Reference documentation for deal.II version GIT relicensing-399-g79d89019c5 2024-04-16 15:00:02+00:00
\(\newcommand{\dealvcentcolon}{\mathrel{\mathop{:}}}\) \(\newcommand{\dealcoloneq}{\dealvcentcolon\mathrel{\mkern-1.2mu}=}\) \(\newcommand{\jump}[1]{\left[\!\left[ #1 \right]\!\right]}\) \(\newcommand{\average}[1]{\left\{\!\left\{ #1 \right\}\!\right\}}\)
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fe_tools.h
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1// ------------------------------------------------------------------------
2//
3// SPDX-License-Identifier: LGPL-2.1-or-later
4// Copyright (C) 2000 - 2023 by the deal.II authors
5//
6// This file is part of the deal.II library.
7//
8// Part of the source code is dual licensed under Apache-2.0 WITH
9// LLVM-exception OR LGPL-2.1-or-later. Detailed license information
10// governing the source code and code contributions can be found in
11// LICENSE.md and CONTRIBUTING.md at the top level directory of deal.II.
12//
13// ------------------------------------------------------------------------
14
15#ifndef dealii_fe_tools_H
16#define dealii_fe_tools_H
17
18
19
20#include <deal.II/base/config.h>
21
26#include <deal.II/base/tensor.h>
27
29
31
33
34#include <memory>
35#include <string>
36#include <vector>
37
38
40
41// Forward declarations
42#ifndef DOXYGEN
43template <typename number>
44class FullMatrix;
45template <int dim>
46class Quadrature;
47template <int dim, int spacedim>
48class FiniteElement;
49template <int dim, int spacedim>
51class DoFHandler;
52template <int dim>
54template <typename number>
56#endif
57
58
77namespace FETools
78{
87 template <int dim, int spacedim = dim>
89 {
90 public:
94 virtual std::unique_ptr<FiniteElement<dim, spacedim>>
95 get(const unsigned int degree) const = 0;
96
102 virtual std::unique_ptr<FiniteElement<dim, spacedim>>
103 get(const Quadrature<1> &quad) const = 0;
104
108 virtual ~FEFactoryBase() override = default;
109 };
110
120 template <class FE>
121 class FEFactory : public FEFactoryBase<FE::dimension, FE::space_dimension>
122 {
123 public:
127 virtual std::unique_ptr<FiniteElement<FE::dimension, FE::space_dimension>>
128 get(const unsigned int degree) const override;
129
134 virtual std::unique_ptr<FiniteElement<FE::dimension, FE::space_dimension>>
135 get(const Quadrature<1> &quad) const override;
136 };
137
153 template <int dim, int spacedim>
154 void
156 std::vector<unsigned int> &renumbering,
157 std::vector<std::vector<unsigned int>> &start_indices);
158
174 template <int dim, int spacedim>
175 void
177 std::vector<types::global_dof_index> &renumbering,
178 std::vector<types::global_dof_index> &block_data,
179 bool return_start_indices = true);
180
194 template <int dim, typename number, int spacedim>
195 void
198 FullMatrix<number> &interpolation_matrix);
199
211 template <int dim, typename number, int spacedim>
212 void
215 FullMatrix<number> &interpolation_matrix);
216
228 template <int dim, typename number, int spacedim>
229 void
232 FullMatrix<number> &difference_matrix);
233
237 template <int dim, typename number, int spacedim>
238 void
241 FullMatrix<number> &matrix);
242
311 template <int dim, int spacedim>
314
353 template <int dim, typename number, int spacedim>
354 void
357 std::vector<std::vector<FullMatrix<number>>> &matrices,
358 const bool isotropic_only = false,
359 const double threshold = 1.e-12);
360
382 template <int dim, typename number, int spacedim>
383 void
387 const unsigned int face_coarse,
