
boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new adaptivepoisson_finite_element_3()))),
12623
boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dofmap>(new adaptivepoisson_dofmap_3()), mesh)))
12624
{
12625
// Do nothing
12626
}
12627
12628
CoefficientSpace___cell_bubble(dolfin::Mesh& mesh):
12629
dolfin::FunctionSpace(dolfin::reference_to_no_delete_pointer(mesh),
12630
boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new adaptivepoisson_finite_element_3()))),
12631
boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dofmap>(new adaptivepoisson_dofmap_3()), mesh)))
12632
{
12633
// Do nothing
12634
}
12635
12636
CoefficientSpace___cell_bubble(boost::shared_ptr<dolfin::Mesh> mesh):
12637
dolfin::FunctionSpace(mesh,
12638
boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new adaptivepoisson_finite_element_3()))),
12639
boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dofmap>(new adaptivepoisson_dofmap_3()), *mesh)))
12640
{
12641
// Do nothing
12642
}
12643
12644
CoefficientSpace___cell_bubble(boost::shared_ptr<const dolfin::Mesh> mesh):
12645
dolfin::FunctionSpace(mesh,
12646
boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new adaptivepoisson_finite_element_3()))),
12647
boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dofmap>(new adaptivepoisson_dofmap_3()), *mesh)))
12648
{
12649
// Do nothing
12650
}
12651
12652
~CoefficientSpace___cell_bubble()
12653
{
12654
}
12655
12656
};
12657
12658
class CoefficientSpace___cell_cone: public dolfin::FunctionSpace
12659
{
12660
public:
12661
12662
CoefficientSpace___cell_cone(const dolfin::Mesh& mesh):
12663
dolfin::FunctionSpace(dolfin::reference_to_no_delete_pointer(mesh),
12664
boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new adaptivepoisson_finite_element_2()))),
12665
boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dofmap>(new adaptivepoisson_dofmap_2()), mesh)))
12666
{
12667
// Do nothing
12668
}
12669
12670
CoefficientSpace___cell_cone(dolfin::Mesh& mesh):
12671
dolfin::FunctionSpace(dolfin::reference_to_no_delete_pointer(mesh),
12672
boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new adaptivepoisson_finite_element_2()))),
12673
boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dofmap>(new adaptivepoisson_dofmap_2()), mesh)))
12674
{
12675
// Do nothing
12676
}
12677
12678
CoefficientSpace___cell_cone(boost::shared_ptr<dolfin::Mesh> mesh):
12679
dolfin::FunctionSpace(mesh,
12680
boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new adaptivepoisson_finite_element_2()))),
12681
boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dofmap>(new adaptivepoisson_dofmap_2()), *mesh)))
12682
{
12683
// Do nothing
12684
}
12685
12686
CoefficientSpace___cell_cone(boost::shared_ptr<const dolfin::Mesh> mesh):
12687
dolfin::FunctionSpace(mesh,
12688
boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new adaptivepoisson_finite_element_2()))),
12689
boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dofmap>(new adaptivepoisson_dofmap_2()), *mesh)))
12690
{
12691
// Do nothing
12692
}
12693
12694
~CoefficientSpace___cell_cone()
12695
{
12696
}
12697
12698
};
12699
12700
class CoefficientSpace___cell_residual: public dolfin::FunctionSpace
12701
{
12702
public:
12703
12704
CoefficientSpace___cell_residual(const dolfin::Mesh& mesh):
12705
dolfin::FunctionSpace(dolfin::reference_to_no_delete_pointer(mesh),
12706
boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new adaptivepoisson_finite_element_4()))),
12707
boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dofmap>(new adaptivepoisson_dofmap_4()), mesh)))
12708
{
12709
// Do nothing
12710
}
12711
12712
CoefficientSpace___cell_residual(dolfin::Mesh& mesh):
12713
dolfin::FunctionSpace(dolfin::reference_to_no_delete_pointer(mesh),
12714
boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new adaptivepoisson_finite_element_4()))),
12715
boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dofmap>(new adaptivepoisson_dofmap_4()), mesh)))
12716
{
12717
// Do nothing
12718
}
12719
12720
CoefficientSpace___cell_residual(boost::shared_ptr<dolfin::Mesh> mesh):
12721
dolfin::FunctionSpace(mesh,
12722
boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new adaptivepoisson_finite_element_4()))),
12723
boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dofmap>(new adaptivepoisson_dofmap_4()), *mesh)))
12724
{
12725
// Do nothing
12726
}
12727
12728
CoefficientSpace___cell_residual(boost::shared_ptr<const dolfin::Mesh> mesh):
12729
dolfin::FunctionSpace(mesh,
12730
boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new adaptivepoisson_finite_element_4()))),
12731
boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dofmap>(new adaptivepoisson_dofmap_4()), *mesh)))
12732
{
12733
// Do nothing
12734
}
12735
12736
~CoefficientSpace___cell_residual()
12737
{
12738
}
12739
12740
};
12741
12742
class CoefficientSpace___discrete_dual_solution: public dolfin::FunctionSpace
12743
{
12744
public:
12745
12746
CoefficientSpace___discrete_dual_solution(const dolfin::Mesh& mesh):
12747
dolfin::FunctionSpace(dolfin::reference_to_no_delete_pointer(mesh),
12748
boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new adaptivepoisson_finite_element_5()))),
12749
boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dofmap>(new adaptivepoisson_dofmap_5()), mesh)))
12750
{
12751
// Do nothing
12752
}
12753
12754
CoefficientSpace___discrete_dual_solution(dolfin::Mesh& mesh):
12755
dolfin::FunctionSpace(dolfin::reference_to_no_delete_pointer(mesh),
12756
boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new adaptivepoisson_finite_element_5()))),
12757
boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dofmap>(new adaptivepoisson_dofmap_5()), mesh)))
12758
{
12759
// Do nothing
12760
}
12761
12762
CoefficientSpace___discrete_dual_solution(boost::shared_ptr<dolfin::Mesh> mesh):
12763
dolfin::FunctionSpace(mesh,
12764
boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new adaptivepoisson_finite_element_5()))),
12765
boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dofmap>(new adaptivepoisson_dofmap_5()), *mesh)))
12766
{
12767
// Do nothing
12768
}
12769
12770
CoefficientSpace___discrete_dual_solution(boost::shared_ptr<const dolfin::Mesh> mesh):
12771
dolfin::FunctionSpace(mesh,
12772
boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new adaptivepoisson_finite_element_5()))),
12773
boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dofmap>(new adaptivepoisson_dofmap_5()), *mesh)))
12774
{
12775
// Do nothing
12776
}
12777
12778
~CoefficientSpace___discrete_dual_solution()
12779
{
12780
}
12781
12782
};
12783
12784
class CoefficientSpace___discrete_primal_solution: public dolfin::FunctionSpace
12785
{
12786
public:
12787
12788
CoefficientSpace___discrete_primal_solution(const dolfin::Mesh& mesh):
12789
dolfin::FunctionSpace(dolfin::reference_to_no_delete_pointer(mesh),
12790
boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new adaptivepoisson_finite_element_5()))),
12791
boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dofmap>(new adaptivepoisson_dofmap_5()), mesh)))
12792
{
12793
// Do nothing
12794
}
12795
12796
CoefficientSpace___discrete_primal_solution(dolfin::Mesh& mesh):
12797
dolfin::FunctionSpace(dolfin::reference_to_no_delete_pointer(mesh),
12798
boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new adaptivepoisson_finite_element_5()))),
12799
boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dofmap>(new adaptivepoisson_dofmap_5()), mesh)))
12800
{
12801
// Do nothing
12802
}
12803
12804
CoefficientSpace___discrete_primal_solution(boost::shared_ptr<dolfin::Mesh> mesh):
12805
dolfin::FunctionSpace(mesh,
12806
boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new adaptivepoisson_finite_element_5()))),
12807
boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dofmap>(new adaptivepoisson_dofmap_5()), *mesh)))
12808
{
12809
// Do nothing
12810
}
12811
12812
CoefficientSpace___discrete_primal_solution(boost::shared_ptr<const dolfin::Mesh> mesh):
12813
dolfin::FunctionSpace(mesh,
12814
boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new adaptivepoisson_finite_element_5()))),
12815
boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dofmap>(new adaptivepoisson_dofmap_5()), *mesh)))
12816
{
12817
// Do nothing
12818
}
12819
12820
~CoefficientSpace___discrete_primal_solution()
12821
{
12822
}
12823
12824
};
12825
12826
class CoefficientSpace___facet_residual: public dolfin::FunctionSpace
12827
{
12828
public:
12829
12830
CoefficientSpace___facet_residual(const dolfin::Mesh& mesh):
12831
dolfin::FunctionSpace(dolfin::reference_to_no_delete_pointer(mesh),
12832
boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new adaptivepoisson_finite_element_4()))),
12833
boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dofmap>(new adaptivepoisson_dofmap_4()), mesh)))
12834
{
12835
// Do nothing
12836
}
12837
12838
CoefficientSpace___facet_residual(dolfin::Mesh& mesh):
12839
dolfin::FunctionSpace(dolfin::reference_to_no_delete_pointer(mesh),
12840
boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new adaptivepoisson_finite_element_4()))),
12841
boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dofmap>(new adaptivepoisson_dofmap_4()), mesh)))
12842
{
12843
// Do nothing
12844
}
12845
12846
CoefficientSpace___facet_residual(boost::shared_ptr<dolfin::Mesh> mesh):
12847
dolfin::FunctionSpace(mesh,
12848
boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new adaptivepoisson_finite_element_4()))),
12849
boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dofmap>(new adaptivepoisson_dofmap_4()), *mesh)))
12850
{
12851
// Do nothing
12852
}
12853
12854
CoefficientSpace___facet_residual(boost::shared_ptr<const dolfin::Mesh> mesh):
12855
dolfin::FunctionSpace(mesh,
12856
boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new adaptivepoisson_finite_element_4()))),
12857
boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dofmap>(new adaptivepoisson_dofmap_4()), *mesh)))
12858
{
12859
// Do nothing
12860
}
12861
12862
~CoefficientSpace___facet_residual()
12863
{
12864
}
12865
12866
};
12867
12868
class CoefficientSpace___improved_dual: public dolfin::FunctionSpace
12869
{
12870
public:
12871
12872
CoefficientSpace___improved_dual(const dolfin::Mesh& mesh):
12873
dolfin::FunctionSpace(dolfin::reference_to_no_delete_pointer(mesh),
12874
boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new adaptivepoisson_finite_element_1()))),
12875
boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dofmap>(new adaptivepoisson_dofmap_1()), mesh)))
12876
{
12877
// Do nothing
12878
}
12879
12880
CoefficientSpace___improved_dual(dolfin::Mesh& mesh):
12881
dolfin::FunctionSpace(dolfin::reference_to_no_delete_pointer(mesh),
12882
boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new adaptivepoisson_finite_element_1()))),
12883
boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dofmap>(new adaptivepoisson_dofmap_1()), mesh)))
12884
{
12885
// Do nothing
12886
}
12887
12888
CoefficientSpace___improved_dual(boost::shared_ptr<dolfin::Mesh> mesh):
12889
dolfin::FunctionSpace(mesh,
12890
boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new adaptivepoisson_finite_element_1()))),
12891
boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dofmap>(new adaptivepoisson_dofmap_1()), *mesh)))
12892
{
12893
// Do nothing
12894
}
12895
12896
CoefficientSpace___improved_dual(boost::shared_ptr<const dolfin::Mesh> mesh):
12897
dolfin::FunctionSpace(mesh,
12898
boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new adaptivepoisson_finite_element_1()))),
12899
boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dofmap>(new adaptivepoisson_dofmap_1()), *mesh)))
12900
{
12901
// Do nothing
12902
}
12903
12904
~CoefficientSpace___improved_dual()
12905
{
12906
}
12907
12908
};
12909
12910
class CoefficientSpace_f: public dolfin::FunctionSpace
12911
{
12912
public:
12913
12914
CoefficientSpace_f(const dolfin::Mesh& mesh):
12915
dolfin::FunctionSpace(dolfin::reference_to_no_delete_pointer(mesh),
12916
boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new adaptivepoisson_finite_element_5()))),
12917
boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dofmap>(new adaptivepoisson_dofmap_5()), mesh)))
12918
{
12919
// Do nothing
12920
}
12921
12922
CoefficientSpace_f(dolfin::Mesh& mesh):
12923
dolfin::FunctionSpace(dolfin::reference_to_no_delete_pointer(mesh),
12924
boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new adaptivepoisson_finite_element_5()))),
12925
boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dofmap>(new adaptivepoisson_dofmap_5()), mesh)))
12926
{
12927
// Do nothing
12928
}
12929
12930
CoefficientSpace_f(boost::shared_ptr<dolfin::Mesh> mesh):
12931
dolfin::FunctionSpace(mesh,
12932
boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new adaptivepoisson_finite_element_5()))),
12933
boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dofmap>(new adaptivepoisson_dofmap_5()), *mesh)))
12934
{
12935
// Do nothing
12936
}
12937
12938
CoefficientSpace_f(boost::shared_ptr<const dolfin::Mesh> mesh):
12939
dolfin::FunctionSpace(mesh,
12940
boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new adaptivepoisson_finite_element_5()))),
12941
boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dofmap>(new adaptivepoisson_dofmap_5()), *mesh)))
12942
{
12943
// Do nothing
12944
}
12945
12946
~CoefficientSpace_f()
12947
{
12948
}
12949
12950
};
12951
12952
class CoefficientSpace_g: public dolfin::FunctionSpace
12953
{
12954
public:
12955
12956
CoefficientSpace_g(const dolfin::Mesh& mesh):
12957
dolfin::FunctionSpace(dolfin::reference_to_no_delete_pointer(mesh),
12958
boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new adaptivepoisson_finite_element_5()))),
12959
boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dofmap>(new adaptivepoisson_dofmap_5()), mesh)))
12960
{
12961
// Do nothing
12962
}
12963
12964
CoefficientSpace_g(dolfin::Mesh& mesh):
12965
dolfin::FunctionSpace(dolfin::reference_to_no_delete_pointer(mesh),
12966
boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new adaptivepoisson_finite_element_5()))),
12967
boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dofmap>(new adaptivepoisson_dofmap_5()), mesh)))
12968
{
12969
// Do nothing
12970
}
12971
12972
CoefficientSpace_g(boost::shared_ptr<dolfin::Mesh> mesh):
12973
dolfin::FunctionSpace(mesh,
12974
boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new adaptivepoisson_finite_element_5()))),
12975
boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dofmap>(new adaptivepoisson_dofmap_5()), *mesh)))
12976
{
12977
// Do nothing
12978
}
12979
12980
CoefficientSpace_g(boost::shared_ptr<const dolfin::Mesh> mesh):
12981
dolfin::FunctionSpace(mesh,
12982
boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new adaptivepoisson_finite_element_5()))),
12983
boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dofmap>(new adaptivepoisson_dofmap_5()), *mesh)))
12984
{
12985
// Do nothing
12986
}
12987
12988
~CoefficientSpace_g()
12989
{
12990
}
12991
12992
};
12993
12994
class Form_0_FunctionSpace_0: public dolfin::FunctionSpace
12995
{
12996
public:
12997
12998
Form_0_FunctionSpace_0(const dolfin::Mesh& mesh):
12999
dolfin::FunctionSpace(dolfin::reference_to_no_delete_pointer(mesh),
13000
boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new adaptivepoisson_finite_element_5()))),
13001
boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dofmap>(new adaptivepoisson_dofmap_5()), mesh)))
13002
{
13003
// Do nothing
13004
}
13005
13006
Form_0_FunctionSpace_0(dolfin::Mesh& mesh):
13007
dolfin::FunctionSpace(dolfin::reference_to_no_delete_pointer(mesh),
13008
boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new adaptivepoisson_finite_element_5()))),
13009
boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dofmap>(new adaptivepoisson_dofmap_5()), mesh)))
13010
{
13011
// Do nothing
13012
}
13013
13014
Form_0_FunctionSpace_0(boost::shared_ptr<dolfin::Mesh> mesh):
13015
dolfin::FunctionSpace(mesh,
13016
boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new adaptivepoisson_finite_element_5()))),
13017
boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dofmap>(new adaptivepoisson_dofmap_5()), *mesh)))
13018
{
13019
// Do nothing
13020
}
13021
13022
Form_0_FunctionSpace_0(boost::shared_ptr<const dolfin::Mesh> mesh):
13023
dolfin::FunctionSpace(mesh,
13024
boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new adaptivepoisson_finite_element_5()))),
13025
boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dofmap>(new adaptivepoisson_dofmap_5()), *mesh)))
13026
{
13027
// Do nothing
13028
}
13029
13030
~Form_0_FunctionSpace_0()
13031
{
13032
}
13033
13034
};
13035
13036
class Form_0_FunctionSpace_1: public dolfin::FunctionSpace
13037
{
13038
public:
13039
13040
Form_0_FunctionSpace_1(const dolfin::Mesh& mesh):
13041
dolfin::FunctionSpace(dolfin::reference_to_no_delete_pointer(mesh),
13042
boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new adaptivepoisson_finite_element_5()))),
13043
boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dofmap>(new adaptivepoisson_dofmap_5()), mesh)))
13044
{
13045
// Do nothing
13046
}
13047
13048
Form_0_FunctionSpace_1(dolfin::Mesh& mesh):
13049
dolfin::FunctionSpace(dolfin::reference_to_no_delete_pointer(mesh),
13050
boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new adaptivepoisson_finite_element_5()))),
13051
boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dofmap>(new adaptivepoisson_dofmap_5()), mesh)))
13052
{
13053
// Do nothing
13054
}
13055
13056
Form_0_FunctionSpace_1(boost::shared_ptr<dolfin::Mesh> mesh):
13057
dolfin::FunctionSpace(mesh,
13058
boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new adaptivepoisson_finite_element_5()))),
13059
boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dofmap>(new adaptivepoisson_dofmap_5()), *mesh)))
13060
{
13061
// Do nothing
13062
}
13063
13064
Form_0_FunctionSpace_1(boost::shared_ptr<const dolfin::Mesh> mesh):
13065
dolfin::FunctionSpace(mesh,
13066
boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new adaptivepoisson_finite_element_5()))),
13067
boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dofmap>(new adaptivepoisson_dofmap_5()), *mesh)))
13068
{
13069
// Do nothing
13070
}
13071
13072
~Form_0_FunctionSpace_1()
13073
{
13074
}
13075
13076
};
13077
13078
class Form_0: public dolfin::Form
13079
{
13080
public:
13081
13082
// Constructor
13083
Form_0(const dolfin::FunctionSpace& V0, const dolfin::FunctionSpace& V1):
13084
dolfin::Form(2, 0)
13085
{
13086
_function_spaces[0] = reference_to_no_delete_pointer(V0);
13087
_function_spaces[1] = reference_to_no_delete_pointer(V1);
13088
13089
_ufc_form = boost::shared_ptr<const ufc::form>(new adaptivepoisson_form_0());
13090
}
13091
13092
// Constructor
13093
Form_0(boost::shared_ptr<const dolfin::FunctionSpace> V0, boost::shared_ptr<const dolfin::FunctionSpace> V1):
13094
dolfin::Form(2, 0)
13095
{
13096
_function_spaces[0] = V0;
13097
_function_spaces[1] = V1;
13098
13099
_ufc_form = boost::shared_ptr<const ufc::form>(new adaptivepoisson_form_0());
13100
}
13101
13102
// Destructor
13103
~Form_0()
13104
{}
13105
13106
/// Return the number of the coefficient with this name
13107
virtual dolfin::uint coefficient_number(const std::string& name) const
13108
{
13109
13110
dolfin::error("No coefficients.");
13111
return 0;
13112
}
13113
13114
/// Return the name of the coefficient with this number
13115
virtual std::string coefficient_name(dolfin::uint i) const
13116
{
13117
13118
dolfin::error("No coefficients.");
13119
return "unnamed";
13120
}
13121
13122
// Typedefs
13123
typedef Form_0_FunctionSpace_0 TestSpace;
13124
typedef Form_0_FunctionSpace_1 TrialSpace;
13125
13126
// Coefficients
13127
};
13128
13129
class Form_1_FunctionSpace_0: public dolfin::FunctionSpace
13130
{
13131
public:
13132
13133
Form_1_FunctionSpace_0(const dolfin::Mesh& mesh):
13134
dolfin::FunctionSpace(dolfin::reference_to_no_delete_pointer(mesh),
13135
boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new adaptivepoisson_finite_element_5()))),
13136
boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dofmap>(new adaptivepoisson_dofmap_5()), mesh)))
13137
{
13138
// Do nothing
13139
}
13140
13141
Form_1_FunctionSpace_0(dolfin::Mesh& mesh):
13142
dolfin::FunctionSpace(dolfin::reference_to_no_delete_pointer(mesh),
13143
boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new adaptivepoisson_finite_element_5()))),
13144
boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dofmap>(new adaptivepoisson_dofmap_5()), mesh)))
13145
{
13146
// Do nothing
13147
}
13148
13149
Form_1_FunctionSpace_0(boost::shared_ptr<dolfin::Mesh> mesh):
13150
dolfin::FunctionSpace(mesh,
13151
boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new adaptivepoisson_finite_element_5()))),
13152
boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dofmap>(new adaptivepoisson_dofmap_5()), *mesh)))
13153
{
13154
// Do nothing
13155
}
13156
13157
Form_1_FunctionSpace_0(boost::shared_ptr<const dolfin::Mesh> mesh):
13158
dolfin::FunctionSpace(mesh,
13159
boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new adaptivepoisson_finite_element_5()))),
13160
boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dofmap>(new adaptivepoisson_dofmap_5()), *mesh)))
13161
{
13162
// Do nothing
13163
}
13164
13165
~Form_1_FunctionSpace_0()
13166
{
13167
}
13168
13169
};
13170
13171
class Form_1: public dolfin::Form
13172
{
13173
public:
13174
13175
// Constructor
13176
Form_1(const dolfin::FunctionSpace& V0):
