Reference documentation for deal.II version 9.5.0
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dof_tools_constraints.cc
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1// ---------------------------------------------------------------------
2//
3// Copyright (C) 1999 - 2023 by the deal.II authors
4//
5// This file is part of the deal.II library.
6//
7// The deal.II library is free software; you can use it, redistribute
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.
13//
14// ---------------------------------------------------------------------
15
16#include <deal.II/base/table.h>
17#include <deal.II/base/template_constraints.h>
18#include <deal.II/base/utilities.h>
19#include <deal.II/base/work_stream.h>
20
21#include <deal.II/dofs/dof_accessor.h>
22#include <deal.II/dofs/dof_handler.h>
23#include <deal.II/dofs/dof_tools.h>
24
25#include <deal.II/fe/fe.h>
26#include <deal.II/fe/fe_tools.h>
27#include <deal.II/fe/fe_values.h>
28
29#include <deal.II/grid/filtered_iterator.h>
30#include <deal.II/grid/grid_tools.h>
31#include <deal.II/grid/intergrid_map.h>
32#include <deal.II/grid/tria.h>
33#include <deal.II/grid/tria_iterator.h>
34
35#include <deal.II/hp/fe_collection.h>
36#include <deal.II/hp/fe_values.h>
37
38#include <deal.II/lac/affine_constraints.h>
39#include <deal.II/lac/vector.h>
40
41#ifdef DEAL_II_WITH_MPI
42# include <deal.II/lac/la_parallel_vector.h>
43#endif
44
45#include <algorithm>
46#include <array>
47#include <memory>
48#include <numeric>
49
50DEAL_II_NAMESPACE_OPEN
51
52
53
54namespace DoFTools
55{
56 namespace internal
57 {
58 namespace
59 {
60 inline bool
61 check_primary_dof_list(
62 const FullMatrix<double> & face_interpolation_matrix,
63 const std::vector<types::global_dof_index> &primary_dof_list)
64 {
65 const unsigned int N = primary_dof_list.size();
66
67 FullMatrix<double> tmp(N, N);
68 for (unsigned int i = 0; i < N; ++i)
69 for (unsigned int j = 0; j < N; ++j)
70 tmp(i, j) = face_interpolation_matrix(primary_dof_list[i], j);
71
72 // then use the algorithm from FullMatrix::gauss_jordan on this matrix
73 // to find out whether it is singular. the algorithm there does pivoting
74 // and at the end swaps rows back into their proper order -- we omit
75 // this step here, since we don't care about the inverse matrix, all we
76 // care about is whether the matrix is regular or singular
77
78 // first get an estimate of the size of the elements of this matrix, for
79 // later checks whether the pivot element is large enough, or whether we
80 // have to fear that the matrix is not regular
81 double diagonal_sum = 0;
82 for (unsigned int i = 0; i < N; ++i)
83 diagonal_sum += std::fabs(tmp(i, i));
84 const double typical_diagonal_element = diagonal_sum / N;
85
86 // initialize the array that holds the permutations that we find during
87 // pivot search
88 std::vector<unsigned int> p(N);
89 for (unsigned int i = 0; i < N; ++i)
90 p[i] = i;
91
92 for (unsigned int j = 0; j < N; ++j)
93 {
94 // pivot search: search that part of the line on and right of the
95 // diagonal for the largest element
96 double max = std::fabs(tmp(j, j));
97 unsigned int r = j;
98 for (unsigned int i = j + 1; i < N; ++i)
99 {
100 if (std::fabs(tmp(i, j)) > max)
101 {
102 max = std::fabs(tmp(i, j));
103 r = i;
104 }
105 }
106 // check whether the pivot is too small. if that is the case, then
107 // the matrix is singular and we shouldn't use this set of primary
108 // dofs
109 if (max < 1.e-12 * typical_diagonal_element)
110 return false;
111
112 // row interchange
113 if (r > j)
114 {
115 for (unsigned int k = 0; k < N; ++k)
116 std::swap(tmp(j, k), tmp(r, k));
117
118 std::swap(p[j], p[r]);
119 }
120
121 // transformation
122 const double hr = 1. / tmp(j, j);
123 tmp(j, j) = hr;
124 for (unsigned int k = 0; k < N; ++k)
125 {
126 if (k == j)
127 continue;
128 for (unsigned int i = 0; i < N; ++i)
129 {
130 if (i == j)
131 continue;
132 tmp(i, k) -= tmp(i, j) * tmp(j, k) * hr;
133 }
134 }
135 for (unsigned int i = 0; i < N; ++i)
136 {
137 tmp(i, j) *= hr;
138 tmp(j, i) *= -hr;
139 }
140 tmp(j, j) = hr;
141 }
142
143 // everything went fine, so we can accept this set of primary dofs (at
144 // least as far as they have already been collected)
145 return true;
146 }
147
148
149
171 template <int dim, int spacedim>
172 void
173 select_primary_dofs_for_face_restriction(
174 const FiniteElement<dim, spacedim> &fe1,
175 const FiniteElement<dim, spacedim> &fe2,
176 const FullMatrix<double> & face_interpolation_matrix,
177 std::vector<bool> & primary_dof_mask)
178 {
179 // TODO: the implementation makes the assumption that all faces have the
180 // same number of dofs
181 AssertDimension(fe1.n_unique_faces(), 1);
182 AssertDimension(fe2.n_unique_faces(), 1);
183 const unsigned int face_no = 0;
184 (void)face_no;
185
186 Assert(fe1.n_dofs_per_face(face_no) >= fe2.n_dofs_per_face(face_no),
187 ExcInternalError());
188 AssertDimension(primary_dof_mask.size(), fe1.n_dofs_per_face(face_no));
189
190 Assert(fe2.n_dofs_per_vertex() <= fe1.n_dofs_per_vertex(),
191 ExcInternalError());
192 Assert(fe2.n_dofs_per_line() <= fe1.n_dofs_per_line(),
193 ExcInternalError());
194 Assert((dim < 3) ||
195 (fe2.n_dofs_per_quad(face_no) <= fe1.n_dofs_per_quad(face_no)),
196 ExcInternalError());
197
198 // the idea here is to designate as many DoFs in fe1 per object (vertex,
199 // line, quad) as primary as there are such dofs in fe2 (indices are
200 // int, because we want to avoid the 'unsigned int < 0 is always false
201 // warning for the cases at the bottom in 1d and 2d)
202 //
203 // as mentioned in the paper, it is not always easy to find a set of
204 // primary dofs that produces an invertible matrix. to this end, we
205 // check in each step whether the matrix is still invertible and simply
206 // discard this dof if the matrix is not invertible anymore.
207 //
208 // the cases where we did have trouble in the past were with adding more
209 // quad dofs when Q3 and Q4 elements meet at a refined face in 3d (see
210 // the hp/crash_12 test that tests that we can do exactly this, and
211 // failed before we had code to compensate for this case). the other
212 // case are system elements: if we have say a Q1Q2 vs a Q2Q3 element,
213 // then we can't just take all primary dofs on a line from a single base
214 // element, since the shape functions of that base element are
215 // independent of that of the other one. this latter case shows up when
216 // running hp/hp_constraints_q_system_06
217
218 std::vector<types::global_dof_index> primary_dof_list;
219 unsigned int index = 0;
220 for (int v = 0;
221 v < static_cast<signed int>(GeometryInfo<dim>::vertices_per_face);
222 ++v)
223 {
224 unsigned int dofs_added = 0;
225 unsigned int i = 0;
226 while (dofs_added < fe2.n_dofs_per_vertex())
227 {
228 // make sure that we were able to find a set of primary dofs and
229 // that the code down below didn't just reject all our efforts
230 Assert(i < fe1.n_dofs_per_vertex(), ExcInternalError());
231
232 // tentatively push this vertex dof
233 primary_dof_list.push_back(index + i);
234
235 // then see what happens. if it succeeds, fine
236 if (check_primary_dof_list(face_interpolation_matrix,
237 primary_dof_list) == true)
238 ++dofs_added;
239 else
240 // well, it didn't. simply pop that dof from the list again
241 // and try with the next dof
242 primary_dof_list.pop_back();
243
244 // forward counter by one
245 ++i;
246 }
247 index += fe1.n_dofs_per_vertex();
248 }
249
250 for (int l = 0;
251 l < static_cast<signed int>(GeometryInfo<dim>::lines_per_face);
252 ++l)
253 {
254 // same algorithm as above
255 unsigned int dofs_added = 0;
256 unsigned int i = 0;
257 while (dofs_added < fe2.n_dofs_per_line())
258 {
259 Assert(i < fe1.n_dofs_per_line(), ExcInternalError());
260
261 primary_dof_list.push_back(index + i);
262 if (check_primary_dof_list(face_interpolation_matrix,
263 primary_dof_list) == true)
264 ++dofs_added;
265 else
266 primary_dof_list.pop_back();
267
268 ++i;
269 }
270 index += fe1.n_dofs_per_line();
271 }
272
273 for (int q = 0;
274 q < static_cast<signed int>(GeometryInfo<dim>::quads_per_face);
275 ++q)
276 {
277 // same algorithm as above
278 unsigned int dofs_added = 0;
279 unsigned int i = 0;
280 while (dofs_added < fe2.n_dofs_per_quad(q))
281 {
282 Assert(i < fe1.n_dofs_per_quad(q), ExcInternalError());
283
284 primary_dof_list.push_back(index + i);
285 if (check_primary_dof_list(face_interpolation_matrix,
286 primary_dof_list) == true)
287 ++dofs_added;
288 else
289 primary_dof_list.pop_back();
290
291 ++i;
292 }
293 index += fe1.n_dofs_per_quad(q);
294 }
295
296 AssertDimension(index, fe1.n_dofs_per_face(face_no));
297 AssertDimension(primary_dof_list.size(), fe2.n_dofs_per_face(face_no));
298
299 // finally copy the list into the mask
300 std::fill(primary_dof_mask.begin(), primary_dof_mask.end(), false);
301 for (const auto dof : primary_dof_list)
302 primary_dof_mask[dof] = true;
303 }
304
305
306
311 template <int dim, int spacedim>
312 void
313 ensure_existence_of_primary_dof_mask(
314 const FiniteElement<dim, spacedim> &fe1,
315 const FiniteElement<dim, spacedim> &fe2,
316 const FullMatrix<double> & face_interpolation_matrix,
317 std::unique_ptr<std::vector<bool>> &primary_dof_mask)
318 {
319 // TODO: the implementation makes the assumption that all faces have the
320 // same number of dofs
321 AssertDimension(fe1.n_unique_faces(), 1);
322 AssertDimension(fe2.n_unique_faces(), 1);
323 const unsigned int face_no = 0;
324
325 if (primary_dof_mask == nullptr)
326 {
327 primary_dof_mask =
328 std::make_unique<std::vector<bool>>(fe1.n_dofs_per_face(face_no));
329 select_primary_dofs_for_face_restriction(fe1,
330 fe2,
331 face_interpolation_matrix,
332 *primary_dof_mask);
333 }
334 }
335
336
337
343 template <int dim, int spacedim>
344 void
345 ensure_existence_of_face_matrix(
346 const FiniteElement<dim, spacedim> & fe1,
347 const FiniteElement<dim, spacedim> & fe2,
348 std::unique_ptr<FullMatrix<double>> &matrix)
349 {
350 // TODO: the implementation makes the assumption that all faces have the
351 // same number of dofs
352 AssertDimension(fe1.n_unique_faces(), 1);
353 AssertDimension(fe2.n_unique_faces(), 1);
354 const unsigned int face_no = 0;
355
356 if (matrix == nullptr)
357 {
358 matrix = std::make_unique<FullMatrix<double>>(
359 fe2.n_dofs_per_face(face_no), fe1.n_dofs_per_face(face_no));
360 fe1.get_face_interpolation_matrix(fe2, *matrix, face_no);
361 }
362 }
363
364
365
369 template <int dim, int spacedim>
370 void
371 ensure_existence_of_subface_matrix(
372 const FiniteElement<dim, spacedim> & fe1,
373 const FiniteElement<dim, spacedim> & fe2,
374 const unsigned int subface,
375 std::unique_ptr<FullMatrix<double>> &matrix)
376 {
377 // TODO: the implementation makes the assumption that all faces have the
378 // same number of dofs
379 AssertDimension(fe1.n_unique_faces(), 1);
380 AssertDimension(fe2.n_unique_faces(), 1);
381 const unsigned int face_no = 0;
382
383 if (matrix == nullptr)
384 {
385 matrix = std::make_unique<FullMatrix<double>>(
386 fe2.n_dofs_per_face(face_no), fe1.n_dofs_per_face(face_no));
387 fe1.get_subface_interpolation_matrix(fe2,
388 subface,
389 *matrix,
390 face_no);
391 }
392 }
393
394
395
401 void
402 ensure_existence_of_split_face_matrix(
403 const FullMatrix<double> &face_interpolation_matrix,
404 const std::vector<bool> & primary_dof_mask,
405 std::unique_ptr<std::pair<FullMatrix<double>, FullMatrix<double>>>
406 &split_matrix)
407 {
408 AssertDimension(primary_dof_mask.size(), face_interpolation_matrix.m());
409 Assert(std::count(primary_dof_mask.begin(),
410 primary_dof_mask.end(),
411 true) ==
412 static_cast<signed int>(face_interpolation_matrix.n()),
413 ExcInternalError());
414
415 if (split_matrix == nullptr)
416 {
417 split_matrix = std::make_unique<
418 std::pair<FullMatrix<double>, FullMatrix<double>>>();
419
420 const unsigned int n_primary_dofs = face_interpolation_matrix.n();
421 const unsigned int n_dofs = face_interpolation_matrix.m();
422
423 Assert(n_primary_dofs <= n_dofs, ExcInternalError());
424
425 // copy and invert the primary component, copy the dependent
426 // component
427 split_matrix->first.reinit(n_primary_dofs, n_primary_dofs);
428 split_matrix->second.reinit(n_dofs - n_primary_dofs,
429 n_primary_dofs);
430
431 unsigned int nth_primary_dof = 0, nth_dependent_dof = 0;
432
433 for (unsigned int i = 0; i < n_dofs; ++i)
434 if (primary_dof_mask[i] == true)
435 {
436 for (unsigned int j = 0; j < n_primary_dofs; ++j)
437 split_matrix->first(nth_primary_dof, j) =
438 face_interpolation_matrix(i, j);
439 ++nth_primary_dof;
440 }
441 else
442 {
443 for (unsigned int j = 0; j < n_primary_dofs; ++j)
444 split_matrix->second(nth_dependent_dof, j) =
445 face_interpolation_matrix(i, j);
446 ++nth_dependent_dof;
447 }
448
449 AssertDimension(nth_primary_dof, n_primary_dofs);
450 AssertDimension(nth_dependent_dof, n_dofs - n_primary_dofs);
451
452 // TODO[WB]: We should make sure very small entries are removed
453 // after inversion
454 split_matrix->first.gauss_jordan();
455 }
456 }
457
458
464 template <int dim, int spacedim>
465 unsigned int
466 n_finite_elements(const DoFHandler<dim, spacedim> &dof_handler)
467 {
468 if (dof_handler.has_hp_capabilities() == true)
469 return dof_handler.get_fe_collection().size();
470 else
471 return 1;
472 }
473
474
475
486 template <typename number1, typename number2>
487 void
488 filter_constraints(
489 const std::vector<types::global_dof_index> &primary_dofs,
490 const std::vector<types::global_dof_index> &dependent_dofs,
491 const FullMatrix<number1> & face_constraints,
492 AffineConstraints<number2> & constraints)
493 {
494 Assert(face_constraints.n() == primary_dofs.size(),
495 ExcDimensionMismatch(primary_dofs.size(), face_constraints.n()));
496 Assert(face_constraints.m() == dependent_dofs.size(),
497 ExcDimensionMismatch(dependent_dofs.size(),
498 face_constraints.m()));
499
500 const unsigned int n_primary_dofs = primary_dofs.size();
501 const unsigned int n_dependent_dofs = dependent_dofs.size();
502
503 // check for a couple conditions that happened in parallel distributed
504 // mode
505 for (unsigned int row = 0; row != n_dependent_dofs; ++row)
506 Assert(dependent_dofs[row] != numbers::invalid_dof_index,
507 ExcInternalError());
508 for (unsigned int col = 0; col != n_primary_dofs; ++col)
509 Assert(primary_dofs[col] != numbers::invalid_dof_index,
510 ExcInternalError());
511
512
513 for (unsigned int row = 0; row != n_dependent_dofs; ++row)
514 if (constraints.is_constrained(dependent_dofs[row]) == false)
515 {
516 // Check if we have an identity constraint, i.e.,
517 // something of the form
518 // U(dependent_dof[row])==U(primary_dof[row]),
519 // where
520 // dependent_dof[row] == primary_dof[row].
521 // This can happen in the hp context where we have previously
522 // unified DoF indices, for example, the middle node on the
523 // face of a Q4 element will have gotten the same index
524 // as the middle node of the Q2 element on the neighbor
525 // cell. But because the other Q4 nodes will still have to be
526 // constrained, so the middle node shows up again here.
527 //
528 // If we find such a constraint, then it is trivially
529 // satisfied, and we can move on to the next dependent
530 // DoF (row). The only thing we should make sure is that the
531 // row of the matrix really just contains this one entry.
