Reference documentation for deal.II version 9.3.3
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polynomials_rt_bubbles.cc
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2//
3// Copyright (C) 2018 - 2020 by the deal.II authors
4//
5// This file is part of the deal.II library.
6//
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8// it, and/or modify it under the terms of the GNU Lesser General
9// Public License as published by the Free Software Foundation; either
10// version 2.1 of the License, or (at your option) any later version.
11// The full text of the license can be found in the file LICENSE.md at
12// the top level directory of deal.II.
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15
16
17#include "deal.II/base/polynomials_rt_bubbles.h"
18
19#include <deal.II/base/quadrature_lib.h>
20#include <deal.II/base/thread_management.h>
21
22#include <iomanip>
23#include <iostream>
24#include <memory>
25
26DEAL_II_NAMESPACE_OPEN
27
28
29template <int dim>
30PolynomialsRT_Bubbles<dim>::PolynomialsRT_Bubbles(const unsigned int k)
31 : TensorPolynomialsBase<dim>(k, n_polynomials(k))
32 , raviart_thomas_space(k - 1)
33 , monomials(k + 2)
34{
35 Assert(dim >= 2, ExcImpossibleInDim(dim));
36
37 for (unsigned int i = 0; i < monomials.size(); ++i)
38 monomials[i] = Polynomials::Monomial<double>(i);
39}
40
41
42
43template <int dim>
44void
45PolynomialsRT_Bubbles<dim>::evaluate(
46 const Point<dim> & unit_point,
47 std::vector<Tensor<1, dim>> &values,
48 std::vector<Tensor<2, dim>> &grads,
49 std::vector<Tensor<3, dim>> &grad_grads,
50 std::vector<Tensor<4, dim>> &third_derivatives,
51 std::vector<Tensor<5, dim>> &fourth_derivatives) const
52{
53 Assert(values.size() == this->n() || values.size() == 0,
54 ExcDimensionMismatch(values.size(), this->n()));
55 Assert(grads.size() == this->n() || grads.size() == 0,
56 ExcDimensionMismatch(grads.size(), this->n()));
57 Assert(grad_grads.size() == this->n() || grad_grads.size() == 0,
58 ExcDimensionMismatch(grad_grads.size(), this->n()));
59 Assert(third_derivatives.size() == this->n() || third_derivatives.size() == 0,
60 ExcDimensionMismatch(third_derivatives.size(), this->n()));
61 Assert(fourth_derivatives.size() == this->n() ||
62 fourth_derivatives.size() == 0,
63 ExcDimensionMismatch(fourth_derivatives.size(), this->n()));
64
65 // Third and fourth derivatives are not implemented
66 (void)third_derivatives;
67 Assert(third_derivatives.size() == 0, ExcNotImplemented());
68 (void)fourth_derivatives;
69 Assert(fourth_derivatives.size() == 0, ExcNotImplemented());
70
71 const unsigned int n_sub = raviart_thomas_space.n();
72 const unsigned int my_degree = this->degree();
73
74 // Guard access to the scratch arrays in the following block
75 // using a mutex to make sure they are not used by multiple threads
76 // at once
77 {
78 static std::mutex mutex;
79 std::lock_guard<std::mutex> lock(mutex);
80
81 static std::vector<Tensor<1, dim>> p_values;
82 static std::vector<Tensor<2, dim>> p_grads;
83 static std::vector<Tensor<3, dim>> p_grad_grads;
84 static std::vector<Tensor<4, dim>> p_third_derivatives;
85 static std::vector<Tensor<5, dim>> p_fourth_derivatives;
86
87 p_values.resize((values.size() == 0) ? 0 : n_sub);
88 p_grads.resize((grads.size() == 0) ? 0 : n_sub);
89 p_grad_grads.resize((grad_grads.size() == 0) ? 0 : n_sub);
90
91 // This is the Raviart-Thomas part of the space
92 raviart_thomas_space.evaluate(unit_point,
93 p_values,
94 p_grads,
95 p_grad_grads,
96 p_third_derivatives,
97 p_fourth_derivatives);
98 for (unsigned int i = 0; i < p_values.size(); ++i)
99 values[i] = p_values[i];
100 for (unsigned int i = 0; i < p_grads.size(); ++i)
101 grads[i] = p_grads[i];
102 for (unsigned int i = 0; i < p_grad_grads.size(); ++i)
103 grad_grads[i] = p_grad_grads[i];
104 }
105
106 // Next we compute the polynomials and derivatives
107 // of the curl part of the space
108 const unsigned int n_derivatives = 3;
109 double monoval_plus[dim][n_derivatives + 1];
110 double monoval[dim][n_derivatives + 1];
111
112 double monoval_i[dim][n_derivatives + 1];
113 double monoval_j[dim][n_derivatives + 1];
114 double monoval_jplus[dim][n_derivatives + 1];
115
116 unsigned int start = n_sub;
117
118 if (dim == 2)
119 {
120 // In 2d the curl part of the space is spanned by the vectors
121 // of two types. The first one is
122 // [ x^i * [y^(k+1)]' ]
123 // [ -[x^i]' * y^(k+1) ]
124 // The second one can be obtained from the first by a cyclic
125 // rotation of the coordinates.