13177
dolfin::Form(1, 0)
13178
{
13179
_function_spaces[0] = reference_to_no_delete_pointer(V0);
13180
13181
_ufc_form = boost::shared_ptr<const ufc::form>(new adaptivepoisson_form_1());
13182
}
13183
13184
// Constructor
13185
Form_1(boost::shared_ptr<const dolfin::FunctionSpace> V0):
13186
dolfin::Form(1, 0)
13187
{
13188
_function_spaces[0] = V0;
13189
13190
_ufc_form = boost::shared_ptr<const ufc::form>(new adaptivepoisson_form_1());
13191
}
13192
13193
// Destructor
13194
~Form_1()
13195
{}
13196
13197
/// Return the number of the coefficient with this name
13198
virtual dolfin::uint coefficient_number(const std::string& name) const
13199
{
13200
13201
dolfin::error("No coefficients.");
13202
return 0;
13203
}
13204
13205
/// Return the name of the coefficient with this number
13206
virtual std::string coefficient_name(dolfin::uint i) const
13207
{
13208
13209
dolfin::error("No coefficients.");
13210
return "unnamed";
13211
}
13212
13213
// Typedefs
13214
typedef Form_1_FunctionSpace_0 TestSpace;
13215
13216
// Coefficients
13217
};
13218
13219
class Form_2_FunctionSpace_0: public dolfin::FunctionSpace
13220
{
13221
public:
13222
13223
Form_2_FunctionSpace_0(const dolfin::Mesh& mesh):
13224
dolfin::FunctionSpace(dolfin::reference_to_no_delete_pointer(mesh),
13225
boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new adaptivepoisson_finite_element_4()))),
13226
boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dofmap>(new adaptivepoisson_dofmap_4()), mesh)))
13227
{
13228
// Do nothing
13229
}
13230
13231
Form_2_FunctionSpace_0(dolfin::Mesh& mesh):
13232
dolfin::FunctionSpace(dolfin::reference_to_no_delete_pointer(mesh),
13233
boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new adaptivepoisson_finite_element_4()))),
13234
boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dofmap>(new adaptivepoisson_dofmap_4()), mesh)))
13235
{
13236
// Do nothing
13237
}
13238
13239
Form_2_FunctionSpace_0(boost::shared_ptr<dolfin::Mesh> mesh):
13240
dolfin::FunctionSpace(mesh,
13241
boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new adaptivepoisson_finite_element_4()))),
13242
boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dofmap>(new adaptivepoisson_dofmap_4()), *mesh)))
13243
{
13244
// Do nothing
13245
}
13246
13247
Form_2_FunctionSpace_0(boost::shared_ptr<const dolfin::Mesh> mesh):
13248
dolfin::FunctionSpace(mesh,
13249
boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new adaptivepoisson_finite_element_4()))),
13250
boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dofmap>(new adaptivepoisson_dofmap_4()), *mesh)))
13251
{
13252
// Do nothing
13253
}
13254
13255
~Form_2_FunctionSpace_0()
13256
{
13257
}
13258
13259
};
13260
13261
class Form_2_FunctionSpace_1: public dolfin::FunctionSpace
13262
{
13263
public:
13264
13265
Form_2_FunctionSpace_1(const dolfin::Mesh& mesh):
13266
dolfin::FunctionSpace(dolfin::reference_to_no_delete_pointer(mesh),
13267
boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new adaptivepoisson_finite_element_4()))),
13268
boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dofmap>(new adaptivepoisson_dofmap_4()), mesh)))
13269
{
13270
// Do nothing
13271
}
13272
13273
Form_2_FunctionSpace_1(dolfin::Mesh& mesh):
13274
dolfin::FunctionSpace(dolfin::reference_to_no_delete_pointer(mesh),
13275
boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new adaptivepoisson_finite_element_4()))),
13276
boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dofmap>(new adaptivepoisson_dofmap_4()), mesh)))
13277
{
13278
// Do nothing
13279
}
13280
13281
Form_2_FunctionSpace_1(boost::shared_ptr<dolfin::Mesh> mesh):
13282
dolfin::FunctionSpace(mesh,
13283
boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new adaptivepoisson_finite_element_4()))),
13284
boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dofmap>(new adaptivepoisson_dofmap_4()), *mesh)))
13285
{
13286
// Do nothing
13287
}
13288
13289
Form_2_FunctionSpace_1(boost::shared_ptr<const dolfin::Mesh> mesh):
13290
dolfin::FunctionSpace(mesh,
13291
boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new adaptivepoisson_finite_element_4()))),
13292
boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dofmap>(new adaptivepoisson_dofmap_4()), *mesh)))
13293
{
13294
// Do nothing
13295
}
13296
13297
~Form_2_FunctionSpace_1()
13298
{
13299
}
13300
13301
};
13302
13303
typedef CoefficientSpace___cell_bubble Form_2_FunctionSpace_2;
13304
13305
class Form_2: public dolfin::Form
13306
{
13307
public:
13308
13309
// Constructor
13310
Form_2(const dolfin::FunctionSpace& V0, const dolfin::FunctionSpace& V1):
13311
dolfin::Form(2, 1), __cell_bubble(*this, 0)
13312
{
13313
_function_spaces[0] = reference_to_no_delete_pointer(V0);
13314
_function_spaces[1] = reference_to_no_delete_pointer(V1);
13315
13316
_ufc_form = boost::shared_ptr<const ufc::form>(new adaptivepoisson_form_2());
13317
}
13318
13319
// Constructor
13320
Form_2(const dolfin::FunctionSpace& V0, const dolfin::FunctionSpace& V1, const dolfin::GenericFunction& __cell_bubble):
13321
dolfin::Form(2, 1), __cell_bubble(*this, 0)
13322
{
13323
_function_spaces[0] = reference_to_no_delete_pointer(V0);
13324
_function_spaces[1] = reference_to_no_delete_pointer(V1);
13325
13326
this->__cell_bubble = __cell_bubble;
13327
13328
_ufc_form = boost::shared_ptr<const ufc::form>(new adaptivepoisson_form_2());
13329
}
13330
13331
// Constructor
13332
Form_2(const dolfin::FunctionSpace& V0, const dolfin::FunctionSpace& V1, boost::shared_ptr<const dolfin::GenericFunction> __cell_bubble):
13333
dolfin::Form(2, 1), __cell_bubble(*this, 0)
13334
{
13335
_function_spaces[0] = reference_to_no_delete_pointer(V0);
13336
_function_spaces[1] = reference_to_no_delete_pointer(V1);
13337
13338
this->__cell_bubble = *__cell_bubble;
13339
13340
_ufc_form = boost::shared_ptr<const ufc::form>(new adaptivepoisson_form_2());
13341
}
13342
13343
// Constructor
13344
Form_2(boost::shared_ptr<const dolfin::FunctionSpace> V0, boost::shared_ptr<const dolfin::FunctionSpace> V1):
13345
dolfin::Form(2, 1), __cell_bubble(*this, 0)
13346
{
13347
_function_spaces[0] = V0;
13348
_function_spaces[1] = V1;
13349
13350
_ufc_form = boost::shared_ptr<const ufc::form>(new adaptivepoisson_form_2());
13351
}
13352
13353
// Constructor
13354
Form_2(boost::shared_ptr<const dolfin::FunctionSpace> V0, boost::shared_ptr<const dolfin::FunctionSpace> V1, const dolfin::GenericFunction& __cell_bubble):
13355
dolfin::Form(2, 1), __cell_bubble(*this, 0)
13356
{
13357
_function_spaces[0] = V0;
13358
_function_spaces[1] = V1;
13359
13360
this->__cell_bubble = __cell_bubble;
13361
13362
_ufc_form = boost::shared_ptr<const ufc::form>(new adaptivepoisson_form_2());
13363
}
13364
13365
// Constructor
13366
Form_2(boost::shared_ptr<const dolfin::FunctionSpace> V0, boost::shared_ptr<const dolfin::FunctionSpace> V1, boost::shared_ptr<const dolfin::GenericFunction> __cell_bubble):
13367
dolfin::Form(2, 1), __cell_bubble(*this, 0)
13368
{
13369
_function_spaces[0] = V0;
13370
_function_spaces[1] = V1;
13371
13372
this->__cell_bubble = *__cell_bubble;
13373
13374
_ufc_form = boost::shared_ptr<const ufc::form>(new adaptivepoisson_form_2());
13375
}
13376
13377
// Destructor
13378
~Form_2()
13379
{}
13380
13381
/// Return the number of the coefficient with this name
13382
virtual dolfin::uint coefficient_number(const std::string& name) const
13383
{
13384
if (name == "__cell_bubble")
13385
return 0;
13386
13387
dolfin::error("Invalid coefficient.");
13388
return 0;
13389
}
13390
13391
/// Return the name of the coefficient with this number
13392
virtual std::string coefficient_name(dolfin::uint i) const
13393
{
13394
switch (i)
13395
{
13396
case 0:
13397
return "__cell_bubble";
13398
}
13399
13400
dolfin::error("Invalid coefficient.");
13401
return "unnamed";
13402
}
13403
13404
// Typedefs
13405
typedef Form_2_FunctionSpace_0 TestSpace;
13406
typedef Form_2_FunctionSpace_1 TrialSpace;
13407
typedef Form_2_FunctionSpace_2 CoefficientSpace___cell_bubble;
13408
13409
// Coefficients
13410
dolfin::CoefficientAssigner __cell_bubble;
13411
};
13412
13413
class Form_3_FunctionSpace_0: public dolfin::FunctionSpace
13414
{
13415
public:
13416
13417
Form_3_FunctionSpace_0(const dolfin::Mesh& mesh):
13418
dolfin::FunctionSpace(dolfin::reference_to_no_delete_pointer(mesh),
13419
boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new adaptivepoisson_finite_element_4()))),
13420
boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dofmap>(new adaptivepoisson_dofmap_4()), mesh)))
13421
{
13422
// Do nothing
13423
}
13424
13425
Form_3_FunctionSpace_0(dolfin::Mesh& mesh):
13426
dolfin::FunctionSpace(dolfin::reference_to_no_delete_pointer(mesh),
13427
boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new adaptivepoisson_finite_element_4()))),
13428
boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dofmap>(new adaptivepoisson_dofmap_4()), mesh)))
13429
{
13430
// Do nothing
13431
}
13432
13433
Form_3_FunctionSpace_0(boost::shared_ptr<dolfin::Mesh> mesh):
13434
dolfin::FunctionSpace(mesh,
13435
boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new adaptivepoisson_finite_element_4()))),
13436
boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dofmap>(new adaptivepoisson_dofmap_4()), *mesh)))
13437
{
13438
// Do nothing
13439
}
13440
13441
Form_3_FunctionSpace_0(boost::shared_ptr<const dolfin::Mesh> mesh):
13442
dolfin::FunctionSpace(mesh,
13443
boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new adaptivepoisson_finite_element_4()))),
13444
boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dofmap>(new adaptivepoisson_dofmap_4()), *mesh)))
13445
{
13446
// Do nothing
13447
}
13448
13449
~Form_3_FunctionSpace_0()
13450
{
13451
}
13452
13453
};
13454
13455
typedef CoefficientSpace_f Form_3_FunctionSpace_1;
13456
13457
typedef CoefficientSpace_g Form_3_FunctionSpace_2;
13458
13459
typedef CoefficientSpace___discrete_primal_solution Form_3_FunctionSpace_3;
13460
13461
typedef CoefficientSpace___cell_bubble Form_3_FunctionSpace_4;
13462
13463
class Form_3: public dolfin::Form
13464
{
13465
public:
13466
13467
// Constructor
13468
Form_3(const dolfin::FunctionSpace& V0):
13469
dolfin::Form(1, 4), f(*this, 0), g(*this, 1), __discrete_primal_solution(*this, 2), __cell_bubble(*this, 3)
13470
{
13471
_function_spaces[0] = reference_to_no_delete_pointer(V0);
13472
13473
_ufc_form = boost::shared_ptr<const ufc::form>(new adaptivepoisson_form_3());
13474
}
13475
13476
// Constructor
13477
Form_3(const dolfin::FunctionSpace& V0, const dolfin::GenericFunction& f, const dolfin::GenericFunction& g, const dolfin::GenericFunction& __discrete_primal_solution, const dolfin::GenericFunction& __cell_bubble):
13478
dolfin::Form(1, 4), f(*this, 0), g(*this, 1), __discrete_primal_solution(*this, 2), __cell_bubble(*this, 3)
