deal.II version GIT relicensing-2220-ge8e5360a96 2024-12-05 09:50:00+00:00
\(\newcommand{\dealvcentcolon}{\mathrel{\mathop{:}}}\) \(\newcommand{\dealcoloneq}{\dealvcentcolon\mathrel{\mkern-1.2mu}=}\) \(\newcommand{\jump}[1]{\left[\!\left[ #1 \right]\!\right]}\) \(\newcommand{\average}[1]{\left\{\!\left\{ #1 \right\}\!\right\}}\)
Loading...
Searching...
No Matches
fe_face.cc
Go to the documentation of this file.
1// ------------------------------------------------------------------------
2//
3// SPDX-License-Identifier: LGPL-2.1-or-later
4// Copyright (C) 2009 - 2024 by the deal.II authors
5//
6// This file is part of the deal.II library.
7//
8// Part of the source code is dual licensed under Apache-2.0 WITH
9// LLVM-exception OR LGPL-2.1-or-later. Detailed license information
10// governing the source code and code contributions can be found in
11// LICENSE.md and CONTRIBUTING.md at the top level directory of deal.II.
12//
13// ------------------------------------------------------------------------
14
15
17
18#include <deal.II/fe/fe_face.h>
20#include <deal.II/fe/fe_poly_face.templates.h>
21#include <deal.II/fe/fe_tools.h>
22
24
25#include <memory>
26#include <sstream>
27
29
30
31namespace internal
32{
33 namespace FE_FaceQImplementation
34 {
35 namespace
36 {
37 std::vector<Point<1>>
38 get_QGaussLobatto_points(const unsigned int degree)
39 {
40 if (degree > 0)
41 return QGaussLobatto<1>(degree + 1).get_points();
42 else
43 return std::vector<Point<1>>(1, Point<1>(0.5));
44 }
45 } // namespace
46 } // namespace FE_FaceQImplementation
47} // namespace internal
48
49template <int dim, int spacedim>
50FE_FaceQ<dim, spacedim>::FE_FaceQ(const unsigned int degree)
51 : FE_PolyFace<TensorProductPolynomials<dim - 1>, dim, spacedim>(
53 Polynomials::generate_complete_Lagrange_basis(
54 internal::FE_FaceQImplementation::get_QGaussLobatto_points(degree))),
55 FiniteElementData<dim>(get_dpo_vector(degree),
56 1,
57 degree,
58 FiniteElementData<dim>::L2),
59 std::vector<bool>(1, true))
60{
61 // initialize unit face support points
62 const unsigned int codim = dim - 1;
63 this->unit_face_support_points[0].resize(
64 Utilities::fixed_power<codim>(this->degree + 1));
65
66 if (this->degree == 0)
67 for (unsigned int d = 0; d < codim; ++d)
68 this->unit_face_support_points[0][0][d] = 0.5;
69 else
70 {
71 std::vector<Point<1>> points =
72 internal::FE_FaceQImplementation::get_QGaussLobatto_points(degree);
73
74 unsigned int k = 0;
75 for (unsigned int iz = 0; iz <= ((codim > 2) ? this->degree : 0); ++iz)
76 for (unsigned int iy = 0; iy <= ((codim > 1) ? this->degree : 0); ++iy)
77 for (unsigned int ix = 0; ix <= this->degree; ++ix)
78 {
80
81 p[0] = points[ix][0];
82 if (codim > 1)
83 p[1] = points[iy][0];
84 if (codim > 2)
85 p[2] = points[iz][0];
86
87 this->unit_face_support_points[0][k++] = p;
88 }
90 }
91
92 // initialize unit support points (this makes it possible to assign initial
93 // values to FE_FaceQ)
96 const unsigned int n_face_dofs = this->unit_face_support_points[0].size();
97 for (unsigned int i = 0; i < n_face_dofs; ++i)
98 for (unsigned int d = 0; d < dim; ++d)
99 {
100 for (unsigned int e = 0, c = 0; e < dim; ++e)
101 if (d != e)
102 {
103 // faces in y-direction are oriented differently
104 unsigned int renumber = i;
105 if (dim == 3 && d == 1)
106 renumber = i / (degree + 1) + (degree + 1) * (i % (degree + 1));
107 this->unit_support_points[n_face_dofs * 2 * d + i][e] =
108 this->unit_face_support_points[0][renumber][c];
109 this->unit_support_points[n_face_dofs * (2 * d + 1) + i][e] =
110 this->unit_face_support_points[0][renumber][c];
111 this->unit_support_points[n_face_dofs * (2 * d + 1) + i][d] = 1;
112 ++c;
113 }
114 }
115}
116
117
118
119template <int dim, int spacedim>
120std::unique_ptr<FiniteElement<dim, spacedim>>
122{
123 return std::make_unique<FE_FaceQ<dim, spacedim>>(this->degree);
124}
125
126
127
128template <int dim, int spacedim>
129std::string
131{
132 // note that the FETools::get_fe_by_name function depends on the
133 // particular format of the string this function returns, so they have to be
134 // kept in synch
135 std::ostringstream namebuf;
136 namebuf << "FE_FaceQ<" << Utilities::dim_string(dim, spacedim) << ">("
137 << this->degree << ")";
138
139 return namebuf.str();
140}
141
142
143
144template <int dim, int spacedim>
145void
147 const FiniteElement<dim, spacedim> &source_fe,
148 FullMatrix<double> &interpolation_matrix,
149 const unsigned int face_no) const
150{
151 get_subface_interpolation_matrix(source_fe,
153 interpolation_matrix,
154 face_no);
155}
156
157
158
159template <int dim, int spacedim>
160void