126 // monoval_i = x^i,
127 // monoval_plus = x^(k+1)
128 for (unsigned int d = 0; d < dim; ++d)
129 monomials[my_degree + 1].value(unit_point(d),
130 n_derivatives,
131 monoval_plus[d]);
132
133 for (unsigned int i = 0; i <= my_degree; ++i, ++start)
134 {
135 for (unsigned int d = 0; d < dim; ++d)
136 monomials[i].value(unit_point(d), n_derivatives, monoval_i[d]);
137
138 if (values.size() != 0)
139 {
140 values[start][0] = monoval_i[0][0] * monoval_plus[1][1];
141 values[start][1] = -monoval_i[0][1] * monoval_plus[1][0];
142
143 values[start + my_degree + 1][0] =
144 -monoval_plus[0][0] * monoval_i[1][1];
145 values[start + my_degree + 1][1] =
146 monoval_plus[0][1] * monoval_i[1][0];
147 }
148
149 if (grads.size() != 0)
150 {
151 grads[start][0][0] = monoval_i[0][1] * monoval_plus[1][1];
152 grads[start][0][1] = monoval_i[0][0] * monoval_plus[1][2];
153 grads[start][1][0] = -monoval_i[0][2] * monoval_plus[1][0];
154 grads[start][1][1] = -monoval_i[0][1] * monoval_plus[1][1];
155
156 grads[start + my_degree + 1][0][0] =
157 -monoval_plus[0][1] * monoval_i[1][1];
158 grads[start + my_degree + 1][0][1] =
159 -monoval_plus[0][0] * monoval_i[1][2];
160 grads[start + my_degree + 1][1][0] =
161 monoval_plus[0][2] * monoval_i[1][0];
162 grads[start + my_degree + 1][1][1] =
163 monoval_plus[0][1] * monoval_i[1][1];
164 }
165
166 if (grad_grads.size() != 0)
167 {
168 grad_grads[start][0][0][0] = monoval_i[0][2] * monoval_plus[1][1];
169 grad_grads[start][0][0][1] = monoval_i[0][1] * monoval_plus[1][2];
170 grad_grads[start][0][1][0] = monoval_i[0][1] * monoval_plus[1][2];
171 grad_grads[start][0][1][1] = monoval_i[0][0] * monoval_plus[1][3];
172 grad_grads[start][1][0][0] =
173 -monoval_i[0][3] * monoval_plus[1][0];
174 grad_grads[start][1][0][1] =
175 -monoval_i[0][2] * monoval_plus[1][1];
176 grad_grads[start][1][1][0] =
177 -monoval_i[0][2] * monoval_plus[1][1];
178 grad_grads[start][1][1][1] =
179 -monoval_i[0][1] * monoval_plus[1][2];
180
181 grad_grads[start + my_degree + 1][0][0][0] =
182 -monoval_plus[0][2] * monoval_i[1][1];
183 grad_grads[start + my_degree + 1][0][0][1] =
184 -monoval_plus[0][1] * monoval_i[1][2];
185 grad_grads[start + my_degree + 1][0][1][0] =
186 -monoval_plus[0][1] * monoval_i[1][2];
187 grad_grads[start + my_degree + 1][0][1][1] =
188 -monoval_plus[0][0] * monoval_i[1][3];
189 grad_grads[start + my_degree + 1][1][0][0] =
190 monoval_plus[0][3] * monoval_i[1][0];
191 grad_grads[start + my_degree + 1][1][0][1] =
192 monoval_plus[0][2] * monoval_i[1][1];
193 grad_grads[start + my_degree + 1][1][1][0] =
194 monoval_plus[0][2] * monoval_i[1][1];
195 grad_grads[start + my_degree + 1][1][1][1] =
196 monoval_plus[0][1] * monoval_i[1][2];
197 }
198 }
199 Assert(start == this->n() - my_degree - 1, ExcInternalError());
200 }
201 else if (dim == 3)
202 {
203 // In 3d the first type of basis vector is
204 // [ x^i * y^j * z^k * (j+k+2) ]
205 // [ -[x^i]' * y^(j+1) * z^k ]
206 // [ -[x^i]' * y^j * z^(k+1) ],
207 // For the second type of basis vector y and z
208 // are swapped. Then for each of these,
209 // two more are obtained by the cyclic rotation
210 // of the coordinates.
211 // monoval = x^k, monoval_plus = x^(k+1)
212 // monoval_* = x^*, monoval_jplus = x^(j+1)
213 for (unsigned int d = 0; d < dim; ++d)
214 {
215 monomials[my_degree + 1].value(unit_point(d),
216 n_derivatives,
217 monoval_plus[d]);
218 monomials[my_degree].value(unit_point(d), n_derivatives, monoval[d]);
219 }
220
221 const unsigned int n_curls = (my_degree + 1) * (2 * my_degree + 1);
222 // Span of @f$\tilde{B}@f$
223 for (unsigned int i = 0; i <= my_degree; ++i)
224 {
225 for (unsigned int d = 0; d < dim; ++d)
226 monomials[i].value(unit_point(d), n_derivatives, monoval_i[d]);
227
228 for (unsigned int j = 0; j <= my_degree; ++j)
229 {
230 for (unsigned int d = 0; d < dim; ++d)
231 {
232 monomials[j].value(unit_point(d),
233 n_derivatives,
234 monoval_j[d]);
235 monomials[j + 1].value(unit_point(d),
236 n_derivatives,
237 monoval_jplus[d]);
238 }
239
240 if (values.size() != 0)
241 {
242 values[start][0] = monoval_i[0][0] * monoval_j[1][0] *
243 monoval[2][0] *
244 static_cast<double>(j + my_degree + 2);
245 values[start][1] =
246 -monoval_i[0][1] * monoval_jplus[1][0] * monoval[2][0];
247 values[start][2] =
248 -monoval_i[0][1] * monoval_j[1][0] * monoval_plus[2][0];
249
250 values[start + n_curls][0] =
251 -monoval_jplus[0][0] * monoval_i[1][1] * monoval[2][0];
252 values[start + n_curls][1] =
253 monoval_j[0][0] * monoval_i[1][0] * monoval[2][0] *
254 static_cast<double>(j + my_degree + 2);
255 values[start + n_curls][2] =
256 -monoval_j[0][0] * monoval_i[1][1] * monoval_plus[2][0];
257
258 values[start + 2 * n_curls][0] =
259 -monoval_jplus[0][0] * monoval[1][0] * monoval_i[2][1];
260 values[start + 2 * n_curls][1] =