532 {
533 bool is_trivial_constraint = false;
534
535 for (unsigned int i = 0; i < n_primary_dofs; ++i)
536 if (face_constraints(row, i) == 1.0)
537 if (dependent_dofs[row] == primary_dofs[i])
538 {
539 is_trivial_constraint = true;
540
541 for (unsigned int ii = 0; ii < n_primary_dofs; ++ii)
542 if (ii != i)
543 Assert(face_constraints(row, ii) == 0.0,
544 ExcInternalError());
545
546 break;
547 }
548
549 if (is_trivial_constraint == true)
550 continue;
551 }
552 // add up the absolute values of all constraints in this line
553 // to get a measure of their absolute size
554 number1 abs_sum = 0;
555 for (unsigned int i = 0; i < n_primary_dofs; ++i)
556 abs_sum += std::abs(face_constraints(row, i));
557
558 // then enter those constraints that are larger than
559 // 1e-14*abs_sum. everything else probably originated from
560 // inexact inversion of matrices and similar effects. having
561 // those constraints in here will only lead to problems
562 // because it makes sparsity patterns fuller than necessary
563 // without producing any significant effect
564 constraints.add_line(dependent_dofs[row]);
565 for (unsigned int i = 0; i < n_primary_dofs; ++i)
566 if ((face_constraints(row, i) != 0) &&
567 (std::fabs(face_constraints(row, i)) >= 1e-14 * abs_sum))
568 constraints.add_entry(dependent_dofs[row],
569 primary_dofs[i],
570 face_constraints(row, i));
571 constraints.set_inhomogeneity(dependent_dofs[row], 0.);
572 }
573 }
574
575 } // namespace
576
577
578 template <typename number>
579 void
580 make_hp_hanging_node_constraints(const DoFHandler<1> &,
581 AffineConstraints<number> &)
582 {
583 // nothing to do for regular dof handlers in 1d
584 }
585
586
587 template <typename number>
588 void
589 make_oldstyle_hanging_node_constraints(const DoFHandler<1> &,
590 AffineConstraints<number> &,
591 std::integral_constant<int, 1>)
592 {
593 // nothing to do for regular dof handlers in 1d
594 }
595
596
597 template <typename number>
598 void
599 make_hp_hanging_node_constraints(const DoFHandler<1, 2> &,
600 AffineConstraints<number> &)
601 {
602 // nothing to do for regular dof handlers in 1d
603 }
604
605
606 template <typename number>
607 void
608 make_oldstyle_hanging_node_constraints(const DoFHandler<1, 2> &,
609 AffineConstraints<number> &,
610 std::integral_constant<int, 1>)
611 {
612 // nothing to do for regular dof handlers in 1d
613 }
614
615
616 template <typename number, int spacedim>
617 void
618 make_hp_hanging_node_constraints(
619 const DoFHandler<1, spacedim> & /*dof_handler*/,
620 AffineConstraints<number> & /*constraints*/)
621 {
622 // nothing to do for dof handlers in 1d
623 }
624
625
626 template <typename number, int spacedim>
627 void
628 make_oldstyle_hanging_node_constraints(
629 const DoFHandler<1, spacedim> & /*dof_handler*/,
630 AffineConstraints<number> & /*constraints*/,
631 std::integral_constant<int, 1>)
632 {
633 // nothing to do for dof handlers in 1d
634 }
635
636 template <int dim_, int spacedim, typename number>
637 void
638 make_oldstyle_hanging_node_constraints(
639 const DoFHandler<dim_, spacedim> &dof_handler,
640 AffineConstraints<number> & constraints,
641 std::integral_constant<int, 2>)
642 {
643 const unsigned int dim = 2;
644
645 std::vector<types::global_dof_index> dofs_on_mother;
646 std::vector<types::global_dof_index> dofs_on_children;
647
648 // loop over all lines; only on lines there can be constraints. We do so
649 // by looping over all active cells and checking whether any of the faces
650 // are refined which can only be from the neighboring cell because this
651 // one is active. In that case, the face is subject to constraints
652 //
653 // note that even though we may visit a face twice if the neighboring
654 // cells are equally refined, we can only visit each face with hanging
655 // nodes once
656 typename DoFHandler<dim_, spacedim>::active_cell_iterator
657 cell = dof_handler.begin_active(),
658 endc = dof_handler.end();
659 for (; cell != endc; ++cell)
660 {
661 // artificial cells can at best neighbor ghost cells, but we're not
662 // interested in these interfaces
663 if (cell->is_artificial())
664 continue;
665
666 for (const unsigned int face : cell->face_indices())
667 if (cell->face(face)->has_children())
668 {
669 // in any case, faces can have at most two active FE indices,
670 // but here the face can have only one (namely the same as that
671 // from the cell we're sitting on), and each of the children can
672 // have only one as well. check this
673 Assert(cell->face(face)->n_active_fe_indices() == 1,
674 ExcInternalError());
675 Assert(cell->face(face)->fe_index_is_active(
676 cell->active_fe_index()) == true,
677 ExcInternalError());
678 for (unsigned int c = 0; c < cell->face(face)->n_children();
679 ++c)
680 if (!cell->neighbor_child_on_subface(face, c)
681 ->is_artificial())
682 Assert(cell->face(face)->child(c)->n_active_fe_indices() ==
683 1,
684 ExcInternalError());
685
686 // right now, all that is implemented is the case that both
687 // sides use the same FE
688 for (unsigned int c = 0; c < cell->face(face)->n_children();
689 ++c)
690 if (!cell->neighbor_child_on_subface(face, c)
691 ->is_artificial())
692 Assert(cell->face(face)->child(c)->fe_index_is_active(
693 cell->active_fe_index()) == true,
694 ExcNotImplemented());
695
696 // ok, start up the work
697 const FiniteElement<dim, spacedim> &fe = cell->get_fe();
698 const types::fe_index fe_index = cell->active_fe_index();
699
700 const unsigned int n_dofs_on_mother =
701 2 * fe.n_dofs_per_vertex() +
702 fe.n_dofs_per_line(),
703 n_dofs_on_children =
704 fe.n_dofs_per_vertex() +
705 2 * fe.n_dofs_per_line();
706
707 dofs_on_mother.resize(n_dofs_on_mother);
708 // we might not use all of those in case of artificial cells, so
709 // do not resize(), but reserve() and use push_back later.
710 dofs_on_children.clear();
711 dofs_on_children.reserve(n_dofs_on_children);
712
713 Assert(n_dofs_on_mother == fe.constraints().n(),
714 ExcDimensionMismatch(n_dofs_on_mother,
715 fe.constraints().n()));
716 Assert(n_dofs_on_children == fe.constraints().m(),
717 ExcDimensionMismatch(n_dofs_on_children,
718 fe.constraints().m()));
719
720 const typename DoFHandler<dim_, spacedim>::line_iterator
721 this_face = cell->face(face);
722
723 // fill the dofs indices. Use same enumeration scheme as in
724 // @p{FiniteElement::constraints()}
725 unsigned int next_index = 0;
726 for (unsigned int vertex = 0; vertex < 2; ++vertex)
727 for (unsigned int dof = 0; dof != fe.n_dofs_per_vertex();
728 ++dof)
729 dofs_on_mother[next_index++] =
730 this_face->vertex_dof_index(vertex, dof, fe_index);
731 for (unsigned int dof = 0; dof != fe.n_dofs_per_line(); ++dof)
732 dofs_on_mother[next_index++] =
733 this_face->dof_index(dof, fe_index);
734 AssertDimension(next_index, dofs_on_mother.size());
735
736 for (unsigned int dof = 0; dof != fe.n_dofs_per_vertex(); ++dof)
737 dofs_on_children.push_back(
738 this_face->child(0)->vertex_dof_index(1, dof, fe_index));
739 for (unsigned int child = 0; child < 2; ++child)
740 {
741 // skip artificial cells
742 if (cell->neighbor_child_on_subface(face, child)
743 ->is_artificial())
744 continue;
745 for (unsigned int dof = 0; dof != fe.n_dofs_per_line();
746 ++dof)
747 dofs_on_children.push_back(
748 this_face->child(child)->dof_index(dof, fe_index));
749 }
750 // note: can get fewer DoFs when we have artificial cells
751 Assert(dofs_on_children.size() <= n_dofs_on_children,
752 ExcInternalError());
753
754 // for each row in the AffineConstraints object for this line:
755 for (unsigned int row = 0; row != dofs_on_children.size();
756 ++row)
757 {
758 constraints.add_line(dofs_on_children[row]);
759 for (unsigned int i = 0; i != dofs_on_mother.size(); ++i)
760 constraints.add_entry(dofs_on_children[row],
761 dofs_on_mother[i],
762 fe.constraints()(row, i));
763
764 constraints.set_inhomogeneity(dofs_on_children[row], 0.);
765 }
766 }
767 else
768 {
769 // this face has no children, but it could still be that it is
770 // shared by two cells that use a different FE index. check a
771 // couple of things, but ignore the case that the neighbor is an
772 // artificial cell
773 if (!cell->at_boundary(face) &&
774 !cell->neighbor(face)->is_artificial())
775 {
776 Assert(cell->face(face)->n_active_fe_indices() == 1,
777 ExcNotImplemented());
778 Assert(cell->face(face)->fe_index_is_active(
779 cell->active_fe_index()) == true,
780 ExcInternalError());
781 }
782 }
783 }
784 }
785
786
787
788 template <int dim_, int spacedim, typename number>
789 void
790 make_oldstyle_hanging_node_constraints(
791 const DoFHandler<dim_, spacedim> &dof_handler,
792 AffineConstraints<number> & constraints,
793 std::integral_constant<int, 3>)
794 {
795 const unsigned int dim = 3;
796
797 std::vector<types::global_dof_index> dofs_on_mother;
798 std::vector<types::global_dof_index> dofs_on_children;
799
800 // loop over all quads; only on quads there can be constraints. We do so
801 // by looping over all active cells and checking whether any of the faces
802 // are refined which can only be from the neighboring cell because this
803 // one is active. In that case, the face is subject to constraints
804 //
805 // note that even though we may visit a face twice if the neighboring
806 // cells are equally refined, we can only visit each face with hanging
807 // nodes once
808 typename DoFHandler<dim_, spacedim>::active_cell_iterator
809 cell = dof_handler.begin_active(),
810 endc = dof_handler.end();
811 for (; cell != endc; ++cell)
812 {
813 // artificial cells can at best neighbor ghost cells, but we're not
814 // interested in these interfaces
815 if (cell->is_artificial())
816 continue;
817
818 for (const unsigned int face : cell->face_indices())
819 if (cell->face(face)->has_children())
820 {
821 // first of all, make sure that we treat a case which is
822 // possible, i.e. either no dofs on the face at all or no
823 // anisotropic refinement
824 if (cell->get_fe().n_dofs_per_face(face) == 0)
825 continue;
826
827 Assert(cell->face(face)->refinement_case() ==
828 RefinementCase<dim - 1>::isotropic_refinement,
829 ExcNotImplemented());
830
831 // in any case, faces can have at most two active FE indices,
832 // but here the face can have only one (namely the same as that
833 // from the cell we're sitting on), and each of the children can
834 // have only one as well. check this
835 AssertDimension(cell->face(face)->n_active_fe_indices(), 1);
836 Assert(cell->face(face)->fe_index_is_active(
837 cell->active_fe_index()) == true,
838 ExcInternalError());
839 for (unsigned int c = 0; c < cell->face(face)->n_children();
840 ++c)
841 if (!cell->neighbor_child_on_subface(face, c)
842 ->is_artificial())
843 AssertDimension(
844 cell->face(face)->child(c)->n_active_fe_indices(), 1);
845
846 // right now, all that is implemented is the case that both
847 // sides use the same fe, and not only that but also that all
848 // lines bounding this face and the children have the same FE
849 for (unsigned int c = 0; c < cell->face(face)->n_children();
850 ++c)
851 if (!cell->neighbor_child_on_subface(face, c)
852 ->is_artificial())
853 {
854 Assert(cell->face(face)->child(c)->fe_index_is_active(
855 cell->active_fe_index()) == true,
856 ExcNotImplemented());
857 for (unsigned int e = 0; e < 4; ++e)
858 {
859 Assert(cell->face(face)
860 ->child(c)
861 ->line(e)
862 ->n_active_fe_indices() == 1,
863 ExcNotImplemented());
864 Assert(cell->face(face)
865 ->child(c)
866 ->line(e)
867 ->fe_index_is_active(
868 cell->active_fe_index()) == true,
869 ExcNotImplemented());
870 }
871 }
872 for (unsigned int e = 0; e < 4; ++e)
873 {
874 Assert(cell->face(face)->line(e)->n_active_fe_indices() ==
875 1,
876 ExcNotImplemented());
877 Assert(cell->face(face)->line(e)->fe_index_is_active(
878 cell->active_fe_index()) == true,
879 ExcNotImplemented());
880 }
881
882 // ok, start up the work
883 const FiniteElement<dim> &fe = cell->get_fe();
884 const types::fe_index fe_index = cell->active_fe_index();
885
886 const unsigned int n_dofs_on_mother = fe.n_dofs_per_face(face);
887 const unsigned int n_dofs_on_children =
888 (5 * fe.n_dofs_per_vertex() + 12 * fe.n_dofs_per_line() +
889 4 * fe.n_dofs_per_quad(face));
890
891 // TODO[TL]: think about this and the following in case of
892 // anisotropic refinement
893
894 dofs_on_mother.resize(n_dofs_on_mother);
895 // we might not use all of those in case of artificial cells, so
896 // do not resize(), but reserve() and use push_back later.
897 dofs_on_children.clear();
898 dofs_on_children.reserve(n_dofs_on_children);
899
900 Assert(n_dofs_on_mother == fe.constraints().n(),
901 ExcDimensionMismatch(n_dofs_on_mother,
902 fe.constraints().n()));
903 Assert(n_dofs_on_children == fe.constraints().m(),
904 ExcDimensionMismatch(n_dofs_on_children,
905 fe.constraints().m()));
906
907 const typename DoFHandler<dim_, spacedim>::face_iterator
908 this_face = cell->face(face);
909
910 // fill the dofs indices. Use same enumeration scheme as in
911 // @p{FiniteElement::constraints()}
912 unsigned int next_index = 0;
913 for (unsigned int vertex = 0; vertex < 4; ++vertex)
914 for (unsigned int dof = 0; dof != fe.n_dofs_per_vertex();
915 ++dof)
916 dofs_on_mother[next_index++] =
917 this_face->vertex_dof_index(vertex, dof, fe_index);
918 for (unsigned int line = 0; line < 4; ++line)
919 for (unsigned int dof = 0; dof != fe.n_dofs_per_line(); ++dof)
920 dofs_on_mother[next_index++] =
921 this_face->line(line)->dof_index(dof, fe_index);
922 for (unsigned int dof = 0; dof != fe.n_dofs_per_quad(face);
923 ++dof)
924 dofs_on_mother[next_index++] =
925 this_face->dof_index(dof, fe_index);
926 AssertDimension(next_index, dofs_on_mother.size());
927
928 // TODO: assert some consistency assumptions
929
930 // TODO[TL]: think about this in case of anisotropic refinement
931
932 Assert(dof_handler.get_triangulation()
933 .get_anisotropic_refinement_flag() ||
934 ((this_face->child(0)->vertex_index(3) ==
935 this_face->child(1)->vertex_index(2)) &&
936 (this_face->child(0)->vertex_index(3) ==
937 this_face->child(2)->vertex_index(1)) &&
938 (this_face->child(0)->vertex_index(3) ==
939 this_face->child(3)->vertex_index(0))),
940 ExcInternalError());
941
942 for (unsigned int dof = 0; dof != fe.n_dofs_per_vertex(); ++dof)
943 dofs_on_children.push_back(
944 this_face->child(0)->vertex_dof_index(3, dof));
945
946 // dof numbers on the centers of the lines bounding this face
947 for (unsigned int line = 0; line < 4; ++line)
948 for (unsigned int dof = 0; dof != fe.n_dofs_per_vertex();
949 ++dof)
950 dofs_on_children.push_back(
951 this_face->line(line)->child(0)->vertex_dof_index(
952 1, dof, fe_index));
953
954 // next the dofs on the lines interior to the face; the order of
955 // these lines is laid down in the FiniteElement class
956 // documentation
957 for (unsigned int dof = 0; dof < fe.n_dofs_per_line(); ++dof)
958 dofs_on_children.push_back(
959 this_face->child(0)->line(1)->dof_index(dof, fe_index));
960 for (unsigned int dof = 0; dof < fe.n_dofs_per_line(); ++dof)
961 dofs_on_children.push_back(
962 this_face->child(2)->line(1)->dof_index(dof, fe_index));
963 for (unsigned int dof = 0; dof < fe.n_dofs_per_line(); ++dof)
964 dofs_on_children.push_back(
965 this_face->child(0)->line(3)->dof_index(dof, fe_index));
966 for (unsigned int dof = 0; dof < fe.n_dofs_per_line(); ++dof)
967 dofs_on_children.push_back(
968 this_face->child(1)->line(3)->dof_index(dof, fe_index));
969
970 // dofs on the bordering lines
971 for (unsigned int line = 0; line < 4; ++line)
972 for (unsigned int child = 0; child < 2; ++child)
973 {
974 for (unsigned int dof = 0; dof != fe.n_dofs_per_line();
975 ++dof)
976 dofs_on_children.push_back(
977 this_face->line(line)->child(child)->dof_index(
978 dof, fe_index));
979 }
980
981 // finally, for the dofs interior to the four child faces
982 for (unsigned int child = 0; child < 4; ++child)
983 {
984 // skip artificial cells
985 if (cell->neighbor_child_on_subface(face, child)
986 ->is_artificial())
987 continue;
988 for (unsigned int dof = 0; dof != fe.n_dofs_per_quad(face);
989 ++dof)
990 dofs_on_children.push_back(
991 this_face->child(child)->dof_index(dof, fe_index));
992 }
993
994 // note: can get fewer DoFs when we have artificial cells:
995 Assert(dofs_on_children.size() <= n_dofs_on_children,
996 ExcInternalError());
997
998 // for each row in the AffineConstraints object for this line:
999 for (unsigned int row = 0; row != dofs_on_children.size();
1000 ++row)
1001 {
1002 constraints.add_line(dofs_on_children[row]);
1003 for (unsigned int i = 0; i != dofs_on_mother.size(); ++i)
1004 constraints.add_entry(dofs_on_children[row],
1005 dofs_on_mother[i],
1006 fe.constraints()(row, i));
1007
1008 constraints.set_inhomogeneity(dofs_on_children[row], 0.);
1009 }
1010 }
1011 else
1012 {
1013 // this face has no children, but it could still be that it is
1014 // shared by two cells that use a different FE index. check a
1015 // couple of things, but ignore the case that the neighbor is an
1016 // artificial cell
1017 if (!cell->at_boundary(face) &&
1018 !cell->neighbor(face)->is_artificial())
1019 {
1020 Assert(cell->face(face)->n_active_fe_indices() == 1,
1021 ExcNotImplemented());
1022 Assert(cell->face(face)->fe_index_is_active(
1023 cell->active_fe_index()) == true,
1024 ExcInternalError());
1025 }
1026 }
1027 }
1028 }
1029
1030
1031
1032 template <int dim, int spacedim, typename number>
1033 void
1034 make_hp_hanging_node_constraints(
1035 const DoFHandler<dim, spacedim> &dof_handler,
1036 AffineConstraints<number> & constraints)
1037 {
1038 // note: this function is going to be hard to understand if you haven't
1039 // read the hp-paper. however, we try to follow the notation laid out
1040 // there, so go read the paper before you try to understand what is going
1041 // on here
1042
1043
1044 // a matrix to be used for constraints below. declared here and simply
1045 // resized down below to avoid permanent re-allocation of memory
1046 FullMatrix<double> constraint_matrix;
1047
1048 // similarly have arrays that will hold primary and dependent dof numbers,
1049 // as well as a scratch array needed for the complicated case below
1050 std::vector<types::global_dof_index> primary_dofs;
1051 std::vector<types::global_dof_index> dependent_dofs;
1052 std::vector<types::global_dof_index> scratch_dofs;
1053
1054 // caches for the face and subface interpolation matrices between
1055 // different (or the same) finite elements. we compute them only once,
1056 // namely the first time they are needed, and then just reuse them
1057 Table<2, std::unique_ptr<FullMatrix<double>>> face_interpolation_matrices(
1058 n_finite_elements(dof_handler), n_finite_elements(dof_handler));
1059 Table<3, std::unique_ptr<FullMatrix<double>>>
1060 subface_interpolation_matrices(
1061 n_finite_elements(dof_handler),
1062 n_finite_elements(dof_handler),
1063 GeometryInfo<dim>::max_children_per_face);
1064
1065 // similarly have a cache for the matrices that are split into their
1066 // primary and dependent parts, and for which the primary part is
1067 // inverted. these two matrices are derived from the face interpolation
1068 // matrix
1069 // as described in the @ref hp_paper "hp-paper"
1070 Table<2,
1071 std::unique_ptr<std::pair<FullMatrix<double>, FullMatrix<double>>>>
1072 split_face_interpolation_matrices(n_finite_elements(dof_handler),
1073 n_finite_elements(dof_handler));
1074
1075 // finally, for each pair of finite elements, have a mask that states
1076 // which of the degrees of freedom on the coarse side of a refined face
1077 // will act as primary dofs.