162 const FiniteElement<dim, spacedim> &x_source_fe,
163 const unsigned int subface,
164 FullMatrix<double> &interpolation_matrix,
165 const unsigned int face_no) const
166{
167 // this function is similar to the respective method in FE_Q
168
169 Assert(interpolation_matrix.n() == this->n_dofs_per_face(face_no),
170 ExcDimensionMismatch(interpolation_matrix.n(),
171 this->n_dofs_per_face(face_no)));
172 Assert(interpolation_matrix.m() == x_source_fe.n_dofs_per_face(face_no),
173 ExcDimensionMismatch(interpolation_matrix.m(),
174 x_source_fe.n_dofs_per_face(face_no)));
175
176 // see if source is a FaceQ element
177 if (const FE_FaceQ<dim, spacedim> *source_fe =
178 dynamic_cast<const FE_FaceQ<dim, spacedim> *>(&x_source_fe))
179 {
180 // Make sure that the element for which the DoFs should be constrained
181 // is the one with the higher polynomial degree. Actually the procedure
182 // will work also if this assertion is not satisfied. But the matrices
183 // produced in that case might lead to problems in the hp-procedures,
184 // which use this method.
185 Assert(
186 this->n_dofs_per_face(face_no) <= source_fe->n_dofs_per_face(face_no),
187 (typename FiniteElement<dim,
188 spacedim>::ExcInterpolationNotImplemented()));
189
190 // generate a quadrature with the unit face support points.
191 const Quadrature<dim - 1> face_quadrature(
192 source_fe->get_unit_face_support_points(face_no));
193
194 // Rule of thumb for FP accuracy, that can be expected for a given
195 // polynomial degree. This value is used to cut off values close to
196 // zero.
197 const double eps = 2e-13 * (this->degree + 1) * (dim - 1);
198
199 // compute the interpolation matrix by simply taking the value at the
200 // support points.
201 for (unsigned int i = 0; i < source_fe->n_dofs_per_face(face_no); ++i)
202 {
203 const Point<dim - 1> p =
205 face_quadrature.point(i) :
207 face_quadrature.point(i), subface);
208
209 for (unsigned int j = 0; j < this->n_dofs_per_face(face_no); ++j)
210 {
211 double matrix_entry = this->poly_space.compute_value(j, p);
212
213 // Correct the interpolated value. I.e. if it is close to 1 or 0,
214 // make it exactly 1 or 0. Unfortunately, this is required to
215 // avoid problems with higher order elements.
216 if (std::fabs(matrix_entry - 1.0) < eps)
217 matrix_entry = 1.0;
218 if (std::fabs(matrix_entry) < eps)
219 matrix_entry = 0.0;
220
221 interpolation_matrix(i, j) = matrix_entry;
222 }
223 }
224
225#ifdef DEBUG
226 // make sure that the row sum of each of the matrices is 1 at this
227 // point. this must be so since the shape functions sum up to 1
228 for (unsigned int j = 0; j < source_fe->n_dofs_per_face(face_no); ++j)
229 {
230 double sum = 0.;
231
232 for (unsigned int i = 0; i < this->n_dofs_per_face(face_no); ++i)
233 sum += interpolation_matrix(j, i);
234
235 Assert(std::fabs(sum - 1) < eps, ExcInternalError());
236 }
237#endif
238 }
239 else if (dynamic_cast<const FE_Nothing<dim> *>(&x_source_fe) != nullptr)
240 {
241 // nothing to do here, the FE_Nothing has no degrees of freedom anyway
242 }
243 else
245 false,
246 (typename FiniteElement<dim,
247 spacedim>::ExcInterpolationNotImplemented()));
248}
249
250
251
252template <int dim, int spacedim>
253bool
255 const unsigned int shape_index,
256 const unsigned int face_index) const
257{
258 return (face_index == (shape_index / this->n_dofs_per_face(face_index)));
259}
260
261
262
263template <int dim, int spacedim>
264std::vector<unsigned int>
266{
267 std::vector<unsigned int> dpo(dim + 1, 0U);
268 dpo[dim - 1] = deg + 1;
269 for (unsigned int i = 1; i < dim - 1; ++i)
270 dpo[dim - 1] *= deg + 1;
271 return dpo;
272}
273
274
275
276template <int dim, int spacedim>
277bool
282
283
284
285template <int dim, int spacedim>
286std::vector<std::pair<unsigned int, unsigned int>>
288 const FiniteElement<dim, spacedim> & /*fe_other*/) const
289{
290 // this element is always discontinuous at vertices
291 return std::vector<std::pair<unsigned int, unsigned int>>();
292}
293
294
295
296template <int dim, int spacedim>
297std::vector<std::pair<unsigned int, unsigned int>>
299 const FiniteElement<dim, spacedim> &fe_other) const
300{
301 Assert(dim >= 2, ExcInternalError());
302
303 // this element is continuous only for the highest dimensional bounding object
304 if (dim > 2)
305 return std::vector<std::pair<unsigned int, unsigned int>>();
306 else
307 {
308 // this is similar to the FE_Q_Base class
309 if (const FE_FaceQ<dim, spacedim> *fe_q_other =
310 dynamic_cast<const FE_FaceQ<dim, spacedim> *>(&fe_other))
311 {
312 // dofs are located along lines, so two dofs are identical if they are
313 // located at identical positions.