261 -monoval_j[0][0] * monoval_plus[1][0] * monoval_i[2][1];
262 values[start + 2 * n_curls][2] =
263 monoval_j[0][0] * monoval[1][0] * monoval_i[2][0] *
264 static_cast<double>(j + my_degree + 2);
265
266 // Only unique triples of powers (i j k)
267 // and (i k j) are allowed, 0 <= i,j <= k
268 if (j != my_degree)
269 {
270 values[start + 1][0] =
271 monoval_i[0][0] * monoval[1][0] * monoval_j[2][0] *
272 static_cast<double>(j + my_degree + 2);
273 values[start + 1][1] =
274 -monoval_i[0][1] * monoval_plus[1][0] * monoval_j[2][0];
275 values[start + 1][2] =
276 -monoval_i[0][1] * monoval[1][0] * monoval_jplus[2][0];
277
278 values[start + n_curls + 1][0] =
279 -monoval_plus[0][0] * monoval_i[1][1] * monoval_j[2][0];
280 values[start + n_curls + 1][1] =
281 monoval[0][0] * monoval_i[1][0] * monoval_j[2][0] *
282 static_cast<double>(j + my_degree + 2);
283 values[start + n_curls + 1][2] =
284 -monoval[0][0] * monoval_i[1][1] * monoval_jplus[2][0];
285
286 values[start + 2 * n_curls + 1][0] =
287 -monoval_plus[0][0] * monoval_j[1][0] * monoval_i[2][1];
288 values[start + 2 * n_curls + 1][1] =
289 -monoval[0][0] * monoval_jplus[1][0] * monoval_i[2][1];
290 values[start + 2 * n_curls + 1][2] =
291 monoval[0][0] * monoval_j[1][0] * monoval_i[2][0] *
292 static_cast<double>(j + my_degree + 2);
293 }
294 }
295
296 if (grads.size() != 0)
297 {
298 grads[start][0][0] = monoval_i[0][1] * monoval_j[1][0] *
299 monoval[2][0] *
300 static_cast<double>(j + my_degree + 2);
301 grads[start][0][1] = monoval_i[0][0] * monoval_j[1][1] *
302 monoval[2][0] *
303 static_cast<double>(j + my_degree + 2);
304 grads[start][0][2] = monoval_i[0][0] * monoval_j[1][0] *
305 monoval[2][1] *
306 static_cast<double>(j + my_degree + 2);
307 grads[start][1][0] =
308 -monoval_i[0][2] * monoval_jplus[1][0] * monoval[2][0];
309 grads[start][1][1] =
310 -monoval_i[0][1] * monoval_jplus[1][1] * monoval[2][0];
311 grads[start][1][2] =
312 -monoval_i[0][1] * monoval_jplus[1][0] * monoval[2][1];
313 grads[start][2][0] =
314 -monoval_i[0][2] * monoval_j[1][0] * monoval_plus[2][0];
315 grads[start][2][1] =
316 -monoval_i[0][1] * monoval_j[1][1] * monoval_plus[2][0];
317 grads[start][2][2] =
318 -monoval_i[0][1] * monoval_j[1][0] * monoval_plus[2][1];
319
320 grads[start + n_curls][0][0] =
321 -monoval_jplus[0][1] * monoval_i[1][1] * monoval[2][0];
322 grads[start + n_curls][0][1] =
323 -monoval_jplus[0][0] * monoval_i[1][2] * monoval[2][0];
324 grads[start + n_curls][0][2] =
325 -monoval_jplus[0][0] * monoval_i[1][1] * monoval[2][1];
326 grads[start + n_curls][1][0] =
327 monoval_j[0][1] * monoval_i[1][0] * monoval[2][0] *
328 static_cast<double>(j + my_degree + 2);
329 grads[start + n_curls][1][1] =
330 monoval_j[0][0] * monoval_i[1][1] * monoval[2][0] *
331 static_cast<double>(j + my_degree + 2);
332 grads[start + n_curls][1][2] =
333 monoval_j[0][0] * monoval_i[1][0] * monoval[2][1] *
334 static_cast<double>(j + my_degree + 2);
335 grads[start + n_curls][2][0] =
336 -monoval_j[0][1] * monoval_i[1][1] * monoval_plus[2][0];
337 grads[start + n_curls][2][1] =
338 -monoval_j[0][0] * monoval_i[1][2] * monoval_plus[2][0];
339 grads[start + n_curls][2][2] =
340 -monoval_j[0][0] * monoval_i[1][1] * monoval_plus[2][1];
341
342 grads[start + 2 * n_curls][0][0] =
343 -monoval_jplus[0][1] * monoval[1][0] * monoval_i[2][1];
344 grads[start + 2 * n_curls][0][1] =
345 -monoval_jplus[0][0] * monoval[1][1] * monoval_i[2][1];
346 grads[start + 2 * n_curls][0][2] =
347 -monoval_jplus[0][0] * monoval[1][0] * monoval_i[2][2];
348 grads[start + 2 * n_curls][1][0] =
349 -monoval_j[0][1] * monoval_plus[1][0] * monoval_i[2][1];
350 grads[start + 2 * n_curls][1][1] =
351 -monoval_j[0][0] * monoval_plus[1][1] * monoval_i[2][1];
352 grads[start + 2 * n_curls][1][2] =
353 -monoval_j[0][0] * monoval_plus[1][0] * monoval_i[2][2];
354 grads[start + 2 * n_curls][2][0] =
355 monoval_j[0][1] * monoval[1][0] * monoval_i[2][0] *
356 static_cast<double>(j + my_degree + 2);
357 grads[start + 2 * n_curls][2][1] =
358 monoval_j[0][0] * monoval[1][1] * monoval_i[2][0] *
359 static_cast<double>(j + my_degree + 2);
360 grads[start + 2 * n_curls][2][2] =
361 monoval_j[0][0] * monoval[1][0] * monoval_i[2][1] *
362 static_cast<double>(j + my_degree + 2);
363
364 if (j != my_degree)
365 {
366 grads[start + 1][0][0] =
367 monoval_i[0][1] * monoval[1][0] * monoval_j[2][0] *
368 static_cast<double>(j + my_degree + 2);
369 grads[start + 1][0][1] =
370 monoval_i[0][0] * monoval[1][1] * monoval_j[2][0] *
371 static_cast<double>(j + my_degree + 2);
372 grads[start + 1][0][2] =
373 monoval_i[0][0] * monoval[1][0] * monoval_j[2][1] *
374 static_cast<double>(j + my_degree + 2);
375 grads[start + 1][1][0] =
376 -monoval_i[0][2] * monoval_plus[1][0] * monoval_j[2][0];
377 grads[start + 1][1][1] =
378 -monoval_i[0][1] * monoval_plus[1][1] * monoval_j[2][0];