1078 Table<2, std::unique_ptr<std::vector<bool>>> primary_dof_masks(
1079 n_finite_elements(dof_handler), n_finite_elements(dof_handler));
1080
1081 // loop over all faces
1082 //
1083 // note that even though we may visit a face twice if the neighboring
1084 // cells are equally refined, we can only visit each face with hanging
1085 // nodes once
1086 for (const auto &cell : dof_handler.active_cell_iterators())
1087 {
1088 // artificial cells can at best neighbor ghost cells, but we're not
1089 // interested in these interfaces
1090 if (cell->is_artificial())
1091 continue;
1092
1093 for (const unsigned int face : cell->face_indices())
1094 if (cell->face(face)->has_children())
1095 {
1096 // first of all, make sure that we treat a case which is
1097 // possible, i.e. either no dofs on the face at all or no
1098 // anisotropic refinement
1099 if (cell->get_fe().n_dofs_per_face(face) == 0)
1100 continue;
1101
1102 Assert(cell->face(face)->refinement_case() ==
1103 RefinementCase<dim - 1>::isotropic_refinement,
1104 ExcNotImplemented());
1105
1106 // so now we've found a face of an active cell that has
1107 // children. that means that there are hanging nodes here.
1108
1109 // in any case, faces can have at most two sets of active FE
1110 // indices, but here the face can have only one (namely the same
1111 // as that from the cell we're sitting on), and each of the
1112 // children can have only one as well. check this
1113 Assert(cell->face(face)->n_active_fe_indices() == 1,
1114 ExcInternalError());
1115 Assert(cell->face(face)->fe_index_is_active(
1116 cell->active_fe_index()) == true,
1117 ExcInternalError());
1118 for (unsigned int c = 0; c < cell->face(face)->n_children();
1119 ++c)
1120 if (!cell->neighbor_child_on_subface(face, c)
1121 ->is_artificial())
1122 Assert(cell->face(face)->child(c)->n_active_fe_indices() ==
1123 1,
1124 ExcInternalError());
1125
1126 // first find out whether we can constrain each of the subfaces
1127 // to the mother face. in the lingo of the hp-paper, this would
1128 // be the simple case. note that we can short-circuit this
1129 // decision if the dof_handler doesn't support hp at all
1130 //
1131 // ignore all interfaces with artificial cells
1132 FiniteElementDomination::Domination mother_face_dominates =
1133 FiniteElementDomination::either_element_can_dominate;
1134
1135 // auxiliary variable which holds FE indices of the mother face
1136 // and its subfaces. This knowledge will be needed in hp-case
1137 // with neither_element_dominates.
1138 std::set<types::fe_index> fe_ind_face_subface;
1139 fe_ind_face_subface.insert(cell->active_fe_index());
1140
1141 if (dof_handler.has_hp_capabilities())
1142 for (unsigned int c = 0;
1143 c < cell->face(face)->n_active_descendants();
1144 ++c)
1145 {
1146 const auto subcell =
1147 cell->neighbor_child_on_subface(face, c);
1148 if (!subcell->is_artificial())
1149 {
1150 mother_face_dominates =
1151 mother_face_dominates &
1152 (cell->get_fe().compare_for_domination(
1153 subcell->get_fe(), /*codim=*/1));
1154 fe_ind_face_subface.insert(
1155 subcell->active_fe_index());
1156 }
1157 }
1158
1159 switch (mother_face_dominates)
1160 {
1161 case FiniteElementDomination::this_element_dominates:
1162 case FiniteElementDomination::either_element_can_dominate:
1163 {
1164 // Case 1 (the simple case and the only case that can
1165 // happen for non-hp-DoFHandlers): The coarse element
1166 // dominates the elements on the subfaces (or they are
1167 // all the same)
1168 //
1169 // so we are going to constrain the DoFs on the face
1170 // children against the DoFs on the face itself
1171 primary_dofs.resize(
1172 cell->get_fe().n_dofs_per_face(face));
1173
1174 cell->face(face)->get_dof_indices(
1175 primary_dofs, cell->active_fe_index());
1176
1177 // Now create constraints for the subfaces and
1178 // assemble it. ignore all interfaces with artificial
1179 // cells because we can only get to such interfaces if
1180 // the current cell is a ghost cell
1181 for (unsigned int c = 0;
1182 c < cell->face(face)->n_children();
1183 ++c)
1184 {
1185 if (cell->neighbor_child_on_subface(face, c)
1186 ->is_artificial())
1187 continue;
1188
1189 const typename DoFHandler<dim, spacedim>::
1190 active_face_iterator subface =
1191 cell->face(face)->child(c);
1192
1193 Assert(subface->n_active_fe_indices() == 1,
1194 ExcInternalError());
1195
1196 const types::fe_index subface_fe_index =
1197 subface->nth_active_fe_index(0);
1198
1199 // we sometime run into the situation where for
1200 // example on one big cell we have a FE_Q(1) and on
1201 // the subfaces we have a mixture of FE_Q(1) and
1202 // FE_Nothing. In that case, the face domination is
1203 // either_element_can_dominate for the whole
1204 // collection of subfaces, but on the particular
1205 // subface between FE_Q(1) and FE_Nothing, there are
1206 // no constraints that we need to take care of. in
1207 // that case, just continue
1208 if (cell->get_fe().compare_for_domination(
1209 subface->get_fe(subface_fe_index),
1210 /*codim=*/1) ==
1211 FiniteElementDomination::no_requirements)
1212 continue;
1213
1214 // Same procedure as for the mother cell. Extract
1215 // the face DoFs from the cell DoFs.
1216 dependent_dofs.resize(
1217 subface->get_fe(subface_fe_index)
1218 .n_dofs_per_face(face, c));
1219 subface->get_dof_indices(dependent_dofs,
1220 subface_fe_index);
1221
1222 for (const types::global_dof_index dependent_dof :
1223 dependent_dofs)
1224 {
1225 (void)dependent_dof;
1226 Assert(dependent_dof !=
1227 numbers::invalid_dof_index,
1228 ExcInternalError());
1229 }
1230
1231 // Now create the element constraint for this
1232 // subface.
1233 //
1234 // As a side remark, one may wonder the following:
1235 // neighbor_child is clearly computed correctly,
1236 // i.e. taking into account face_orientation (just
1237 // look at the implementation of that function).
1238 // however, we don't care about this here, when we
1239 // ask for subface_interpolation on subface c. the
1240 // question rather is: do we have to translate 'c'
1241 // here as well?
1242 //
1243 // the answer is in fact 'no'. if one does that,
1244 // results are wrong: constraints are added twice
1245 // for the same pair of nodes but with differing
1246 // weights. in addition, one can look at the
1247 // deal.II/project_*_03 tests that look at exactly
1248 // this case: there, we have a mesh with at least
1249 // one face_orientation==false and hanging nodes,
1250 // and the results of those tests show that the
1251 // result of projection verifies the approximation
1252 // properties of a finite element onto that mesh
1253 ensure_existence_of_subface_matrix(
1254 cell->get_fe(),
1255 subface->get_fe(subface_fe_index),
1256 c,
1257 subface_interpolation_matrices
1258 [cell->active_fe_index()][subface_fe_index][c]);
1259
1260 // Add constraints to global AffineConstraints
1261 // object.
1262 filter_constraints(primary_dofs,
1263 dependent_dofs,
1264 *(subface_interpolation_matrices
1265 [cell->active_fe_index()]
1266 [subface_fe_index][c]),
1267 constraints);
1268 } // loop over subfaces
1269
1270 break;
1271 } // Case 1
1272
1273 case FiniteElementDomination::other_element_dominates:
1274 case FiniteElementDomination::neither_element_dominates:
1275 {
1276 // Case 2 (the "complex" case): at least one (the
1277 // neither_... case) of the finer elements or all of
1278 // them (the other_... case) is dominating. See the hp-
1279 // paper for a way how to deal with this situation
1280 //
1281 // since this is something that can only happen for hp-
1282 // dof handlers, add a check here...
1283 Assert(dof_handler.has_hp_capabilities() == true,
1284 ExcInternalError());
1285
1286 const ::hp::FECollection<dim, spacedim>
1287 &fe_collection = dof_handler.get_fe_collection();
1288 // we first have to find the finite element that is able
1289 // to generate a space that all the other ones can be
1290 // constrained to. At this point we potentially have
1291 // different scenarios:
1292 //
1293 // 1) sub-faces dominate mother face and there is a
1294 // dominating FE among sub faces. We could loop over sub
1295 // faces to find the needed FE index. However, this will
1296 // not work in the case when ...
1297 //
1298 // 2) there is no dominating FE among sub faces (e.g.
1299 // Q1xQ2 vs Q2xQ1), but subfaces still dominate mother
1300 // face (e.g. Q2xQ2). To cover this case we would have
1301 // to find the least dominating element amongst all
1302 // finite elements on sub faces.
1303 //
1304 // 3) Finally, it could happen that we got here because
1305 // neither_element_dominates (e.g. Q1xQ1xQ2 and Q1xQ2xQ1
1306 // for subfaces and Q2xQ1xQ1 for mother face). This
1307 // requires finding the least dominating element amongst
1308 // all finite elements on sub faces and the mother face.
1309 //
1310 // Note that the last solution covers the first two
1311 // scenarios, thus we stick with it assuming that we
1312 // won't lose much time/efficiency.
1313 // TODO: Change set to types::fe_index
1314 const types::fe_index dominating_fe_index =
1315 fe_collection.find_dominating_fe_extended(
1316 {fe_ind_face_subface.begin(),
1317 fe_ind_face_subface.end()},
1318 /*codim=*/1);
1319
1320 AssertThrow(
1321 dominating_fe_index != numbers::invalid_fe_index,
1322 ExcMessage(
1323 "Could not find a least face dominating FE."));
1324
1325 const FiniteElement<dim, spacedim> &dominating_fe =
1326 dof_handler.get_fe(dominating_fe_index);
1327
1328 // first get the interpolation matrix from the mother to
1329 // the virtual dofs
1330 Assert(dominating_fe.n_dofs_per_face(face) <=
1331 cell->get_fe().n_dofs_per_face(face),
1332 ExcInternalError());
1333
1334 ensure_existence_of_face_matrix(
1335 dominating_fe,
1336 cell->get_fe(),
1337 face_interpolation_matrices[dominating_fe_index]
1338 [cell->active_fe_index()]);
1339
1340 // split this matrix into primary and dependent
1341 // components. invert the primary component
1342 ensure_existence_of_primary_dof_mask(
1343 cell->get_fe(),
1344 dominating_fe,
1345 (*face_interpolation_matrices
1346 [dominating_fe_index][cell->active_fe_index()]),
1347 primary_dof_masks[dominating_fe_index]
1348 [cell->active_fe_index()]);
1349
1350 ensure_existence_of_split_face_matrix(
1351 *face_interpolation_matrices[dominating_fe_index]
1352 [cell->active_fe_index()],
1353 (*primary_dof_masks[dominating_fe_index]
1354 [cell->active_fe_index()]),
1355 split_face_interpolation_matrices
1356 [dominating_fe_index][cell->active_fe_index()]);
1357
1358 const FullMatrix<double>
1359 &restrict_mother_to_virtual_primary_inv =
1360 (split_face_interpolation_matrices
1361 [dominating_fe_index][cell->active_fe_index()]
1362 ->first);
1363
1364 const FullMatrix<double>
1365 &restrict_mother_to_virtual_dependent =
1366 (split_face_interpolation_matrices
1367 [dominating_fe_index][cell->active_fe_index()]
1368 ->second);
1369
1370 // now compute the constraint matrix as the product
1371 // between the inverse matrix and the dependent part
1372 constraint_matrix.reinit(
1373 cell->get_fe().n_dofs_per_face(face) -
1374 dominating_fe.n_dofs_per_face(face),
1375 dominating_fe.n_dofs_per_face(face));
1376 restrict_mother_to_virtual_dependent.mmult(
1377 constraint_matrix,
1378 restrict_mother_to_virtual_primary_inv);
1379
1380 // then figure out the global numbers of primary and
1381 // dependent dofs and apply constraints
1382 scratch_dofs.resize(
1383 cell->get_fe().n_dofs_per_face(face));
1384 cell->face(face)->get_dof_indices(
1385 scratch_dofs, cell->active_fe_index());
1386
1387 // split dofs into primary and dependent components
1388 primary_dofs.clear();
1389 dependent_dofs.clear();
1390 for (unsigned int i = 0;
1391 i < cell->get_fe().n_dofs_per_face(face);
1392 ++i)
1393 if ((*primary_dof_masks[dominating_fe_index]
1394 [cell
1395 ->active_fe_index()])[i] ==
1396 true)
1397 primary_dofs.push_back(scratch_dofs[i]);
1398 else
1399 dependent_dofs.push_back(scratch_dofs[i]);
1400
1401 AssertDimension(primary_dofs.size(),
1402 dominating_fe.n_dofs_per_face(face));
1403 AssertDimension(dependent_dofs.size(),
1404 cell->get_fe().n_dofs_per_face(face) -
1405 dominating_fe.n_dofs_per_face(face));
1406
1407 filter_constraints(primary_dofs,
1408 dependent_dofs,
1409 constraint_matrix,
1410 constraints);
1411
1412
1413
1414 // next we have to deal with the subfaces. do as
1415 // discussed in the hp-paper
1416 for (unsigned int sf = 0;
1417 sf < cell->face(face)->n_children();
1418 ++sf)
1419 {
1420 // ignore interfaces with artificial cells as well
1421 // as interfaces between ghost cells in 2d
1422 if (cell->neighbor_child_on_subface(face, sf)
1423 ->is_artificial() ||
1424 (dim == 2 && cell->is_ghost() &&
1425 cell->neighbor_child_on_subface(face, sf)
1426 ->is_ghost()))
1427 continue;
1428
1429 Assert(cell->face(face)
1430 ->child(sf)
1431 ->n_active_fe_indices() == 1,
1432 ExcInternalError());
1433
1434 const types::fe_index subface_fe_index =
1435 cell->face(face)->child(sf)->nth_active_fe_index(
1436 0);
1437 const FiniteElement<dim, spacedim> &subface_fe =
1438 dof_handler.get_fe(subface_fe_index);
1439
1440 // first get the interpolation matrix from the
1441 // subface to the virtual dofs
1442 Assert(dominating_fe.n_dofs_per_face(face) <=
1443 subface_fe.n_dofs_per_face(face),
1444 ExcInternalError());
1445 ensure_existence_of_subface_matrix(
1446 dominating_fe,
1447 subface_fe,
1448 sf,
1449 subface_interpolation_matrices
1450 [dominating_fe_index][subface_fe_index][sf]);
1451
1452 const FullMatrix<double>
1453 &restrict_subface_to_virtual = *(
1454 subface_interpolation_matrices
1455 [dominating_fe_index][subface_fe_index][sf]);
1456
1457 constraint_matrix.reinit(
1458 subface_fe.n_dofs_per_face(face),
1459 dominating_fe.n_dofs_per_face(face));
1460
1461 restrict_subface_to_virtual.mmult(
1462 constraint_matrix,
1463 restrict_mother_to_virtual_primary_inv);
1464
1465 dependent_dofs.resize(
1466 subface_fe.n_dofs_per_face(face));
1467 cell->face(face)->child(sf)->get_dof_indices(
1468 dependent_dofs, subface_fe_index);
1469
1470 filter_constraints(primary_dofs,
1471 dependent_dofs,
1472 constraint_matrix,
1473 constraints);
1474 } // loop over subfaces
1475
1476 break;
1477 } // Case 2
1478
1479 case FiniteElementDomination::no_requirements:
1480 // there are no continuity requirements between the two
1481 // elements. record no constraints
1482 break;
1483
1484 default:
1485 // we shouldn't get here
1486 Assert(false, ExcInternalError());
1487 }
1488 }
1489 else
1490 {
1491 // this face has no children, but it could still be that it is
1492 // shared by two cells that use a different FE index
1493 Assert(cell->face(face)->fe_index_is_active(
1494 cell->active_fe_index()) == true,
1495 ExcInternalError());
1496
1497 // see if there is a neighbor that is an artificial cell. in
1498 // that case, we're not interested in this interface. we test
1499 // this case first since artificial cells may not have an
1500 // active FE index set, etc
1501 if (!cell->at_boundary(face) &&
1502 cell->neighbor(face)->is_artificial())
1503 continue;
1504
1505 // Only if there is a neighbor with a different active FE index
1506 // and the same h-level, some action has to be taken.