314 // Therefore, read the points in unit_support_points for the
315 // first coordinate direction. We take the lexicographic ordering of
316 // the points in the second direction (i.e., y-direction) since we
317 // know that the first p+1 dofs are located at the left (x=0) face.
318 const unsigned int p = this->degree;
319 const unsigned int q = fe_q_other->degree;
320
321 std::vector<std::pair<unsigned int, unsigned int>> identities;
322
323 const std::vector<unsigned int> &index_map_inverse =
324 this->poly_space.get_numbering_inverse();
325 const std::vector<unsigned int> &index_map_inverse_other =
326 fe_q_other->poly_space.get_numbering_inverse();
327
328 for (unsigned int i = 0; i < p + 1; ++i)
329 for (unsigned int j = 0; j < q + 1; ++j)
330 if (std::fabs(
331 this->unit_support_points[index_map_inverse[i]][dim - 1] -
332 fe_q_other->unit_support_points[index_map_inverse_other[j]]
333 [dim - 1]) < 1e-14)
334 identities.emplace_back(i, j);
335
336 return identities;
337 }
338 else if (dynamic_cast<const FE_Nothing<dim> *>(&fe_other) != nullptr)
339 {
340 // the FE_Nothing has no degrees of freedom, so there are no
341 // equivalencies to be recorded
342 return std::vector<std::pair<unsigned int, unsigned int>>();
343 }
344 else if (fe_other.n_unique_faces() == 1 &&
345 fe_other.n_dofs_per_face(0) == 0)
346 {
347 // if the other element has no elements on faces at all,
348 // then it would be impossible to enforce any kind of
349 // continuity even if we knew exactly what kind of element
350 // we have -- simply because the other element declares
351 // that it is discontinuous because it has no DoFs on
352 // its faces. in that case, just state that we have no
353 // constraints to declare
354 return std::vector<std::pair<unsigned int, unsigned int>>();
355 }
356 else
357 {
359 return std::vector<std::pair<unsigned int, unsigned int>>();
360 }
361 }
362}
363
364
365
366template <int dim, int spacedim>
367std::vector<std::pair<unsigned int, unsigned int>>
369 const FiniteElement<dim, spacedim> &fe_other,
370 const unsigned int) const
371{
372 Assert(dim >= 3, ExcInternalError());
373
374 // this element is continuous only for the highest dimensional bounding object
375 if (dim > 3)
376 return std::vector<std::pair<unsigned int, unsigned int>>();
377 else
378 {
379 // this is similar to the FE_Q_Base class
380 if (const FE_FaceQ<dim, spacedim> *fe_q_other =
381 dynamic_cast<const FE_FaceQ<dim, spacedim> *>(&fe_other))
382 {
383 // this works exactly like the line case above, except that now we
384 // have to have two indices i1, i2 and j1, j2 to characterize the dofs
385 // on the face of each of the finite elements. since they are ordered
386 // lexicographically along the first line and we have a tensor
387 // product, the rest is rather straightforward
388 const unsigned int p = this->degree;
389 const unsigned int q = fe_q_other->degree;
390
391 std::vector<std::pair<unsigned int, unsigned int>> identities;
392
393 const std::vector<unsigned int> &index_map_inverse =
394 this->poly_space.get_numbering_inverse();
395 const std::vector<unsigned int> &index_map_inverse_other =
396 fe_q_other->poly_space.get_numbering_inverse();
397
398 std::vector<std::pair<unsigned int, unsigned int>> identities_1d;
399
400 for (unsigned int i = 0; i < p + 1; ++i)
401 for (unsigned int j = 0; j < q + 1; ++j)
402 if (std::fabs(
403 this->unit_support_points[index_map_inverse[i]][dim - 2] -
404 fe_q_other->unit_support_points[index_map_inverse_other[j]]
405 [dim - 2]) < 1e-14)
406 identities_1d.emplace_back(i, j);
407
408 for (unsigned int n1 = 0; n1 < identities_1d.size(); ++n1)
409 for (unsigned int n2 = 0; n2 < identities_1d.size(); ++n2)
410 identities.emplace_back(identities_1d[n1].first * (p + 1) +
411 identities_1d[n2].first,
412 identities_1d[n1].second * (q + 1) +
413 identities_1d[n2].second);
414
415 return identities;
416 }
417 else if (dynamic_cast<const FE_Nothing<dim> *>(&fe_other) != nullptr)
418 {
419 // the FE_Nothing has no degrees of freedom, so there are no
420 // equivalencies to be recorded
421 return std::vector<std::pair<unsigned int, unsigned int>>();
422 }
423 else if (fe_other.n_unique_faces() == 1 &&
424 fe_other.n_dofs_per_face(0) == 0)
425 {
426 // if the other element has no elements on faces at all,
427 // then it would be impossible to enforce any kind of