379 grads[start + 1][1][2] =
380 -monoval_i[0][1] * monoval_plus[1][0] * monoval_j[2][1];
381 grads[start + 1][2][0] =
382 -monoval_i[0][2] * monoval[1][0] * monoval_jplus[2][0];
383 grads[start + 1][2][1] =
384 -monoval_i[0][1] * monoval[1][1] * monoval_jplus[2][0];
385 grads[start + 1][2][2] =
386 -monoval_i[0][1] * monoval[1][0] * monoval_jplus[2][1];
387
388 grads[start + n_curls + 1][0][0] =
389 -monoval_plus[0][1] * monoval_i[1][1] * monoval_j[2][0];
390 grads[start + n_curls + 1][0][1] =
391 -monoval_plus[0][0] * monoval_i[1][2] * monoval_j[2][0];
392 grads[start + n_curls + 1][0][2] =
393 -monoval_plus[0][0] * monoval_i[1][1] * monoval_j[2][1];
394 grads[start + n_curls + 1][1][0] =
395 monoval[0][1] * monoval_i[1][0] * monoval_j[2][0] *
396 static_cast<double>(j + my_degree + 2);
397 grads[start + n_curls + 1][1][1] =
398 monoval[0][0] * monoval_i[1][1] * monoval_j[2][0] *
399 static_cast<double>(j + my_degree + 2);
400 grads[start + n_curls + 1][1][2] =
401 monoval[0][0] * monoval_i[1][0] * monoval_j[2][1] *
402 static_cast<double>(j + my_degree + 2);
403 grads[start + n_curls + 1][2][0] =
404 -monoval[0][1] * monoval_i[1][1] * monoval_jplus[2][0];
405 grads[start + n_curls + 1][2][1] =
406 -monoval[0][0] * monoval_i[1][2] * monoval_jplus[2][0];
407 grads[start + n_curls + 1][2][2] =
408 -monoval[0][0] * monoval_i[1][1] * monoval_jplus[2][1];
409
410 grads[start + 2 * n_curls + 1][0][0] =
411 -monoval_plus[0][1] * monoval_j[1][0] * monoval_i[2][1];
412 grads[start + 2 * n_curls + 1][0][1] =
413 -monoval_plus[0][0] * monoval_j[1][1] * monoval_i[2][1];
414 grads[start + 2 * n_curls + 1][0][2] =
415 -monoval_plus[0][0] * monoval_j[1][0] * monoval_i[2][2];
416 grads[start + 2 * n_curls + 1][1][0] =
417 -monoval[0][1] * monoval_jplus[1][0] * monoval_i[2][1];
418 grads[start + 2 * n_curls + 1][1][1] =
419 -monoval[0][0] * monoval_jplus[1][1] * monoval_i[2][1];
420 grads[start + 2 * n_curls + 1][1][2] =
421 -monoval[0][0] * monoval_jplus[1][0] * monoval_i[2][2];
422 grads[start + 2 * n_curls + 1][2][0] =
423 monoval[0][1] * monoval_j[1][0] * monoval_i[2][0] *
424 static_cast<double>(j + my_degree + 2);
425 grads[start + 2 * n_curls + 1][2][1] =
426 monoval[0][0] * monoval_j[1][1] * monoval_i[2][0] *
427 static_cast<double>(j + my_degree + 2);
428 grads[start + 2 * n_curls + 1][2][2] =
429 monoval[0][0] * monoval_j[1][0] * monoval_i[2][1] *
430 static_cast<double>(j + my_degree + 2);
431 }
432 }
433
434 if (grad_grads.size() != 0)
435 {
436 grad_grads[start][0][0][0] =
437 monoval_i[0][2] * monoval_j[1][0] * monoval[2][0] *
438 static_cast<double>(j + my_degree + 2);
439 grad_grads[start][0][0][1] =
440 monoval_i[0][1] * monoval_j[1][1] * monoval[2][0] *
441 static_cast<double>(j + my_degree + 2);
442 grad_grads[start][0][0][2] =
443 monoval_i[0][1] * monoval_j[1][0] * monoval[2][1] *
444 static_cast<double>(j + my_degree + 2);
445 grad_grads[start][0][1][0] =
446 monoval_i[0][1] * monoval_j[1][1] * monoval[2][0] *
447 static_cast<double>(j + my_degree + 2);
448 grad_grads[start][0][1][1] =
449 monoval_i[0][0] * monoval_j[1][2] * monoval[2][0] *
450 static_cast<double>(j + my_degree + 2);
451 grad_grads[start][0][1][2] =
452 monoval_i[0][0] * monoval_j[1][1] * monoval[2][1] *
453 static_cast<double>(j + my_degree + 2);
454 grad_grads[start][0][2][0] =
455 monoval_i[0][1] * monoval_j[1][0] * monoval[2][1] *
456 static_cast<double>(j + my_degree + 2);
457 grad_grads[start][0][2][1] =
458 monoval_i[0][0] * monoval_j[1][1] * monoval[2][1] *
459 static_cast<double>(j + my_degree + 2);
460 grad_grads[start][0][2][2] =
461 monoval_i[0][0] * monoval_j[1][0] * monoval[2][2] *
462 static_cast<double>(j + my_degree + 2);
463 grad_grads[start][1][0][0] =
464 -monoval_i[0][3] * monoval_jplus[1][0] * monoval[2][0];
465 grad_grads[start][1][0][1] =
466 -monoval_i[0][2] * monoval_jplus[1][1] * monoval[2][0];
467 grad_grads[start][1][0][2] =
468 -monoval_i[0][2] * monoval_jplus[1][0] * monoval[2][1];
469 grad_grads[start][1][1][0] =
470 -monoval_i[0][2] * monoval_jplus[1][1] * monoval[2][0];
471 grad_grads[start][1][1][1] =
472 -monoval_i[0][1] * monoval_jplus[1][2] * monoval[2][0];
473 grad_grads[start][1][1][2] =
474 -monoval_i[0][1] * monoval_jplus[1][1] * monoval[2][1];
475 grad_grads[start][1][2][0] =
476 -monoval_i[0][2] * monoval_jplus[1][0] * monoval[2][1];
477 grad_grads[start][1][2][1] =
478 -monoval_i[0][1] * monoval_jplus[1][1] * monoval[2][1];
479 grad_grads[start][1][2][2] =
480 -monoval_i[0][1] * monoval_jplus[1][0] * monoval[2][2];
481 grad_grads[start][2][0][0] =
482 -monoval_i[0][3] * monoval_j[1][0] * monoval_plus[2][0];
483 grad_grads[start][2][0][1] =
484 -monoval_i[0][2] * monoval_j[1][1] * monoval_plus[2][0];
485 grad_grads[start][2][0][2] =
486 -monoval_i[0][2] * monoval_j[1][0] * monoval_plus[2][1];
487 grad_grads[start][2][1][0] =
