deal.II version GIT relicensing-6834-g5b78e6bcdf 2026-10-01 11:20:01+00:00
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polynomials_bdm.cc
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1// -----------------------------------------------------------------------------
2//
3// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception OR LGPL-2.1-or-later
4// Copyright (C) 2004 - 2024 by the deal.II authors
5//
6// This file is part of the deal.II library.
7//
8// Detailed license information governing the source code and contributions
9// can be found in LICENSE.md and CONTRIBUTING.md at the top level directory.
10//
11// -----------------------------------------------------------------------------
12
13
14#include <deal.II/base/geometry_info.h>
15#include <deal.II/base/polynomial_space.h>
16#include <deal.II/base/polynomials_bdm.h>
17#include <deal.II/base/quadrature_lib.h>
18
19#include <iomanip>
20#include <iostream>
21#include <memory>
22
23DEAL_II_NAMESPACE_OPEN
24
25
26template <int dim>
27PolynomialsBDM<dim>::PolynomialsBDM(const unsigned int k)
28 : TensorPolynomialsBase<dim>(k + 1, n_polynomials(k))
29 , polynomial_space(Polynomials::Legendre::generate_complete_basis(k))
30 , monomials((dim == 2) ? (1) : (k + 2))
31 , p_values(polynomial_space.n())
32 , p_grads(polynomial_space.n())
33 , p_grad_grads(polynomial_space.n())
34{
35 switch (dim)
36 {
37 case 2:
38 monomials[0] = Polynomials::Monomial<double>(k + 1);
39 break;
40 case 3:
41 for (unsigned int i = 0; i < monomials.size(); ++i)
42 monomials[i] = Polynomials::Monomial<double>(i);
43 break;
44 default:
45 DEAL_II_NOT_IMPLEMENTED();
46 }
47}
48
49
50
51template <int dim>
52void
53PolynomialsBDM<dim>::evaluate(
54 const Point<dim> &unit_point,
55 std::vector<Tensor<1, dim>> &values,
56 std::vector<Tensor<2, dim>> &grads,
57 std::vector<Tensor<3, dim>> &grad_grads,
58 std::vector<Tensor<4, dim>> &third_derivatives,
59 std::vector<Tensor<5, dim>> &fourth_derivatives) const
60{
61 Assert(values.size() == this->n() || values.empty(),
62 ExcDimensionMismatch(values.size(), this->n()));
63 Assert(grads.size() == this->n() || grads.empty(),
64 ExcDimensionMismatch(grads.size(), this->n()));
65 Assert(grad_grads.size() == this->n() || grad_grads.empty(),
66 ExcDimensionMismatch(grad_grads.size(), this->n()));
67 Assert(third_derivatives.size() == this->n() || third_derivatives.empty(),
68 ExcDimensionMismatch(third_derivatives.size(), this->n()));
69 Assert(fourth_derivatives.size() == this->n() || fourth_derivatives.empty(),
70 ExcDimensionMismatch(fourth_derivatives.size(), this->n()));
71
72 // third and fourth derivatives not implemented
73 (void)third_derivatives;
74 Assert(third_derivatives.empty(), ExcNotImplemented());
75 (void)fourth_derivatives;
76 Assert(fourth_derivatives.empty(), ExcNotImplemented());
77
78 const unsigned int n_sub = polynomial_space.n();
79
80 // guard access to the scratch arrays in the following block using a
81 // mutex to make sure they are not used by multiple threads at once
82 {
83 std::scoped_lock lock(mutex);
84
85 p_values.resize((values.empty()) ? 0 : n_sub);
86 p_grads.resize((grads.empty()) ? 0 : n_sub);
87 p_grad_grads.resize((grad_grads.empty()) ? 0 : n_sub);
88
89 // Compute values of complete space and insert into tensors. Result
90 // will have first all polynomials in the x-component, then y and z.