428 // continuity even if we knew exactly what kind of element
429 // we have -- simply because the other element declares
430 // that it is discontinuous because it has no DoFs on
431 // its faces. in that case, just state that we have no
432 // constraints to declare
433 return std::vector<std::pair<unsigned int, unsigned int>>();
434 }
435 else
436 {
438 return std::vector<std::pair<unsigned int, unsigned int>>();
439 }
440 }
441}
442
443
444
445template <int dim, int spacedim>
448 const FiniteElement<dim, spacedim> &fe_other,
449 const unsigned int codim) const
450{
451 Assert(codim <= dim, ExcImpossibleInDim(dim));
452
453 // vertex/line/face/cell domination
454 // --------------------------------
455 if (const FE_FaceQ<dim, spacedim> *fe_faceq_other =
456 dynamic_cast<const FE_FaceQ<dim, spacedim> *>(&fe_other))
457 {
458 if (this->degree < fe_faceq_other->degree)
460 else if (this->degree == fe_faceq_other->degree)
462 else
464 }
465 else if (const FE_Nothing<dim> *fe_nothing =
466 dynamic_cast<const FE_Nothing<dim> *>(&fe_other))
467 {
468 if (fe_nothing->is_dominating())
470 else
471 // the FE_Nothing has no degrees of freedom and it is typically used
472 // in a context where we don't require any continuity along the
473 // interface
475 }
476
479}
480
481template <int dim, int spacedim>
482std::pair<Table<2, bool>, std::vector<unsigned int>>
484{
485 Table<2, bool> constant_modes(1, this->n_dofs_per_cell());
486 for (unsigned int i = 0; i < this->n_dofs_per_cell(); ++i)
487 constant_modes(0, i) = true;
488 return std::pair<Table<2, bool>, std::vector<unsigned int>>(
489 constant_modes, std::vector<unsigned int>(1, 0));
490}
491
492template <int dim, int spacedim>
493void
495 const std::vector<Vector<double>> &support_point_values,
496 std::vector<double> &nodal_values) const
497{
498 AssertDimension(support_point_values.size(),
499 this->get_unit_support_points().size());
500 AssertDimension(support_point_values.size(), nodal_values.size());
501 AssertDimension(this->n_dofs_per_cell(), nodal_values.size());
502
503 for (unsigned int i = 0; i < this->n_dofs_per_cell(); ++i)
504 {
505 AssertDimension(support_point_values[i].size(), 1);
506
507 nodal_values[i] = support_point_values[i](0);
508 }
509}
510
511// ----------------------------- FE_FaceQ<1,spacedim> ------------------------
512
513template <int spacedim>
514FE_FaceQ<1, spacedim>::FE_FaceQ(const unsigned int degree)
515 : FiniteElement<1, spacedim>(
516 FiniteElementData<1>(get_dpo_vector(degree),
517 1,
518 degree,
519 FiniteElementData<1>::L2),
520 std::vector<bool>(1, true),
521 std::vector<ComponentMask>(1, ComponentMask(1, true)))
522{
523 this->unit_face_support_points[0].resize(1);
524
525 // initialize unit support points (this makes it possible to assign initial
526 // values to FE_FaceQ)
528 this->unit_support_points[1] = Point<1>(1.);
529}
530
531
532
533template <int spacedim>
534std::unique_ptr<FiniteElement<1, spacedim>>
536{
537 return std::make_unique<FE_FaceQ<1, spacedim>>(this->degree);
538}
539
540
541
542template <int spacedim>
543std::string
545{
546 // note that the FETools::get_fe_by_name function depends on the
547 // particular format of the string this function returns, so they have to be
548 // kept in synch
549 std::ostringstream namebuf;
550 namebuf << "FE_FaceQ<" << Utilities::dim_string(1, spacedim) << ">("
551 << this->degree << ")";
552
553 return namebuf.str();
554}
555
556
557
558template <int spacedim>
559void
561 const FiniteElement<1, spacedim> &source_fe,
562 FullMatrix<double> &interpolation_matrix,
563 const unsigned int face_no) const
564{
565 get_subface_interpolation_matrix(source_fe,
567 interpolation_matrix,
568 face_no);
569}
570
571
572
573template <int spacedim>
574void
576 const FiniteElement<1, spacedim> &x_source_fe,
577 const unsigned int /*subface*/,
578 FullMatrix<double> &interpolation_matrix,
579 const unsigned int face_no) const
580{
581 Assert(interpolation_matrix.n() == this->n_dofs_per_face(face_no),
582 ExcDimensionMismatch(interpolation_matrix.n(),
583 this->n_dofs_per_face(face_no)));
584 Assert(interpolation_matrix.m() == x_source_fe.n_dofs_per_face(face_no),
585 ExcDimensionMismatch(interpolation_matrix.m(),
586 x_source_fe.n_dofs_per_face(face_no)));
587 interpolation_matrix(0, 0) = 1.;
588}
589
590
591
592template <int spacedim>