13479
{
13480
_function_spaces[0] = reference_to_no_delete_pointer(V0);
13481
13482
this->f = f;
13483
this->g = g;
13484
this->__discrete_primal_solution = __discrete_primal_solution;
13485
this->__cell_bubble = __cell_bubble;
13486
13487
_ufc_form = boost::shared_ptr<const ufc::form>(new adaptivepoisson_form_3());
13488
}
13489
13490
// Constructor
13491
Form_3(const dolfin::FunctionSpace& V0, boost::shared_ptr<const dolfin::GenericFunction> f, boost::shared_ptr<const dolfin::GenericFunction> g, boost::shared_ptr<const dolfin::GenericFunction> __discrete_primal_solution, boost::shared_ptr<const dolfin::GenericFunction> __cell_bubble):
13492
dolfin::Form(1, 4), f(*this, 0), g(*this, 1), __discrete_primal_solution(*this, 2), __cell_bubble(*this, 3)
13493
{
13494
_function_spaces[0] = reference_to_no_delete_pointer(V0);
13495
13496
this->f = *f;
13497
this->g = *g;
13498
this->__discrete_primal_solution = *__discrete_primal_solution;
13499
this->__cell_bubble = *__cell_bubble;
13500
13501
_ufc_form = boost::shared_ptr<const ufc::form>(new adaptivepoisson_form_3());
13502
}
13503
13504
// Constructor
13505
Form_3(boost::shared_ptr<const dolfin::FunctionSpace> V0):
13506
dolfin::Form(1, 4), f(*this, 0), g(*this, 1), __discrete_primal_solution(*this, 2), __cell_bubble(*this, 3)
13507
{
13508
_function_spaces[0] = V0;
13509
13510
_ufc_form = boost::shared_ptr<const ufc::form>(new adaptivepoisson_form_3());
13511
}
13512
13513
// Constructor
13514
Form_3(boost::shared_ptr<const dolfin::FunctionSpace> V0, const dolfin::GenericFunction& f, const dolfin::GenericFunction& g, const dolfin::GenericFunction& __discrete_primal_solution, const dolfin::GenericFunction& __cell_bubble):
13515
dolfin::Form(1, 4), f(*this, 0), g(*this, 1), __discrete_primal_solution(*this, 2), __cell_bubble(*this, 3)
13516
{
13517
_function_spaces[0] = V0;
13518
13519
this->f = f;
13520
this->g = g;
13521
this->__discrete_primal_solution = __discrete_primal_solution;
13522
this->__cell_bubble = __cell_bubble;
13523
13524
_ufc_form = boost::shared_ptr<const ufc::form>(new adaptivepoisson_form_3());
13525
}
13526
13527
// Constructor
13528
Form_3(boost::shared_ptr<const dolfin::FunctionSpace> V0, boost::shared_ptr<const dolfin::GenericFunction> f, boost::shared_ptr<const dolfin::GenericFunction> g, boost::shared_ptr<const dolfin::GenericFunction> __discrete_primal_solution, boost::shared_ptr<const dolfin::GenericFunction> __cell_bubble):
13529
dolfin::Form(1, 4), f(*this, 0), g(*this, 1), __discrete_primal_solution(*this, 2), __cell_bubble(*this, 3)
13530
{
13531
_function_spaces[0] = V0;
13532
13533
this->f = *f;
13534
this->g = *g;
13535
this->__discrete_primal_solution = *__discrete_primal_solution;
13536
this->__cell_bubble = *__cell_bubble;
13537
13538
_ufc_form = boost::shared_ptr<const ufc::form>(new adaptivepoisson_form_3());
13539
}
13540
13541
// Destructor
13542
~Form_3()
13543
{}
13544
13545
/// Return the number of the coefficient with this name
13546
virtual dolfin::uint coefficient_number(const std::string& name) const
13547
{
13548
if (name == "f")
13549
return 0;
13550
else if (name == "g")
13551
return 1;
13552
else if (name == "__discrete_primal_solution")
13553
return 2;
13554
else if (name == "__cell_bubble")
13555
return 3;
13556
13557
dolfin::error("Invalid coefficient.");
13558
return 0;
13559
}
13560
13561
/// Return the name of the coefficient with this number
13562
virtual std::string coefficient_name(dolfin::uint i) const
13563
{
13564
switch (i)
13565
{
13566
case 0:
13567
return "f";
13568
case 1:
13569
return "g";
13570
case 2:
13571
return "__discrete_primal_solution";
13572
case 3:
13573
return "__cell_bubble";
13574
}
13575
13576
dolfin::error("Invalid coefficient.");
13577
return "unnamed";
13578
}
13579
13580
// Typedefs
13581
typedef Form_3_FunctionSpace_0 TestSpace;
13582
typedef Form_3_FunctionSpace_1 CoefficientSpace_f;
13583
typedef Form_3_FunctionSpace_2 CoefficientSpace_g;
13584
typedef Form_3_FunctionSpace_3 CoefficientSpace___discrete_primal_solution;
13585
typedef Form_3_FunctionSpace_4 CoefficientSpace___cell_bubble;
13586
13587
// Coefficients
13588
dolfin::CoefficientAssigner f;
13589
dolfin::CoefficientAssigner g;
13590
dolfin::CoefficientAssigner __discrete_primal_solution;
13591
dolfin::CoefficientAssigner __cell_bubble;
13592
};
13593
13594
class Form_4_FunctionSpace_0: public dolfin::FunctionSpace
13595
{
13596
public:
13597
13598
Form_4_FunctionSpace_0(const dolfin::Mesh& mesh):
13599
dolfin::FunctionSpace(dolfin::reference_to_no_delete_pointer(mesh),
13600
boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new adaptivepoisson_finite_element_4()))),
13601
boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dofmap>(new adaptivepoisson_dofmap_4()), mesh)))
13602
{
13603
// Do nothing
13604
}
13605
13606
Form_4_FunctionSpace_0(dolfin::Mesh& mesh):
13607
dolfin::FunctionSpace(dolfin::reference_to_no_delete_pointer(mesh),
13608
boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new adaptivepoisson_finite_element_4()))),
13609
boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dofmap>(new adaptivepoisson_dofmap_4()), mesh)))
13610
{
13611
// Do nothing
13612
}
13613
13614
Form_4_FunctionSpace_0(boost::shared_ptr<dolfin::Mesh> mesh):
13615
dolfin::FunctionSpace(mesh,
13616
boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new adaptivepoisson_finite_element_4()))),
13617
boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dofmap>(new adaptivepoisson_dofmap_4()), *mesh)))
13618
{
13619
// Do nothing
13620
}
13621
13622
Form_4_FunctionSpace_0(boost::shared_ptr<const dolfin::Mesh> mesh):
13623
dolfin::FunctionSpace(mesh,
13624
boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new adaptivepoisson_finite_element_4()))),
13625
boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dofmap>(new adaptivepoisson_dofmap_4()), *mesh)))
13626
{
13627
// Do nothing
13628
}
13629
13630
~Form_4_FunctionSpace_0()
13631
{
13632
}
13633
13634
};
13635
13636
class Form_4_FunctionSpace_1: public dolfin::FunctionSpace
13637
{
13638
public:
13639
13640
Form_4_FunctionSpace_1(const dolfin::Mesh& mesh):
13641
dolfin::FunctionSpace(dolfin::reference_to_no_delete_pointer(mesh),
13642
boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new adaptivepoisson_finite_element_4()))),
13643
boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dofmap>(new adaptivepoisson_dofmap_4()), mesh)))
13644
{
13645
// Do nothing
13646
}
13647
13648
Form_4_FunctionSpace_1(dolfin::Mesh& mesh):
13649
dolfin::FunctionSpace(dolfin::reference_to_no_delete_pointer(mesh),
13650
boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new adaptivepoisson_finite_element_4()))),
13651
boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dofmap>(new adaptivepoisson_dofmap_4()), mesh)))
13652
{
13653
// Do nothing
13654
}
13655
13656
Form_4_FunctionSpace_1(boost::shared_ptr<dolfin::Mesh> mesh):
13657
dolfin::FunctionSpace(mesh,
13658
boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new adaptivepoisson_finite_element_4()))),
13659
boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dofmap>(new adaptivepoisson_dofmap_4()), *mesh)))
13660
{
13661
// Do nothing
13662
}
13663
13664
Form_4_FunctionSpace_1(boost::shared_ptr<const dolfin::Mesh> mesh):
13665
dolfin::FunctionSpace(mesh,
13666
boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new adaptivepoisson_finite_element_4()))),
13667
boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dofmap>(new adaptivepoisson_dofmap_4()), *mesh)))
13668
{
13669
// Do nothing
13670
}
13671
13672
~Form_4_FunctionSpace_1()
13673
{
13674
}
13675
13676
};
13677
13678
typedef CoefficientSpace___cell_cone Form_4_FunctionSpace_2;
13679
13680
class Form_4: public dolfin::Form
13681
{
13682
public:
13683
13684
// Constructor
13685
Form_4(const dolfin::FunctionSpace& V0, const dolfin::FunctionSpace& V1):
13686
dolfin::Form(2, 1), __cell_cone(*this, 0)
13687
{
13688
_function_spaces[0] = reference_to_no_delete_pointer(V0);
13689
_function_spaces[1] = reference_to_no_delete_pointer(V1);
13690
13691
_ufc_form = boost::shared_ptr<const ufc::form>(new adaptivepoisson_form_4());
13692
}
13693
13694
// Constructor
13695
Form_4(const dolfin::FunctionSpace& V0, const dolfin::FunctionSpace& V1, const dolfin::GenericFunction& __cell_cone):
13696
dolfin::Form(2, 1), __cell_cone(*this, 0)
13697
{
13698
_function_spaces[0] = reference_to_no_delete_pointer(V0);
13699
_function_spaces[1] = reference_to_no_delete_pointer(V1);
13700
13701
this->__cell_cone = __cell_cone;
13702
13703
_ufc_form = boost::shared_ptr<const ufc::form>(new adaptivepoisson_form_4());
13704
}
13705
13706
// Constructor
13707
Form_4(const dolfin::FunctionSpace& V0, const dolfin::FunctionSpace& V1, boost::shared_ptr<const dolfin::GenericFunction> __cell_cone):
13708
dolfin::Form(2, 1), __cell_cone(*this, 0)
13709
{
13710
_function_spaces[0] = reference_to_no_delete_pointer(V0);
13711
_function_spaces[1] = reference_to_no_delete_pointer(V1);
13712
13713
this->__cell_cone = *__cell_cone;
13714
13715
_ufc_form = boost::shared_ptr<const ufc::form>(new adaptivepoisson_form_4());
13716
}
13717
13718
// Constructor
13719
Form_4(boost::shared_ptr<const dolfin::FunctionSpace> V0, boost::shared_ptr<const dolfin::FunctionSpace> V1):
13720
dolfin::Form(2, 1), __cell_cone(*this, 0)
13721
{
13722
_function_spaces[0] = V0;
13723
_function_spaces[1] = V1;
13724
13725
_ufc_form = boost::shared_ptr<const ufc::form>(new adaptivepoisson_form_4());
13726
}
13727
13728
// Constructor
13729
Form_4(boost::shared_ptr<const dolfin::FunctionSpace> V0, boost::shared_ptr<const dolfin::FunctionSpace> V1, const dolfin::GenericFunction& __cell_cone):
13730
dolfin::Form(2, 1), __cell_cone(*this, 0)
13731
{
13732
_function_spaces[0] = V0;
13733
_function_spaces[1] = V1;
13734
13735
this->__cell_cone = __cell_cone;
13736
13737
_ufc_form = boost::shared_ptr<const ufc::form>(new adaptivepoisson_form_4());
13738
}
13739
13740
// Constructor
13741
Form_4(boost::shared_ptr<const dolfin::FunctionSpace> V0, boost::shared_ptr<const dolfin::FunctionSpace> V1, boost::shared_ptr<const dolfin::GenericFunction> __cell_cone):
13742
dolfin::Form(2, 1), __cell_cone(*this, 0)
13743
{
13744
_function_spaces[0] = V0;
13745
_function_spaces[1] = V1;
13746
13747
this->__cell_cone = *__cell_cone;
13748
13749
_ufc_form = boost::shared_ptr<const ufc::form>(new adaptivepoisson_form_4());
13750
}
13751
13752
// Destructor
13753
~Form_4()
13754
{}
13755
13756
/// Return the number of the coefficient with this name
13757
virtual dolfin::uint coefficient_number(const std::string& name) const
13758
{
13759
if (name == "__cell_cone")
13760
return 0;
13761
13762
dolfin::error("Invalid coefficient.");
13763
return 0;
13764
}
13765
13766