1507 if ((dof_handler.has_hp_capabilities()) &&
1508 !cell->face(face)->at_boundary() &&
1509 (cell->neighbor(face)->active_fe_index() !=
1510 cell->active_fe_index()) &&
1511 (!cell->face(face)->has_children() &&
1512 !cell->neighbor_is_coarser(face)))
1513 {
1514 const typename DoFHandler<dim,
1515 spacedim>::level_cell_iterator
1516 neighbor = cell->neighbor(face);
1517
1518 // see which side of the face we have to constrain
1519 switch (
1520 cell->get_fe().compare_for_domination(neighbor->get_fe(),
1521 /*codim=*/1))
1522 {
1523 case FiniteElementDomination::this_element_dominates:
1524 {
1525 // Get DoFs on dominating and dominated side of the
1526 // face
1527 primary_dofs.resize(
1528 cell->get_fe().n_dofs_per_face(face));
1529 cell->face(face)->get_dof_indices(
1530 primary_dofs, cell->active_fe_index());
1531
1532 // break if the n_primary_dofs == 0, because we are
1533 // attempting to constrain to an element that has no
1534 // face dofs
1535 if (primary_dofs.size() == 0)
1536 break;
1537
1538 dependent_dofs.resize(
1539 neighbor->get_fe().n_dofs_per_face(face));
1540 cell->face(face)->get_dof_indices(
1541 dependent_dofs, neighbor->active_fe_index());
1542
1543 // make sure the element constraints for this face
1544 // are available
1545 ensure_existence_of_face_matrix(
1546 cell->get_fe(),
1547 neighbor->get_fe(),
1548 face_interpolation_matrices
1549 [cell->active_fe_index()]
1550 [neighbor->active_fe_index()]);
1551
1552 // Add constraints to global constraint matrix.
1553 filter_constraints(
1554 primary_dofs,
1555 dependent_dofs,
1556 *(face_interpolation_matrices
1557 [cell->active_fe_index()]
1558 [neighbor->active_fe_index()]),
1559 constraints);
1560
1561 break;
1562 }
1563
1564 case FiniteElementDomination::other_element_dominates:
1565 {
1566 // we don't do anything here since we will come back
1567 // to this face from the other cell, at which time
1568 // we will fall into the first case clause above
1569 break;
1570 }
1571
1572 case FiniteElementDomination::
1573 either_element_can_dominate:
1574 {
1575 // it appears as if neither element has any
1576 // constraints on its neighbor. this may be because
1577 // neither element has any DoFs on faces at all. or
1578 // that the two elements are actually the same,
1579 // although they happen to run under different
1580 // fe_indices (this is what happens in
1581 // hp/hp_hanging_nodes_01 for example).
1582 //
1583 // another possibility is what happens in crash_13.
1584 // there, we have FESystem(FE_Q(1),FE_DGQ(0)) vs.
1585 // FESystem(FE_Q(1),FE_DGQ(1)). neither of them
1586 // dominates the other.
1587 //
1588 // a final possibility is that we have something
1589 // like FESystem(FE_Q(1),FE_Q(1)) vs
1590 // FESystem(FE_Q(1),FE_Nothing()), see
1591 // hp/fe_nothing_18/19.
1592 //
1593 // in any case, the point is that it doesn't matter.
1594 // there is nothing to do here.
1595 break;
1596 }
1597
1598 case FiniteElementDomination::neither_element_dominates:
1599 {
1600 // make sure we don't get here twice from each cell
1601 if (cell < neighbor)
1602 break;
1603
1604 // our best bet is to find the common space among
1605 // other FEs in FECollection and then constrain both
1606 // FEs to that one. More precisely, we follow the
1607 // strategy outlined on page 17 of the hp-paper:
1608 // First we find the dominant FE space S. Then we
1609 // divide our dofs in primary and dependent such
1610 // that I^{face,primary}_{S^{face}->S} is
1611 // invertible. And finally constrain dependent dofs
1612 // to primary dofs based on the interpolation
1613 // matrix.
1614
1615 const types::fe_index this_fe_index =
1616 cell->active_fe_index();
1617 const types::fe_index neighbor_fe_index =
1618 neighbor->active_fe_index();
1619 std::set<types::fe_index> fes;
1620 fes.insert(this_fe_index);
1621 fes.insert(neighbor_fe_index);
1622 const ::hp::FECollection<dim, spacedim>
1623 &fe_collection = dof_handler.get_fe_collection();
1624
1625 // TODO: Change set to types::fe_index
1626 const types::fe_index dominating_fe_index =
1627 fe_collection.find_dominating_fe_extended(
1628 {fes.begin(), fes.end()}, /*codim=*/1);
1629
1630 AssertThrow(
1631 dominating_fe_index != numbers::invalid_fe_index,
1632 ExcMessage(
1633 "Could not find the dominating FE for " +
1634 cell->get_fe().get_name() + " and " +
1635 neighbor->get_fe().get_name() +
1636 " inside FECollection."));
1637
1638 const FiniteElement<dim, spacedim> &dominating_fe =
1639 fe_collection[dominating_fe_index];
1640
1641 // TODO: until we hit the second face, the code is a
1642 // copy-paste from h-refinement case...
1643
1644 // first get the interpolation matrix from main FE
1645 // to the virtual dofs
1646 Assert(dominating_fe.n_dofs_per_face(face) <=
1647 cell->get_fe().n_dofs_per_face(face),
1648 ExcInternalError());
1649
1650 ensure_existence_of_face_matrix(
1651 dominating_fe,
1652 cell->get_fe(),
1653 face_interpolation_matrices
1654 [dominating_fe_index][cell->active_fe_index()]);
1655
1656 // split this matrix into primary and dependent
1657 // components. invert the primary component
1658 ensure_existence_of_primary_dof_mask(
1659 cell->get_fe(),
1660 dominating_fe,
1661 (*face_interpolation_matrices
1662 [dominating_fe_index]
1663 [cell->active_fe_index()]),
1664 primary_dof_masks[dominating_fe_index]
1665 [cell->active_fe_index()]);
1666
1667 ensure_existence_of_split_face_matrix(
1668 *face_interpolation_matrices
1669 [dominating_fe_index][cell->active_fe_index()],
1670 (*primary_dof_masks[dominating_fe_index]
1671 [cell->active_fe_index()]),
1672 split_face_interpolation_matrices
1673 [dominating_fe_index][cell->active_fe_index()]);
1674
1675 const FullMatrix<
1676 double> &restrict_mother_to_virtual_primary_inv =
1677 (split_face_interpolation_matrices
1678 [dominating_fe_index][cell->active_fe_index()]
1679 ->first);
1680
1681 const FullMatrix<
1682 double> &restrict_mother_to_virtual_dependent =
1683 (split_face_interpolation_matrices
1684 [dominating_fe_index][cell->active_fe_index()]
1685 ->second);
1686
1687 // now compute the constraint matrix as the product
1688 // between the inverse matrix and the dependent part
1689 constraint_matrix.reinit(
1690 cell->get_fe().n_dofs_per_face(face) -
1691 dominating_fe.n_dofs_per_face(face),
1692 dominating_fe.n_dofs_per_face(face));
1693 restrict_mother_to_virtual_dependent.mmult(
1694 constraint_matrix,
1695 restrict_mother_to_virtual_primary_inv);
1696
1697 // then figure out the global numbers of primary and
1698 // dependent dofs and apply constraints
1699 scratch_dofs.resize(
1700 cell->get_fe().n_dofs_per_face(face));
1701 cell->face(face)->get_dof_indices(
1702 scratch_dofs, cell->active_fe_index());
1703
1704 // split dofs into primary and dependent components
1705 primary_dofs.clear();
1706 dependent_dofs.clear();
1707 for (unsigned int i = 0;
1708 i < cell->get_fe().n_dofs_per_face(face);
1709 ++i)
1710 if ((*primary_dof_masks[dominating_fe_index]
1711 [cell->active_fe_index()])
1712 [i] == true)
1713 primary_dofs.push_back(scratch_dofs[i]);
1714 else
1715 dependent_dofs.push_back(scratch_dofs[i]);
1716
1717 AssertDimension(primary_dofs.size(),
1718 dominating_fe.n_dofs_per_face(
1719 face));
1720 AssertDimension(
1721 dependent_dofs.size(),
1722 cell->get_fe().n_dofs_per_face(face) -
1723 dominating_fe.n_dofs_per_face(face));
1724
1725 filter_constraints(primary_dofs,
1726 dependent_dofs,
1727 constraint_matrix,
1728 constraints);
1729
1730 // now do the same for another FE this is pretty
1731 // much the same we do above to resolve h-refinement
1732 // constraints
1733 Assert(dominating_fe.n_dofs_per_face(face) <=
1734 neighbor->get_fe().n_dofs_per_face(face),
1735 ExcInternalError());
1736
1737 ensure_existence_of_face_matrix(
1738 dominating_fe,
1739 neighbor->get_fe(),
1740 face_interpolation_matrices
1741 [dominating_fe_index]
1742 [neighbor->active_fe_index()]);
1743
1744 const FullMatrix<double>
1745 &restrict_secondface_to_virtual =
1746 *(face_interpolation_matrices
1747 [dominating_fe_index]
1748 [neighbor->active_fe_index()]);
1749
1750 constraint_matrix.reinit(
1751 neighbor->get_fe().n_dofs_per_face(face),
1752 dominating_fe.n_dofs_per_face(face));
1753
1754 restrict_secondface_to_virtual.mmult(
1755 constraint_matrix,
1756 restrict_mother_to_virtual_primary_inv);
1757
1758 dependent_dofs.resize(
1759 neighbor->get_fe().n_dofs_per_face(face));
1760 cell->face(face)->get_dof_indices(
1761 dependent_dofs, neighbor->active_fe_index());
1762
1763 filter_constraints(primary_dofs,
1764 dependent_dofs,
1765 constraint_matrix,
1766 constraints);
1767
1768 break;
1769 }
1770
1771 case FiniteElementDomination::no_requirements:
1772 {
1773 // nothing to do here
1774 break;
1775 }
1776
1777 default:
1778 // we shouldn't get here
1779 Assert(false, ExcInternalError());
1780 }
1781 }
1782 }
1783 }
1784 }
1785 } // namespace internal
1786
1787
1788
1789 template <int dim, int spacedim, typename number>
1790 void
1791 make_hanging_node_constraints(const DoFHandler<dim, spacedim> &dof_handler,
1792 AffineConstraints<number> & constraints)
1793 {
1794 Assert(dof_handler.has_active_dofs(),
1795 ExcMessage(
1796 "The given DoFHandler does not have any DoFs. Did you forget to "
1797 "call dof_handler.distribute_dofs()?"));
1798
1799 // Decide whether to use the new or old make_hanging_node_constraints
1800 // function. If all the FiniteElement or all elements in a FECollection
1801 // support the new face constraint matrix, the new code will be used.
1802 // Otherwise, the old implementation is used for the moment.
1803 if (dof_handler.get_fe_collection().hp_constraints_are_implemented())
1804 internal::make_hp_hanging_node_constraints(dof_handler, constraints);
1805 else
1806 internal::make_oldstyle_hanging_node_constraints(
1807 dof_handler, constraints, std::integral_constant<int, dim>());
1808 }
1809
1810
1811
1812 namespace
1813 {
1839 template <typename FaceIterator, typename number>
1840 void
1841 set_periodicity_constraints(
1842 const FaceIterator & face_1,
1843 const std_cxx20::type_identity_t<FaceIterator> &face_2,
1844 const FullMatrix<double> & transformation,
1845 AffineConstraints<number> & affine_constraints,
1846 const ComponentMask & component_mask,
1847 const bool face_orientation,
1848 const bool face_flip,
1849 const bool face_rotation,
1850 const number periodicity_factor)
1851 {
1852 static const int dim = FaceIterator::AccessorType::dimension;
1853 static const int spacedim = FaceIterator::AccessorType::space_dimension;
1854
1855 // we should be in the case where face_1 is active, i.e. has no children:
1856 Assert(!face_1->has_children(), ExcInternalError());
1857
1858 Assert(face_1->n_active_fe_indices() == 1, ExcInternalError());
1859
1860 // TODO: the implementation makes the assumption that all faces have the
1861 // same number of dofs
1862 AssertDimension(
1863 face_1->get_fe(face_1->nth_active_fe_index(0)).n_unique_faces(), 1);
1864 AssertDimension(
1865 face_2->get_fe(face_2->nth_active_fe_index(0)).n_unique_faces(), 1);
1866 const unsigned int face_no = 0;
1867
1868 // If face_2 does have children, then we need to iterate over these
1869 // children and set periodic constraints in the inverse direction:
1870
1871 if (face_2->has_children())
1872 {
1873 Assert(face_2->n_children() ==
1874 GeometryInfo<dim>::max_children_per_face,
1875 ExcNotImplemented());
1876
1877 const unsigned int dofs_per_face =
1878 face_1->get_fe(face_1->nth_active_fe_index(0))
1879 .n_dofs_per_face(face_no);
1880 FullMatrix<double> child_transformation(dofs_per_face, dofs_per_face);
1881 FullMatrix<double> subface_interpolation(dofs_per_face,
1882 dofs_per_face);
1883
1884 for (unsigned int c = 0; c < face_2->n_children(); ++c)
1885 {
1886 // get the interpolation matrix recursively from the one that
1887 // interpolated from face_1 to face_2 by multiplying from the left
1888 // with the one that interpolates from face_2 to its child
1889 const auto &fe = face_1->get_fe(face_1->nth_active_fe_index(0));
1890 fe.get_subface_interpolation_matrix(fe,
1891 c,
1892 subface_interpolation,
1893 face_no);
1894 subface_interpolation.mmult(child_transformation, transformation);
1895
1896 set_periodicity_constraints(face_1,
1897 face_2->child(c),
1898 child_transformation,
1899 affine_constraints,
1900 component_mask,
1901 face_orientation,
1902 face_flip,
1903 face_rotation,
1904 periodicity_factor);
1905 }
1906 return;
1907 }
1908
1909 //
1910 // If we reached this point then both faces are active. Now all
1911 // that is left is to match the corresponding DoFs of both faces.
1912 //
1913
1914 const types::fe_index face_1_index = face_1->nth_active_fe_index(0);
1915 const types::fe_index face_2_index = face_2->nth_active_fe_index(0);
1916 Assert(face_1->get_fe(face_1_index) == face_2->get_fe(face_2_index),
1917 ExcMessage(
1918 "Matching periodic cells need to use the same finite element"));
1919
1920 const FiniteElement<dim, spacedim> &fe = face_1->get_fe(face_1_index);
1921
1922 Assert(component_mask.represents_n_components(fe.n_components()),
1923 ExcMessage(
1924 "The number of components in the mask has to be either "
1925 "zero or equal to the number of components in the finite "
1926 "element."));
1927
1928 const unsigned int dofs_per_face = fe.n_dofs_per_face(face_no);
1929
1930 std::vector<types::global_dof_index> dofs_1(dofs_per_face);
1931 std::vector<types::global_dof_index> dofs_2(dofs_per_face);
1932
1933 face_1->get_dof_indices(dofs_1, face_1_index);
1934 face_2->get_dof_indices(dofs_2, face_2_index);
1935
1936 // If either of the two faces has an invalid dof index, stop. This is
1937 // so that there is no attempt to match artificial cells of parallel
1938 // distributed triangulations.
1939 //
1940 // While it seems like we ought to be able to avoid even calling
1941 // set_periodicity_constraints for artificial faces, this situation
1942 // can arise when a face that is being made periodic is only
1943 // partially touched by the local subdomain.
1944 // make_periodicity_constraints will be called recursively even for
1945 // the section of the face that is not touched by the local
1946 // subdomain.
1947 //
1948 // Until there is a better way to determine if the cells that
1949 // neighbor a face are artificial, we simply test to see if the face
1950 // does not have a valid dof initialization.
1951
1952 for (unsigned int i = 0; i < dofs_per_face; ++i)
1953 if (dofs_1[i] == numbers::invalid_dof_index ||
1954 dofs_2[i] == numbers::invalid_dof_index)
1955 {
1956 return;
1957 }
1958
1959 // Well, this is a hack:
1960 //
1961 // There is no
1962 // face_to_face_index(face_index,
1963 // face_orientation,
1964 // face_flip,
1965 // face_rotation)
1966 // function in FiniteElementData, so we have to use
1967 // face_to_cell_index(face_index, face
1968 // face_orientation,
1969 // face_flip,
1970 // face_rotation)
1971 // But this will give us an index on a cell - something we cannot work
1972 // with directly. But luckily we can match them back :-]
1973
1974 std::map<unsigned int, unsigned int> cell_to_rotated_face_index;
1975
1976 // Build up a cell to face index for face_2:
1977 for (unsigned int i = 0; i < dofs_per_face; ++i)
1978 {
1979 const unsigned int cell_index =
1980 fe.face_to_cell_index(i,
1981 0, /* It doesn't really matter, just
1982 * assume we're on the first face...
1983 */
1984 true,
1985 false,
1986 false // default orientation
1987 );
1988 cell_to_rotated_face_index[cell_index] = i;
1989 }
1990
1991 //
1992 // Loop over all dofs on face 2 and constrain them against all
1993 // matching dofs on face 1:
1994 //
1995
1996 for (unsigned int i = 0; i < dofs_per_face; ++i)
1997 {
1998 // Obey the component mask
1999 if ((component_mask.n_selected_components(fe.n_components()) !=
2000 fe.n_components()) &&
2001 !component_mask[fe.face_system_to_component_index(i, face_no)
2002 .first])
2003 continue;
2004
2005 // We have to be careful to treat so called "identity
2006 // constraints" special. These are constraints of the form
2007 // x1 == constraint_factor * x_2. In this case, if the constraint
2008 // x2 == 1./constraint_factor * x1 already exists we are in trouble.