91 polynomial_space.evaluate(unit_point,
92 p_values,
93 p_grads,
94 p_grad_grads,
95 p_third_derivatives,
96 p_fourth_derivatives);
97
98 std::fill(values.begin(), values.end(), Tensor<1, dim>());
99 for (unsigned int i = 0; i < p_values.size(); ++i)
100 for (unsigned int j = 0; j < dim; ++j)
101 values[i + j * n_sub][j] = p_values[i];
102
103 std::fill(grads.begin(), grads.end(), Tensor<2, dim>());
104 for (unsigned int i = 0; i < p_grads.size(); ++i)
105 for (unsigned int j = 0; j < dim; ++j)
106 grads[i + j * n_sub][j] = p_grads[i];
107
108 std::fill(grad_grads.begin(), grad_grads.end(), Tensor<3, dim>());
109 for (unsigned int i = 0; i < p_grad_grads.size(); ++i)
110 for (unsigned int j = 0; j < dim; ++j)
111 grad_grads[i + j * n_sub][j] = p_grad_grads[i];
112 }
113
114 // This is the first polynomial not covered by the P_k subspace
115 unsigned int start = dim * n_sub;
116
117 // Store values of auxiliary polynomials and their three derivatives
118 std::vector<std::vector<double>> monovali(dim, std::vector<double>(4));
119 std::vector<std::vector<double>> monovalk(dim, std::vector<double>(4));
120
121 if (dim == 1)
122 {
123 // Despite the fact that we are instantiating this class for 1, 2 and
124 // 3 space dimensions we only support dimension 2 and 3.
125 Assert(false,
126 ::ExcMessage("PolynomialsBDF::evaluate is only "
127 "available for dim == 2, or dim == 3"));
128 }
129 else if (dim == 2)
130 {
131 for (unsigned int d = 0; d < dim; ++d)
132 monomials[0].value(unit_point[d], monovali[d]);
133 if (values.size() != 0)
134 {
135 values[start][0] = monovali[0][0];
136 values[start][1] = -unit_point[1] * monovali[0][1];
137 values[start + 1][0] = unit_point[0] * monovali[1][1];
138 values[start + 1][1] = -monovali[1][0];
139 }
140 if (grads.size() != 0)
141 {
142 grads[start][0][0] = monovali[0][1];
143 grads[start][0][1] = 0.;
144 grads[start][1][0] = -unit_point[1] * monovali[0][2];
145 grads[start][1][1] = -monovali[0][1];
146 grads[start + 1][0][0] = monovali[1][1];
147 grads[start + 1][0][1] = unit_point[0] * monovali[1][2];
148 grads[start + 1][1][0] = 0.;
149 grads[start + 1][1][1] = -monovali[1][1];
150 }
151 if (grad_grads.size() != 0)
152 {
153 grad_grads[start][0][0][0] = monovali[0][2];
154 grad_grads[start][0][0][1] = 0.;
155 grad_grads[start][0][1][0] = 0.;
156 grad_grads[start][0][1][1] = 0.;
157 grad_grads[start][1][0][0] = -unit_point[1] * monovali[0][3];
158 grad_grads[start][1][0][1] = -monovali[0][2];
159 grad_grads[start][1][1][0] = -monovali[0][2];
160 grad_grads[start][1][1][1] = 0.;
161 grad_grads[start + 1][0][0][0] = 0;
162 grad_grads[start + 1][0][0][1] = monovali[1][2];
163 grad_grads[start + 1][0][1][0] = monovali[1][2];
164 grad_grads[start + 1][0][1][1] = unit_point[0] * monovali[1][3];
165 grad_grads[start + 1][1][0][0] = 0.;
166 grad_grads[start + 1][1][0][1] = 0.;
167 grad_grads[start + 1][1][1][0] = 0.;
168 grad_grads[start + 1][1][1][1] = -monovali[1][2];
169 }
170 }
171 else if (dim == 3)
172 {
173 // The number of curls in each component. Note that the table in
174 // BrezziFortin91 has a typo, but the text has the right basis