488 -monoval_i[0][2] * monoval_j[1][1] * monoval_plus[2][0];
489 grad_grads[start][2][1][1] =
490 -monoval_i[0][1] * monoval_j[1][2] * monoval_plus[2][0];
491 grad_grads[start][2][1][2] =
492 -monoval_i[0][1] * monoval_j[1][1] * monoval_plus[2][1];
493 grad_grads[start][2][2][0] =
494 -monoval_i[0][2] * monoval_j[1][0] * monoval_plus[2][1];
495 grad_grads[start][2][2][1] =
496 -monoval_i[0][1] * monoval_j[1][1] * monoval_plus[2][1];
497 grad_grads[start][2][2][2] =
498 -monoval_i[0][1] * monoval_j[1][0] * monoval_plus[2][2];
499
500 grad_grads[start + n_curls][0][0][0] =
501 -monoval_jplus[0][2] * monoval_i[1][1] * monoval[2][0];
502 grad_grads[start + n_curls][0][0][1] =
503 -monoval_jplus[0][1] * monoval_i[1][2] * monoval[2][0];
504 grad_grads[start + n_curls][0][0][2] =
505 -monoval_jplus[0][1] * monoval_i[1][1] * monoval[2][1];
506 grad_grads[start + n_curls][0][1][0] =
507 -monoval_jplus[0][1] * monoval_i[1][2] * monoval[2][0];
508 grad_grads[start + n_curls][0][1][1] =
509 -monoval_jplus[0][0] * monoval_i[1][3] * monoval[2][0];
510 grad_grads[start + n_curls][0][1][2] =
511 -monoval_jplus[0][0] * monoval_i[1][2] * monoval[2][1];
512 grad_grads[start + n_curls][0][2][0] =
513 -monoval_jplus[0][1] * monoval_i[1][1] * monoval[2][1];
514 grad_grads[start + n_curls][0][2][1] =
515 -monoval_jplus[0][0] * monoval_i[1][2] * monoval[2][1];
516 grad_grads[start + n_curls][0][2][2] =
517 -monoval_jplus[0][0] * monoval_i[1][1] * monoval[2][2];
518 grad_grads[start + n_curls][1][0][0] =
519 monoval_j[0][2] * monoval_i[1][0] * monoval[2][0] *
520 static_cast<double>(j + my_degree + 2);
521 grad_grads[start + n_curls][1][0][1] =
522 monoval_j[0][1] * monoval_i[1][1] * monoval[2][0] *
523 static_cast<double>(j + my_degree + 2);
524 grad_grads[start + n_curls][1][0][2] =
525 monoval_j[0][1] * monoval_i[1][0] * monoval[2][1] *
526 static_cast<double>(j + my_degree + 2);
527 grad_grads[start + n_curls][1][1][0] =
528 monoval_j[0][1] * monoval_i[1][1] * monoval[2][0] *
529 static_cast<double>(j + my_degree + 2);
530 grad_grads[start + n_curls][1][1][1] =
531 monoval_j[0][0] * monoval_i[1][2] * monoval[2][0] *
532 static_cast<double>(j + my_degree + 2);
533 grad_grads[start + n_curls][1][1][2] =
534 monoval_j[0][0] * monoval_i[1][1] * monoval[2][1] *
535 static_cast<double>(j + my_degree + 2);
536 grad_grads[start + n_curls][1][2][0] =
537 monoval_j[0][1] * monoval_i[1][0] * monoval[2][1] *
538 static_cast<double>(j + my_degree + 2);
539 grad_grads[start + n_curls][1][2][1] =
540 monoval_j[0][0] * monoval_i[1][1] * monoval[2][1] *
541 static_cast<double>(j + my_degree + 2);
542 grad_grads[start + n_curls][1][2][2] =
543 monoval_j[0][0] * monoval_i[1][0] * monoval[2][2] *
544 static_cast<double>(j + my_degree + 2);
545 grad_grads[start + n_curls][2][0][0] =
546 -monoval_j[0][2] * monoval_i[1][1] * monoval_plus[2][0];
547 grad_grads[start + n_curls][2][0][1] =
548 -monoval_j[0][1] * monoval_i[1][2] * monoval_plus[2][0];
549 grad_grads[start + n_curls][2][0][2] =
550 -monoval_j[0][1] * monoval_i[1][1] * monoval_plus[2][1];
551 grad_grads[start + n_curls][2][1][0] =
552 -monoval_j[0][1] * monoval_i[1][2] * monoval_plus[2][0];
553 grad_grads[start + n_curls][2][1][1] =
554 -monoval_j[0][0] * monoval_i[1][3] * monoval_plus[2][0];
555 grad_grads[start + n_curls][2][1][2] =
556 -monoval_j[0][0] * monoval_i[1][2] * monoval_plus[2][1];
557 grad_grads[start + n_curls][2][2][0] =
558 -monoval_j[0][1] * monoval_i[1][1] * monoval_plus[2][1];
559 grad_grads[start + n_curls][2][2][1] =
560 -monoval_j[0][0] * monoval_i[1][2] * monoval_plus[2][1];
561 grad_grads[start + n_curls][2][2][2] =
562 -monoval_j[0][0] * monoval_i[1][1] * monoval_plus[2][2];
563
564 grad_grads[start + 2 * n_curls][0][0][0] =
565 -monoval_jplus[0][2] * monoval[1][0] * monoval_i[2][1];
566 grad_grads[start + 2 * n_curls][0][0][1] =
567 -monoval_jplus[0][1] * monoval[1][1] * monoval_i[2][1];
568 grad_grads[start + 2 * n_curls][0][0][2] =
569 -monoval_jplus[0][1] * monoval[1][0] * monoval_i[2][2];
570 grad_grads[start + 2 * n_curls][0][1][0] =
571 -monoval_jplus[0][1] * monoval[1][1] * monoval_i[2][1];
572 grad_grads[start + 2 * n_curls][0][1][1] =
573 -monoval_jplus[0][0] * monoval[1][2] * monoval_i[2][1];
574 grad_grads[start + 2 * n_curls][0][1][2] =
575 -monoval_jplus[0][0] * monoval[1][1] * monoval_i[2][2];
576 grad_grads[start + 2 * n_curls][0][2][0] =
577 -monoval_jplus[0][1] * monoval[1][0] * monoval_i[2][2];
578 grad_grads[start + 2 * n_curls][0][2][1] =
579 -monoval_jplus[0][0] * monoval[1][1] * monoval_i[2][2];
580 grad_grads[start + 2 * n_curls][0][2][2] =
581 -monoval_jplus[0][0] * monoval[1][0] * monoval_i[2][3];
582 grad_grads[start + 2 * n_curls][1][0][0] =
583 -monoval_j[0][2] * monoval_plus[1][0] * monoval_i[2][1];
584 grad_grads[start + 2 * n_curls][1][0][1] =