2009 //
2010 // Consequently, we have to check that we have indeed such an
2011 // "identity constraint". We do this by looping over all entries
2012 // of the row of the transformation matrix and check whether we
2013 // find exactly one nonzero entry. If this is the case, set
2014 // "is_identity_constrained" to true and record the corresponding
2015 // index and constraint_factor.
2016
2017 bool is_identity_constrained = false;
2018 unsigned int target = numbers::invalid_unsigned_int;
2019 number constraint_factor = periodicity_factor;
2020
2021 constexpr double eps = 1.e-13;
2022 for (unsigned int jj = 0; jj < dofs_per_face; ++jj)
2023 {
2024 const auto entry = transformation(i, jj);
2025 if (std::abs(entry) > eps)
2026 {
2027 if (is_identity_constrained)
2028 {
2029 // We did encounter more than one nonzero entry, so
2030 // the dof is not identity constrained. Set the
2031 // boolean to false and break out of the for loop.
2032 is_identity_constrained = false;
2033 break;
2034 }
2035 is_identity_constrained = true;
2036 target = jj;
2037 constraint_factor = entry * periodicity_factor;
2038 }
2039 }
2040
2041 // Next, we work on all constraints that are not identity
2042 // constraints, i.e., constraints that involve an interpolation
2043 // step that constrains the current dof (on face 2) to more than
2044 // one dof on face 1.
2045
2046 if (!is_identity_constrained)
2047 {
2048 // The current dof is already constrained. There is nothing
2049 // left to do.
2050 if (affine_constraints.is_constrained(dofs_2[i]))
2051 continue;
2052
2053 // Enter the constraint piece by piece:
2054 affine_constraints.add_line(dofs_2[i]);
2055
2056 for (unsigned int jj = 0; jj < dofs_per_face; ++jj)
2057 {
2058 // Get the correct dof index on face_1 respecting the
2059 // given orientation:
2060 const unsigned int j =
2061 cell_to_rotated_face_index[fe.face_to_cell_index(
2062 jj, 0, face_orientation, face_flip, face_rotation)];
2063
2064 if (std::abs(transformation(i, jj)) > eps)
2065 affine_constraints.add_entry(dofs_2[i],
2066 dofs_1[j],
2067 transformation(i, jj));
2068 }
2069
2070 // Continue with next dof.
2071 continue;
2072 }
2073
2074 // We are left with an "identity constraint".
2075
2076 // Get the correct dof index on face_1 respecting the given
2077 // orientation:
2078 const unsigned int j =
2079 cell_to_rotated_face_index[fe.face_to_cell_index(
2080 target, 0, face_orientation, face_flip, face_rotation)];
2081
2082 auto dof_left = dofs_1[j];
2083 auto dof_right = dofs_2[i];
2084
2085 // If dof_left is already constrained, or dof_left < dof_right we
2086 // flip the order to ensure that dofs are constrained in a stable
2087 // manner on different MPI processes.
2088 if (affine_constraints.is_constrained(dof_left) ||
2089 (dof_left < dof_right &&
2090 !affine_constraints.is_constrained(dof_right)))
2091 {
2092 std::swap(dof_left, dof_right);
2093 constraint_factor = 1. / constraint_factor;
2094 }
2095
2096 // Next, we try to enter the constraint
2097 // dof_left = constraint_factor * dof_right;
2098
2099 // If both degrees of freedom are constrained, there is nothing we
2100 // can do. Simply continue with the next dof.
2101 if (affine_constraints.is_constrained(dof_left) &&
2102 affine_constraints.is_constrained(dof_right))
2103 continue;
2104
2105 // We have to be careful that adding the current identity
2106 // constraint does not create a constraint cycle. Thus, check for
2107 // a dependency cycle:
2108
2109 bool constraints_are_cyclic = true;
2110 number cycle_constraint_factor = constraint_factor;
2111
2112 for (auto test_dof = dof_right; test_dof != dof_left;)
2113 {
2114 if (!affine_constraints.is_constrained(test_dof))
2115 {
2116 constraints_are_cyclic = false;
2117 break;
2118 }
2119
2120 const auto &constraint_entries =
2121 *affine_constraints.get_constraint_entries(test_dof);
2122 if (constraint_entries.size() == 1)
2123 {
2124 test_dof = constraint_entries[0].first;
2125 cycle_constraint_factor *= constraint_entries[0].second;
2126 }
2127 else
2128 {
2129 constraints_are_cyclic = false;
2130 break;
2131 }
2132 }
2133
2134 // In case of a dependency cycle we, either
2135 // - do nothing if cycle_constraint_factor == 1. In this case all
2136 // degrees
2137 // of freedom are already periodically constrained,
2138 // - otherwise, force all dofs to zero (by setting dof_left to
2139 // zero). The reasoning behind this is the fact that
2140 // cycle_constraint_factor != 1 occurs in situations such as
2141 // x1 == x2 and x2 == -1. * x1. This system is only solved by
2142 // x_1 = x_2 = 0.
2143
2144 if (constraints_are_cyclic)
2145 {
2146 if (std::abs(cycle_constraint_factor - number(1.)) > eps)
2147 affine_constraints.add_line(dof_left);
2148 }
2149 else
2150 {
2151 affine_constraints.add_line(dof_left);
2152 affine_constraints.add_entry(dof_left,
2153 dof_right,
2154 constraint_factor);
2155 // The number 1e10 in the assert below is arbitrary. If the
2156 // absolute value of constraint_factor is too large, then probably
2157 // the absolute value of periodicity_factor is too large or too
2158 // small. This would be equivalent to an evanescent wave that has
2159 // a very small wavelength. A quick calculation shows that if
2160 // |periodicity_factor| > 1e10 -> |np.exp(ikd)|> 1e10, therefore k
2161 // is imaginary (evanescent wave) and the evanescent wavelength is
2162 // 0.27 times smaller than the dimension of the structure,
2163 // lambda=((2*pi)/log(1e10))*d. Imaginary wavenumbers can be
2164 // interesting in some cases
2165 // (https://doi.org/10.1103/PhysRevA.94.033813).In order to
2166 // implement the case of in which the wavevector can be imaginary
2167 // it would be necessary to rewrite this function and the dof
2168 // ordering method should be modified.
2169 // Let's take the following constraint a*x1 + b*x2 = 0. You could
2170 // just always pick x1 = b/a*x2, but in practice this is not so
2171 // stable if a could be a small number -- intended to be zero, but
2172 // just very small due to roundoff. Of course, constraining x2 in
2173 // terms of x1 has the same problem. So one chooses x1 = b/a*x2 if
2174 // |b|<|a|, and x2 = a/b*x1 if |a|<|b|.
2175 Assert(std::abs(constraint_factor) < 1e10,
2176 ExcMessage("The periodicity constraint is too large. "
2177 "The parameter periodicity_factor might "
2178 "be too large or too small."));
2179 }
2180 } /* for dofs_per_face */
2181 }
2182
2183
2184
2185 // Internally used in make_periodicity_constraints.
2186 //
2187 // Build up a (possibly rotated) interpolation matrix that is used in
2188 // set_periodicity_constraints with the help of user supplied matrix and
2189 // first_vector_components.
2190 template <int dim, int spacedim>
2191 FullMatrix<double>
2192 compute_transformation(
2193 const FiniteElement<dim, spacedim> &fe,
2194 const FullMatrix<double> & matrix,
2195 const std::vector<unsigned int> & first_vector_components)
2196 {
2197 // TODO: the implementation makes the assumption that all faces have the
2198 // same number of dofs
2199 AssertDimension(fe.n_unique_faces(), 1);
2200 const unsigned int face_no = 0;
2201
2202 Assert(matrix.m() == matrix.n(), ExcInternalError());
2203
2204 const unsigned int n_dofs_per_face = fe.n_dofs_per_face(face_no);
2205
2206 if (matrix.m() == n_dofs_per_face)
2207 {
2208 // In case of m == n == n_dofs_per_face the supplied matrix is already
2209 // an interpolation matrix, so we use it directly:
2210 return matrix;
2211 }
2212
2213 if (first_vector_components.empty() && matrix.m() == 0)
2214 {
2215 // Just the identity matrix in case no rotation is specified:
2216 return IdentityMatrix(n_dofs_per_face);
2217 }
2218
2219 // The matrix describes a rotation and we have to build a transformation
2220 // matrix, we assume that for a 0* rotation we would have to build the
2221 // identity matrix
2222
2223 Assert(matrix.m() == spacedim, ExcInternalError())
2224
2225 Quadrature<dim - 1>
2226 quadrature(fe.get_unit_face_support_points(face_no));
2227
2228 // have an array that stores the location of each vector-dof tuple we want
2229 // to rotate.
2230 using DoFTuple = std::array<unsigned int, spacedim>;
2231
2232 // start with a pristine interpolation matrix...
2233 FullMatrix<double> transformation = IdentityMatrix(n_dofs_per_face);
2234
2235 for (unsigned int i = 0; i < n_dofs_per_face; ++i)
2236 {
2237 std::vector<unsigned int>::const_iterator comp_it =
2238 std::find(first_vector_components.begin(),
2239 first_vector_components.end(),
2240 fe.face_system_to_component_index(i, face_no).first);
2241 if (comp_it != first_vector_components.end())
2242 {
2243 const unsigned int first_vector_component = *comp_it;
2244
2245 // find corresponding other components of vector
2246 DoFTuple vector_dofs;
2247 vector_dofs[0] = i;
2248 unsigned int n_found = 1;
2249
2250 Assert(
2251 *comp_it + spacedim <= fe.n_components(),
2252 ExcMessage(
2253 "Error: the finite element does not have enough components "
2254 "to define rotated periodic boundaries."));
2255
2256 for (unsigned int k = 0; k < n_dofs_per_face; ++k)
2257 if ((k != i) && (quadrature.point(k) == quadrature.point(i)) &&
2258 (fe.face_system_to_component_index(k, face_no).first >=
2259 first_vector_component) &&
2260 (fe.face_system_to_component_index(k, face_no).first <
2261 first_vector_component + spacedim))
2262 {
2263 vector_dofs[fe.face_system_to_component_index(k, face_no)
2264 .first -
2265 first_vector_component] = k;
2266 n_found++;
2267 if (n_found == dim)
2268 break;
2269 }
2270
2271 // ... and rotate all dofs belonging to vector valued components
2272 // that are selected by first_vector_components:
2273 for (unsigned int i = 0; i < spacedim; ++i)
2274 {
2275 transformation[vector_dofs[i]][vector_dofs[i]] = 0.;
2276 for (unsigned int j = 0; j < spacedim; ++j)
2277 transformation[vector_dofs[i]][vector_dofs[j]] =
2278 matrix[i][j];
2279 }
2280 }
2281 }
2282 return transformation;
2283 }
2284 } /*namespace*/
2285
2286
2287 // Low level interface:
2288
2289
2290 template <typename FaceIterator, typename number>
2291 void
2292 make_periodicity_constraints(
2293 const FaceIterator & face_1,
2294 const std_cxx20::type_identity_t<FaceIterator> &face_2,
2295 AffineConstraints<number> & affine_constraints,
2296 const ComponentMask & component_mask,
2297 const bool face_orientation,
2298 const bool face_flip,
2299 const bool face_rotation,
2300 const FullMatrix<double> & matrix,
2301 const std::vector<unsigned int> & first_vector_components,
2302 const number periodicity_factor)
2303 {
2304 static const int dim = FaceIterator::AccessorType::dimension;
2305 static const int spacedim = FaceIterator::AccessorType::space_dimension;
2306
2307 Assert((dim != 1) || (face_orientation == true && face_flip == false &&
2308 face_rotation == false),
2309 ExcMessage("The supplied orientation "
2310 "(face_orientation, face_flip, face_rotation) "
2311 "is invalid for 1d"));
2312
2313 Assert((dim != 2) || (face_orientation == true && face_rotation == false),
2314 ExcMessage("The supplied orientation "
2315 "(face_orientation, face_flip, face_rotation) "
2316 "is invalid for 2d"));
2317
2318 Assert(face_1 != face_2,
2319 ExcMessage("face_1 and face_2 are equal! Cannot constrain DoFs "
2320 "on the very same face"));
2321
2322 Assert(face_1->at_boundary() && face_2->at_boundary(),
2323 ExcMessage("Faces for periodicity constraints must be on the "
2324 "boundary"));
2325
2326 Assert(matrix.m() == matrix.n(),
2327 ExcMessage("The supplied (rotation or interpolation) matrix must "
2328 "be a square matrix"));
2329
2330 Assert(first_vector_components.empty() || matrix.m() == spacedim,
2331 ExcMessage("first_vector_components is nonempty, so matrix must "
2332 "be a rotation matrix exactly of size spacedim"));
2333
2334#ifdef DEBUG
2335 if (!face_1->has_children())
2336 {
2337 // TODO: the implementation makes the assumption that all faces have the
2338 // same number of dofs
2339 AssertDimension(
2340 face_1->get_fe(face_1->nth_active_fe_index(0)).n_unique_faces(), 1);
2341 const unsigned int face_no = 0;
2342
2343 Assert(face_1->n_active_fe_indices() == 1, ExcInternalError());
2344 const unsigned int n_dofs_per_face =
2345 face_1->get_fe(face_1->nth_active_fe_index(0))
2346 .n_dofs_per_face(face_no);
2347
2348 Assert(matrix.m() == 0 ||
2349 (first_vector_components.empty() &&
2350 matrix.m() == n_dofs_per_face) ||
2351 (!first_vector_components.empty() && matrix.m() == spacedim),
2352 ExcMessage(
2353 "The matrix must have either size 0 or spacedim "
2354 "(if first_vector_components is nonempty) "
2355 "or the size must be equal to the # of DoFs on the face "
2356 "(if first_vector_components is empty)."));
2357 }
2358
2359 if (!face_2->has_children())
2360 {
2361 // TODO: the implementation makes the assumption that all faces have the
2362 // same number of dofs
2363 AssertDimension(
2364 face_2->get_fe(face_2->nth_active_fe_index(0)).n_unique_faces(), 1);
2365 const unsigned int face_no = 0;
2366
2367 Assert(face_2->n_active_fe_indices() == 1, ExcInternalError());
2368 const unsigned int n_dofs_per_face =
2369 face_2->get_fe(face_2->nth_active_fe_index(0))
2370 .n_dofs_per_face(face_no);
2371
2372 Assert(matrix.m() == 0 ||
2373 (first_vector_components.empty() &&
2374 matrix.m() == n_dofs_per_face) ||
2375 (!first_vector_components.empty() && matrix.m() == spacedim),
2376 ExcMessage(
2377 "The matrix must have either size 0 or spacedim "
2378 "(if first_vector_components is nonempty) "
2379 "or the size must be equal to the # of DoFs on the face "
2380 "(if first_vector_components is empty)."));
2381 }
2382#endif
2383
2384 // A lookup table on how to go through the child faces depending on the
2385 // orientation:
2386
2387 static const int lookup_table_2d[2][2] = {
2388 // flip:
2389 {0, 1}, // false
2390 {1, 0}, // true
2391 };
2392
2393 static const int lookup_table_3d[2][2][2][4] = {
2394 // orientation flip rotation
2395 {
2396 {
2397 {0, 2, 1, 3}, // false false false
2398 {2, 3, 0, 1}, // false false true
2399 },
2400 {
2401 {3, 1, 2, 0}, // false true false
2402 {1, 0, 3, 2}, // false true true
2403 },
2404 },
2405 {
2406 {
2407 {0, 1, 2, 3}, // true false false
2408 {1, 3, 0, 2}, // true false true
2409 },
2410 {
2411 {3, 2, 1, 0}, // true true false
2412 {2, 0, 3, 1}, // true true true
2413 },
2414 },
2415 };
2416
2417 if (face_1->has_children() && face_2->has_children())
2418 {
2419 // In the case that both faces have children, we loop over all children
2420 // and apply make_periodicty_constrains recursively:
2421
2422 Assert(face_1->n_children() ==
2423 GeometryInfo<dim>::max_children_per_face &&
2424 face_2->n_children() ==
2425 GeometryInfo<dim>::max_children_per_face,
2426 ExcNotImplemented());
2427
2428 for (unsigned int i = 0; i < GeometryInfo<dim>::max_children_per_face;
2429 ++i)
2430 {
2431 // Lookup the index for the second face
2432 unsigned int j;
2433 switch (dim)
2434 {
2435 case 2:
2436 j = lookup_table_2d[face_flip][i];
2437 break;
2438 case 3:
2439 j = lookup_table_3d[face_orientation][face_flip]
2440 [face_rotation][i];
2441 break;
2442 default:
2443 AssertThrow(false, ExcNotImplemented());
2444 }
2445
2446 make_periodicity_constraints(face_1->child(i),
2447 face_2->child(j),
2448 affine_constraints,
2449 component_mask,
2450 face_orientation,
2451 face_flip,
2452 face_rotation,
2453 matrix,
2454 first_vector_components,
2455 periodicity_factor);
2456 }
2457 }
2458 else
2459 {
2460 // Otherwise at least one of the two faces is active and we need to do
2461 // some work and enter the constraints!
2462
2463 // The finite element that matters is the one on the active face:
2464 const FiniteElement<dim, spacedim> &fe =
2465 face_1->has_children() ?
2466 face_2->get_fe(face_2->nth_active_fe_index(0)) :
2467 face_1->get_fe(face_1->nth_active_fe_index(0));
2468
2469 // TODO: the implementation makes the assumption that all faces have the
2470 // same number of dofs
2471 AssertDimension(fe.n_unique_faces(), 1);
2472 const unsigned int face_no = 0;
2473
2474 const unsigned int n_dofs_per_face = fe.n_dofs_per_face(face_no);
2475
2476 // Sometimes we just have nothing to do (for all finite elements, or
2477 // systems which accidentally don't have any dofs on the boundary).