175
176 // Note that the next basis function is always obtained from the
177 // previous by cyclic rotation of the coordinates
178 const unsigned int n_curls = monomials.size() - 1;
179 for (unsigned int i = 0; i < n_curls; ++i, start += dim)
180 {
181 for (unsigned int d = 0; d < dim; ++d)
182 {
183 // p(t) = t^(i+1)
184 monomials[i + 1].value(unit_point[d], monovali[d]);
185 // q(t) = t^(k-i)
186 monomials[this->degree() - 1 - i].value(unit_point[d],
187 monovalk[d]);
188 }
189
190 if (values.size() != 0)
191 {
192 // x p'(y) q(z)
193 values[start][0] =
194 unit_point[0] * monovali[1][1] * monovalk[2][0];
195 // - p(y) q(z)
196 values[start][1] = -monovali[1][0] * monovalk[2][0];
197 values[start][2] = 0.;
198
199 // y p'(z) q(x)
200 values[start + 1][1] =
201 unit_point[1] * monovali[2][1] * monovalk[0][0];
202 // - p(z) q(x)
203 values[start + 1][2] = -monovali[2][0] * monovalk[0][0];
204 values[start + 1][0] = 0.;
205
206 // z p'(x) q(y)
207 values[start + 2][2] =
208 unit_point[2] * monovali[0][1] * monovalk[1][0];
209 // -p(x) q(y)
210 values[start + 2][0] = -monovali[0][0] * monovalk[1][0];
211 values[start + 2][1] = 0.;
212 }
213
214 if (grads.size() != 0)
215 {
216 grads[start][0][0] = monovali[1][1] * monovalk[2][0];
217 grads[start][0][1] =
218 unit_point[0] * monovali[1][2] * monovalk[2][0];
219 grads[start][0][2] =
220 unit_point[0] * monovali[1][1] * monovalk[2][1];
221 grads[start][1][0] = 0.;
222 grads[start][1][1] = -monovali[1][1] * monovalk[2][0];
223 grads[start][1][2] = -monovali[1][0] * monovalk[2][1];
224 grads[start][2][0] = 0.;
225 grads[start][2][1] = 0.;
226 grads[start][2][2] = 0.;
227
228 grads[start + 1][1][1] = monovali[2][1] * monovalk[0][0];
229 grads[start + 1][1][2] =
230 unit_point[1] * monovali[2][2] * monovalk[0][0];
231 grads[start + 1][1][0] =
232 unit_point[1] * monovali[2][1] * monovalk[0][1];
233 grads[start + 1][2][1] = 0.;
234 grads[start + 1][2][2] = -monovali[2][1] * monovalk[0][0];
235 grads[start + 1][2][0] = -monovali[2][0] * monovalk[0][1];
236 grads[start + 1][0][1] = 0.;
237 grads[start + 1][0][2] = 0.;
238 grads[start + 1][0][0] = 0.;
239
240 grads[start + 2][2][2] = monovali[0][1] * monovalk[1][0];
241 grads[start + 2][2][0] =
242 unit_point[2] * monovali[0][2] * monovalk[1][0];
243 grads[start + 2][2][1] =
244 unit_point[2] * monovali[0][1] * monovalk[1][1];
245 grads[start + 2][0][2] = 0.;
246 grads[start + 2][0][0] = -monovali[0][1] * monovalk[1][0];
247 grads[start + 2][0][1] = -monovali[0][0] * monovalk[1][1];
248 grads[start + 2][1][2] = 0.;
249 grads[start + 2][1][0] = 0.;
250 grads[start + 2][1][1] = 0.;
251 }
252
253 if (grad_grads.size() != 0)
254 {
255 grad_grads[start][0][0][0] = 0.;
256 grad_grads[start][0][0][1] = monovali[1][2] * monovalk[2][0];
257 grad_grads[start][0][0][2] = monovali[1][1] * monovalk[2][1];
258 grad_grads[start][0][1][0] = monovali[1][2] * monovalk[2][0];
259 grad_grads[start][0][1][1] =
260 unit_point[0] * monovali[1][3] * monovalk[2][0];
261 grad_grads[start][0][1][2] =
262 unit_point[0] * monovali[1][2] * monovalk[2][1];