388 const unsigned int face_fine,
389 const double threshold = 1.e-12);
390
422 template <int dim, typename number, int spacedim>
423 void
426 std::vector<std::vector<FullMatrix<number>>> &matrices,
427 const bool isotropic_only = false);
428
514 template <int dim, int spacedim>
515 void
518 const Quadrature<dim> &lhs_quadrature,
519 const Quadrature<dim> &rhs_quadrature,
521
529 template <int dim, int spacedim>
530 void
533 const Quadrature<dim> &quadrature,
534 FullMatrix<double> &I_q);
535
549 template <int dim>
550 void
552 const FullMatrix<double> &projection_matrix,
553 const std::vector<Tensor<1, dim>> &vector_of_tensors_at_qp,
554 std::vector<Tensor<1, dim>> &vector_of_tensors_at_nodes);
555
556
557
561 template <int dim>
562 void
564 const FullMatrix<double> &projection_matrix,
565 const std::vector<SymmetricTensor<2, dim>> &vector_of_tensors_at_qp,
566 std::vector<SymmetricTensor<2, dim>> &vector_of_tensors_at_nodes);
567
568
569
579 template <int dim, int spacedim>
580 void
583 const Quadrature<dim - 1> &lhs_quadrature,
584 const Quadrature<dim - 1> &rhs_quadrature,
586 const unsigned int face,
588
589
590
606 template <int dim, int spacedim, typename number>
607 void
609 const FiniteElement<dim, spacedim> &finite_element,
610 const std::vector<Vector<number>> &support_point_values,
611 std::vector<number> &dof_values);
612
613
614
652 template <int dim, int spacedim, class InVector, class OutVector>
653 void
655 const InVector &u1,
656 const DoFHandler<dim, spacedim> &dof2,
657 OutVector &u2);
658
678 template <int dim, int spacedim, class InVector, class OutVector>
679 void
681 const DoFHandler<dim, spacedim> &dof1,
682 const InVector &u1,
683 const DoFHandler<dim, spacedim> &dof2,
685 OutVector &u2);
686
700 template <int dim, class InVector, class OutVector, int spacedim>
701 void
703 const InVector &u1,
705 OutVector &u1_interpolated);
706
719 template <int dim, class InVector, class OutVector, int spacedim>
720 void
722 const DoFHandler<dim, spacedim> &dof1,
724 const InVector &u1,
725 const DoFHandler<dim, spacedim> &dof2,
727 OutVector &u1_interpolated);
728
738 template <int dim, class InVector, class OutVector, int spacedim>
739 void
741 const InVector &z1,
743 OutVector &z1_difference);
744
757 template <int dim, class InVector, class OutVector, int spacedim>
758 void
760 const DoFHandler<dim, spacedim> &dof1,
762 const InVector &z1,
763 const DoFHandler<dim, spacedim> &dof2,
765 OutVector &z1_difference);
766
767
768
777 template <int dim, class InVector, class OutVector, int spacedim>
778 void
780 const InVector &u1,
781 const DoFHandler<dim, spacedim> &dof2,
782 OutVector &u2);
783
844 template <int dim, class InVector, class OutVector, int spacedim>
845 void
847 const InVector &z1,
848 const DoFHandler<dim, spacedim> &dof2,
849 OutVector &z2);
850
863 template <int dim, class InVector, class OutVector, int spacedim>
864 void
866 const DoFHandler<dim, spacedim> &dof1,
867 const InVector &z1,
868 const DoFHandler<dim, spacedim> &dof2,
870 OutVector &z2);
871
887 template <int dim>
888 std::vector<unsigned int>
890
897 template <int dim>
898 std::vector<unsigned int>
900
976 namespace Compositing
977 {
994 template <int dim, int spacedim>
997 const std::vector<const FiniteElement<dim, spacedim> *> &fes,
998 const std::vector<unsigned int> &multiplicities,
999 const bool do_tensor_product = true);
1000
1006 template <int dim, int spacedim>
1009 const std::initializer_list<
1010 std::pair<std::unique_ptr<FiniteElement<dim, spacedim>>, unsigned int>>