2478 if (n_dofs_per_face == 0)
2479 return;
2480
2481 const FullMatrix<double> transformation =
2482 compute_transformation(fe, matrix, first_vector_components);
2483
2484 if (!face_2->has_children())
2485 {
2486 // Performance hack: We do not need to compute an inverse if the
2487 // matrix is the identity matrix.
2488 if (first_vector_components.empty() && matrix.m() == 0)
2489 {
2490 set_periodicity_constraints(face_2,
2491 face_1,
2492 transformation,
2493 affine_constraints,
2494 component_mask,
2495 face_orientation,
2496 face_flip,
2497 face_rotation,
2498 periodicity_factor);
2499 }
2500 else
2501 {
2502 FullMatrix<double> inverse(transformation.m());
2503 inverse.invert(transformation);
2504
2505 set_periodicity_constraints(face_2,
2506 face_1,
2507 inverse,
2508 affine_constraints,
2509 component_mask,
2510 face_orientation,
2511 face_flip,
2512 face_rotation,
2513 periodicity_factor);
2514 }
2515 }
2516 else
2517 {
2518 Assert(!face_1->has_children(), ExcInternalError());
2519
2520 // Important note:
2521 // In 3d we have to take care of the fact that face_rotation gives
2522 // the relative rotation of face_1 to face_2, i.e. we have to invert
2523 // the rotation when constraining face_2 to face_1. Therefore
2524 // face_flip has to be toggled if face_rotation is true: In case of
2525 // inverted orientation, nothing has to be done.
2526 set_periodicity_constraints(face_1,
2527 face_2,
2528 transformation,
2529 affine_constraints,
2530 component_mask,
2531 face_orientation,
2532 face_orientation ?
2533 face_rotation ^ face_flip :
2534 face_flip,
2535 face_rotation,
2536 periodicity_factor);
2537 }
2538 }
2539 }
2540
2541
2542
2543 template <int dim, int spacedim, typename number>
2544 void
2545 make_periodicity_constraints(
2546 const std::vector<GridTools::PeriodicFacePair<
2547 typename DoFHandler<dim, spacedim>::cell_iterator>> &periodic_faces,
2548 AffineConstraints<number> & constraints,
2549 const ComponentMask & component_mask,
2550 const std::vector<unsigned int> &first_vector_components,
2551 const number periodicity_factor)
2552 {
2553 // Loop over all periodic faces...
2554 for (auto &pair : periodic_faces)
2555 {
2556 using FaceIterator = typename DoFHandler<dim, spacedim>::face_iterator;
2557 const FaceIterator face_1 = pair.cell[0]->face(pair.face_idx[0]);
2558 const FaceIterator face_2 = pair.cell[1]->face(pair.face_idx[1]);
2559
2560 Assert(face_1->at_boundary() && face_2->at_boundary(),
2561 ExcInternalError());
2562
2563 Assert(face_1 != face_2, ExcInternalError());
2564
2565 // ... and apply the low level make_periodicity_constraints function to
2566 // every matching pair:
2567 make_periodicity_constraints(face_1,
2568 face_2,
2569 constraints,
2570 component_mask,
2571 pair.orientation[0],
2572 pair.orientation[1],
2573 pair.orientation[2],
2574 pair.matrix,
2575 first_vector_components,
2576 periodicity_factor);
2577 }
2578 }
2579
2580
2581 // High level interface variants:
2582
2583
2584 template <int dim, int spacedim, typename number>
2585 void
2586 make_periodicity_constraints(const DoFHandler<dim, spacedim> & dof_handler,
2587 const types::boundary_id b_id1,
2588 const types::boundary_id b_id2,
2589 const unsigned int direction,
2590 ::AffineConstraints<number> &constraints,
2591 const ComponentMask &component_mask,
2592 const number periodicity_factor)
2593 {
2594 AssertIndexRange(direction, spacedim);
2595
2596 Assert(b_id1 != b_id2,
2597 ExcMessage("The boundary indicators b_id1 and b_id2 must be "
2598 "different to denote different boundaries."));
2599
2600 std::vector<GridTools::PeriodicFacePair<
2601 typename DoFHandler<dim, spacedim>::cell_iterator>>
2602 matched_faces;
2603
2604 // Collect matching periodic cells on the coarsest level:
2605 GridTools::collect_periodic_faces(
2606 dof_handler, b_id1, b_id2, direction, matched_faces);
2607
2608 make_periodicity_constraints<dim, spacedim>(matched_faces,
2609 constraints,
2610 component_mask,
2611 std::vector<unsigned int>(),
2612 periodicity_factor);
2613 }
2614
2615
2616
2617 template <int dim, int spacedim, typename number>
2618 void
2619 make_periodicity_constraints(const DoFHandler<dim, spacedim> &dof_handler,
2620 const types::boundary_id b_id,
2621 const unsigned int direction,
2622 AffineConstraints<number> & constraints,
2623 const ComponentMask & component_mask,
2624 const number periodicity_factor)
2625 {
2626 AssertIndexRange(direction, spacedim);
2627
2628 Assert(dim == spacedim, ExcNotImplemented());
2629
2630 std::vector<GridTools::PeriodicFacePair<
2631 typename DoFHandler<dim, spacedim>::cell_iterator>>
2632 matched_faces;
2633
2634 // Collect matching periodic cells on the coarsest level:
2635 GridTools::collect_periodic_faces(dof_handler,
2636 b_id,
2637 direction,
2638 matched_faces);
2639
2640 make_periodicity_constraints<dim, spacedim>(matched_faces,
2641 constraints,
2642 component_mask,
2643 std::vector<unsigned int>(),
2644 periodicity_factor);
2645 }
2646
2647
2648
2649 namespace internal
2650 {
2651 namespace Assembler
2652 {
2653 struct Scratch
2654 {};
2655
2656
2657 template <int dim, int spacedim>
2658 struct CopyData
2659 {
2660 unsigned int dofs_per_cell;
2661 std::vector<types::global_dof_index> parameter_dof_indices;
2662#ifdef DEAL_II_WITH_MPI
2663 std::vector<::LinearAlgebra::distributed::Vector<double>>
2664 global_parameter_representation;
2665#else
2666 std::vector<::Vector<double>> global_parameter_representation;
2667#endif
2668 };
2669 } // namespace Assembler
2670
2671 namespace
2672 {
2678 template <int dim, int spacedim>
2679 void
2680 compute_intergrid_weights_3(
2681 const typename DoFHandler<dim, spacedim>::active_cell_iterator &cell,
2682 const Assembler::Scratch &,
2683 Assembler::CopyData<dim, spacedim> & copy_data,
2684 const unsigned int coarse_component,
2685 const FiniteElement<dim, spacedim> & coarse_fe,
2686 const InterGridMap<DoFHandler<dim, spacedim>> &coarse_to_fine_grid_map,
2687 const std::vector<::Vector<double>> & parameter_dofs)
2688 {
2689 // for each cell on the parameter grid: find out which degrees of
2690 // freedom on the fine grid correspond in which way to the degrees of
2691 // freedom on the parameter grid
2692 //
2693 // since for continuous FEs some dofs exist on more than one cell, we
2694 // have to track which ones were already visited. the problem is that if
2695 // we visit a dof first on one cell and compute its weight with respect
2696 // to some global dofs to be non-zero, and later visit the dof again on
2697 // another cell and (since we are on another cell) recompute the weights
2698 // with respect to the same dofs as above to be zero now, we have to
2699 // preserve them. we therefore overwrite all weights if they are nonzero
2700 // and do not enforce zero weights since that might be only due to the
2701 // fact that we are on another cell.
2702 //
2703 // example:
2704 // coarse grid
2705 // | | |
2706 // *-----*-----*
2707 // | cell|cell |
2708 // | 1 | 2 |
2709 // | | |
2710 // 0-----1-----*
2711 //
2712 // fine grid
2713 // | | | | |
2714 // *--*--*--*--*
2715 // | | | | |
2716 // *--*--*--*--*
2717 // | | | | |
2718 // *--x--y--*--*
2719 //
2720 // when on cell 1, we compute the weights of dof 'x' to be 1/2 from
2721 // parameter dofs 0 and 1, respectively. however, when later we are on
2722 // cell 2, we again compute the prolongation of shape function 1
2723 // restricted to cell 2 to the globla grid and find that the weight of
2724 // global dof 'x' now is zero. however, we should not overwrite the old
2725 // value.
2726 //
2727 // we therefore always only set nonzero values. why adding up is not
2728 // useful: dof 'y' would get weight 1 from parameter dof 1 on both cells
2729 // 1 and 2, but the correct weight is nevertheless only 1.
2730
2731 // vector to hold the representation of a single degree of freedom on
2732 // the coarse grid (for the selected fe) on the fine grid
2733
2734 copy_data.dofs_per_cell = coarse_fe.n_dofs_per_cell();
2735 copy_data.parameter_dof_indices.resize(copy_data.dofs_per_cell);
2736
2737 // get the global indices of the parameter dofs on this parameter grid
2738 // cell
2739 cell->get_dof_indices(copy_data.parameter_dof_indices);
2740
2741 // loop over all dofs on this cell and check whether they are
2742 // interesting for us
2743 for (unsigned int local_dof = 0; local_dof < copy_data.dofs_per_cell;
2744 ++local_dof)
2745 if (coarse_fe.system_to_component_index(local_dof).first ==
2746 coarse_component)
2747 {
2748 // the how-many-th parameter is this on this cell?
2749 const unsigned int local_parameter_dof =
2750 coarse_fe.system_to_component_index(local_dof).second;
2751
2752 copy_data.global_parameter_representation[local_parameter_dof] =
2753 0.;
2754
2755 // distribute the representation of @p{local_parameter_dof} on the
2756 // parameter grid cell
2757 // @p{cell} to the global data space
2758 coarse_to_fine_grid_map[cell]->set_dof_values_by_interpolation(
2759 parameter_dofs[local_parameter_dof],
2760 copy_data.global_parameter_representation[local_parameter_dof]);
2761 }
2762 }
2763
2764
2765
2771 template <int dim, int spacedim>
2772 void
2773 copy_intergrid_weights_3(
2774 const Assembler::CopyData<dim, spacedim> & copy_data,
2775 const unsigned int coarse_component,
2776 const FiniteElement<dim, spacedim> & coarse_fe,
2777 const std::vector<types::global_dof_index> &weight_mapping,
2778 const bool is_called_in_parallel,
2779 std::vector<std::map<types::global_dof_index, float>> &weights)
2780 {
2781 unsigned int pos = 0;
2782 for (unsigned int local_dof = 0; local_dof < copy_data.dofs_per_cell;
2783 ++local_dof)
2784 if (coarse_fe.system_to_component_index(local_dof).first ==
2785 coarse_component)
2786 {
2787 // now that we've got the global representation of each parameter
2788 // dof, we've only got to clobber the non-zero entries in that
2789 // vector and store the result
2790 //
2791 // what we have learned: if entry @p{i} of the global vector holds
2792 // the value @p{v[i]}, then this is the weight with which the
2793 // present dof contributes to @p{i}. there may be several such
2794 // @p{i}s and their weights' sum should be one. Then, @p{v[i]}
2795 // should be equal to @p{\sum_j w_{ij} p[j]} with @p{p[j]} be the
2796 // values of the degrees of freedom on the coarse grid. we can
2797 // thus compute constraints which link the degrees of freedom
2798 // @p{v[i]} on the fine grid to those on the coarse grid,
2799 // @p{p[j]}. Now to use these as real constraints, rather than as
2800 // additional equations, we have to identify representants among
2801 // the @p{i} for each @p{j}. this will be done by simply taking
2802 // the first @p{i} for which @p{w_{ij}==1}.
2803 //
2804 // guard modification of the weights array by a Mutex. since it
2805 // should happen rather rarely that there are several threads
2806 // operating on different intergrid weights, have only one mutex
2807 // for all of them
2808 for (types::global_dof_index i = 0;
2809 i < copy_data.global_parameter_representation[pos].size();
2810 ++i)
2811 // set this weight if it belongs to a parameter dof.
2812 if (weight_mapping[i] != numbers::invalid_dof_index)
2813 {
2814 // only overwrite old value if not by zero
2815 if (copy_data.global_parameter_representation[pos](i) != 0)
2816 {
2817 const types::global_dof_index
2818 wi = copy_data.parameter_dof_indices[local_dof],
2819 wj = weight_mapping[i];
2820 weights[wi][wj] =
2821 copy_data.global_parameter_representation[pos](i);
2822 }
2823 }
2824 else if (!is_called_in_parallel)
2825 {
2826 // Note that when this function operates with distributed
2827 // fine grid, this assertion is switched off since the
2828 // condition does not necessarily hold
2829 Assert(copy_data.global_parameter_representation[pos](i) ==
2830 0,
2831 ExcInternalError());
2832 }
2833
2834 ++pos;
2835 }
2836 }
2837
2838
2839
2845 template <int dim, int spacedim>
2846 void
2847 compute_intergrid_weights_2(
2848 const DoFHandler<dim, spacedim> & coarse_grid,
2849 const unsigned int coarse_component,
2850 const InterGridMap<DoFHandler<dim, spacedim>> &coarse_to_fine_grid_map,
2851 const std::vector<::Vector<double>> & parameter_dofs,
2852 const std::vector<types::global_dof_index> & weight_mapping,
2853 std::vector<std::map<types::global_dof_index, float>> &weights)
2854 {
2855 Assembler::Scratch scratch;
2856 Assembler::CopyData<dim, spacedim> copy_data;
2857
2858 unsigned int n_interesting_dofs = 0;
2859 for (unsigned int local_dof = 0;
2860 local_dof < coarse_grid.get_fe().n_dofs_per_cell();
2861 ++local_dof)
2862 if (coarse_grid.get_fe().system_to_component_index(local_dof).first ==
2863 coarse_component)
2864 ++n_interesting_dofs;
2865
2866 copy_data.global_parameter_representation.resize(n_interesting_dofs);
2867
2868 bool is_called_in_parallel = false;
2869 for (std::size_t i = 0;
2870 i < copy_data.global_parameter_representation.size();
2871 ++i)
2872 {
2873#ifdef DEAL_II_WITH_MPI
2874 MPI_Comm communicator = MPI_COMM_SELF;
2875 try
2876 {
2877 const typename ::parallel::TriangulationBase<dim,
2878 spacedim>
2879 &tria = dynamic_cast<const typename ::parallel::
2880 TriangulationBase<dim, spacedim> &>(
2881 coarse_to_fine_grid_map.get_destination_grid()
2882 .get_triangulation());
2883 communicator = tria.get_communicator();
2884 is_called_in_parallel = true;
2885 }
2886 catch (std::bad_cast &)
2887 {
2888 // Nothing bad happened: the user used serial Triangulation
2889 }
2890
2891
2892 IndexSet locally_relevant_dofs;
2893 DoFTools::extract_locally_relevant_dofs(
2894 coarse_to_fine_grid_map.get_destination_grid(),
2895 locally_relevant_dofs);
2896
2897 copy_data.global_parameter_representation[i].reinit(
2898 coarse_to_fine_grid_map.get_destination_grid()
2899 .locally_owned_dofs(),
2900 locally_relevant_dofs,
2901 communicator);
2902#else
2903 const types::global_dof_index n_fine_dofs = weight_mapping.size();
2904 copy_data.global_parameter_representation[i].reinit(n_fine_dofs);
2905#endif
2906 }
2907
2908 auto worker =
2909 [coarse_component,
2910 &coarse_grid,
2911 &coarse_to_fine_grid_map,
2912 &parameter_dofs](
2913 const typename DoFHandler<dim, spacedim>::active_cell_iterator
2914 & cell,
2915 const Assembler::Scratch & scratch_data,
2916 Assembler::CopyData<dim, spacedim> &copy_data) {
2917 compute_intergrid_weights_3<dim, spacedim>(cell,
2918 scratch_data,
2919 copy_data,
2920 coarse_component,
2921 coarse_grid.get_fe(),
2922 coarse_to_fine_grid_map,
2923 parameter_dofs);
2924 };
2925
2926 auto copier =
2927 [coarse_component,
2928 &coarse_grid,
2929 &weight_mapping,
2930 is_called_in_parallel,
2931 &weights](const Assembler::CopyData<dim, spacedim> &copy_data) {
2932 copy_intergrid_weights_3<dim, spacedim>(copy_data,
2933 coarse_component,
2934 coarse_grid.get_fe(),
2935 weight_mapping,
2936 is_called_in_parallel,
2937 weights);
2938 };
2939
2940 WorkStream::run(coarse_grid.begin_active(),
2941 coarse_grid.end(),
2942 worker,
2943 copier,
2944 scratch,
2945 copy_data);
2946
2947#ifdef DEAL_II_WITH_MPI
2948 for (std::size_t i = 0;
2949 i < copy_data.global_parameter_representation.size();
2950 ++i)
2951 copy_data.global_parameter_representation[i].update_ghost_values();
2952#endif
2953 }
2954
2955
2956
2962 template <int dim, int spacedim>
2963 unsigned int
2964 compute_intergrid_weights_1(
2965 const DoFHandler<dim, spacedim> & coarse_grid,
2966 const unsigned int coarse_component,
2967 const DoFHandler<dim, spacedim> & fine_grid,
2968 const unsigned int fine_component,
2969 const InterGridMap<DoFHandler<dim, spacedim>> &coarse_to_fine_grid_map,
2970 std::vector<std::map<types::global_dof_index, float>> &weights,
2971 std::vector<types::global_dof_index> & weight_mapping)
2972 {
2973 // aliases to the finite elements used by the dof handlers:
2974 const FiniteElement<dim, spacedim> &coarse_fe = coarse_grid.get_fe(),
2975 &fine_fe = fine_grid.get_fe();
2976
2977 // global numbers of dofs
2978 const types::global_dof_index n_coarse_dofs = coarse_grid.n_dofs(),
2979 n_fine_dofs = fine_grid.n_dofs();
2980
2981 // local numbers of dofs
2982 const unsigned int fine_dofs_per_cell = fine_fe.n_dofs_per_cell();
2983
2984 // alias the number of dofs per cell belonging to the coarse_component
2985 // which is to be the restriction of the fine grid:
2986 const unsigned int coarse_dofs_per_cell_component =
2987 coarse_fe
2988 .base_element(
2989 coarse_fe.component_to_base_index(coarse_component).first)
2990 .n_dofs_per_cell();
2991
2992
2993 // Try to find out whether the grids stem from the same coarse grid.
