v0.14.0
BernsteinBezier.cpp
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1 /** \file BernsteinBezier.cpp
2 \brief Bernstein-Bezier polynomials for H1 space
3
4 Implementation based on \cite ainsworth2011bernstein
5
6 */
7
8 template <int D, int Side>
9 MoFEMErrorCode BernsteinBezier::generateIndicesVertex(const int N, int *alpha) {
11  alpha[(D + 1) * Side + Side] = N;
13 }
14
15 template <int D, int Side>
16 MoFEMErrorCode BernsteinBezier::generateIndicesEdgeOnSimplex(const int N,
17  int *alpha) {
18  constexpr int edge_nodes[6][2] = {{0, 1}, {1, 2}, {2, 0},
19  {0, 3}, {1, 3}, {2, 3}};
21  std::fill(alpha, &alpha[(D + 1) * NBEDGE_H1(N)], 0);
22  for (int n = N - 1; n != 0; --n) {
23
24  // + o o o o +
25
26  alpha[edge_nodes[Side][0]] = n;
27  alpha[edge_nodes[Side][1]] = N - n;
28  alpha += D + 1;
29  }
31 }
32
33 template <int D, int Side>
34 MoFEMErrorCode BernsteinBezier::generateIndicesTriOnSimplex(const int N,
35  int *alpha) {
36  constexpr int tri_nodes[4][3] = {{0, 1, 3}, {1, 2, 3}, {0, 2, 3}, {0, 1, 2}};
38  std::fill(alpha, &alpha[(D + 1) * NBFACETRI_H1(N)], 0);
39  for (int n0 = 1; n0 != N - 1; ++n0) {
40  for (int n1 = 1; n1 != N - n0; ++n1) {
41
42  // +
43  // + +
44  // + o +
45  // + o o +
46  // + o o o +
47  // + + + + + +
48
49  alpha[tri_nodes[Side][0]] = n0;
50  alpha[tri_nodes[Side][1]] = n1;
51  alpha[tri_nodes[Side][2]] = N - n0 - n1;
52
53  alpha += D + 1;
54  }
55  }
57 }
58
59 MoFEMErrorCode BernsteinBezier::generateIndicesTetOnSimplex(const int N,
60  int *alpha) {
62  std::fill(alpha, &alpha[4 * NBVOLUMETET_H1(N)], 0);
63  for (int n0 = 1; n0 != N - 1; ++n0) {
64  for (int n1 = 1; n1 != N - n0; ++n1) {
65  for (int n2 = 1; n2 != N - n0 - n1; ++n2) {
66  alpha[0] = n0;
67  alpha[1] = n1;
68  alpha[2] = n2;
69  alpha[3] = N - n0 - n1 - n2;
70  alpha += 4;
71  }
72  }
73  }
75 }
76
77 MoFEMErrorCode BernsteinBezier::generateIndicesVertexEdge(const int N,
78  int *alpha) {
80  CHKERR generateIndicesVertex<1, 0>(N, alpha);
81  CHKERR generateIndicesVertex<1, 1>(N, alpha);
83 }
84
85 MoFEMErrorCode BernsteinBezier::generateIndicesEdgeEdge(const int N,
86  int *alpha) {
87  return generateIndicesEdgeOnSimplex<1, 0>(N, alpha);
88 }
89
90 MoFEMErrorCode BernsteinBezier::generateIndicesVertexTri(const int N,
91  int *alpha) {
93  CHKERR generateIndicesVertex<2, 0>(N, alpha);
94  CHKERR generateIndicesVertex<2, 1>(N, alpha);
95  CHKERR generateIndicesVertex<2, 2>(N, alpha);
97 }
98
99 MoFEMErrorCode BernsteinBezier::generateIndicesEdgeTri(const int N[],
100  int *alpha[]) {
102  CHKERR generateIndicesEdgeOnSimplex<2, 0>(N[0], alpha[0]);
103  CHKERR generateIndicesEdgeOnSimplex<2, 1>(N[1], alpha[1]);
104  CHKERR generateIndicesEdgeOnSimplex<2, 2>(N[2], alpha[2]);
106 }
107
108 MoFEMErrorCode BernsteinBezier::generateIndicesEdgeTri(const int side,
109  const int N,
110  int *alpha) {
111  switch (side) {
112  case 0:
113  return generateIndicesEdgeOnSimplex<2, 0>(N, alpha);
114  case 1:
115  return generateIndicesEdgeOnSimplex<2, 1>(N, alpha);
116  case 2:
117  return generateIndicesEdgeOnSimplex<2, 2>(N, alpha);
118  default:
119  SETERRQ(PETSC_COMM_SELF, MOFEM_DATA_INCONSISTENCY,
120  "Wrong side number, on triangle are edges from 0 to 2");
121  }
122 }
123
124 MoFEMErrorCode BernsteinBezier::generateIndicesTriTri(const int N, int *alpha) {
125  return generateIndicesTriOnSimplex<2, 3>(N, alpha);
126 }
127
128 MoFEMErrorCode BernsteinBezier::generateIndicesVertexTet(const int N,