/// Return the name of the coefficient with this number
13767
virtual std::string coefficient_name(dolfin::uint i) const
13768
{
13769
switch (i)
13770
{
13771
case 0:
13772
return "__cell_cone";
13773
}
13774
13775
dolfin::error("Invalid coefficient.");
13776
return "unnamed";
13777
}
13778
13779
// Typedefs
13780
typedef Form_4_FunctionSpace_0 TestSpace;
13781
typedef Form_4_FunctionSpace_1 TrialSpace;
13782
typedef Form_4_FunctionSpace_2 CoefficientSpace___cell_cone;
13783
13784
// Coefficients
13785
dolfin::CoefficientAssigner __cell_cone;
13786
};
13787
13788
class Form_5_FunctionSpace_0: public dolfin::FunctionSpace
13789
{
13790
public:
13791
13792
Form_5_FunctionSpace_0(const dolfin::Mesh& mesh):
13793
dolfin::FunctionSpace(dolfin::reference_to_no_delete_pointer(mesh),
13794
boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new adaptivepoisson_finite_element_4()))),
13795
boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dofmap>(new adaptivepoisson_dofmap_4()), mesh)))
13796
{
13797
// Do nothing
13798
}
13799
13800
Form_5_FunctionSpace_0(dolfin::Mesh& mesh):
13801
dolfin::FunctionSpace(dolfin::reference_to_no_delete_pointer(mesh),
13802
boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new adaptivepoisson_finite_element_4()))),
13803
boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dofmap>(new adaptivepoisson_dofmap_4()), mesh)))
13804
{
13805
// Do nothing
13806
}
13807
13808
Form_5_FunctionSpace_0(boost::shared_ptr<dolfin::Mesh> mesh):
13809
dolfin::FunctionSpace(mesh,
13810
boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new adaptivepoisson_finite_element_4()))),
13811
boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dofmap>(new adaptivepoisson_dofmap_4()), *mesh)))
13812
{
13813
// Do nothing
13814
}
13815
13816
Form_5_FunctionSpace_0(boost::shared_ptr<const dolfin::Mesh> mesh):
13817
dolfin::FunctionSpace(mesh,
13818
boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new adaptivepoisson_finite_element_4()))),
13819
boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dofmap>(new adaptivepoisson_dofmap_4()), *mesh)))
13820
{
13821
// Do nothing
13822
}
13823
13824
~Form_5_FunctionSpace_0()
13825
{
13826
}
13827
13828
};
13829
13830
typedef CoefficientSpace_f Form_5_FunctionSpace_1;
13831
13832
typedef CoefficientSpace_g Form_5_FunctionSpace_2;
13833
13834
typedef CoefficientSpace___discrete_primal_solution Form_5_FunctionSpace_3;
13835
13836
typedef CoefficientSpace___cell_residual Form_5_FunctionSpace_4;
13837
13838
typedef CoefficientSpace___cell_cone Form_5_FunctionSpace_5;
13839
13840
class Form_5: public dolfin::Form
13841
{
13842
public:
13843
13844
// Constructor
13845
Form_5(const dolfin::FunctionSpace& V0):
13846
dolfin::Form(1, 5), f(*this, 0), g(*this, 1), __discrete_primal_solution(*this, 2), __cell_residual(*this, 3), __cell_cone(*this, 4)
13847
{
13848
_function_spaces[0] = reference_to_no_delete_pointer(V0);
13849
13850
_ufc_form = boost::shared_ptr<const ufc::form>(new adaptivepoisson_form_5());
13851
}
13852
13853
// Constructor
13854
Form_5(const dolfin::FunctionSpace& V0, const dolfin::GenericFunction& f, const dolfin::GenericFunction& g, const dolfin::GenericFunction& __discrete_primal_solution, const dolfin::GenericFunction& __cell_residual, const dolfin::GenericFunction& __cell_cone):
13855
dolfin::Form(1, 5), f(*this, 0), g(*this, 1), __discrete_primal_solution(*this, 2), __cell_residual(*this, 3), __cell_cone(*this, 4)
13856
{
13857
_function_spaces[0] = reference_to_no_delete_pointer(V0);
13858
13859
this->f = f;
13860
this->g = g;
13861
this->__discrete_primal_solution = __discrete_primal_solution;
13862
this->__cell_residual = __cell_residual;
13863
this->__cell_cone = __cell_cone;
13864
13865
_ufc_form = boost::shared_ptr<const ufc::form>(new adaptivepoisson_form_5());
13866
}
13867
13868
// Constructor
13869
Form_5(const dolfin::FunctionSpace& V0, boost::shared_ptr<const dolfin::GenericFunction> f, boost::shared_ptr<const dolfin::GenericFunction> g, boost::shared_ptr<const dolfin::GenericFunction> __discrete_primal_solution, boost::shared_ptr<const dolfin::GenericFunction> __cell_residual, boost::shared_ptr<const dolfin::GenericFunction> __cell_cone):
13870
dolfin::Form(1, 5), f(*this, 0), g(*this, 1), __discrete_primal_solution(*this, 2), __cell_residual(*this, 3), __cell_cone(*this, 4)
13871
{
13872
_function_spaces[0] = reference_to_no_delete_pointer(V0);
13873
13874
this->f = *f;
13875
this->g = *g;
13876
this->__discrete_primal_solution = *__discrete_primal_solution;
13877
this->__cell_residual = *__cell_residual;
13878
this->__cell_cone = *__cell_cone;
13879
13880
_ufc_form = boost::shared_ptr<const ufc::form>(new adaptivepoisson_form_5());
13881
}
13882
13883
// Constructor
13884
Form_5(boost::shared_ptr<const dolfin::FunctionSpace> V0):
13885
dolfin::Form(1, 5), f(*this, 0), g(*this, 1), __discrete_primal_solution(*this, 2), __cell_residual(*this, 3), __cell_cone(*this, 4)
13886
{
13887
_function_spaces[0] = V0;
13888
13889
_ufc_form = boost::shared_ptr<const ufc::form>(new adaptivepoisson_form_5());
13890
}
13891
13892
// Constructor
13893
Form_5(boost::shared_ptr<const dolfin::FunctionSpace> V0, const dolfin::GenericFunction& f, const dolfin::GenericFunction& g, const dolfin::GenericFunction& __discrete_primal_solution, const dolfin::GenericFunction& __cell_residual, const dolfin::GenericFunction& __cell_cone):
13894
dolfin::Form(1, 5), f(*this, 0), g(*this, 1), __discrete_primal_solution(*this, 2), __cell_residual(*this, 3), __cell_cone(*this, 4)
13895
{
13896
_function_spaces[0] = V0;
13897
13898
this->f = f;
13899
this->g = g;
13900
this->__discrete_primal_solution = __discrete_primal_solution;
13901
this->__cell_residual = __cell_residual;
13902
this->__cell_cone = __cell_cone;
13903
13904
_ufc_form = boost::shared_ptr<const ufc::form>(new adaptivepoisson_form_5());
13905
}
13906
13907
// Constructor
13908
Form_5(boost::shared_ptr<const dolfin::FunctionSpace> V0, boost::shared_ptr<const dolfin::GenericFunction> f, boost::shared_ptr<const dolfin::GenericFunction> g, boost::shared_ptr<const dolfin::GenericFunction> __discrete_primal_solution, boost::shared_ptr<const dolfin::GenericFunction> __cell_residual, boost::shared_ptr<const dolfin::GenericFunction> __cell_cone):
13909
dolfin::Form(1, 5), f(*this, 0), g(*this, 1), __discrete_primal_solution(*this, 2), __cell_residual(*this, 3), __cell_cone(*this, 4)
13910
{
13911
_function_spaces[0] = V0;
13912
13913
this->f = *f;
13914
this->g = *g;
13915
this->__discrete_primal_solution = *__discrete_primal_solution;
13916
this->__cell_residual = *__cell_residual;
13917
this->__cell_cone = *__cell_cone;
13918
13919
_ufc_form = boost::shared_ptr<const ufc::form>(new adaptivepoisson_form_5());
13920
}
13921
13922
// Destructor
13923
~Form_5()
13924
{}
13925
13926
/// Return the number of the coefficient with this name
13927
virtual dolfin::uint coefficient_number(const std::string& name) const
13928
{
13929
if (name == "f")
13930
return 0;
13931
else if (name == "g")
13932
return 1;
13933
else if (name == "__discrete_primal_solution")
13934
return 2;
13935
else if (name == "__cell_residual")
13936
return 3;
13937
else if (name == "__cell_cone")
13938
return 4;
13939
13940
dolfin::error("Invalid coefficient.");
13941
return 0;
13942
}
13943
13944
/// Return the name of the coefficient with this number
13945
virtual std::string coefficient_name(dolfin::uint i) const
13946
{
13947
switch (i)
13948
{
13949
case 0:
13950
return "f";
13951
case 1:
13952
return "g";
13953
case 2:
13954
return "__discrete_primal_solution";
13955
case 3:
13956
return "__cell_residual";
13957
case 4:
13958
return "__cell_cone";
13959
}
13960
13961
dolfin::error("Invalid coefficient.");
13962
return "unnamed";
13963
}
13964
13965
// Typedefs
13966
typedef Form_5_FunctionSpace_0 TestSpace;
13967
typedef Form_5_FunctionSpace_1 CoefficientSpace_f;
13968
typedef Form_5_FunctionSpace_2 CoefficientSpace_g;
13969
typedef Form_5_FunctionSpace_3 CoefficientSpace___discrete_primal_solution;
13970
typedef Form_5_FunctionSpace_4 CoefficientSpace___cell_residual;
13971
typedef Form_5_FunctionSpace_5 CoefficientSpace___cell_cone;
13972
13973
// Coefficients
13974
dolfin::CoefficientAssigner f;
13975
dolfin::CoefficientAssigner g;
13976
dolfin::CoefficientAssigner __discrete_primal_solution;
13977
dolfin::CoefficientAssigner __cell_residual;
13978
dolfin::CoefficientAssigner __cell_cone;
13979
};
13980
13981
typedef CoefficientSpace_f Form_6_FunctionSpace_0;
13982
13983
typedef CoefficientSpace_g Form_6_FunctionSpace_1;
13984
13985
typedef CoefficientSpace___discrete_primal_solution Form_6_FunctionSpace_2;
13986
13987
typedef CoefficientSpace___improved_dual Form_6_FunctionSpace_3;
13988
13989
class Form_6: public dolfin::Form
13990
{
13991
public:
13992
13993
// Constructor
13994
Form_6(const dolfin::Mesh& mesh):
13995
dolfin::Form(0, 4), f(*this, 0), g(*this, 1), __discrete_primal_solution(*this, 2), __improved_dual(*this, 3)
13996
{
13997
_mesh = reference_to_no_delete_pointer(mesh);
13998
_ufc_form = boost::shared_ptr<const ufc::form>(new adaptivepoisson_form_6());
13999
}
14000
14001
// Constructor
14002
Form_6(const dolfin::Mesh& mesh, const dolfin::GenericFunction& f, const dolfin::GenericFunction& g, const dolfin::GenericFunction& __discrete_primal_solution, const dolfin::GenericFunction& __improved_dual):
14003
dolfin::Form(0, 4), f(*this, 0), g(*this, 1), __discrete_primal_solution(*this, 2), __improved_dual(*this, 3)
14004
{
14005
_mesh = reference_to_no_delete_pointer(mesh);
14006
this->f = f;
14007
this->g = g;
14008
this->__discrete_primal_solution = __discrete_primal_solution;
14009
this->__improved_dual = __improved_dual;
14010
14011
_ufc_form = boost::shared_ptr<const ufc::form>(new adaptivepoisson_form_6());
14012
}
14013
14014
// Constructor
14015
Form_6(const dolfin::Mesh& mesh, boost::shared_ptr<const dolfin::GenericFunction> f, boost::shared_ptr<const dolfin::GenericFunction> g, boost::shared_ptr<const dolfin::GenericFunction> __discrete_primal_solution, boost::shared_ptr<const dolfin::GenericFunction> __improved_dual):
14016
dolfin::Form(0, 4), f(*this, 0), g(*this, 1), __discrete_primal_solution(*this, 2), __improved_dual(*this, 3)
14017
{
14018
_mesh = reference_to_no_delete_pointer(mesh);
14019
this->f = *f;
14020
this->g = *g;
14021
this->__discrete_primal_solution = *__discrete_primal_solution;
14022
this->__improved_dual = *__improved_dual;
14023
14024
_ufc_form = boost::shared_ptr<const ufc::form>(new adaptivepoisson_form_6());
14025
}
14026
14027
// Constructor
14028
Form_6(boost::shared_ptr<const dolfin::Mesh> mesh):
14029
dolfin::Form(0, 4), f(*this, 0), g(*this, 1), __discrete_primal_solution(*this, 2), __improved_dual(*this, 3)
14030
{
14031
_mesh = mesh;
14032