593bool
594FE_FaceQ<1, spacedim>::has_support_on_face(const unsigned int shape_index,
595 const unsigned int face_index) const
596{
597 AssertIndexRange(shape_index, 2);
598 return (face_index == shape_index);
599}
600
601
602
603template <int spacedim>
604std::vector<unsigned int>
606{
607 std::vector<unsigned int> dpo(2, 0U);
608 dpo[0] = 1;
609 return dpo;
610}
611
612
613
614template <int spacedim>
615bool
620
621template <int spacedim>
622std::vector<std::pair<unsigned int, unsigned int>>
624 const FiniteElement<1, spacedim> & /*fe_other*/) const
625{
626 // this element is always discontinuous at vertices
627 return std::vector<std::pair<unsigned int, unsigned int>>(1,
628 std::make_pair(0U,
629 0U));
630}
631
632
633
634template <int spacedim>
635std::vector<std::pair<unsigned int, unsigned int>>
637 const FiniteElement<1, spacedim> &) const
638{
639 // this element is continuous only for the highest dimensional bounding object
640 return std::vector<std::pair<unsigned int, unsigned int>>();
641}
642
643
644
645template <int spacedim>
646std::vector<std::pair<unsigned int, unsigned int>>
649 const unsigned int) const
650{
651 // this element is continuous only for the highest dimensional bounding object
652 return std::vector<std::pair<unsigned int, unsigned int>>();
653}
654
655
656
657template <int spacedim>
658std::pair<Table<2, bool>, std::vector<unsigned int>>
660{
661 Table<2, bool> constant_modes(1, this->n_dofs_per_cell());
662 for (unsigned int i = 0; i < this->n_dofs_per_cell(); ++i)
663 constant_modes(0, i) = true;
664 return std::pair<Table<2, bool>, std::vector<unsigned int>>(
665 constant_modes, std::vector<unsigned int>(1, 0));
666}
667
668
669
670template <int spacedim>
684
685
686template <int spacedim>
687void
691 const Quadrature<1> &,
692 const Mapping<1, spacedim> &,
697 spacedim>
698 &) const
699{
700 // Do nothing, since we do not have values in the interior
701}
702
703
704
705template <int spacedim>
706void
709 const unsigned int face,
710 const hp::QCollection<0> &,
711 const Mapping<1, spacedim> &,
714 const typename FiniteElement<1, spacedim>::InternalDataBase &fe_internal,
716 spacedim>
717 &output_data) const
718{
719 const unsigned int foffset = face;
720 if (fe_internal.update_each & update_values)
721 {
722 for (unsigned int k = 0; k < this->n_dofs_per_cell(); ++k)
723 output_data.shape_values(k, 0) = 0.;
724 output_data.shape_values(foffset, 0) = 1;
725 }
726}
727
728
729template <int spacedim>
730void
733 const unsigned int,
734 const unsigned int,
735 const Quadrature<0> &,
736 const Mapping<1, spacedim> &,
741 spacedim>
742 &) const
743{
744 Assert(false, ExcMessage("There are no sub-face values to fill in 1d!"));
745}
746
747
748
749// --------------------------------------- FE_FaceP --------------------------
750
751template <int dim, int spacedim>
752FE_FaceP<dim, spacedim>::FE_FaceP(const unsigned int degree)
753 : FE_PolyFace<PolynomialSpace<dim - 1>, dim, spacedim>(
754 PolynomialSpace<dim - 1>(
755 Polynomials::Legendre::generate_complete_basis(degree)),
756 FiniteElementData<dim>(get_dpo_vector(degree),
757 1,
758 degree,
759 FiniteElementData<dim>::L2),
760 std::vector<bool>(1, true))
761{}
762
763
764
765template <int dim, int spacedim>
766std::unique_ptr<FiniteElement<dim, spacedim>>
768{
769 return std::make_unique<FE_FaceP<dim, spacedim>>(this->degree);
770}
771
772
773
774template <int dim, int spacedim>
775std::string
777{
778 // note that the FETools::get_fe_by_name function depends on the
779 // particular format of the string this function returns, so they have to be
780 // kept in synch
781 std::ostringstream namebuf;
782 namebuf << "FE_FaceP<" << Utilities::dim_string(dim, spacedim) << ">("
783 << this->degree << ")";
784
785 return namebuf.str();
786}
787
788
789
790template <int dim, int spacedim>
791bool
793 const unsigned int shape_index,
794 const unsigned int face_index) const
795{
796 return (face_index == (shape_index / this->n_dofs_per_face(face_index)));
797}
798
799
800
801template <int dim, int spacedim>
802std::vector<unsigned int>
804{
805 std::vector<unsigned int> dpo(dim + 1, 0U);
806 dpo[dim - 1] = deg + 1;
807 for (unsigned int i = 1; i < dim - 1; ++i)
808 {
809 dpo[dim - 1] *= deg + 1 + i;
810 dpo[dim - 1] /= i + 1;
811 }
812 return dpo;
813}
814
815
816
817template <int dim, int spacedim>