2994 // This is a rather crude test, but better than nothing
2995 Assert(coarse_grid.get_triangulation().n_cells(0) ==
2996 fine_grid.get_triangulation().n_cells(0),
2997 ExcGridsDontMatch());
2998
2999 // check whether the map correlates the right objects
3000 Assert(&coarse_to_fine_grid_map.get_source_grid() == &coarse_grid,
3001 ExcGridsDontMatch());
3002 Assert(&coarse_to_fine_grid_map.get_destination_grid() == &fine_grid,
3003 ExcGridsDontMatch());
3004
3005
3006 // check whether component numbers are valid
3007 AssertIndexRange(coarse_component, coarse_fe.n_components());
3008 AssertIndexRange(fine_component, fine_fe.n_components());
3009
3010 // check whether respective finite elements are equal
3011 Assert(coarse_fe.base_element(
3012 coarse_fe.component_to_base_index(coarse_component).first) ==
3013 fine_fe.base_element(
3014 fine_fe.component_to_base_index(fine_component).first),
3015 ExcFiniteElementsDontMatch());
3016
3017#ifdef DEBUG
3018 // if in debug mode, check whether the coarse grid is indeed coarser
3019 // everywhere than the fine grid
3020 for (const auto &cell : coarse_grid.active_cell_iterators())
3021 Assert(cell->level() <= coarse_to_fine_grid_map[cell]->level(),
3022 ExcGridNotCoarser());
3023#endif
3024
3025 /*
3026 * From here on: the term `parameter' refers to the selected component
3027 * on the coarse grid and its analogon on the fine grid. The naming of
3028 * variables containing this term is due to the fact that
3029 * `selected_component' is longer, but also due to the fact that the
3030 * code of this function was initially written for a program where the
3031 * component which we wanted to match between grids was actually the
3032 * `parameter' variable.
3033 *
3034 * Likewise, the terms `parameter grid' and `state grid' refer to the
3035 * coarse and fine grids, respectively.
3036 *
3037 * Changing the names of variables would in principle be a good idea,
3038 * but would not make things simpler and would be another source of
3039 * errors. If anyone feels like doing so: patches would be welcome!
3040 */
3041
3042
3043
3044 // set up vectors of cell-local data; each vector represents one degree
3045 // of freedom of the coarse-grid variable in the fine-grid element
3046 std::vector<::Vector<double>> parameter_dofs(
3047 coarse_dofs_per_cell_component,
3048 ::Vector<double>(fine_dofs_per_cell));
3049 // for each coarse dof: find its position within the fine element and
3050 // set this value to one in the respective vector (all other values are
3051 // zero by construction)
3052 for (unsigned int local_coarse_dof = 0;
3053 local_coarse_dof < coarse_dofs_per_cell_component;
3054 ++local_coarse_dof)
3055 for (unsigned int fine_dof = 0; fine_dof < fine_fe.n_dofs_per_cell();
3056 ++fine_dof)
3057 if (fine_fe.system_to_component_index(fine_dof) ==
3058 std::make_pair(fine_component, local_coarse_dof))
3059 {
3060 parameter_dofs[local_coarse_dof](fine_dof) = 1.;
3061 break;
3062 }
3063
3064
3065 // find out how many DoFs there are on the grids belonging to the
3066 // components we want to match
3067 unsigned int n_parameters_on_fine_grid = 0;
3068 {
3069 // have a flag for each dof on the fine grid and set it to true if
3070 // this is an interesting dof. finally count how many true's there
3071 std::vector<bool> dof_is_interesting(fine_grid.n_dofs(), false);
3072 std::vector<types::global_dof_index> local_dof_indices(
3073 fine_fe.n_dofs_per_cell());
3074
3075 for (const auto &cell : fine_grid.active_cell_iterators() |
3076 IteratorFilters::LocallyOwnedCell())
3077 {
3078 cell->get_dof_indices(local_dof_indices);
3079 for (unsigned int i = 0; i < fine_fe.n_dofs_per_cell(); ++i)
3080 if (fine_fe.system_to_component_index(i).first ==
3081 fine_component)
3082 dof_is_interesting[local_dof_indices[i]] = true;
3083 }
3084
3085 n_parameters_on_fine_grid = std::count(dof_is_interesting.begin(),
3086 dof_is_interesting.end(),
3087 true);
3088 }
3089
3090
3091 // set up the weights mapping
3092 weights.clear();
3093 weights.resize(n_coarse_dofs);
3094
3095 weight_mapping.clear();
3096 weight_mapping.resize(n_fine_dofs, numbers::invalid_dof_index);
3097
3098 {
3099 std::vector<types::global_dof_index> local_dof_indices(
3100 fine_fe.n_dofs_per_cell());
3101 unsigned int next_free_index = 0;
3102 for (const auto &cell : fine_grid.active_cell_iterators() |
3103 IteratorFilters::LocallyOwnedCell())
3104 {
3105 cell->get_dof_indices(local_dof_indices);
3106 for (unsigned int i = 0; i < fine_fe.n_dofs_per_cell(); ++i)
3107 // if this DoF is a parameter dof and has not yet been
3108 // numbered, then do so
3109 if ((fine_fe.system_to_component_index(i).first ==
3110 fine_component) &&
3111 (weight_mapping[local_dof_indices[i]] ==
3112 numbers::invalid_dof_index))
3113 {
3114 weight_mapping[local_dof_indices[i]] = next_free_index;
3115 ++next_free_index;
3116 }
3117 }
3118
3119 Assert(next_free_index == n_parameters_on_fine_grid,
3120 ExcInternalError());
3121 }
3122
3123
3124 // for each cell on the parameter grid: find out which degrees of
3125 // freedom on the fine grid correspond in which way to the degrees of
3126 // freedom on the parameter grid
3127 //
3128 // do this in a separate function to allow for multithreading there. see
3129 // this function also if you want to read more information on the
3130 // algorithm used.
3131 compute_intergrid_weights_2(coarse_grid,
3132 coarse_component,
3133 coarse_to_fine_grid_map,
3134 parameter_dofs,
3135 weight_mapping,
3136 weights);
3137
3138
3139 // ok, now we have all weights for each dof on the fine grid. if in
3140 // debug mode lets see if everything went smooth, i.e. each dof has sum
3141 // of weights one
3142 //
3143 // in other words this means that if the sum of all shape functions on
3144 // the parameter grid is one (which is always the case), then the
3145 // representation on the state grid should be as well (division of
3146 // unity)
3147 //
3148 // if the parameter grid has more than one component, then the
3149 // respective dofs of the other components have sum of weights zero, of
3150 // course. we do not explicitly ask which component a dof belongs to,
3151 // but this at least tests some errors
3152#ifdef DEBUG
3153 for (unsigned int col = 0; col < n_parameters_on_fine_grid; ++col)
3154 {
3155 double sum = 0;
3156 for (types::global_dof_index row = 0; row < n_coarse_dofs; ++row)
3157 if (weights[row].find(col) != weights[row].end())
3158 sum += weights[row][col];
3159 Assert((std::fabs(sum - 1) < 1.e-12) ||
3160 ((coarse_fe.n_components() > 1) && (sum == 0)),
3161 ExcInternalError());
3162 }
3163#endif
3164
3165
3166 return n_parameters_on_fine_grid;
3167 }
3168
3169
3170 } // namespace
3171 } // namespace internal
3172
3173
3174
3175 template <int dim, int spacedim>
3176 void
3177 compute_intergrid_constraints(
3178 const DoFHandler<dim, spacedim> & coarse_grid,
3179 const unsigned int coarse_component,
3180 const DoFHandler<dim, spacedim> & fine_grid,
3181 const unsigned int fine_component,
3182 const InterGridMap<DoFHandler<dim, spacedim>> &coarse_to_fine_grid_map,
3183 AffineConstraints<double> & constraints)
3184 {
3185 Assert(coarse_grid.get_fe_collection().size() == 1 &&
3186 fine_grid.get_fe_collection().size() == 1,
3187 ExcMessage("This function is not yet implemented for DoFHandlers "
3188 "using hp-capabilities."));
3189 // store the weights with which a dof on the parameter grid contributes to a
3190 // dof on the fine grid. see the long doc below for more info
3191 //
3192 // allocate as many rows as there are parameter dofs on the coarse grid and
3193 // as many columns as there are parameter dofs on the fine grid.
3194 //
3195 // weight_mapping is used to map the global (fine grid) parameter dof
3196 // indices to the columns
3197 //
3198 // in the original implementation, the weights array was actually of
3199 // FullMatrix<double> type. this wasted huge amounts of memory, but was
3200 // fast. nonetheless, since the memory consumption was quadratic in the
3201 // number of degrees of freedom, this was not very practical, so we now use
3202 // a vector of rows of the matrix, and in each row a vector of pairs
3203 // (colnum,value). this seems like the best tradeoff between memory and
3204 // speed, as it is now linear in memory and still fast enough.
3205 //
3206 // to save some memory and since the weights are usually (negative) powers
3207 // of 2, we choose the value type of the matrix to be @p{float} rather than
3208 // @p{double}.
3209 std::vector<std::map<types::global_dof_index, float>> weights;
3210
3211 // this is this mapping. there is one entry for each dof on the fine grid;
3212 // if it is a parameter dof, then its value is the column in weights for
3213 // that parameter dof, if it is any other dof, then its value is -1,
3214 // indicating an error
3215 std::vector<types::global_dof_index> weight_mapping;
3216
3217 const unsigned int n_parameters_on_fine_grid =
3218 internal::compute_intergrid_weights_1(coarse_grid,
3219 coarse_component,
3220 fine_grid,
3221 fine_component,
3222 coarse_to_fine_grid_map,
3223 weights,
3224 weight_mapping);
3225 (void)n_parameters_on_fine_grid;
3226
3227 // global numbers of dofs
3228 const types::global_dof_index n_coarse_dofs = coarse_grid.n_dofs(),
3229 n_fine_dofs = fine_grid.n_dofs();
3230
3231
3232 // get an array in which we store which dof on the coarse grid is a
3233 // parameter and which is not
3234 IndexSet coarse_dof_is_parameter;
3235 {
3236 std::vector<bool> mask(coarse_grid.get_fe(0).n_components(), false);
3237 mask[coarse_component] = true;
3238
3239 coarse_dof_is_parameter =
3240 extract_dofs<dim, spacedim>(coarse_grid, ComponentMask(mask));
3241 }
3242
3243 // now we know that the weights in each row constitute a constraint. enter
3244 // this into the constraints object
3245 //
3246 // first task: for each parameter dof on the parameter grid, find a
3247 // representant on the fine, global grid. this is possible since we use
3248 // conforming finite element. we take this representant to be the first
3249 // element in this row with weight identical to one. the representant will
3250 // become an unconstrained degree of freedom, while all others will be
3251 // constrained to this dof (and possibly others)
3252 std::vector<types::global_dof_index> representants(
3253 n_coarse_dofs, numbers::invalid_dof_index);
3254 for (types::global_dof_index parameter_dof = 0;
3255 parameter_dof < n_coarse_dofs;
3256 ++parameter_dof)
3257 if (coarse_dof_is_parameter.is_element(parameter_dof))
3258 {
3259 // if this is the line of a parameter dof on the coarse grid, then it
3260 // should have at least one dependent node on the fine grid
3261 Assert(weights[parameter_dof].size() > 0, ExcInternalError());
3262
3263 // find the column where the representant is mentioned
3264 std::map<types::global_dof_index, float>::const_iterator i =
3265 weights[parameter_dof].begin();
3266 for (; i != weights[parameter_dof].end(); ++i)
3267 if (i->second == 1)
3268 break;
3269 Assert(i != weights[parameter_dof].end(), ExcInternalError());
3270 const types::global_dof_index column = i->first;
3271
3272 // now we know in which column of weights the representant is, but we
3273 // don't know its global index. get it using the inverse operation of
3274 // the weight_mapping
3275 types::global_dof_index global_dof = 0;
3276 for (; global_dof < weight_mapping.size(); ++global_dof)
3277 if (weight_mapping[global_dof] ==
3278 static_cast<types::global_dof_index>(column))
3279 break;
3280 Assert(global_dof < weight_mapping.size(), ExcInternalError());
3281
3282 // now enter the representants global index into our list
3283 representants[parameter_dof] = global_dof;
3284 }
3285 else
3286 {
3287 // consistency check: if this is no parameter dof on the coarse grid,
3288 // then the respective row must be empty!
3289 Assert(weights[parameter_dof].size() == 0, ExcInternalError());
3290 }
3291
3292
3293
3294 // note for people that want to optimize this function: the largest part of
3295 // the computing time is spent in the following, rather innocent block of
3296 // code. basically, it must be the AffineConstraints::add_entry call which
3297 // takes the bulk of the time, but it is not known to the author how to make
3298 // it faster...
3299 std::vector<std::pair<types::global_dof_index, double>> constraint_line;
3300 for (types::global_dof_index global_dof = 0; global_dof < n_fine_dofs;
3301 ++global_dof)
3302 if (weight_mapping[global_dof] != numbers::invalid_dof_index)
3303 // this global dof is a parameter dof, so it may carry a constraint note
3304 // that for each global dof, the sum of weights shall be one, so we can
3305 // find out whether this dof is constrained in the following way: if the
3306 // only weight in this row is a one, and the representant for the
3307 // parameter dof of the line in which this one is is the present dof,
3308 // then we consider this dof to be unconstrained. otherwise, all other
3309 // dofs are constrained
3310 {
3311 const types::global_dof_index col = weight_mapping[global_dof];
3312 Assert(col < n_parameters_on_fine_grid, ExcInternalError());
3313
3314 types::global_dof_index first_used_row = 0;
3315
3316 {
3317 Assert(weights.size() > 0, ExcInternalError());
3318 std::map<types::global_dof_index, float>::const_iterator col_entry =
3319 weights[0].end();
3320 for (; first_used_row < n_coarse_dofs; ++first_used_row)
3321 {
3322 col_entry = weights[first_used_row].find(col);
3323 if (col_entry != weights[first_used_row].end())
3324 break;
3325 }
3326
3327 Assert(col_entry != weights[first_used_row].end(),
3328 ExcInternalError());
3329
3330 if ((col_entry->second == 1) &&
3331 (representants[first_used_row] == global_dof))
3332 // dof unconstrained or constrained to itself (in case this cell
3333 // is mapped to itself, rather than to children of itself)
3334 continue;
3335 }
3336
3337
3338 // otherwise enter all constraints
3339 constraints.add_line(global_dof);
3340
3341 constraint_line.clear();
3342 for (types::global_dof_index row = first_used_row;
3343 row < n_coarse_dofs;
3344 ++row)
3345 {
3346 const std::map<types::global_dof_index, float>::const_iterator j =
3347 weights[row].find(col);
3348 if ((j != weights[row].end()) && (j->second != 0))
3349 constraint_line.emplace_back(representants[row], j->second);
3350 }
3351
3352 constraints.add_entries(global_dof, constraint_line);
3353 }
3354 }
3355
3356
3357
3358 template <int dim, int spacedim>
3359 void
3360 compute_intergrid_transfer_representation(
3361 const DoFHandler<dim, spacedim> & coarse_grid,
3362 const unsigned int coarse_component,
3363 const DoFHandler<dim, spacedim> & fine_grid,
3364 const unsigned int fine_component,
3365 const InterGridMap<DoFHandler<dim, spacedim>> &coarse_to_fine_grid_map,
3366 std::vector<std::map<types::global_dof_index, float>>
3367 &transfer_representation)
3368 {
3369 Assert(coarse_grid.get_fe_collection().size() == 1 &&
3370 fine_grid.get_fe_collection().size() == 1,
3371 ExcMessage("This function is not yet implemented for DoFHandlers "
3372 "using hp-capabilities."));
3373 // store the weights with which a dof on the parameter grid contributes to a
3374 // dof on the fine grid. see the long doc below for more info
3375 //
3376 // allocate as many rows as there are parameter dofs on the coarse grid and
3377 // as many columns as there are parameter dofs on the fine grid.
3378 //
3379 // weight_mapping is used to map the global (fine grid) parameter dof
3380 // indices to the columns
3381 //
3382 // in the original implementation, the weights array was actually of
3383 // FullMatrix<double> type. this wasted huge amounts of memory, but was
3384 // fast. nonetheless, since the memory consumption was quadratic in the
3385 // number of degrees of freedom, this was not very practical, so we now use
3386 // a vector of rows of the matrix, and in each row a vector of pairs
3387 // (colnum,value). this seems like the best tradeoff between memory and
3388 // speed, as it is now linear in memory and still fast enough.
3389 //
3390 // to save some memory and since the weights are usually (negative) powers
3391 // of 2, we choose the value type of the matrix to be @p{float} rather than
3392 // @p{double}.