_ufc_form = boost::shared_ptr<const ufc::form>(new adaptivepoisson_form_6());
14033
}
14034
14035
// Constructor
14036
Form_6(boost::shared_ptr<const dolfin::Mesh> mesh, const dolfin::GenericFunction& f, const dolfin::GenericFunction& g, const dolfin::GenericFunction& __discrete_primal_solution, const dolfin::GenericFunction& __improved_dual):
14037
dolfin::Form(0, 4), f(*this, 0), g(*this, 1), __discrete_primal_solution(*this, 2), __improved_dual(*this, 3)
14038
{
14039
_mesh = mesh;
14040
this->f = f;
14041
this->g = g;
14042
this->__discrete_primal_solution = __discrete_primal_solution;
14043
this->__improved_dual = __improved_dual;
14044
14045
_ufc_form = boost::shared_ptr<const ufc::form>(new adaptivepoisson_form_6());
14046
}
14047
14048
// Constructor
14049
Form_6(boost::shared_ptr<const dolfin::Mesh> mesh, boost::shared_ptr<const dolfin::GenericFunction> f, boost::shared_ptr<const dolfin::GenericFunction> g, boost::shared_ptr<const dolfin::GenericFunction> __discrete_primal_solution, boost::shared_ptr<const dolfin::GenericFunction> __improved_dual):
14050
dolfin::Form(0, 4), f(*this, 0), g(*this, 1), __discrete_primal_solution(*this, 2), __improved_dual(*this, 3)
14051
{
14052
_mesh = mesh;
14053
this->f = *f;
14054
this->g = *g;
14055
this->__discrete_primal_solution = *__discrete_primal_solution;
14056
this->__improved_dual = *__improved_dual;
14057
14058
_ufc_form = boost::shared_ptr<const ufc::form>(new adaptivepoisson_form_6());
14059
}
14060
14061
// Destructor
14062
~Form_6()
14063
{}
14064
14065
/// Return the number of the coefficient with this name
14066
virtual dolfin::uint coefficient_number(const std::string& name) const
14067
{
14068
if (name == "f")
14069
return 0;
14070
else if (name == "g")
14071
return 1;
14072
else if (name == "__discrete_primal_solution")
14073
return 2;
14074
else if (name == "__improved_dual")
14075
return 3;
14076
14077
dolfin::error("Invalid coefficient.");
14078
return 0;
14079
}
14080
14081
/// Return the name of the coefficient with this number
14082
virtual std::string coefficient_name(dolfin::uint i) const
14083
{
14084
switch (i)
14085
{
14086
case 0:
14087
return "f";
14088
case 1:
14089
return "g";
14090
case 2:
14091
return "__discrete_primal_solution";
14092
case 3:
14093
return "__improved_dual";
14094
}
14095
14096
dolfin::error("Invalid coefficient.");
14097
return "unnamed";
14098
}
14099
14100
// Typedefs
14101
typedef Form_6_FunctionSpace_0 CoefficientSpace_f;
14102
typedef Form_6_FunctionSpace_1 CoefficientSpace_g;
14103
typedef Form_6_FunctionSpace_2 CoefficientSpace___discrete_primal_solution;
14104
typedef Form_6_FunctionSpace_3 CoefficientSpace___improved_dual;
14105
14106
// Coefficients
14107
dolfin::CoefficientAssigner f;
14108
dolfin::CoefficientAssigner g;
14109
dolfin::CoefficientAssigner __discrete_primal_solution;
14110
dolfin::CoefficientAssigner __improved_dual;
14111
};
14112
14113
class Form_7_FunctionSpace_0: public dolfin::FunctionSpace
14114
{
14115
public:
14116
14117
Form_7_FunctionSpace_0(const dolfin::Mesh& mesh):
14118
dolfin::FunctionSpace(dolfin::reference_to_no_delete_pointer(mesh),
14119
boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new adaptivepoisson_finite_element_0()))),
14120
boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dofmap>(new adaptivepoisson_dofmap_0()), mesh)))
14121
{
14122
// Do nothing
14123
}
14124
14125
Form_7_FunctionSpace_0(dolfin::Mesh& mesh):
14126
dolfin::FunctionSpace(dolfin::reference_to_no_delete_pointer(mesh),
14127
boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new adaptivepoisson_finite_element_0()))),
14128
boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dofmap>(new adaptivepoisson_dofmap_0()), mesh)))
14129
{
14130
// Do nothing
14131
}
14132
14133
Form_7_FunctionSpace_0(boost::shared_ptr<dolfin::Mesh> mesh):
14134
dolfin::FunctionSpace(mesh,
14135
boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new adaptivepoisson_finite_element_0()))),
14136
boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dofmap>(new adaptivepoisson_dofmap_0()), *mesh)))
14137
{
14138
// Do nothing
14139
}
14140
14141
Form_7_FunctionSpace_0(boost::shared_ptr<const dolfin::Mesh> mesh):
14142
dolfin::FunctionSpace(mesh,
14143
boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new adaptivepoisson_finite_element_0()))),
14144
boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dofmap>(new adaptivepoisson_dofmap_0()), *mesh)))
14145
{
14146
// Do nothing
14147
}
14148
14149
~Form_7_FunctionSpace_0()
14150
{
14151
}
14152
14153
};
14154
14155
typedef CoefficientSpace___improved_dual Form_7_FunctionSpace_1;
14156
14157
typedef CoefficientSpace___cell_residual Form_7_FunctionSpace_2;
14158
14159
typedef CoefficientSpace___facet_residual Form_7_FunctionSpace_3;
14160
14161
typedef CoefficientSpace___discrete_dual_solution Form_7_FunctionSpace_4;
14162
14163
class Form_7: public dolfin::Form
14164
{
14165
public:
14166
14167
// Constructor
14168
Form_7(const dolfin::FunctionSpace& V0):
14169
dolfin::Form(1, 4), __improved_dual(*this, 0), __cell_residual(*this, 1), __facet_residual(*this, 2), __discrete_dual_solution(*this, 3)
14170
{
14171
_function_spaces[0] = reference_to_no_delete_pointer(V0);
14172
14173
_ufc_form = boost::shared_ptr<const ufc::form>(new adaptivepoisson_form_7());
14174
}
14175
14176
// Constructor
14177
Form_7(const dolfin::FunctionSpace& V0, const dolfin::GenericFunction& __improved_dual, const dolfin::GenericFunction& __cell_residual, const dolfin::GenericFunction& __facet_residual, const dolfin::GenericFunction& __discrete_dual_solution):
14178
dolfin::Form(1, 4), __improved_dual(*this, 0), __cell_residual(*this, 1), __facet_residual(*this, 2), __discrete_dual_solution(*this, 3)
14179
{
14180
_function_spaces[0] = reference_to_no_delete_pointer(V0);
14181
14182
this->__improved_dual = __improved_dual;
14183
this->__cell_residual = __cell_residual;
14184
this->__facet_residual = __facet_residual;
14185
this->__discrete_dual_solution = __discrete_dual_solution;
14186
14187
_ufc_form = boost::shared_ptr<const ufc::form>(new adaptivepoisson_form_7());
14188
}
14189
14190
// Constructor
14191
Form_7(const dolfin::FunctionSpace& V0, boost::shared_ptr<const dolfin::GenericFunction> __improved_dual, boost::shared_ptr<const dolfin::GenericFunction> __cell_residual, boost::shared_ptr<const dolfin::GenericFunction> __facet_residual, boost::shared_ptr<const dolfin::GenericFunction> __discrete_dual_solution):
14192
dolfin::Form(1, 4), __improved_dual(*this, 0), __cell_residual(*this, 1), __facet_residual(*this, 2), __discrete_dual_solution(*this, 3)
14193
{
14194
_function_spaces[0] = reference_to_no_delete_pointer(V0);
14195
14196
this->__improved_dual = *__improved_dual;
14197
this->__cell_residual = *__cell_residual;
14198
this->__facet_residual = *__facet_residual;
14199
this->__discrete_dual_solution = *__discrete_dual_solution;
14200
14201
_ufc_form = boost::shared_ptr<const ufc::form>(new adaptivepoisson_form_7());
14202
}
14203
14204
// Constructor
14205
Form_7(boost::shared_ptr<const dolfin::FunctionSpace> V0):
14206
dolfin::Form(1, 4), __improved_dual(*this, 0), __cell_residual(*this, 1), __facet_residual(*this, 2), __discrete_dual_solution(*this, 3)
14207
{
14208
_function_spaces[0] = V0;
14209
14210
_ufc_form = boost::shared_ptr<const ufc::form>(new adaptivepoisson_form_7());
14211
}
14212
14213
// Constructor
14214
Form_7(boost::shared_ptr<const dolfin::FunctionSpace> V0, const dolfin::GenericFunction& __improved_dual, const dolfin::GenericFunction& __cell_residual, const dolfin::GenericFunction& __facet_residual, const dolfin::GenericFunction& __discrete_dual_solution):
14215
dolfin::Form(1, 4), __improved_dual(*this, 0), __cell_residual(*this, 1), __facet_residual(*this, 2), __discrete_dual_solution(*this, 3)
14216
{
14217
_function_spaces[0] = V0;
14218
14219
this->__improved_dual = __improved_dual;
14220
this->__cell_residual = __cell_residual;
14221
this->__facet_residual = __facet_residual;
14222
this->__discrete_dual_solution = __discrete_dual_solution;
14223
14224
_ufc_form = boost::shared_ptr<const ufc::form>(new adaptivepoisson_form_7());
14225
}
14226
14227
// Constructor
14228
Form_7(boost::shared_ptr<const dolfin::FunctionSpace> V0, boost::shared_ptr<const dolfin::GenericFunction> __improved_dual, boost::shared_ptr<const dolfin::GenericFunction> __cell_residual, boost::shared_ptr<const dolfin::GenericFunction> __facet_residual, boost::shared_ptr<const dolfin::GenericFunction> __discrete_dual_solution):
14229
dolfin::Form(1, 4), __improved_dual(*this, 0), __cell_residual(*this, 1), __facet_residual(*this, 2), __discrete_dual_solution(*this, 3)
14230
{
14231
_function_spaces[0] = V0;
14232
14233
this->__improved_dual = *__improved_dual;
14234
this->__cell_residual = *__cell_residual;
14235
this->__facet_residual = *__facet_residual;
14236
this->__discrete_dual_solution = *__discrete_dual_solution;
14237
14238
_ufc_form = boost::shared_ptr<const ufc::form>(new adaptivepoisson_form_7());
14239
}
14240
14241
// Destructor
14242
~Form_7()
14243
{}
14244
14245
/// Return the number of the coefficient with this name
14246
virtual dolfin::uint coefficient_number(const std::string& name) const
14247
{
14248
if (name == "__improved_dual")
14249
return 0;
14250
else if (name == "__cell_residual")
14251
return 1;
14252
else if (name == "__facet_residual")
14253
return 2;
14254
else if (name == "__discrete_dual_solution")
14255
return 3;
14256
14257
dolfin::error("Invalid coefficient.");
14258
return 0;
14259
}
14260
14261
/// Return the name of the coefficient with this number
14262
virtual std::string coefficient_name(dolfin::uint i) const
14263
{
14264
switch (i)
14265
{
14266
case 0:
14267
return "__improved_dual";
14268
case 1:
14269
return "__cell_residual";
14270
case 2:
14271
return "__facet_residual";
14272
case 3:
14273
return "__discrete_dual_solution";
14274
}
14275
14276
dolfin::error("Invalid coefficient.");
14277
return "unnamed";
14278
}
14279
14280
// Typedefs
14281
typedef Form_7_FunctionSpace_0 TestSpace;
14282
typedef Form_7_FunctionSpace_1 CoefficientSpace___improved_dual;
14283
typedef Form_7_FunctionSpace_2 CoefficientSpace___cell_residual;
14284
typedef Form_7_FunctionSpace_3 CoefficientSpace___facet_residual;
14285
typedef Form_7_FunctionSpace_4 CoefficientSpace___discrete_dual_solution;
14286
14287
// Coefficients
14288
dolfin::CoefficientAssigner __improved_dual;
14289
dolfin::CoefficientAssigner __cell_residual;
14290
dolfin::CoefficientAssigner __facet_residual;
14291
dolfin::CoefficientAssigner __discrete_dual_solution;
14292
};
14293
14294
class Form_8_FunctionSpace_0: public dolfin::FunctionSpace
14295
{
14296
public:
14297
14298
Form_8_FunctionSpace_0(const dolfin::Mesh& mesh):
14299
dolfin::FunctionSpace(dolfin::reference_to_no_delete_pointer(mesh),