818bool
823
824
825
826template <int dim, int spacedim>
829 const FiniteElement<dim, spacedim> &fe_other,
830 const unsigned int codim) const
831{
832 Assert(codim <= dim, ExcImpossibleInDim(dim));
833
834 // vertex/line/face/cell domination
835 // --------------------------------
836 if (const FE_FaceP<dim, spacedim> *fe_facep_other =
837 dynamic_cast<const FE_FaceP<dim, spacedim> *>(&fe_other))
838 {
839 if (this->degree < fe_facep_other->degree)
841 else if (this->degree == fe_facep_other->degree)
843 else
845 }
846 else if (const FE_Nothing<dim> *fe_nothing =
847 dynamic_cast<const FE_Nothing<dim> *>(&fe_other))
848 {
849 if (fe_nothing->is_dominating())
851 else
852 // the FE_Nothing has no degrees of freedom and it is typically used
853 // in a context where we don't require any continuity along the
854 // interface
856 }
857
860}
861
862
863
864template <int dim, int spacedim>
865void
867 const FiniteElement<dim, spacedim> &source_fe,
868 FullMatrix<double> &interpolation_matrix,
869 const unsigned int face_no) const
870{
871 get_subface_interpolation_matrix(source_fe,
873 interpolation_matrix,
874 face_no);
875}
876
877
878
879template <int dim, int spacedim>
880void
882 const FiniteElement<dim, spacedim> &x_source_fe,
883 const unsigned int subface,
884 FullMatrix<double> &interpolation_matrix,
885 const unsigned int face_no) const
886{
887 // this function is similar to the respective method in FE_Q
888
889 Assert(interpolation_matrix.n() == this->n_dofs_per_face(face_no),
890 ExcDimensionMismatch(interpolation_matrix.n(),
891 this->n_dofs_per_face(face_no)));
892 Assert(interpolation_matrix.m() == x_source_fe.n_dofs_per_face(face_no),
893 ExcDimensionMismatch(interpolation_matrix.m(),
894 x_source_fe.n_dofs_per_face(face_no)));
895
896 // see if source is a FaceP element
897 if (const FE_FaceP<dim, spacedim> *source_fe =
898 dynamic_cast<const FE_FaceP<dim, spacedim> *>(&x_source_fe))
899 {
900 // Make sure that the element for which the DoFs should be constrained
901 // is the one with the higher polynomial degree. Actually the procedure
902 // will work also if this assertion is not satisfied. But the matrices
903 // produced in that case might lead to problems in the hp-procedures,
904 // which use this method.
905 Assert(
906 this->n_dofs_per_face(face_no) <= source_fe->n_dofs_per_face(face_no),
907 (typename FiniteElement<dim,
908 spacedim>::ExcInterpolationNotImplemented()));
909
910 // do this as in FETools by solving a least squares problem where we
911 // force the source FE polynomial to be equal the given FE on all
912 // quadrature points
913 const QGauss<dim - 1> face_quadrature(source_fe->degree + 1);
914
915 // Rule of thumb for FP accuracy, that can be expected for a given
916 // polynomial degree. This value is used to cut off values close to
917 // zero.
918 const double eps = 2e-13 * (this->degree + 1) * (dim - 1);
919
920 FullMatrix<double> mass(face_quadrature.size(),
921 source_fe->n_dofs_per_face(face_no));
922
923 for (unsigned int k = 0; k < face_quadrature.size(); ++k)
924 {
925 const Point<dim - 1> p =
927 face_quadrature.point(k) :
929 face_quadrature.point(k), subface);
930
931 for (unsigned int j = 0; j < source_fe->n_dofs_per_face(face_no); ++j)
932 mass(k, j) = source_fe->poly_space.compute_value(j, p);
933 }
934
935 Householder<double> H(mass);
936 Vector<double> v_in(face_quadrature.size());
937 Vector<double> v_out(source_fe->n_dofs_per_face(face_no));
938
939
940 // compute the interpolation matrix by evaluating on the fine side and
941 // then solving the least squares problem
942 for (unsigned int i = 0; i < this->n_dofs_per_face(face_no); ++i)
943 {
944 for (unsigned int k = 0; k < face_quadrature.size(); ++k)
945 {
946 const Point<dim - 1> p =
948 face_quadrature.point(k) :
950 face_quadrature.point(k), subface);
951 v_in(k) = this->poly_space.compute_value(i, p);
952 }
953 [[maybe_unused]] const double result = H.least_squares(v_out, v_in);
954 Assert(result < 1e-12, FETools::ExcLeastSquaresError(result));
955
956 for (unsigned int j = 0; j < source_fe->n_dofs_per_face(face_no); ++j)
957 {
958 double matrix_entry = v_out(j);
959
960 // Correct the interpolated value. I.e. if it is close to 1 or 0,
961 // make it exactly 1 or 0. Unfortunately, this is required to
962 // avoid problems with higher order elements.