1011 &fe_systems);
1012
1016 template <int dim, int spacedim>
1019 const unsigned int N1,
1020 const FiniteElement<dim, spacedim> *fe2 = nullptr,
1021 const unsigned int N2 = 0,
1022 const FiniteElement<dim, spacedim> *fe3 = nullptr,
1023 const unsigned int N3 = 0,
1024 const FiniteElement<dim, spacedim> *fe4 = nullptr,
1025 const unsigned int N4 = 0,
1026 const FiniteElement<dim, spacedim> *fe5 = nullptr,
1027 const unsigned int N5 = 0);
1028
1041 template <int dim, int spacedim>
1042 std::vector<bool>
1044 const std::vector<const FiniteElement<dim, spacedim> *> &fes,
1045 const std::vector<unsigned int> &multiplicities);
1046
1052 template <int dim, int spacedim>
1053 std::vector<bool>
1055 const std::initializer_list<
1056 std::pair<std::unique_ptr<FiniteElement<dim, spacedim>>, unsigned int>>
1057 &fe_systems);
1058
1073 template <int dim, int spacedim>
1074 std::vector<bool>
1077 const unsigned int N1,
1078 const FiniteElement<dim, spacedim> *fe2 = nullptr,
1079 const unsigned int N2 = 0,
1080 const FiniteElement<dim, spacedim> *fe3 = nullptr,
1081 const unsigned int N3 = 0,
1082 const FiniteElement<dim, spacedim> *fe4 = nullptr,
1083 const unsigned int N4 = 0,
1084 const FiniteElement<dim, spacedim> *fe5 = nullptr,
1085 const unsigned int N5 = 0);
1086
1087
1104 template <int dim, int spacedim>
1105 std::vector<ComponentMask>
1107 const std::vector<const FiniteElement<dim, spacedim> *> &fes,
1108 const std::vector<unsigned int> &multiplicities,
1109 const bool do_tensor_product = true);
1110
1116 template <int dim, int spacedim>
1117 std::vector<ComponentMask>
1119 const std::initializer_list<
1120 std::pair<std::unique_ptr<FiniteElement<dim, spacedim>>, unsigned int>>
1121 &fe_systems);
1122
1141 template <int dim, int spacedim>
1142 std::vector<ComponentMask>
1145 const unsigned int N1,
1146 const FiniteElement<dim, spacedim> *fe2 = nullptr,
1147 const unsigned int N2 = 0,
1148 const FiniteElement<dim, spacedim> *fe3 = nullptr,
1149 const unsigned int N3 = 0,
1150 const FiniteElement<dim, spacedim> *fe4 = nullptr,
1151 const unsigned int N4 = 0,
1152 const FiniteElement<dim, spacedim> *fe5 = nullptr,
1153 const unsigned int N5 = 0,
1154 const bool do_tensor_product = true);
1155
1172 template <int dim, int spacedim>
1173 void
1175 std::vector<std::pair<std::pair<unsigned int, unsigned int>,
1176 unsigned int>> &system_to_base_table,
1177 std::vector<std::pair<unsigned int, unsigned int>>
1178 &system_to_component_table,
1179 std::vector<std::pair<std::pair<unsigned int, unsigned int>,
1180 unsigned int>> &component_to_base_table,
1181 const FiniteElement<dim, spacedim> &finite_element,
1182 const bool do_tensor_product = true);
1183
1199 template <int dim, int spacedim>
1200 void
1202 std::vector<std::pair<std::pair<unsigned int, unsigned int>,
1203 unsigned int>> &face_system_to_base_table,
1204 std::vector<std::pair<unsigned int, unsigned int>>
1205 &face_system_to_component_table,
1206 const FiniteElement<dim, spacedim> &finite_element,
1207 const bool do_tensor_product = true,
1208 const unsigned int face_no = 0 /*TODO*/);
1209
1210 } // namespace Compositing
1211
1212
1246 template <int dim, int spacedim = dim>
1247 std::unique_ptr<FiniteElement<dim, spacedim>>
1248 get_fe_by_name(const std::string &name);
1249
1292 template <int dim, int spacedim>
1293 void
1294 add_fe_name(const std::string &name,
1295 const FEFactoryBase<dim, spacedim> *factory);
1296
1307 std::string,