263 grad_grads[start][0][2][0] = monovali[1][1] * monovalk[2][1];
264 grad_grads[start][0][2][1] =
265 unit_point[0] * monovali[1][2] * monovalk[2][1];
266 grad_grads[start][0][2][2] =
267 unit_point[0] * monovali[1][1] * monovalk[2][2];
268 grad_grads[start][1][0][0] = 0.;
269 grad_grads[start][1][0][1] = 0.;
270 grad_grads[start][1][0][2] = 0.;
271 grad_grads[start][1][1][0] = 0.;
272 grad_grads[start][1][1][1] = -monovali[1][2] * monovalk[2][0];
273 grad_grads[start][1][1][2] = -monovali[1][1] * monovalk[2][1];
274 grad_grads[start][1][2][0] = 0.;
275 grad_grads[start][1][2][1] = -monovali[1][1] * monovalk[2][1];
276 grad_grads[start][1][2][2] = -monovali[1][0] * monovalk[2][2];
277 grad_grads[start][2][0][0] = 0.;
278 grad_grads[start][2][0][1] = 0.;
279 grad_grads[start][2][0][2] = 0.;
280 grad_grads[start][2][1][0] = 0.;
281 grad_grads[start][2][1][1] = 0.;
282 grad_grads[start][2][1][2] = 0.;
283 grad_grads[start][2][2][0] = 0.;
284 grad_grads[start][2][2][1] = 0.;
285 grad_grads[start][2][2][2] = 0.;
286
287 grad_grads[start + 1][0][0][0] = 0.;
288 grad_grads[start + 1][0][0][1] = 0.;
289 grad_grads[start + 1][0][0][2] = 0.;
290 grad_grads[start + 1][0][1][0] = 0.;
291 grad_grads[start + 1][0][1][1] = 0.;
292 grad_grads[start + 1][0][1][2] = 0.;
293 grad_grads[start + 1][0][2][0] = 0.;
294 grad_grads[start + 1][0][2][1] = 0.;
295 grad_grads[start + 1][0][2][2] = 0.;
296 grad_grads[start + 1][1][0][0] =
297 unit_point[1] * monovali[2][1] * monovalk[0][2];
298 grad_grads[start + 1][1][0][1] = monovali[2][1] * monovalk[0][1];
299 grad_grads[start + 1][1][0][2] =
300 unit_point[1] * monovali[2][2] * monovalk[0][1];
301 grad_grads[start + 1][1][1][0] = monovalk[0][1] * monovali[2][1];
302 grad_grads[start + 1][1][1][1] = 0.;
303 grad_grads[start + 1][1][1][2] = monovalk[0][0] * monovali[2][2];
304 grad_grads[start + 1][1][2][0] =
305 unit_point[1] * monovalk[0][1] * monovali[2][2];
306 grad_grads[start + 1][1][2][1] = monovalk[0][0] * monovali[2][2];
307 grad_grads[start + 1][1][2][2] =
308 unit_point[1] * monovalk[0][0] * monovali[2][3];
309 grad_grads[start + 1][2][0][0] = -monovalk[0][2] * monovali[2][0];
310 grad_grads[start + 1][2][0][1] = 0.;
311 grad_grads[start + 1][2][0][2] = -monovalk[0][1] * monovali[2][1];
312 grad_grads[start + 1][2][1][0] = 0.;
313 grad_grads[start + 1][2][1][1] = 0.;
314 grad_grads[start + 1][2][1][2] = 0.;
315 grad_grads[start + 1][2][2][0] = -monovalk[0][1] * monovali[2][1];
316 grad_grads[start + 1][2][2][1] = 0.;
317 grad_grads[start + 1][2][2][2] = -monovalk[0][0] * monovali[2][2];
318
319 grad_grads[start + 2][0][0][0] = -monovali[0][2] * monovalk[1][0];
320 grad_grads[start + 2][0][0][1] = -monovali[0][1] * monovalk[1][1];
321 grad_grads[start + 2][0][0][2] = 0.;
322 grad_grads[start + 2][0][1][0] = -monovali[0][1] * monovalk[1][1];
323 grad_grads[start + 2][0][1][1] = -monovali[0][0] * monovalk[1][2];
324 grad_grads[start + 2][0][1][2] = 0.;
325 grad_grads[start + 2][0][2][0] = 0.;
326 grad_grads[start + 2][0][2][1] = 0.;
327 grad_grads[start + 2][0][2][2] = 0.;
328 grad_grads[start + 2][1][0][0] = 0.;
329 grad_grads[start + 2][1][0][1] = 0.;