963 if (std::fabs(matrix_entry - 1.0) < eps)
964 matrix_entry = 1.0;
965 if (std::fabs(matrix_entry) < eps)
966 matrix_entry = 0.0;
967
968 interpolation_matrix(j, i) = matrix_entry;
969 }
970 }
971 }
972 else if (dynamic_cast<const FE_Nothing<dim> *>(&x_source_fe) != nullptr)
973 {
974 // nothing to do here, the FE_Nothing has no degrees of freedom anyway
975 }
976 else
978 false,
979 (typename FiniteElement<dim,
980 spacedim>::ExcInterpolationNotImplemented()));
981}
982
983
984
985template <int dim, int spacedim>
986std::pair<Table<2, bool>, std::vector<unsigned int>>
988{
989 Table<2, bool> constant_modes(1, this->n_dofs_per_cell());
990 for (const unsigned int face : GeometryInfo<dim>::face_indices())
991 constant_modes(0, face * this->n_dofs_per_face(face)) = true;
992 return std::pair<Table<2, bool>, std::vector<unsigned int>>(
993 constant_modes, std::vector<unsigned int>(1, 0));
994}
995
996
997
998template <int spacedim>
999FE_FaceP<1, spacedim>::FE_FaceP(const unsigned int degree)
1000 : FE_FaceQ<1, spacedim>(degree)
1001{}
1002
1003
1004
1005template <int spacedim>
1006std::string
1008{
1009 // note that the FETools::get_fe_by_name function depends on the
1010 // particular format of the string this function returns, so they have to be
1011 // kept in synch
1012 std::ostringstream namebuf;
1013 namebuf << "FE_FaceP<" << Utilities::dim_string(1, spacedim) << ">("
1014 << this->degree << ")";
1015
1016 return namebuf.str();
1017}
1018
1019
1020
1021// explicit instantiations
1022#include "fe_face.inst"
1023
1024
virtual std::pair< Table< 2, bool >, std::vector< unsigned int > > get_constant_modes() const override
Definition fe_face.cc:987
virtual bool hp_constraints_are_implemented() const override
Definition fe_face.cc:819
virtual bool has_support_on_face(const unsigned int shape_index, const unsigned int face_index) const override
Definition fe_face.cc:792
virtual FiniteElementDomination::Domination compare_for_domination(const FiniteElement< dim, spacedim > &fe_other, const unsigned int codim=0) const override final
Definition fe_face.cc:828
virtual std::string get_name() const override
Definition fe_face.cc:776
static std::vector< unsigned int > get_dpo_vector(const unsigned int deg)
Definition fe_face.cc:803
virtual void get_subface_interpolation_matrix(const FiniteElement< dim, spacedim > &source, const unsigned int subface, FullMatrix< double > &matrix, const unsigned int face_no=0) const override
Definition fe_face.cc:881
virtual std::unique_ptr< FiniteElement< dim, spacedim > > clone() const override
Definition fe_face.cc:767
FE_FaceP(unsigned int p)
Definition fe_face.cc:752
virtual void get_face_interpolation_matrix(const FiniteElement< dim, spacedim > &source, FullMatrix< double > &matrix, const unsigned int face_no=0) const override
Definition fe_face.cc:866
virtual FiniteElementDomination::Domination compare_for_domination(const FiniteElement< dim, spacedim > &fe_other, const unsigned int codim=0) const override final
Definition fe_face.cc:447
virtual std::string get_name() const override
Definition fe_face.cc:130
static std::vector< unsigned int > get_dpo_vector(const unsigned int deg)
Definition fe_face.cc:265
virtual void convert_generalized_support_point_values_to_dof_values(const std::vector< Vector< double > > &support_point_values, std::vector< double > &nodal_values) const override
Definition fe_face.cc:494
virtual std::pair< Table< 2, bool >, std::vector< unsigned int > > get_constant_modes() const override
Definition fe_face.cc:483
virtual void get_face_interpolation_matrix(const FiniteElement< dim, spacedim > &source, FullMatrix< double > &matrix, const unsigned int face_no=0) const override
Definition fe_face.cc:146
virtual std::vector< std::pair< unsigned int, unsigned int > > hp_line_dof_identities(const FiniteElement< dim, spacedim > &fe_other) const override
Definition fe_face.cc:298
FE_FaceQ(const unsigned int p)
Definition fe_face.cc:50
virtual std::unique_ptr< FiniteElement< dim, spacedim > > clone() const override
Definition fe_face.cc:121
virtual void get_subface_interpolation_matrix(const FiniteElement< dim, spacedim > &source, const unsigned int subface, FullMatrix< double > &matrix, const unsigned int face_no=0) const override