1308 << "Can't re-generate a finite element from the string '"
1309 << arg1 << "'.");
1310
1323 char,
1324 int,
1325 << "The dimension " << arg1
1326 << " in the finite element string must match "
1327 << "the space dimension " << arg2 << '.');
1328
1335
1349
1357 "You are using continuous elements on a grid with "
1358 "hanging nodes but without providing hanging node "
1359 "constraints. Use the respective function with "
1360 "additional AffineConstraints argument(s), instead.");
1373 int,
1374 int,
1375 int,
1376 int,
1377 << "This is a " << arg1 << 'x' << arg2 << " matrix, "
1378 << "but should be a " << arg3 << 'x' << arg4 << " matrix.");
1379
1386 double,
1387 << "Least squares fit leaves a gap of " << arg1);
1388
1395 int,
1396 int,
1397 << arg1 << " must be greater than " << arg2);
1398} // namespace FETools
1399
1400
1401#ifndef DOXYGEN
1402
1403namespace FETools
1404{
1405 template <class FE>
1406 std::unique_ptr<FiniteElement<FE::dimension, FE::space_dimension>>
1407 FEFactory<FE>::get(const unsigned int degree) const
1408 {
1409 return std::make_unique<FE>(degree);
1410 }
1411
1412 namespace Compositing
1413 {
1414 template <int dim, int spacedim>
1415 std::vector<bool>
1417 const std::initializer_list<
1418 std::pair<std::unique_ptr<FiniteElement<dim, spacedim>>, unsigned int>>
1419 &fe_systems)
1420 {
1421 std::vector<const FiniteElement<dim, spacedim> *> fes;
1422 std::vector<unsigned int> multiplicities;
1423
1424 const auto extract =
1425 [&fes, &multiplicities](
1426 const std::pair<std::unique_ptr<FiniteElement<dim, spacedim>>,
1427 unsigned int> &fe_system) {
1428 fes.push_back(fe_system.first.get());
1429 multiplicities.push_back(fe_system.second);
1430 };
1431
1432 for (const auto &p : fe_systems)
1433 extract(p);
1434
1435 return compute_restriction_is_additive_flags(fes, multiplicities);
1436 }
1437
1438
1439
1440 template <int dim, int spacedim>
1443 const std::initializer_list<
1444 std::pair<std::unique_ptr<FiniteElement<dim, spacedim>>, unsigned int>>
1445 &fe_systems)
1446 {
1447 std::vector<const FiniteElement<dim, spacedim> *> fes;
1448 std::vector<unsigned int> multiplicities;
1449
1450 const auto extract =
1451 [&fes, &multiplicities](
1452 const std::pair<std::unique_ptr<FiniteElement<dim, spacedim>>,
1453 unsigned int> &fe_system) {
1454 fes.push_back(fe_system.first.get());
1455 multiplicities.push_back(fe_system.second);
1456 };
1457
1458 for (const auto &p : fe_systems)
1459 extract(p);
1460
1461 return multiply_dof_numbers(fes, multiplicities, true);
1462 }
1463
1464
1465
1466 template <int dim, int spacedim>
1467 std::vector<ComponentMask>
1469 const std::initializer_list<
1470 std::pair<std::unique_ptr<FiniteElement<dim, spacedim>>, unsigned int>>
1471 &fe_systems)
1472 {
1473 std::vector<const FiniteElement<dim, spacedim> *> fes;
1474 std::vector<unsigned int> multiplicities;
1475
1476 const auto extract =
1477 [&fes, &multiplicities](
1478 const std::pair<std::unique_ptr<FiniteElement<dim, spacedim>>,
1479 unsigned int> &fe_system) {
1480 fes.push_back(fe_system.first.get());
1481 multiplicities.push_back(fe_system.second);
1482 };
1483
1484 for (const auto &p : fe_systems)
1485 extract(p);
1486
1487 return compute_nonzero_components(fes, multiplicities, true);
1488 }
1489 } // namespace Compositing
1490} // namespace FETools
1491
1492#endif
1493
1497
1498#endif /* dealii_fe_tools_H */
virtual ~FEFactoryBase() override=default
virtual std::unique_ptr< FiniteElement< dim, spacedim > > get(const Quadrature< 1 > &quad) const =0