129  int *alpha) {
131  CHKERR generateIndicesVertex<3, 0>(N, alpha);
132  CHKERR generateIndicesVertex<3, 1>(N, alpha);
133  CHKERR generateIndicesVertex<3, 2>(N, alpha);
134  CHKERR generateIndicesVertex<3, 3>(N, alpha);
136 }
137
138 MoFEMErrorCode BernsteinBezier::generateIndicesEdgeTet(const int N[],
139  int *alpha[]) {
141  CHKERR generateIndicesEdgeOnSimplex<3, 0>(N[0], alpha[0]);
142  CHKERR generateIndicesEdgeOnSimplex<3, 1>(N[1], alpha[1]);
143  CHKERR generateIndicesEdgeOnSimplex<3, 2>(N[2], alpha[2]);
144  CHKERR generateIndicesEdgeOnSimplex<3, 3>(N[3], alpha[3]);
145  CHKERR generateIndicesEdgeOnSimplex<3, 4>(N[4], alpha[4]);
146  CHKERR generateIndicesEdgeOnSimplex<3, 5>(N[5], alpha[5]);
148 }
149
150 MoFEMErrorCode BernsteinBezier::generateIndicesEdgeTet(const int side,
151  const int N,
152  int *alpha) {
154  switch (side) {
155  case 0:
156  return generateIndicesEdgeOnSimplex<3, 0>(N, alpha);
157  case 1:
158  return generateIndicesEdgeOnSimplex<3, 1>(N, alpha);
159  case 2:
160  return generateIndicesEdgeOnSimplex<3, 2>(N, alpha);
161  case 3:
162  return generateIndicesEdgeOnSimplex<3, 3>(N, alpha);
163  case 4:
164  return generateIndicesEdgeOnSimplex<3, 4>(N, alpha);
165  case 5:
166  return generateIndicesEdgeOnSimplex<3, 5>(N, alpha);
167  default:
168  SETERRQ(PETSC_COMM_SELF, MOFEM_DATA_INCONSISTENCY,
169  "Wrong side number, on tetrahedron are edges from 0 to 5");
170  }
172 }
173
174 MoFEMErrorCode BernsteinBezier::generateIndicesTriTet(const int N[],
175  int *alpha[]) {
177  CHKERR generateIndicesTriOnSimplex<3, 0>(N[0], alpha[0]);
178  CHKERR generateIndicesTriOnSimplex<3, 1>(N[1], alpha[1]);
179  CHKERR generateIndicesTriOnSimplex<3, 2>(N[2], alpha[2]);
180  CHKERR generateIndicesTriOnSimplex<3, 3>(N[3], alpha[3]);
182 }
183
184 MoFEMErrorCode BernsteinBezier::generateIndicesTriTet(const int side,
185  const int N, int *alpha) {
187  switch (side) {
188  case 0:
189  return generateIndicesTriOnSimplex<3, 0>(N, alpha);
190  case 1:
191  return generateIndicesTriOnSimplex<3, 1>(N, alpha);
192  case 2:
193  return generateIndicesTriOnSimplex<3, 2>(N, alpha);
194  case 3:
195  return generateIndicesTriOnSimplex<3, 3>(N, alpha);
196  default:
197  SETERRQ(PETSC_COMM_SELF, MOFEM_DATA_INCONSISTENCY,
198  "Wrong side number, on tetrahedron are from from 0 to 3");
199  }
201 }
202
203 MoFEMErrorCode BernsteinBezier::generateIndicesTetTet(const int N, int *alpha) {
204  return generateIndicesTetOnSimplex(N, alpha);
205 }
206
207 template <int D>
208 MoFEMErrorCode BernsteinBezier::genrateDerivativeIndices(
209  const int N, const int n_alpha, const int *alpha, const int *diff,
210  const int n_alpha_diff, const int *alpha_diff, double *c) {
212
213  std::fill(c, &c[n_alpha * n_alpha_diff], 0);
214  int abs_diff = diff[0];
215  for (int d = 1; d != D + 1; ++d)
216  abs_diff += diff[d];
217
218  const double b = boost::math::factorial<double>(N) /
219  boost::math::factorial<double>(N - abs_diff);
220
221  for (int i = 0; i != n_alpha; ++i) {
222  for (int j = 0; j != n_alpha_diff; ++j) {
223  int d = 0;
224  for (; d != D + 1; ++d)
225  if (alpha_diff[(D + 1) * j + d] + diff[d] != alpha[(D + 1) * i + d])
226  break;
227  if (d == D + 1) {
228  c[i * n_alpha_diff + j] = b;
229  break;
230  }
231  }
232  }
233
235 }
236
237 MoFEMErrorCode BernsteinBezier::genrateDerivativeIndicesEdges(
238  const int N, const int n_alpha, const int *alpha, const int *diff,