14300
boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new adaptivepoisson_finite_element_5()))),
14301
boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dofmap>(new adaptivepoisson_dofmap_5()), mesh)))
14302
{
14303
// Do nothing
14304
}
14305
14306
Form_8_FunctionSpace_0(dolfin::Mesh& mesh):
14307
dolfin::FunctionSpace(dolfin::reference_to_no_delete_pointer(mesh),
14308
boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new adaptivepoisson_finite_element_5()))),
14309
boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dofmap>(new adaptivepoisson_dofmap_5()), mesh)))
14310
{
14311
// Do nothing
14312
}
14313
14314
Form_8_FunctionSpace_0(boost::shared_ptr<dolfin::Mesh> mesh):
14315
dolfin::FunctionSpace(mesh,
14316
boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new adaptivepoisson_finite_element_5()))),
14317
boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dofmap>(new adaptivepoisson_dofmap_5()), *mesh)))
14318
{
14319
// Do nothing
14320
}
14321
14322
Form_8_FunctionSpace_0(boost::shared_ptr<const dolfin::Mesh> mesh):
14323
dolfin::FunctionSpace(mesh,
14324
boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new adaptivepoisson_finite_element_5()))),
14325
boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dofmap>(new adaptivepoisson_dofmap_5()), *mesh)))
14326
{
14327
// Do nothing
14328
}
14329
14330
~Form_8_FunctionSpace_0()
14331
{
14332
}
14333
14334
};
14335
14336
class Form_8_FunctionSpace_1: public dolfin::FunctionSpace
14337
{
14338
public:
14339
14340
Form_8_FunctionSpace_1(const dolfin::Mesh& mesh):
14341
dolfin::FunctionSpace(dolfin::reference_to_no_delete_pointer(mesh),
14342
boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new adaptivepoisson_finite_element_5()))),
14343
boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dofmap>(new adaptivepoisson_dofmap_5()), mesh)))
14344
{
14345
// Do nothing
14346
}
14347
14348
Form_8_FunctionSpace_1(dolfin::Mesh& mesh):
14349
dolfin::FunctionSpace(dolfin::reference_to_no_delete_pointer(mesh),
14350
boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new adaptivepoisson_finite_element_5()))),
14351
boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dofmap>(new adaptivepoisson_dofmap_5()), mesh)))
14352
{
14353
// Do nothing
14354
}
14355
14356
Form_8_FunctionSpace_1(boost::shared_ptr<dolfin::Mesh> mesh):
14357
dolfin::FunctionSpace(mesh,
14358
boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new adaptivepoisson_finite_element_5()))),
14359
boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dofmap>(new adaptivepoisson_dofmap_5()), *mesh)))
14360
{
14361
// Do nothing
14362
}
14363
14364
Form_8_FunctionSpace_1(boost::shared_ptr<const dolfin::Mesh> mesh):
14365
dolfin::FunctionSpace(mesh,
14366
boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new adaptivepoisson_finite_element_5()))),
14367
boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dofmap>(new adaptivepoisson_dofmap_5()), *mesh)))
14368
{
14369
// Do nothing
14370
}
14371
14372
~Form_8_FunctionSpace_1()
14373
{
14374
}
14375
14376
};
14377
14378
class Form_8: public dolfin::Form
14379
{
14380
public:
14381
14382
// Constructor
14383
Form_8(const dolfin::FunctionSpace& V0, const dolfin::FunctionSpace& V1):
14384
dolfin::Form(2, 0)
14385
{
14386
_function_spaces[0] = reference_to_no_delete_pointer(V0);
14387
_function_spaces[1] = reference_to_no_delete_pointer(V1);
14388
14389
_ufc_form = boost::shared_ptr<const ufc::form>(new adaptivepoisson_form_8());
14390
}
14391
14392
// Constructor
14393
Form_8(boost::shared_ptr<const dolfin::FunctionSpace> V0, boost::shared_ptr<const dolfin::FunctionSpace> V1):
14394
dolfin::Form(2, 0)
14395
{
14396
_function_spaces[0] = V0;
14397
_function_spaces[1] = V1;
14398
14399
_ufc_form = boost::shared_ptr<const ufc::form>(new adaptivepoisson_form_8());
14400
}
14401
14402
// Destructor
14403
~Form_8()
14404
{}
14405
14406
/// Return the number of the coefficient with this name
14407
virtual dolfin::uint coefficient_number(const std::string& name) const
14408
{
14409
14410
dolfin::error("No coefficients.");
14411
return 0;
14412
}
14413
14414
/// Return the name of the coefficient with this number
14415
virtual std::string coefficient_name(dolfin::uint i) const
14416
{
14417
14418
dolfin::error("No coefficients.");
14419
return "unnamed";
14420
}
14421
14422
// Typedefs
14423
typedef Form_8_FunctionSpace_0 TestSpace;
14424
typedef Form_8_FunctionSpace_1 TrialSpace;
14425
14426
// Coefficients
14427
};
14428
14429
class Form_9_FunctionSpace_0: public dolfin::FunctionSpace
14430
{
14431
public:
14432
14433
Form_9_FunctionSpace_0(const dolfin::Mesh& mesh):
14434
dolfin::FunctionSpace(dolfin::reference_to_no_delete_pointer(mesh),
14435
boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new adaptivepoisson_finite_element_5()))),
14436
boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dofmap>(new adaptivepoisson_dofmap_5()), mesh)))
14437
{
14438
// Do nothing
14439
}
14440
14441
Form_9_FunctionSpace_0(dolfin::Mesh& mesh):
14442
dolfin::FunctionSpace(dolfin::reference_to_no_delete_pointer(mesh),
14443
boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new adaptivepoisson_finite_element_5()))),
14444
boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dofmap>(new adaptivepoisson_dofmap_5()), mesh)))
14445
{
14446
// Do nothing
14447
}
14448
14449
Form_9_FunctionSpace_0(boost::shared_ptr<dolfin::Mesh> mesh):
14450
dolfin::FunctionSpace(mesh,
14451
boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new adaptivepoisson_finite_element_5()))),
14452
boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dofmap>(new adaptivepoisson_dofmap_5()), *mesh)))
14453
{
14454
// Do nothing
14455
}
14456
14457
Form_9_FunctionSpace_0(boost::shared_ptr<const dolfin::Mesh> mesh):
14458
dolfin::FunctionSpace(mesh,
14459
boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new adaptivepoisson_finite_element_5()))),
14460
boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dofmap>(new adaptivepoisson_dofmap_5()), *mesh)))
14461
{
14462
// Do nothing
14463
}
14464
14465
~Form_9_FunctionSpace_0()
14466
{
14467
}
14468
14469
};
14470
14471
typedef CoefficientSpace_f Form_9_FunctionSpace_1;
14472
14473
typedef CoefficientSpace_g Form_9_FunctionSpace_2;
14474
14475
class Form_9: public dolfin::Form
14476
{
14477
public:
14478
14479
// Constructor
14480
Form_9(const dolfin::FunctionSpace& V0):
14481
dolfin::Form(1, 2), f(*this, 0), g(*this, 1)
14482
{
14483
_function_spaces[0] = reference_to_no_delete_pointer(V0);
14484
14485
_ufc_form = boost::shared_ptr<const ufc::form>(new adaptivepoisson_form_9());
14486
}
14487
14488
// Constructor
14489
Form_9(const dolfin::FunctionSpace& V0, const dolfin::GenericFunction& f, const dolfin::GenericFunction& g):
14490
dolfin::Form(1, 2), f(*this, 0), g(*this, 1)
14491
{
14492
_function_spaces[0] = reference_to_no_delete_pointer(V0);
14493
14494
this->f = f;
14495
this->g = g;
14496
14497
_ufc_form = boost::shared_ptr<const ufc::form>(new adaptivepoisson_form_9());
14498
}
14499
14500
// Constructor
14501
Form_9(const dolfin::FunctionSpace& V0, boost::shared_ptr<const dolfin::GenericFunction> f, boost::shared_ptr<const dolfin::GenericFunction> g):
14502
dolfin::Form(1, 2), f(*this, 0), g(*this, 1)
14503
{
14504
_function_spaces[0] = reference_to_no_delete_pointer(V0);
14505
14506
this->f = *f;
14507
this->g = *g;
14508
14509
_ufc_form = boost::shared_ptr<const ufc::form>(new adaptivepoisson_form_9());
14510
}
14511
14512
// Constructor
14513
Form_9(boost::shared_ptr<const dolfin::FunctionSpace> V0):
14514
dolfin::Form(1, 2), f(*this, 0), g(*this, 1)
14515
{
14516
_function_spaces[0] = V0;
14517
14518
_ufc_form = boost::shared_ptr<const ufc::form>(new adaptivepoisson_form_9());
14519
}
14520
14521
// Constructor
14522
Form_9(boost::shared_ptr<const dolfin::FunctionSpace> V0, const dolfin::GenericFunction& f, const dolfin::GenericFunction& g):
14523
dolfin::Form(1, 2), f(*this, 0), g(*this, 1)
14524
{
14525
_function_spaces[0] = V0;
14526
14527
this->f = f;
14528
this->g = g;
14529
14530
_ufc_form = boost::shared_ptr<const ufc::form>(new adaptivepoisson_form_9());
14531
}
14532
14533
// Constructor
14534
Form_9(boost::shared_ptr<const dolfin::FunctionSpace> V0, boost::shared_ptr<const dolfin::GenericFunction> f, boost::shared_ptr<const dolfin::GenericFunction> g):
14535
dolfin::Form(1, 2), f(*this, 0), g(*this, 1)
14536
{
14537
_function_spaces[0] = V0;
14538
14539
this->f = *f;
14540
this->g = *g;
14541
14542
_ufc_form = boost::shared_ptr<const ufc::form>(new adaptivepoisson_form_9());
14543
}
14544
14545
// Destructor
14546
~Form_9()
14547
{}
14548
14549
/// Return the number of the coefficient with this name
14550
virtual dolfin::uint coefficient_number(const std::string& name) const
14551
{
14552
if (name == "f")
14553
return 0;
14554
else if (name == "g")
14555
return 1;
14556
14557
dolfin::error("Invalid coefficient.");
14558
return 0;
14559
}
14560
14561
/// Return the name of the coefficient with this number
14562
virtual std::string coefficient_name(dolfin::uint i) const
14563
{
14564
switch (i)
14565
{
14566
case 0:
14567
return "f";
14568
case 1:
14569
return "g";
14570
}
14571
14572
dolfin::error("Invalid coefficient.");
14573
return "unnamed";
14574
}
14575
14576
// Typedefs
14577
typedef Form_9_FunctionSpace_0 TestSpace;
14578
typedef Form_9_FunctionSpace_1 CoefficientSpace_f;
14579
typedef Form_9_FunctionSpace_2 CoefficientSpace_g;
14580
14581
// Coefficients
14582
dolfin::CoefficientAssigner f;
14583
dolfin::CoefficientAssigner g;
14584
};
14585
14586
typedef CoefficientSpace___discrete_primal_solution Form_10_FunctionSpace_0;
14587
14588
class Form_10: public dolfin::GoalFunctional
14589
{
14590
public:
14591
14592
// Constructor
14593
Form_10(const dolfin::Mesh& mesh):
14594
dolfin::GoalFunctional(0, 1), __discrete_primal_solution(*this, 0)
14595
{
14596
_mesh = reference_to_no_delete_pointer(mesh);
14597
_ufc_form = boost::shared_ptr<const ufc::form>(new adaptivepoisson_form_10());
14598
}
14599
14600
// Constructor
14601
Form_10(const dolfin::Mesh& mesh, const dolfin::GenericFunction& __discrete_primal_solution):
14602
dolfin::GoalFunctional(0, 1), __discrete_primal_solution(*this, 0)
14603
{
14604
_mesh = reference_to_no_delete_pointer(mesh);
14605
this->__discrete_primal_solution = __discrete_primal_solution;
14606
14607
_ufc_form = boost::shared_ptr<const ufc::form>(new adaptivepoisson_form_10());
14608
}
14609
14610
// Constructor
14611
Form_10(const dolfin::Mesh& mesh, boost::shared_ptr<const dolfin::GenericFunction> __discrete_primal_solution):
14612
dolfin::GoalFunctional(0, 1), __discrete_primal_solution(*this, 0)
14613
{
14614
_mesh = reference_to_no_delete_pointer(mesh);
14615