virtual std::unique_ptr< FiniteElement< dim, spacedim > > get(const unsigned int degree) const =0
virtual std::unique_ptr< FiniteElement< FE::dimension, FE::space_dimension > > get(const Quadrature< 1 > &quad) const override
virtual std::unique_ptr< FiniteElement< FE::dimension, FE::space_dimension > > get(const unsigned int degree) const override
#define DEAL_II_NAMESPACE_OPEN
Definition config.h:502
#define DEAL_II_CXX20_REQUIRES(condition)
Definition config.h:177
#define DEAL_II_NAMESPACE_CLOSE
Definition config.h:503
#define DeclException0(Exception0)
Definition exceptions.h:471
static ::ExceptionBase & ExcTriangulationMismatch()
static ::ExceptionBase & ExcInvalidFEName(std::string arg1)
#define DeclException4(Exception4, type1, type2, type3, type4, outsequence)
Definition exceptions.h:585
static ::ExceptionBase & ExcInvalidFEDimension(char arg1, int arg2)
static ::ExceptionBase & ExcLeastSquaresError(double arg1)
#define DeclException2(Exception2, type1, type2, outsequence)
Definition exceptions.h:539
static ::ExceptionBase & ExcFENotPrimitive()
static ::ExceptionBase & ExcHangingNodesNotAllowed()
#define DeclExceptionMsg(Exception, defaulttext)
Definition exceptions.h:494
static ::ExceptionBase & ExcInvalidFE()
static ::ExceptionBase & ExcGridNotRefinedAtLeastOnce()
static ::ExceptionBase & ExcMatrixDimensionMismatch(int arg1, int arg2, int arg3, int arg4)
#define DeclException1(Exception1, type1, outsequence)
Definition exceptions.h:516
static ::ExceptionBase & ExcNotGreaterThan(int arg1, int arg2)
typename ActiveSelector::active_cell_iterator active_cell_iterator
void build_face_tables(std::vector< std::pair< std::pair< unsigned int, unsigned int >, unsigned int > > &face_system_to_base_table, std::vector< std::pair< unsigned int, unsigned int > > &face_system_to_component_table, const FiniteElement< dim, spacedim > &finite_element, const bool do_tensor_product=true, const unsigned int face_no=0)
std::vector< ComponentMask > compute_nonzero_components(const std::vector< const FiniteElement< dim, spacedim > * > &fes, const std::vector< unsigned int > &multiplicities, const bool do_tensor_product=true)
std::vector< bool > compute_restriction_is_additive_flags(const std::vector< const FiniteElement< dim, spacedim > * > &fes, const std::vector< unsigned int > &multiplicities)
void build_cell_tables(std::vector< std::pair< std::pair< unsigned int, unsigned int >, unsigned int > > &system_to_base_table, std::vector< std::pair< unsigned int, unsigned int > > &system_to_component_table, std::vector< std::pair< std::pair< unsigned int, unsigned int >, unsigned int > > &component_to_base_table, const FiniteElement< dim, spacedim > &finite_element, const bool do_tensor_product=true)
FiniteElementData< dim > multiply_dof_numbers(const std::vector< const FiniteElement< dim, spacedim > * > &fes, const std::vector< unsigned int > &multiplicities, const bool do_tensor_product=true)
void interpolation_difference(const DoFHandler< dim, spacedim > &dof1, const InVector &z1, const FiniteElement< dim, spacedim > &fe2, OutVector &z1_difference)
void compute_projection_from_quadrature_points(const FullMatrix< double > &projection_matrix, const std::vector< Tensor< 1, dim > > &vector_of_tensors_at_qp, std::vector< Tensor< 1, dim > > &vector_of_tensors_at_nodes)
void project_dg(const DoFHandler< dim, spacedim > &dof1, const InVector &u1, const DoFHandler< dim, spacedim > &dof2, OutVector &u2)