Definition fe_face.cc:161
virtual bool has_support_on_face(const unsigned int shape_index, const unsigned int face_index) const override
Definition fe_face.cc:254
virtual std::vector< std::pair< unsigned int, unsigned int > > hp_vertex_dof_identities(const FiniteElement< dim, spacedim > &fe_other) const override
Definition fe_face.cc:287
virtual std::vector< std::pair< unsigned int, unsigned int > > hp_quad_dof_identities(const FiniteElement< dim, spacedim > &fe_other, const unsigned int face_no=0) const override
Definition fe_face.cc:368
virtual bool hp_constraints_are_implemented() const override
Definition fe_face.cc:278
const unsigned int degree
Definition fe_data.h:452
unsigned int n_dofs_per_face(unsigned int face_no=0, unsigned int child=0) const
unsigned int n_unique_faces() const
virtual void fill_fe_values(const typename Triangulation< dim, spacedim >::cell_iterator &cell, const CellSimilarity::Similarity cell_similarity, const Quadrature< dim > &quadrature, const Mapping< dim, spacedim > &mapping, const typename Mapping< dim, spacedim >::InternalDataBase &mapping_internal, const internal::FEValuesImplementation::MappingRelatedData< dim, spacedim > &mapping_data, const InternalDataBase &fe_internal, ::internal::FEValuesImplementation::FiniteElementRelatedData< dim, spacedim > &output_data) const =0
std::vector< std::vector< Point< dim - 1 > > > unit_face_support_points
Definition fe.h:2495
virtual void fill_fe_face_values(const typename Triangulation< dim, spacedim >::cell_iterator &cell, const unsigned int face_no, const hp::QCollection< dim - 1 > &quadrature, const Mapping< dim, spacedim > &mapping, const typename Mapping< dim, spacedim >::InternalDataBase &mapping_internal, const internal::FEValuesImplementation::MappingRelatedData< dim, spacedim > &mapping_data, const InternalDataBase &fe_internal, ::internal::FEValuesImplementation::FiniteElementRelatedData< dim, spacedim > &output_data) const
virtual void fill_fe_subface_values(const typename Triangulation< dim, spacedim >::cell_iterator &cell, const unsigned int face_no, const unsigned int sub_no, const Quadrature< dim - 1 > &quadrature, const Mapping< dim, spacedim > &mapping, const typename Mapping< dim, spacedim >::InternalDataBase &mapping_internal, const internal::FEValuesImplementation::MappingRelatedData< dim, spacedim > &mapping_data, const InternalDataBase &fe_internal, ::internal::FEValuesImplementation::FiniteElementRelatedData< dim, spacedim > &output_data) const =0
virtual UpdateFlags requires_update_flags(const UpdateFlags update_flags) const =0
std::vector< Point< dim > > unit_support_points
Definition fe.h:2488
size_type n() const
size_type m() const
double least_squares(Vector< number2 > &dst, const Vector< number2 > &src) const
Abstract base class for mapping classes.
Definition mapping.h:318
Definition point.h:111
#define DEAL_II_NAMESPACE_OPEN
Definition config.h:498
#define DEAL_II_NAMESPACE_CLOSE
Definition config.h:499
Point< 2 > second
Definition grid_out.cc:4630
#define Assert(cond, exc)
static ::ExceptionBase & ExcLeastSquaresError(double arg1)
static ::ExceptionBase & ExcImpossibleInDim(int arg1)
#define AssertDimension(dim1, dim2)
#define AssertIndexRange(index, range)
static ::ExceptionBase & ExcInternalError()
static ::ExceptionBase & ExcDimensionMismatch(std::size_t arg1, std::size_t arg2)
static ::ExceptionBase & ExcMessage(std::string arg1)
#define AssertThrow(cond, exc)
UpdateFlags
@ update_hessians
Second derivatives of shape functions.
@ update_values
Shape function values.
@ update_normal_vectors
Normal vectors.
@ update_JxW_values
Transformed quadrature weights.
@ update_covariant_transformation
Covariant transformation.
@ update_gradients
Shape function gradients.
#define DEAL_II_NOT_IMPLEMENTED()
std::size_t size
Definition mpi.cc:734
std::string dim_string(const int dim, const int spacedim)
Definition utilities.cc:555
static const unsigned int invalid_unsigned_int
Definition types.h:220
STL namespace.
static std_cxx20::ranges::iota_view< unsigned int, unsigned int > face_indices()
static Point< dim > child_to_cell_coordinates(const Point< dim > &p, const unsigned int child_index, const RefinementCase< dim > refine_case=RefinementCase< dim >::isotropic_refinement)