330 grad_grads[start + 2][1][0][2] = 0.;
331 grad_grads[start + 2][1][1][0] = 0.;
332 grad_grads[start + 2][1][1][1] = 0.;
333 grad_grads[start + 2][1][1][2] = 0.;
334 grad_grads[start + 2][1][2][0] = 0.;
335 grad_grads[start + 2][1][2][1] = 0.;
336 grad_grads[start + 2][1][2][2] = 0.;
337 grad_grads[start + 2][2][0][0] =
338 unit_point[2] * monovali[0][3] * monovalk[1][0];
339 grad_grads[start + 2][2][0][1] =
340 unit_point[2] * monovali[0][2] * monovalk[1][1];
341 grad_grads[start + 2][2][0][2] = monovali[0][2] * monovalk[1][0];
342 grad_grads[start + 2][2][1][0] =
343 unit_point[2] * monovali[0][2] * monovalk[1][1];
344 grad_grads[start + 2][2][1][1] =
345 unit_point[2] * monovali[0][1] * monovalk[1][2];
346 grad_grads[start + 2][2][1][2] = monovali[0][1] * monovalk[1][1];
347 grad_grads[start + 2][2][2][0] = monovali[0][2] * monovalk[1][0];
348 grad_grads[start + 2][2][2][1] = monovali[0][1] * monovalk[1][1];
349 grad_grads[start + 2][2][2][2] = 0.;
350 }
351 }
352 Assert(start == this->n(), ExcInternalError());
353 }
354}
355
356
357template <int dim>
358unsigned int
359PolynomialsBDM<dim>::n_polynomials(const unsigned int k)
360{
361 if (dim == 1)
362 return k + 1;
363 if (dim == 2)
364 return (k + 1) * (k + 2) + 2;
365 if (dim == 3)
366 return ((k + 1) * (k + 2) * (k + 3)) / 2 + 3 * (k + 1);
367 DEAL_II_NOT_IMPLEMENTED();
368 return 0;
369}
370
371
372template <int dim>
373std::unique_ptr<TensorPolynomialsBase<dim>>
374PolynomialsBDM<dim>::clone() const
375{
376 return std::make_unique<PolynomialsBDM<dim>>(*this);
377}
378
379
380template class PolynomialsBDM<1>;
381template class PolynomialsBDM<2>;
382template class PolynomialsBDM<3>;
383
384
385DEAL_II_NAMESPACE_CLOSE
Point
Definition point.h:111
PolynomialsBDM::monomials
std::vector< Polynomials::Polynomial< double > > monomials
Definition polynomials_bdm.h:155
PolynomialsBDM::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_bdm.cc:53
PolynomialsBDM::clone
virtual std::unique_ptr< TensorPolynomialsBase< dim > > clone() const override
Definition polynomials_bdm.cc:374
PolynomialsBDM::PolynomialsBDM
PolynomialsBDM(const unsigned int k)
Definition polynomials_bdm.cc:27
PolynomialsBDM::n_polynomials
static unsigned int n_polynomials(const unsigned int degree)
Definition polynomials_bdm.cc:359
DEAL_II_NAMESPACE_OPEN
#define DEAL_II_NAMESPACE_OPEN
Definition config.h:38
DEAL_II_NAMESPACE_CLOSE
#define DEAL_II_NAMESPACE_CLOSE
Definition config.h:39
DEAL_II_NOT_IMPLEMENTED
#define DEAL_II_NOT_IMPLEMENTED()
Definition exception_macros.h:705
geometry_info.h
StandardExceptions::ExcNotImplemented
static ::ExceptionBase & ExcNotImplemented()
Assert
#define Assert(cond, exc)
Definition exception_macros.h:543
StandardExceptions::ExcInternalError
static ::ExceptionBase & ExcInternalError()
StandardExceptions::ExcDimensionMismatch
static ::ExceptionBase & ExcDimensionMismatch(std::size_t arg1, std::size_t arg2)
StandardExceptions::ExcMessage
static ::ExceptionBase & ExcMessage(std::string arg1)
polynomial_space.h
polynomials_bdm.h
quadrature_lib.h
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