void get_back_interpolation_matrix(const FiniteElement< dim, spacedim > &fe1, const FiniteElement< dim, spacedim > &fe2, FullMatrix< number > &interpolation_matrix)
void get_projection_matrix(const FiniteElement< dim, spacedim > &fe1, const FiniteElement< dim, spacedim > &fe2, FullMatrix< number > &matrix)
void compute_component_wise(const FiniteElement< dim, spacedim > &fe, std::vector< unsigned int > &renumbering, std::vector< std::vector< unsigned int > > &start_indices)
void add_fe_name(const std::string &name, const FEFactoryBase< dim, spacedim > *factory)
std::vector< unsigned int > hierarchic_to_lexicographic_numbering(unsigned int degree)
void convert_generalized_support_point_values_to_dof_values(const FiniteElement< dim, spacedim > &finite_element, const std::vector< Vector< number > > &support_point_values, std::vector< number > &dof_values)
void compute_interpolation_to_quadrature_points_matrix(const FiniteElement< dim, spacedim > &fe, const Quadrature< dim > &quadrature, FullMatrix< double > &I_q)
std::unique_ptr< FiniteElement< dim, spacedim > > get_fe_by_name(const std::string &name)
void compute_projection_from_quadrature_points_matrix(const FiniteElement< dim, spacedim > &fe, const Quadrature< dim > &lhs_quadrature, const Quadrature< dim > &rhs_quadrature, FullMatrix< double > &X)
void get_interpolation_matrix(const FiniteElement< dim, spacedim > &fe1, const FiniteElement< dim, spacedim > &fe2, FullMatrix< number > &interpolation_matrix)
void extrapolate(const DoFHandler< dim, spacedim > &dof1, const InVector &z1, const DoFHandler< dim, spacedim > &dof2, OutVector &z2)
void compute_embedding_matrices(const FiniteElement< dim, spacedim > &fe, std::vector< std::vector< FullMatrix< number > > > &matrices, const bool isotropic_only=false, const double threshold=1.e-12)
void compute_face_embedding_matrices(const FiniteElement< dim, spacedim > &fe, FullMatrix< number >(&matrices)[GeometryInfo< dim >::max_children_per_face], const unsigned int face_coarse, const unsigned int face_fine, const double threshold=1.e-12)
void interpolate(const DoFHandler< dim, spacedim > &dof1, const InVector &u1, const DoFHandler< dim, spacedim > &dof2, OutVector &u2)
void compute_block_renumbering(const FiniteElement< dim, spacedim > &fe, std::vector< types::global_dof_index > &renumbering, std::vector< types::global_dof_index > &block_data, bool return_start_indices=true)
std::vector< unsigned int > lexicographic_to_hierarchic_numbering(unsigned int degree)
void compute_projection_from_face_quadrature_points_matrix(const FiniteElement< dim, spacedim > &fe, const Quadrature< dim - 1 > &lhs_quadrature, const Quadrature< dim - 1 > &rhs_quadrature, const typename DoFHandler< dim, spacedim >::active_cell_iterator &cell, const unsigned int face, FullMatrix< double > &X)
FullMatrix< double > compute_node_matrix(const FiniteElement< dim, spacedim > &fe)
void get_interpolation_difference_matrix(const FiniteElement< dim, spacedim > &fe1, const FiniteElement< dim, spacedim > &fe2, FullMatrix< number > &difference_matrix)
void back_interpolate(const DoFHandler< dim, spacedim > &dof1, const InVector &u1, const FiniteElement< dim, spacedim > &fe2, OutVector &u1_interpolated)
void compute_projection_matrices(const FiniteElement< dim, spacedim > &fe, std::vector< std::vector< FullMatrix< number > > > &matrices, const bool isotropic_only=false)
spacedim const Point< spacedim > & p
Definition grid_tools.h:990
constexpr ReturnType< rank, T >::value_type & extract(T &t, const ArrayType &indices)