239  const int n_alpha_diff, const int *alpha_diff, double *c) {
240  return genrateDerivativeIndices<1>(N, n_alpha, alpha, diff, n_alpha_diff,
241  alpha_diff, c);
242 }
243
244 MoFEMErrorCode BernsteinBezier::genrateDerivativeIndicesTri(
245  const int N, const int n_alpha, const int *alpha, const int *diff,
246  const int n_alpha_diff, const int *alpha_diff, double *c) {
247  return genrateDerivativeIndices<2>(N, n_alpha, alpha, diff, n_alpha_diff,
248  alpha_diff, c);
249 }
250
251 MoFEMErrorCode BernsteinBezier::genrateDerivativeIndicesTet(
252  const int N, const int n_alpha, const int *alpha, const int *diff,
253  const int n_alpha_diff, const int *alpha_diff, double *c) {
254  return genrateDerivativeIndices<3>(N, n_alpha, alpha, diff, n_alpha_diff,
255  alpha_diff, c);
256 }
257
258 template <int D>
260 BernsteinBezier::domainPoints(const int N, const int n_x, const int n_alpha,
261  const int *alpha, const double *x_k,
262  double *x_alpha) {
265
267  x_alpha, &x_alpha[1], &x_alpha[2]);
268  for (int n0 = 0; n0 != n_alpha; ++n0) {
269  t_x_alpha(i) = 0;
271  x_k, &x_k[1], &x_k[2]);
272  for (int n1 = 0; n1 != n_x; ++n1) {
273  t_x_alpha(i) += static_cast<double>(*alpha) * t_x_k(i);
274  ++t_x_k;
275  ++alpha;
276  }
277  t_x_alpha(i) /= static_cast<double>(N);
278  ++t_x_alpha;
279  }
280
282 }
283
284 MoFEMErrorCode BernsteinBezier::domainPoints3d(const int N, const int n_x,
285  const int n_alpha,
286  const int *alpha,
287  const double *x_k,
288  double *x_alpha) {
289  return domainPoints<3>(N, n_x, n_alpha, alpha, x_k, x_alpha);
290 }
291
292 template <int D, bool GRAD_BASE>
294 BernsteinBezier::baseFunctions(const int N, const int gdim, const int n_alpha,
295  const int *alpha, const double *lambda,
296  const double *grad_lambda, double *base,
299
300  const int *const alpha0 = alpha;
301  const double fN = boost::math::factorial<double>(N);
302  constexpr int MAX_ALPHA = 12;
303  int max_alpha = *std::max_element(alpha, &alpha[(D + 1) * n_alpha]);
304  if(max_alpha > MAX_ALPHA)
305  SETERRQ1(PETSC_COMM_SELF, MOFEM_DATA_INCONSISTENCY,
306  "Is assumed maximal order not to be bigger than %d", MAX_ALPHA);
307  std::array<double, (D + 1) * (MAX_ALPHA + 1)> pow_alpha;
308  std::array<double, (MAX_ALPHA + 1)> factorial_alpha;
309  std::array<double, D + 1> terms, diff_terms;
311
312  factorial_alpha[0] = 1;
313  if (max_alpha >= 1)
314  factorial_alpha[1] = 1;
315  if (max_alpha >= 2)
316  for (int a = 2; a <= max_alpha; ++a)
317  factorial_alpha[a] = factorial_alpha[a - 1] * a;
318
319  for (int g = 0; g != gdim; ++g) {
320
321  for (int n = 0; n != D + 1; ++n, ++lambda) {
322  const size_t shift = (MAX_ALPHA + 1) * n;
323  double *pow_alpha_ptr = &pow_alpha[shift];
324  *pow_alpha_ptr = 1;
325
326  if (max_alpha >= 1) {
327  ++pow_alpha_ptr;
328  *pow_alpha_ptr = *lambda;
329  }
330
331  if (max_alpha >= 2)
332  for (int a = 2; a <= max_alpha; ++a) {
333  const double p = (*pow_alpha_ptr) * (*lambda);
334  ++pow_alpha_ptr;
335  *pow_alpha_ptr = p;
336  }
337  }
338
339  for (int n0 = 0; n0 != n_alpha; ++n0) {
340
342
343  double f = factorial_alpha[(*alpha)];
344  double *terms_ptr = terms.data();
345  double *diff_terms_ptr = diff_terms.data();
346  *terms_ptr = pow_alpha[(*alpha)];
348  if (*alpha > 0)
349  *diff_terms_ptr = (*alpha) * pow_alpha[(*alpha) - 1];
350  else
351  *diff_terms_ptr = 0;
352  }
353  *base = *terms_ptr;
354  ++alpha;