585 -monoval_j[0][1] * monoval_plus[1][1] * monoval_i[2][1];
586 grad_grads[start + 2 * n_curls][1][0][2] =
587 -monoval_j[0][1] * monoval_plus[1][0] * monoval_i[2][2];
588 grad_grads[start + 2 * n_curls][1][1][0] =
589 -monoval_j[0][1] * monoval_plus[1][1] * monoval_i[2][1];
590 grad_grads[start + 2 * n_curls][1][1][1] =
591 -monoval_j[0][0] * monoval_plus[1][2] * monoval_i[2][1];
592 grad_grads[start + 2 * n_curls][1][1][2] =
593 -monoval_j[0][0] * monoval_plus[1][1] * monoval_i[2][2];
594 grad_grads[start + 2 * n_curls][1][2][0] =
595 -monoval_j[0][1] * monoval_plus[1][0] * monoval_i[2][2];
596 grad_grads[start + 2 * n_curls][1][2][1] =
597 -monoval_j[0][0] * monoval_plus[1][1] * monoval_i[2][2];
598 grad_grads[start + 2 * n_curls][1][2][2] =
599 -monoval_j[0][0] * monoval_plus[1][0] * monoval_i[2][3];
600 grad_grads[start + 2 * n_curls][2][0][0] =
601 monoval_j[0][2] * monoval[1][0] * monoval_i[2][0] *
602 static_cast<double>(j + my_degree + 2);
603 grad_grads[start + 2 * n_curls][2][0][1] =
604 monoval_j[0][1] * monoval[1][1] * monoval_i[2][0] *
605 static_cast<double>(j + my_degree + 2);
606 grad_grads[start + 2 * n_curls][2][0][2] =
607 monoval_j[0][1] * monoval[1][0] * monoval_i[2][1] *
608 static_cast<double>(j + my_degree + 2);
609 grad_grads[start + 2 * n_curls][2][1][0] =
610 monoval_j[0][1] * monoval[1][1] * monoval_i[2][0] *
611 static_cast<double>(j + my_degree + 2);
612 grad_grads[start + 2 * n_curls][2][1][1] =
613 monoval_j[0][0] * monoval[1][2] * monoval_i[2][0] *
614 static_cast<double>(j + my_degree + 2);
615 grad_grads[start + 2 * n_curls][2][1][2] =
616 monoval_j[0][0] * monoval[1][1] * monoval_i[2][1] *
617 static_cast<double>(j + my_degree + 2);
618 grad_grads[start + 2 * n_curls][2][2][0] =
619 monoval_j[0][1] * monoval[1][0] * monoval_i[2][1] *
620 static_cast<double>(j + my_degree + 2);
621 grad_grads[start + 2 * n_curls][2][2][1] =
622 monoval_j[0][0] * monoval[1][1] * monoval_i[2][1] *
623 static_cast<double>(j + my_degree + 2);
624 grad_grads[start + 2 * n_curls][2][2][2] =
625 monoval_j[0][0] * monoval[1][0] * monoval_i[2][2] *
626 static_cast<double>(j + my_degree + 2);
627
628 if (j != my_degree)
629 {
630 grad_grads[start + 1][0][0][0] =
631 monoval_i[0][2] * monoval[1][0] * monoval_j[2][0] *
632 static_cast<double>(j + my_degree + 2);
633 grad_grads[start + 1][0][0][1] =
634 monoval_i[0][1] * monoval[1][1] * monoval_j[2][0] *
635 static_cast<double>(j + my_degree + 2);
636 grad_grads[start + 1][0][0][2] =
637 monoval_i[0][1] * monoval[1][0] * monoval_j[2][1] *
638 static_cast<double>(j + my_degree + 2);
639 grad_grads[start + 1][0][1][0] =
640 monoval_i[0][1] * monoval[1][1] * monoval_j[2][0] *
641 static_cast<double>(j + my_degree + 2);
642 grad_grads[start + 1][0][1][1] =
643 monoval_i[0][0] * monoval[1][2] * monoval_j[2][0] *
644 static_cast<double>(j + my_degree + 2);
645 grad_grads[start + 1][0][1][2] =
646 monoval_i[0][0] * monoval[1][1] * monoval_j[2][1] *
647 static_cast<double>(j + my_degree + 2);
648 grad_grads[start + 1][0][2][0] =
649 monoval_i[0][1] * monoval[1][0] * monoval_j[2][1] *
650 static_cast<double>(j + my_degree + 2);
651 grad_grads[start + 1][0][2][1] =
652 monoval_i[0][0] * monoval[1][1] * monoval_j[2][1] *
653 static_cast<double>(j + my_degree + 2);
654 grad_grads[start + 1][0][2][2] =
655 monoval_i[0][0] * monoval[1][0] * monoval_j[2][2] *
656 static_cast<double>(j + my_degree + 2);
657 grad_grads[start + 1][1][0][0] =
658 -monoval_i[0][3] * monoval_plus[1][0] * monoval_j[2][0];
659 grad_grads[start + 1][1][0][1] =
660 -monoval_i[0][2] * monoval_plus[1][1] * monoval_j[2][0];
661 grad_grads[start + 1][1][0][2] =
662 -monoval_i[0][2] * monoval_plus[1][0] * monoval_j[2][1];
663 grad_grads[start + 1][1][1][0] =
664 -monoval_i[0][2] * monoval_plus[1][1] * monoval_j[2][0];
665 grad_grads[start + 1][1][1][1] =
666 -monoval_i[0][1] * monoval_plus[1][2] * monoval_j[2][0];
667 grad_grads[start + 1][1][1][2] =
668 -monoval_i[0][1] * monoval_plus[1][1] * monoval_j[2][1];
669 grad_grads[start + 1][1][2][0] =
670 -monoval_i[0][2] * monoval_plus[1][0] * monoval_j[2][1];
671 grad_grads[start + 1][1][2][1] =
672 -monoval_i[0][1] * monoval_plus[1][1] * monoval_j[2][1];
673 grad_grads[start + 1][1][2][2] =
674 -monoval_i[0][1] * monoval_plus[1][0] * monoval_j[2][2];
675 grad_grads[start + 1][2][0][0] =
676 -monoval_i[0][3] * monoval[1][0] * monoval_jplus[2][0];
677 grad_grads[start + 1][2][0][1] =
678 -monoval_i[0][2] * monoval[1][1] * monoval_jplus[2][0];
679 grad_grads[start + 1][2][0][2] =
680 -monoval_i[0][2] * monoval[1][0] * monoval_jplus[2][1];
681 grad_grads[start + 1][2][1][0] =
682 -monoval_i[0][2] * monoval[1][1] * monoval_jplus[2][0];
683 grad_grads[start + 1][2][1][1] =
684 -monoval_i[0][1] * monoval[1][2] * monoval_jplus[2][0];
685 grad_grads[start + 1][2][1][2] =