this->__discrete_primal_solution = *__discrete_primal_solution;
14616
14617
_ufc_form = boost::shared_ptr<const ufc::form>(new adaptivepoisson_form_10());
14618
}
14619
14620
// Constructor
14621
Form_10(boost::shared_ptr<const dolfin::Mesh> mesh):
14622
dolfin::GoalFunctional(0, 1), __discrete_primal_solution(*this, 0)
14623
{
14624
_mesh = mesh;
14625
_ufc_form = boost::shared_ptr<const ufc::form>(new adaptivepoisson_form_10());
14626
}
14627
14628
// Constructor
14629
Form_10(boost::shared_ptr<const dolfin::Mesh> mesh, const dolfin::GenericFunction& __discrete_primal_solution):
14630
dolfin::GoalFunctional(0, 1), __discrete_primal_solution(*this, 0)
14631
{
14632
_mesh = mesh;
14633
this->__discrete_primal_solution = __discrete_primal_solution;
14634
14635
_ufc_form = boost::shared_ptr<const ufc::form>(new adaptivepoisson_form_10());
14636
}
14637
14638
// Constructor
14639
Form_10(boost::shared_ptr<const dolfin::Mesh> mesh, boost::shared_ptr<const dolfin::GenericFunction> __discrete_primal_solution):
14640
dolfin::GoalFunctional(0, 1), __discrete_primal_solution(*this, 0)
14641
{
14642
_mesh = mesh;
14643
this->__discrete_primal_solution = *__discrete_primal_solution;
14644
14645
_ufc_form = boost::shared_ptr<const ufc::form>(new adaptivepoisson_form_10());
14646
}
14647
14648
// Destructor
14649
~Form_10()
14650
{}
14651
14652
/// Return the number of the coefficient with this name
14653
virtual dolfin::uint coefficient_number(const std::string& name) const
14654
{
14655
if (name == "__discrete_primal_solution")
14656
return 0;
14657
14658
dolfin::error("Invalid coefficient.");
14659
return 0;
14660
}
14661
14662
/// Return the name of the coefficient with this number
14663
virtual std::string coefficient_name(dolfin::uint i) const
14664
{
14665
switch (i)
14666
{
14667
case 0:
14668
return "__discrete_primal_solution";
14669
}
14670
14671
dolfin::error("Invalid coefficient.");
14672
return "unnamed";
14673
}
14674
14675
// Typedefs
14676
typedef Form_10_FunctionSpace_0 CoefficientSpace___discrete_primal_solution;
14677
14678
// Coefficients
14679
dolfin::CoefficientAssigner __discrete_primal_solution;
14680
14681
/// Initialize all error control forms, attach coefficients and
14682
/// (re-)set error control
14683
virtual void update_ec(const dolfin::Form& a, const dolfin::Form& L)
14684
{
14685
// This stuff is created here and shipped elsewhere
14686
boost::shared_ptr<dolfin::Form> a_star; // Dual lhs
14687
boost::shared_ptr<dolfin::Form> L_star; // Dual rhs
14688
boost::shared_ptr<dolfin::FunctionSpace> V_Ez_h; // Extrapolation space
14689
boost::shared_ptr<dolfin::Function> Ez_h; // Extrapolated dual
14690
boost::shared_ptr<dolfin::Form> residual; // Residual (as functional)
14691
boost::shared_ptr<dolfin::FunctionSpace> V_R_T; // Trial space for cell residual
14692
boost::shared_ptr<dolfin::Form> a_R_T; // Cell residual lhs
14693
boost::shared_ptr<dolfin::Form> L_R_T; // Cell residual rhs
14694
boost::shared_ptr<dolfin::FunctionSpace> V_b_T; // Function space for cell bubble
14695
boost::shared_ptr<dolfin::Function> b_T; // Cell bubble
14696
boost::shared_ptr<dolfin::FunctionSpace> V_R_dT; // Trial space for facet residual
14697
boost::shared_ptr<dolfin::Form> a_R_dT; // Facet residual lhs
14698
boost::shared_ptr<dolfin::Form> L_R_dT; // Facet residual rhs
14699
boost::shared_ptr<dolfin::FunctionSpace> V_b_e; // Function space for cell cone
14700
boost::shared_ptr<dolfin::Function> b_e; // Cell cone
14701
boost::shared_ptr<dolfin::FunctionSpace> V_eta_T; // Function space for indicators
14702
boost::shared_ptr<dolfin::Form> eta_T; // Indicator form
14703
14704
// Some handy views
14705
const dolfin::FunctionSpace& Vhat(*(a.function_space(0))); // Primal test
14706
const dolfin::FunctionSpace& V(*(a.function_space(1))); // Primal trial
14707
const dolfin::Mesh& mesh(V.mesh());
14708
std::string name;
14709
14710
// Initialize dual forms
14711
a_star.reset(new Form_0(V, Vhat));
14712
L_star.reset(new Form_1(V));
14713
14714
// Attach coefficients from a to a_star and from M to L_star
14715
dolfin::uint coefficient_number = 0;
14716
14717
for (dolfin::uint i = 0; i < a.num_coefficients(); i++)
14718
{
14719
name = a.coefficient_name(i);
14720
// Don't attach discrete primal solution here (not computed.)
14721
if (name == "__discrete_primal_solution")
14722
continue;
14723
14724
try {
14725
coefficient_number = a_star->coefficient_number(name);
14726
} catch (...) {
14727
std::cout << "Attaching coefficient named: " << name << " to a_star";
14728
std::cout << " failed! But this might be expected." << std::endl;
14729
continue;
14730
}
14731
a_star->set_coefficient(name, a.coefficient(i));
14732
}
14733
14734
14735
for (dolfin::uint i = 0; i < (*this).num_coefficients(); i++)
14736
{
14737
name = (*this).coefficient_name(i);
14738
// Don't attach discrete primal solution here (not computed.)
14739
if (name == "__discrete_primal_solution")
14740
continue;
14741
14742
try {
14743
coefficient_number = L_star->coefficient_number(name);
14744
} catch (...) {
14745
std::cout << "Attaching coefficient named: " << name << " to L_star";
14746
std::cout << " failed! But this might be expected." << std::endl;
14747
continue;
14748
}
14749
L_star->set_coefficient(name, (*this).coefficient(i));
14750
}
14751
14752
14753
// Initialize residual
14754
residual.reset(new Form_6(mesh));
14755
14756
// Attach coefficients (from a and L) in residual
14757
14758
for (dolfin::uint i = 0; i < a.num_coefficients(); i++)
14759
{
14760
name = a.coefficient_name(i);
14761
// Don't attach discrete primal solution here (not computed.)
14762
if (name == "__discrete_primal_solution")
14763
continue;
14764
14765
try {
14766
coefficient_number = residual->coefficient_number(name);
14767
} catch (...) {
14768
std::cout << "Attaching coefficient named: " << name << " to residual";
14769
std::cout << " failed! But this might be expected." << std::endl;
14770
continue;
14771
}
14772
residual->set_coefficient(name, a.coefficient(i));
14773
}
14774
14775
14776
for (dolfin::uint i = 0; i < L.num_coefficients(); i++)
14777
{
14778
name = L.coefficient_name(i);
14779
// Don't attach discrete primal solution here (not computed.)
14780
if (name == "__discrete_primal_solution")
14781
continue;
14782
14783
try {
14784
coefficient_number = residual->coefficient_number(name);
14785
} catch (...) {
14786
std::cout << "Attaching coefficient named: " << name << " to residual";
14787
std::cout << " failed! But this might be expected." << std::endl;
14788
continue;
14789
}
14790
residual->set_coefficient(name, L.coefficient(i));
14791
}
14792
14793
14794
// Initialize extrapolation space and (fake) extrapolation
14795
V_Ez_h.reset(new CoefficientSpace___improved_dual(mesh));
14796
Ez_h.reset(new dolfin::Function(V_Ez_h));
14797
residual->set_coefficient("__improved_dual", Ez_h);
14798
14799
// Create bilinear and linear form for computing cell residual R_T
14800
V_R_T.reset(new Form_3::TestSpace(mesh));
14801
a_R_T.reset(new Form_2(V_R_T, V_R_T));
14802
L_R_T.reset(new Form_3(V_R_T));
14803
14804
// Initialize bubble and attach to a_R_T and L_R_T
14805
V_b_T.reset(new CoefficientSpace___cell_bubble(mesh));
14806
b_T.reset(new dolfin::Function(V_b_T));
14807
b_T->vector() = 1.0;
14808
14809
// Attach coefficients (from a and L) to L_R_T
14810
14811
for (dolfin::uint i = 0; i < a.num_coefficients(); i++)
14812
{
14813
name = a.coefficient_name(i);
14814
// Don't attach discrete primal solution here (not computed.)
14815
if (name == "__discrete_primal_solution")
14816
continue;
14817
14818
try {
14819
coefficient_number = L_R_T->coefficient_number(name);
14820
} catch (...) {
14821
std::cout << "Attaching coefficient named: " << name << " to L_R_T";
14822
std::cout << " failed! But this might be expected." << std::endl;
14823
continue;
14824
}
14825
L_R_T->set_coefficient(name, a.coefficient(i));
14826
}
14827
14828
14829
for (dolfin::uint i = 0; i < L.num_coefficients(); i++)
14830
{
14831
name = L.coefficient_name(i);
14832
// Don't attach discrete primal solution here (not computed.)
14833
if (name == "__discrete_primal_solution")
14834
continue;
14835
14836
try {
14837
coefficient_number = L_R_T->coefficient_number(name);
14838
} catch (...) {
14839
std::cout << "Attaching coefficient named: " << name << " to L_R_T";
14840
std::cout << " failed! But this might be expected." << std::endl;
14841
continue;
14842
}
14843
L_R_T->set_coefficient(name, L.coefficient(i));
14844
}
14845
14846
14847
// Attach bubble function to _a_R_T and _L_R_T
14848
a_R_T->set_coefficient("__cell_bubble", b_T);
14849
L_R_T->set_coefficient("__cell_bubble", b_T);
14850
14851
// Create bilinear and linear form for computing facet residual R_dT
14852
V_R_dT.reset(new Form_5::TestSpace(mesh));
14853
a_R_dT.reset(new Form_4(V_R_dT, V_R_dT));
14854
L_R_dT.reset(new Form_5(V_R_dT));
14855
14856
// Attach coefficients (from a and L) to L_R_dT
14857
14858
for (dolfin::uint i = 0; i < a.num_coefficients(); i++)
14859
{
14860
name = a.coefficient_name(i);
14861
// Don't attach discrete primal solution here (not computed.)
14862
if (name == "__discrete_primal_solution")
14863
continue;
14864
14865
try {
14866
coefficient_number = L_R_dT->coefficient_number(name);
14867
} catch (...) {
14868
std::cout << "Attaching coefficient named: " << name << " to L_R_dT";
14869
std::cout << " failed! But this might be expected." << std::endl;
14870
continue;
14871
}
14872
L_R_dT->set_coefficient(name, a.coefficient(i));
14873
}
14874
14875
14876
for (dolfin::uint i = 0; i < L.num_coefficients(); i++)
14877
{
14878
name = L.coefficient_name(i);
14879
// Don't attach discrete primal solution here (not computed.)
14880
if (name == "__discrete_primal_solution")
14881
continue;
14882
14883
try {
14884
coefficient_number = L_R_dT->coefficient_number(name);
14885
} catch (...) {
14886
std::cout << "Attaching coefficient named: " << name << " to L_R_dT";
14887
std::cout << " failed! But this might be expected." << std::endl;
14888
continue;
14889
}
14890
L_R_dT->set_coefficient(name, L.coefficient(i));
14891
}
14892
14893
14894
// Initialize (fake) cone and attach to a_R_dT and L_R_dT
14895
V_b_e.reset(new CoefficientSpace___cell_cone(mesh));
14896
b_e.reset(new dolfin::Function(V_b_e));
14897
a_R_dT->set_coefficient("__cell_cone", b_e);
14898
L_R_dT->set_coefficient("__cell_cone", b_e);
14899
14900
// Create error indicator form
14901
V_eta_T.reset(new Form_7::TestSpace(mesh));
14902
eta_T.reset(new Form_7(V_eta_T));
14903
14904
// Update error control
14905
_ec.reset(new dolfin::ErrorControl(a_star, L_star, residual,
14906
a_R_T, L_R_T, a_R_dT, L_R_dT, eta_T,
14907
true));
14908
14909
}
14910
14911
};
14912
14913
14914
}
14915
14916
#endif
Loggerhead is a web-based interface for Breezy
Version: 2.0.1