355  ++terms_ptr;
356  ++diff_terms_ptr;
357
358  for (int n1 = 1; n1 < D + 1;
359  ++n1, ++alpha, ++terms_ptr, ++diff_terms_ptr) {
360  f *= factorial_alpha[(*alpha)];
361  const size_t shift = (MAX_ALPHA + 1) * n1;
362  *terms_ptr = pow_alpha[shift + (*alpha)];
364  if (*alpha > 0)
365  *diff_terms_ptr = (*alpha) * pow_alpha[shift + (*alpha) - 1];
366  else
367  *diff_terms_ptr = 0;
368  }
369  *base *= *terms_ptr;
370  }
371
372  const double b = fN / f;
373  *base *= b;
374  ++base;
375
377  double *terms_ptr = terms.data();
378  double *diff_terms_ptr = diff_terms.data();
379  double z = *diff_terms_ptr;
380  ++terms_ptr;
381  ++diff_terms_ptr;
382  for (int n2 = 1; n2 != D + 1; ++n2, ++terms_ptr)
383  z *= *terms_ptr;
384
385  for (int d = 0; d != D; ++d, ++grad_lambda)
387
388  for (int n1 = 1; n1 < D + 1; ++n1) {
389  z = *diff_terms_ptr;
390
391  int n2 = 0;
392  for (terms_ptr = terms.data(); n2 != n1; ++n2, ++terms_ptr)
393  z *= *terms_ptr;
394
395  ++n2;
396  ++terms_ptr;
397
398  for (; n2 < D + 1; ++n2, ++terms_ptr)
399  z *= *terms_ptr;
400
401  for (int d = 0; d != D; ++d, ++grad_lambda)
403
404  ++diff_terms_ptr;
405  }
406  for (int d = 0; d != D; ++d)
409  }
410
411  }
412
413  alpha = alpha0;
414  }
415
417 }
418
419 MoFEMErrorCode BernsteinBezier::baseFunctionsEdge(
420  const int N, const int gdim, const int n_alpha, const int *alpha,
421  const double *lambda, const double *grad_lambda, double *base,
424  return baseFunctions<1, true>(N, gdim, n_alpha, alpha, lambda, grad_lambda,
426  else
427  return baseFunctions<1, false>(N, gdim, n_alpha, alpha, lambda, grad_lambda,
429 }
430
431 MoFEMErrorCode BernsteinBezier::baseFunctionsTri(
432  const int N, const int gdim, const int n_alpha, const int *alpha,
433  const double *lambda, const double *grad_lambda, double *base,
436  return baseFunctions<2, true>(N, gdim, n_alpha, alpha, lambda, grad_lambda,
438  else
439  return baseFunctions<2, false>(N, gdim, n_alpha, alpha, lambda, grad_lambda,
441 }
442
443 MoFEMErrorCode BernsteinBezier::baseFunctionsTet(
444  const int N, const int gdim, const int n_alpha, const int *alpha,
445  const double *lambda, const double *grad_lambda, double *base,
448  return baseFunctions<3, true>(N, gdim, n_alpha, alpha, lambda, grad_lambda,
450  else
451  return baseFunctions<3, false>(N, gdim, n_alpha, alpha, lambda, grad_lambda,
453 }
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Last executable line of each PETSc function used for error handling. Replaces return()
Definition: definitions.h:460
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#define NBEDGE_H1(P)
Numer of base function on edge for H1 space.
Definition: h1_hdiv_hcurl_l2.h:55
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Definition: Tensor1_value.hpp:8
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MoFEM/PETSc error code.
Definition: Exceptions.hpp:56
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Number of base functions on tetrahedron for H1 space.
Definition: h1_hdiv_hcurl_l2.h:75
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Inline error check.
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#define NBFACETRI_H1(P)
Number of base function on triangle for H1 space.
Definition: h1_hdiv_hcurl_l2.h:60
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First executable line of each MoFEM function, used for error handling. Final line of MoFEM functions ...
Definition: definitions.h:453