686 -monoval_i[0][1] * monoval[1][1] * monoval_jplus[2][1];
687 grad_grads[start + 1][2][2][0] =
688 -monoval_i[0][2] * monoval[1][0] * monoval_jplus[2][1];
689 grad_grads[start + 1][2][2][1] =
690 -monoval_i[0][1] * monoval[1][1] * monoval_jplus[2][1];
691 grad_grads[start + 1][2][2][2] =
692 -monoval_i[0][1] * monoval[1][0] * monoval_jplus[2][2];
693
694 grad_grads[start + n_curls + 1][0][0][0] =
695 -monoval_plus[0][2] * monoval_i[1][1] * monoval_j[2][0];
696 grad_grads[start + n_curls + 1][0][0][1] =
697 -monoval_plus[0][1] * monoval_i[1][2] * monoval_j[2][0];
698 grad_grads[start + n_curls + 1][0][0][2] =
699 -monoval_plus[0][1] * monoval_i[1][1] * monoval_j[2][1];
700 grad_grads[start + n_curls + 1][0][1][0] =
701 -monoval_plus[0][1] * monoval_i[1][2] * monoval_j[2][0];
702 grad_grads[start + n_curls + 1][0][1][1] =
703 -monoval_plus[0][0] * monoval_i[1][3] * monoval_j[2][0];
704 grad_grads[start + n_curls + 1][0][1][2] =
705 -monoval_plus[0][0] * monoval_i[1][2] * monoval_j[2][1];
706 grad_grads[start + n_curls + 1][0][2][0] =
707 -monoval_plus[0][1] * monoval_i[1][1] * monoval_j[2][1];
708 grad_grads[start + n_curls + 1][0][2][1] =
709 -monoval_plus[0][0] * monoval_i[1][2] * monoval_j[2][1];
710 grad_grads[start + n_curls + 1][0][2][2] =
711 -monoval_plus[0][0] * monoval_i[1][1] * monoval_j[2][2];
712 grad_grads[start + n_curls + 1][1][0][0] =
713 monoval[0][2] * monoval_i[1][0] * monoval_j[2][0] *
714 static_cast<double>(j + my_degree + 2);
715 grad_grads[start + n_curls + 1][1][0][1] =
716 monoval[0][1] * monoval_i[1][1] * monoval_j[2][0] *
717 static_cast<double>(j + my_degree + 2);
718 grad_grads[start + n_curls + 1][1][0][2] =
719 monoval[0][1] * monoval_i[1][0] * monoval_j[2][1] *
720 static_cast<double>(j + my_degree + 2);
721 grad_grads[start + n_curls + 1][1][1][0] =
722 monoval[0][1] * monoval_i[1][1] * monoval_j[2][0] *
723 static_cast<double>(j + my_degree + 2);
724 grad_grads[start + n_curls + 1][1][1][1] =
725 monoval[0][0] * monoval_i[1][2] * monoval_j[2][0] *
726 static_cast<double>(j + my_degree + 2);
727 grad_grads[start + n_curls + 1][1][1][2] =
728 monoval[0][0] * monoval_i[1][1] * monoval_j[2][1] *
729 static_cast<double>(j + my_degree + 2);
730 grad_grads[start + n_curls + 1][1][2][0] =
731 monoval[0][1] * monoval_i[1][0] * monoval_j[2][1] *
732 static_cast<double>(j + my_degree + 2);
733 grad_grads[start + n_curls + 1][1][2][1] =
734 monoval[0][0] * monoval_i[1][1] * monoval_j[2][1] *
735 static_cast<double>(j + my_degree + 2);
736 grad_grads[start + n_curls + 1][1][2][2] =
737 monoval[0][0] * monoval_i[1][0] * monoval_j[2][2] *
738 static_cast<double>(j + my_degree + 2);
739 grad_grads[start + n_curls + 1][2][0][0] =
740 -monoval[0][2] * monoval_i[1][1] * monoval_jplus[2][0];
741 grad_grads[start + n_curls + 1][2][0][1] =
742 -monoval[0][1] * monoval_i[1][2] * monoval_jplus[2][0];
743 grad_grads[start + n_curls + 1][2][0][2] =
744 -monoval[0][1] * monoval_i[1][1] * monoval_jplus[2][1];
745 grad_grads[start + n_curls + 1][2][1][0] =
746 -monoval[0][1] * monoval_i[1][2] * monoval_jplus[2][0];
747 grad_grads[start + n_curls + 1][2][1][1] =
748 -monoval[0][0] * monoval_i[1][3] * monoval_jplus[2][0];
749 grad_grads[start + n_curls + 1][2][1][2] =
750 -monoval[0][0] * monoval_i[1][2] * monoval_jplus[2][1];
751 grad_grads[start + n_curls + 1][2][2][0] =
752 -monoval[0][1] * monoval_i[1][1] * monoval_jplus[2][1];
753 grad_grads[start + n_curls + 1][2][2][1] =
754 -monoval[0][0] * monoval_i[1][2] * monoval_jplus[2][1];
755 grad_grads[start + n_curls + 1][2][2][2] =
756 -monoval[0][0] * monoval_i[1][1] * monoval_jplus[2][2];
757
758 grad_grads[start + 2 * n_curls + 1][0][0][0] =
759 -monoval_plus[0][2] * monoval_j[1][0] * monoval_i[2][1];
760 grad_grads[start + 2 * n_curls + 1][0][0][1] =
761 -monoval_plus[0][1] * monoval_j[1][1] * monoval_i[2][1];
762 grad_grads[start + 2 * n_curls + 1][0][0][2] =
763 -monoval_plus[0][1] * monoval_j[1][0] * monoval_i[2][2];
764 grad_grads[start + 2 * n_curls + 1][0][1][0] =
765 -monoval_plus[0][1] * monoval_j[1][1] * monoval_i[2][1];
766 grad_grads[start + 2 * n_curls + 1][0][1][1] =
767 -monoval_plus[0][0] * monoval_j[1][2] * monoval_i[2][1];
768 grad_grads[start + 2 * n_curls + 1][0][1][2] =
769 -monoval_plus[0][0] * monoval_j[1][1] * monoval_i[2][2];
770 grad_grads[start + 2 * n_curls + 1][0][2][0] =
771 -monoval_plus[0][1] * monoval_j[1][0] * monoval_i[2][2];
772 grad_grads[start + 2 * n_curls + 1][0][2][1] =
773 -monoval_plus[0][0] * monoval_j[1][1] * monoval_i[2][2];
774 grad_grads[start + 2 * n_curls + 1][0][2][2] =
775 -monoval_plus[0][0] * monoval_j[1][0] * monoval_i[2][3];
776 grad_grads[start + 2 * n_curls + 1][1][0][0] =
777 -monoval[0][2] * monoval_jplus[1][0] * monoval_i[2][1];
778 grad_grads[start + 2 * n_curls + 1][1][0][1] =
779 -monoval[0][1] * monoval_jplus[1][1] * monoval_i[2][1];