3393 std::vector<std::map<types::global_dof_index, float>> weights;
3394
3395 // this is this mapping. there is one entry for each dof on the fine grid;
3396 // if it is a parameter dof, then its value is the column in weights for
3397 // that parameter dof, if it is any other dof, then its value is -1,
3398 // indicating an error
3399 std::vector<types::global_dof_index> weight_mapping;
3400
3401 internal::compute_intergrid_weights_1(coarse_grid,
3402 coarse_component,
3403 fine_grid,
3404 fine_component,
3405 coarse_to_fine_grid_map,
3406 weights,
3407 weight_mapping);
3408
3409 // now compute the requested representation
3410 const types::global_dof_index n_global_parm_dofs =
3411 std::count_if(weight_mapping.begin(),
3412 weight_mapping.end(),
3413 [](const types::global_dof_index dof) {
3414 return dof != numbers::invalid_dof_index;
3415 });
3416
3417 // first construct the inverse mapping of weight_mapping
3418 std::vector<types::global_dof_index> inverse_weight_mapping(
3419 n_global_parm_dofs, numbers::invalid_dof_index);
3420 for (types::global_dof_index i = 0; i < weight_mapping.size(); ++i)
3421 {
3422 const types::global_dof_index parameter_dof = weight_mapping[i];
3423 // if this global dof is a parameter
3424 if (parameter_dof != numbers::invalid_dof_index)
3425 {
3426 Assert(parameter_dof < n_global_parm_dofs, ExcInternalError());
3427 Assert((inverse_weight_mapping[parameter_dof] ==
3428 numbers::invalid_dof_index),
3429 ExcInternalError());
3430
3431 inverse_weight_mapping[parameter_dof] = i;
3432 }
3433 }
3434
3435 // next copy over weights array and replace respective numbers
3436 const types::global_dof_index n_rows = weight_mapping.size();
3437
3438 transfer_representation.clear();
3439 transfer_representation.resize(n_rows);
3440
3441 const types::global_dof_index n_coarse_dofs = coarse_grid.n_dofs();
3442 for (types::global_dof_index i = 0; i < n_coarse_dofs; ++i)
3443 {
3444 std::map<types::global_dof_index, float>::const_iterator j =
3445 weights[i].begin();
3446 for (; j != weights[i].end(); ++j)
3447 {
3448 const types::global_dof_index p = inverse_weight_mapping[j->first];
3449 Assert(p < n_rows, ExcInternalError());
3450
3451 transfer_representation[p][i] = j->second;
3452 }
3453 }
3454 }
3455
3456
3457
3458 template <int dim, int spacedim, typename number>
3459 void
3460 make_zero_boundary_constraints(
3461 const DoFHandler<dim, spacedim> &dof,
3462 const types::boundary_id boundary_id,
3463 AffineConstraints<number> & zero_boundary_constraints,
3464 const ComponentMask & component_mask)
3465 {
3466 Assert(component_mask.represents_n_components(dof.get_fe(0).n_components()),
3467 ExcMessage("The number of components in the mask has to be either "
3468 "zero or equal to the number of components in the finite "
3469 "element."));
3470
3471 const unsigned int n_components = dof.get_fe_collection().n_components();
3472
3473 Assert(component_mask.n_selected_components(n_components) > 0,
3474 ComponentMask::ExcNoComponentSelected());
3475
3476 // a field to store the indices on the face
3477 std::vector<types::global_dof_index> face_dofs;
3478 face_dofs.reserve(dof.get_fe_collection().max_dofs_per_face());
3479 // a field to store the indices on the cell
3480 std::vector<types::global_dof_index> cell_dofs;
3481 cell_dofs.reserve(dof.get_fe_collection().max_dofs_per_cell());
3482
3483 typename DoFHandler<dim, spacedim>::active_cell_iterator
3484 cell = dof.begin_active(),
3485 endc = dof.end();
3486 for (; cell != endc; ++cell)
3487 if (!cell->is_artificial() && cell->at_boundary())
3488 {
3489 const FiniteElement<dim, spacedim> &fe = cell->get_fe();
3490
3491 // get global indices of dofs on the cell
3492 cell_dofs.resize(fe.n_dofs_per_cell());
3493 cell->get_dof_indices(cell_dofs);
3494
3495 for (const auto face_no : cell->face_indices())
3496 {
3497 const typename DoFHandler<dim, spacedim>::face_iterator face =
3498 cell->face(face_no);
3499
3500 // if face is on the boundary and satisfies the correct boundary
3501 // id property
3502 if (face->at_boundary() &&
3503 ((boundary_id == numbers::invalid_boundary_id) ||
3504 (face->boundary_id() == boundary_id)))
3505 {
3506 // get indices and physical location on this face
3507 face_dofs.resize(fe.n_dofs_per_face(face_no));
3508 face->get_dof_indices(face_dofs, cell->active_fe_index());
3509
3510 // enter those dofs into the list that match the component
3511 // signature.
3512 for (const types::global_dof_index face_dof : face_dofs)
3513 {
3514 // Find out if a dof has a contribution in this component,
3515 // and if so, add it to the list
3516 const std::vector<types::global_dof_index>::iterator
3517 it_index_on_cell = std::find(cell_dofs.begin(),
3518 cell_dofs.end(),
3519 face_dof);
3520 Assert(it_index_on_cell != cell_dofs.end(),
3521 ExcInvalidIterator());
3522 const unsigned int index_on_cell =
3523 std::distance(cell_dofs.begin(), it_index_on_cell);
3524 const ComponentMask &nonzero_component_array =
3525 cell->get_fe().get_nonzero_components(index_on_cell);
3526 bool nonzero = false;
3527 for (unsigned int c = 0; c < n_components; ++c)
3528 if (nonzero_component_array[c] && component_mask[c])
3529 {
3530 nonzero = true;
3531 break;
3532 }
3533
3534 if (nonzero)
3535 zero_boundary_constraints.add_line(face_dof);
3536 }
3537 }
3538 }
3539 }
3540 }
3541
3542
3543
3544 template <int dim, int spacedim, typename number>
3545 void
3546 make_zero_boundary_constraints(
3547 const DoFHandler<dim, spacedim> &dof,
3548 AffineConstraints<number> & zero_boundary_constraints,
3549 const ComponentMask & component_mask)
3550 {
3551 make_zero_boundary_constraints(dof,
3552 numbers::invalid_boundary_id,
3553 zero_boundary_constraints,
3554 component_mask);
3555 }
3556
3557
3558} // end of namespace DoFTools
3559
3560
3561
3562// explicit instantiations
3563
3564#include "dof_tools_constraints.inst"
3565
3566
3567
3568DEAL_II_NAMESPACE_CLOSE
affine_constraints.h
AffineConstraints::add_entries
void add_entries(const size_type constrained_dof_index, const std::vector< std::pair< size_type, number > > &col_weight_pairs)
AffineConstraints::add_line
void add_line(const size_type line_n)
Definition affine_constraints.h:2046
AffineConstraints::add_entry
void add_entry(const size_type constrained_dof_index, const size_type column, const number weight)
Definition affine_constraints.h:2078
AffineConstraints::set_inhomogeneity
void set_inhomogeneity(const size_type constrained_dof_index, const number value)
Definition affine_constraints.h:2120
AffineConstraints::is_constrained
bool is_constrained(const size_type line_n) const
Definition affine_constraints.h:2181
AffineConstraints::get_constraint_entries
const std::vector< std::pair< size_type, number > > * get_constraint_entries(const size_type line_n) const
Definition affine_constraints.h:2211
ComponentMask::represents_n_components
bool represents_n_components(const unsigned int n) const
ComponentMask::n_selected_components
unsigned int n_selected_components(const unsigned int overall_number_of_components=numbers::invalid_unsigned_int) const
DoFHandler::end
cell_iterator end() const
DoFHandler::get_fe_collection
const hp::FECollection< dim, spacedim > & get_fe_collection() const
DoFHandler::has_active_dofs
bool has_active_dofs() const
DoFHandler::get_fe
const FiniteElement< dim, spacedim > & get_fe(const types::fe_index index=0) const
DoFHandler::get_triangulation
const Triangulation< dim, spacedim > & get_triangulation() const
DoFHandler::begin_active
active_cell_iterator begin_active(const unsigned int level=0) const
DoFHandler::has_hp_capabilities
bool has_hp_capabilities() const
DoFHandler::n_dofs
types::global_dof_index n_dofs() const
FiniteElementData::n_dofs_per_vertex
unsigned int n_dofs_per_vertex() const
FiniteElementData::n_dofs_per_cell
unsigned int n_dofs_per_cell() const
FiniteElementData::n_dofs_per_line
unsigned int n_dofs_per_line() const
FiniteElementData::n_dofs_per_face
unsigned int n_dofs_per_face(unsigned int face_no=0, unsigned int child=0) const
FiniteElementData::n_components
unsigned int n_components() const
FiniteElementData::n_unique_faces
unsigned int n_unique_faces() const
FiniteElementData::n_dofs_per_quad
unsigned int n_dofs_per_quad(unsigned int face_no=0) const
FiniteElement::get_nonzero_components
const ComponentMask & get_nonzero_components(const unsigned int i) const
FiniteElement::base_element
virtual const FiniteElement< dim, spacedim > & base_element(const unsigned int index) const
FiniteElement::component_to_base_index
std::pair< unsigned int, unsigned int > component_to_base_index(const unsigned int component) const
FiniteElement::face_to_cell_index
virtual unsigned int face_to_cell_index(const unsigned int face_dof_index, const unsigned int face, const bool face_orientation=true, const bool face_flip=false, const bool face_rotation=false) const
FiniteElement::get_subface_interpolation_matrix
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
FiniteElement::system_to_component_index
std::pair< unsigned int, unsigned int > system_to_component_index(const unsigned int index) const
FiniteElement::constraints
const FullMatrix< double > & constraints(const ::internal::SubfaceCase< dim > &subface_case=::internal::SubfaceCase< dim >::case_isotropic) const
FiniteElement::get_face_interpolation_matrix
virtual void get_face_interpolation_matrix(const FiniteElement< dim, spacedim > &source, FullMatrix< double > &matrix, const unsigned int face_no=0) const
FiniteElement::face_system_to_component_index
std::pair< unsigned int, unsigned int > face_system_to_component_index(const unsigned int index, const unsigned int face_no=0) const
FullMatrix::mmult
void mmult(FullMatrix< number2 > &C, const FullMatrix< number2 > &B, const bool adding=false) const
FullMatrix::n
size_type n() const
FullMatrix::invert
void invert(const FullMatrix< number2 > &M)
FullMatrix::m
size_type m() const
IndexSet::is_element
bool is_element(const size_type index) const
Definition index_set.h:1776
MPI_Comm
Triangulation::get_communicator
virtual MPI_Comm get_communicator() const
Triangulation::get_anisotropic_refinement_flag
bool get_anisotropic_refinement_flag() const
Triangulation::n_cells
unsigned int n_cells() const
hp::Collection::size
unsigned int size() const
Definition collection.h:265
hp::FECollection::find_dominating_fe_extended
unsigned int find_dominating_fe_extended(const std::set< unsigned int > &fes, const unsigned int codim=0) const
Definition fe_collection.cc:291
hp::FECollection::hp_constraints_are_implemented
bool hp_constraints_are_implemented() const
Definition fe_collection.h:1052
hp::FECollection::max_dofs_per_face
unsigned int max_dofs_per_face() const
Definition fe_collection.h:1023
hp::FECollection::n_components
unsigned int n_components() const
Definition fe_collection.h:901
hp::FECollection::max_dofs_per_cell
unsigned int max_dofs_per_cell() const
Definition fe_collection.h:1038
DEAL_II_NAMESPACE_OPEN
#define DEAL_II_NAMESPACE_OPEN
Definition config.h:472
DEAL_II_NAMESPACE_CLOSE
#define DEAL_II_NAMESPACE_CLOSE
Definition config.h:473
dof_accessor.h
dof_handler.h
dof_tools.h
fe_values.h
fe_collection.h
fe_tools.h
filtered_iterator.h
level
unsigned int level
Definition grid_out.cc:4618
cell_index
unsigned int cell_index
Definition grid_tools.cc:1196
grid_tools.h
DoFHandler::active_cell_iterators
IteratorRange< active_cell_iterator > active_cell_iterators() const
StandardExceptions::ExcInvalidIterator
static ::ExceptionBase & ExcInvalidIterator()
DoFTools::ExcGridNotCoarser
static ::ExceptionBase & ExcGridNotCoarser()
StandardExceptions::ExcNotImplemented
static ::ExceptionBase & ExcNotImplemented()
Assert
#define Assert(cond, exc)
Definition exceptions.h:1614
AssertDimension
#define AssertDimension(dim1, dim2)
Definition exceptions.h:1787
AssertIndexRange
#define AssertIndexRange(index, range)
Definition exceptions.h:1855
StandardExceptions::ExcInternalError
static ::ExceptionBase & ExcInternalError()
DoFTools::ExcFiniteElementsDontMatch
static ::ExceptionBase & ExcFiniteElementsDontMatch()
ComponentMask::ExcNoComponentSelected
static ::ExceptionBase & ExcNoComponentSelected()
StandardExceptions::ExcDimensionMismatch
static ::ExceptionBase & ExcDimensionMismatch(std::size_t arg1, std::size_t arg2)
DoFTools::ExcGridsDontMatch
static ::ExceptionBase & ExcGridsDontMatch()
StandardExceptions::ExcMessage
static ::ExceptionBase & ExcMessage(std::string arg1)
AssertThrow
#define AssertThrow(cond, exc)
Definition exceptions.h:1703
DoFHandler::cell_iterator
typename ActiveSelector::cell_iterator cell_iterator
Definition dof_handler.h:469
DoFHandler::line_iterator
typename ActiveSelector::line_iterator line_iterator
Definition dof_handler.h:360
DoFHandler::face_iterator
typename ActiveSelector::face_iterator face_iterator
Definition dof_handler.h:487
DoFHandler::active_cell_iterator
typename ActiveSelector::active_cell_iterator active_cell_iterator
Definition dof_handler.h:441
DoFTools::compute_intergrid_transfer_representation
void compute_intergrid_transfer_representation(const DoFHandler< dim, spacedim > &coarse_grid, const unsigned int coarse_component, const DoFHandler< dim, spacedim > &fine_grid, const unsigned int fine_component, const InterGridMap< DoFHandler< dim, spacedim > > &coarse_to_fine_grid_map, std::vector< std::map< types::global_dof_index, float > > &transfer_representation)
Definition dof_tools_constraints.cc:3360
DoFTools::make_zero_boundary_constraints
void make_zero_boundary_constraints(const DoFHandler< dim, spacedim > &dof, const types::boundary_id boundary_id, AffineConstraints< number > &zero_boundary_constraints, const ComponentMask &component_mask=ComponentMask())
Definition dof_tools_constraints.cc:3460
DoFTools::make_hanging_node_constraints
void make_hanging_node_constraints(const DoFHandler< dim, spacedim > &dof_handler, AffineConstraints< number > &constraints)
Definition dof_tools_constraints.cc:1791
DoFTools::compute_intergrid_constraints
void compute_intergrid_constraints(const DoFHandler< dim, spacedim > &coarse_grid, const unsigned int coarse_component, const DoFHandler< dim, spacedim > &fine_grid, const unsigned int fine_component, const InterGridMap< DoFHandler< dim, spacedim > > &coarse_to_fine_grid_map, AffineConstraints< double > &constraints)
Definition dof_tools_constraints.cc:3177
fe_values.h
intergrid_map.h
la_parallel_vector.h
DoFTools::internal::make_hp_hanging_node_constraints
void make_hp_hanging_node_constraints(const DoFHandler< 1 > &, AffineConstraints< number > &)
Definition dof_tools_constraints.cc:580
DoFTools::internal::make_oldstyle_hanging_node_constraints
void make_oldstyle_hanging_node_constraints(const DoFHandler< 1 > &, AffineConstraints< number > &, std::integral_constant< int, 1 >)
Definition dof_tools_constraints.cc:589
DoFTools::extract_locally_relevant_dofs
IndexSet extract_locally_relevant_dofs(const DoFHandler< dim, spacedim > &dof_handler)
Definition dof_tools.cc:1136
DoFTools::make_periodicity_constraints
void make_periodicity_constraints(const FaceIterator &face_1, const std_cxx20::type_identity_t< FaceIterator > &face_2, AffineConstraints< number > &constraints, const ComponentMask &component_mask=ComponentMask(), const bool face_orientation=true, const bool face_flip=false, const bool face_rotation=false, const FullMatrix< double > &matrix=FullMatrix< double >(), const std::vector< unsigned int > &first_vector_components=std::vector< unsigned int >(), const number periodicity_factor=1.)
Definition dof_tools_constraints.cc:2292
GridTools::collect_periodic_faces
void collect_periodic_faces(const MeshType &mesh, const types::boundary_id b_id1, const types::boundary_id b_id2, const unsigned int direction, std::vector< PeriodicFacePair< typename MeshType::cell_iterator > > &matched_pairs, const Tensor< 1, MeshType::space_dimension > &offset=::Tensor< 1, MeshType::space_dimension >(), const FullMatrix< double > &matrix=FullMatrix< double >())
Definition grid_tools_dof_handlers.cc:2232
LAPACKSupport::matrix
@ matrix
Contents is actually a matrix.
Definition lapack_support.h:58
Physics::Elasticity::Kinematics::l
Tensor< 2, dim, Number > l(const Tensor< 2, dim, Number > &F, const Tensor< 2, dim, Number > &dF_dt)
TrilinosWrappers::internal::end
VectorType::value_type * end(VectorType &V)
Definition trilinos_sparse_matrix.cc:65
Utilities::MPI::sum
T sum(const T &t, const MPI_Comm mpi_communicator)
WorkStream::run
void run(const std::vector< std::vector< Iterator > > &colored_iterators, Worker worker, Copier copier, const ScratchData &sample_scratch_data, const CopyData &sample_copy_data, const unsigned int queue_length=2 *MultithreadInfo::n_threads(), const unsigned int chunk_size=8)
Definition work_stream.h:1270
numbers::invalid_boundary_id
const types::boundary_id invalid_boundary_id
Definition types.h:261
numbers::invalid_fe_index
const types::fe_index invalid_fe_index
Definition types.h:228
numbers::invalid_unsigned_int
static const unsigned int invalid_unsigned_int
Definition types.h:213
numbers::invalid_dof_index
const types::global_dof_index invalid_dof_index
Definition types.h:233
std_cxx20::type_identity_t
typename type_identity< T >::type type_identity_t
Definition type_traits.h:96
std
STL namespace.
std::abs
::VectorizedArray< Number, width > abs(const ::VectorizedArray< Number, width > &)
Definition vectorization.h:6008
types::fe_index
unsigned short int fe_index
Definition types.h:60
DoFTools::internal::Assembler::CopyData::global_parameter_representation
std::vector<::LinearAlgebra::distributed::Vector< double > > global_parameter_representation
Definition dof_tools_constraints.cc:2664
DoFTools::internal::Assembler::CopyData::parameter_dof_indices
std::vector< types::global_dof_index > parameter_dof_indices
Definition dof_tools_constraints.cc:2661
GeometryInfo::n_children
static unsigned int n_children(const RefinementCase< dim > &refinement_case)
template_constraints.h
tria
const ::Triangulation< dim, spacedim > & tria
Definition tria_description.cc:704
tria_iterator.h
work_stream.h
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