780 grad_grads[start + 2 * n_curls + 1][1][0][2] =
781 -monoval[0][1] * monoval_jplus[1][0] * monoval_i[2][2];
782 grad_grads[start + 2 * n_curls + 1][1][1][0] =
783 -monoval[0][1] * monoval_jplus[1][1] * monoval_i[2][1];
784 grad_grads[start + 2 * n_curls + 1][1][1][1] =
785 -monoval[0][0] * monoval_jplus[1][2] * monoval_i[2][1];
786 grad_grads[start + 2 * n_curls + 1][1][1][2] =
787 -monoval[0][0] * monoval_jplus[1][1] * monoval_i[2][2];
788 grad_grads[start + 2 * n_curls + 1][1][2][0] =
789 -monoval[0][1] * monoval_jplus[1][0] * monoval_i[2][2];
790 grad_grads[start + 2 * n_curls + 1][1][2][1] =
791 -monoval[0][0] * monoval_jplus[1][1] * monoval_i[2][2];
792 grad_grads[start + 2 * n_curls + 1][1][2][2] =
793 -monoval[0][0] * monoval_jplus[1][0] * monoval_i[2][3];
794 grad_grads[start + 2 * n_curls + 1][2][0][0] =
795 monoval[0][2] * monoval_j[1][0] * monoval_i[2][0] *
796 static_cast<double>(j + my_degree + 2);
797 grad_grads[start + 2 * n_curls + 1][2][0][1] =
798 monoval[0][1] * monoval_j[1][1] * monoval_i[2][0] *
799 static_cast<double>(j + my_degree + 2);
800 grad_grads[start + 2 * n_curls + 1][2][0][2] =
801 monoval[0][1] * monoval_j[1][0] * monoval_i[2][1] *
802 static_cast<double>(j + my_degree + 2);
803 grad_grads[start + 2 * n_curls + 1][2][1][0] =
804 monoval[0][1] * monoval_j[1][1] * monoval_i[2][0] *
805 static_cast<double>(j + my_degree + 2);
806 grad_grads[start + 2 * n_curls + 1][2][1][1] =
807 monoval[0][0] * monoval_j[1][2] * monoval_i[2][0] *
808 static_cast<double>(j + my_degree + 2);
809 grad_grads[start + 2 * n_curls + 1][2][1][2] =
810 monoval[0][0] * monoval_j[1][1] * monoval_i[2][1] *
811 static_cast<double>(j + my_degree + 2);
812 grad_grads[start + 2 * n_curls + 1][2][2][0] =
813 monoval[0][1] * monoval_j[1][0] * monoval_i[2][1] *
814 static_cast<double>(j + my_degree + 2);
815 grad_grads[start + 2 * n_curls + 1][2][2][1] =
816 monoval[0][0] * monoval_j[1][1] * monoval_i[2][1] *
817 static_cast<double>(j + my_degree + 2);
818 grad_grads[start + 2 * n_curls + 1][2][2][2] =
819 monoval[0][0] * monoval_j[1][0] * monoval_i[2][2] *
820 static_cast<double>(j + my_degree + 2);
821 }
822 }
823
824 if (j == my_degree)
825 start += 1;
826 else
827 start += 2;
828 }
829 }
830 Assert(start == this->n() - 2 * n_curls, ExcInternalError());
831 }
832}
833
834
835
836template <int dim>
837unsigned int
838PolynomialsRT_Bubbles<dim>::n_polynomials(const unsigned int k)
839{
840 if (dim == 1 || dim == 2 || dim == 3)
841 return dim * Utilities::fixed_power<dim>(k + 1);
842
843 Assert(false, ExcNotImplemented());
844 return 0;
845}
846
847
848template <int dim>
849std::unique_ptr<TensorPolynomialsBase<dim>>
850PolynomialsRT_Bubbles<dim>::clone() const
851{
852 return std::make_unique<PolynomialsRT_Bubbles<dim>>(*this);
853}
854
855
856template class PolynomialsRT_Bubbles<1>;
857template class PolynomialsRT_Bubbles<2>;
858template class PolynomialsRT_Bubbles<3>;
859
860
861DEAL_II_NAMESPACE_CLOSE
Point
Definition: point.h:111
PolynomialsRT_Bubbles
Definition: polynomials_rt_bubbles.h:87
PolynomialsRT_Bubbles::clone
virtual std::unique_ptr< TensorPolynomialsBase< dim > > clone() const override
Definition: polynomials_rt_bubbles.cc:850
PolynomialsRT_Bubbles::PolynomialsRT_Bubbles
PolynomialsRT_Bubbles(const unsigned int k)
Definition: polynomials_rt_bubbles.cc:30
PolynomialsRT_Bubbles::evaluate
void evaluate(const Point< dim > &unit_point, std::vector< Tensor< 1, dim > > &values, std::vector< Tensor< 2, dim > > &grads, std::vector< Tensor< 3, dim > > &grad_grads, std::vector< Tensor< 4, dim > > &third_derivatives, std::vector< Tensor< 5, dim > > &fourth_derivatives) const override
Definition: polynomials_rt_bubbles.cc:45
PolynomialsRT_Bubbles::n_polynomials
static unsigned int n_polynomials(const unsigned int degree)
Definition: polynomials_rt_bubbles.cc:838
PolynomialsRT_Bubbles::monomials
std::vector< Polynomials::Polynomial< double > > monomials
Definition: polynomials_rt_bubbles.h:145
DEAL_II_NAMESPACE_OPEN
#define DEAL_II_NAMESPACE_OPEN
Definition: config.h:402
DEAL_II_NAMESPACE_CLOSE
#define DEAL_II_NAMESPACE_CLOSE
Definition: config.h:403
StandardExceptions::ExcNotImplemented
static ::ExceptionBase & ExcNotImplemented()
Assert
#define Assert(cond, exc)
Definition: exceptions.h:1465
StandardExceptions::ExcImpossibleInDim
static ::ExceptionBase & ExcImpossibleInDim(int arg1)
StandardExceptions::ExcInternalError
static ::ExceptionBase & ExcInternalError()
StandardExceptions::ExcDimensionMismatch
static ::ExceptionBase & ExcDimensionMismatch(std::size_t arg1, std::size_t arg2)
Physics::Elasticity::Kinematics::d
SymmetricTensor< 2, dim, Number > d(const Tensor< 2, dim, Number > &F, const Tensor< 2, dim, Number > &dF_dt)
polynomials_rt_bubbles.h
quadrature_lib.h
thread_management.h
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