Reference documentation for deal.II version Git d3aed38b93 2021-10-28 13:33:27 +0200
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fe_tools.h
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15 
16 #ifndef dealii_fe_tools_H
17 #define dealii_fe_tools_H
18 
19 
20 
21 #include <deal.II/base/config.h>
22 
27 #include <deal.II/base/tensor.h>
28 
30 
32 
34 
35 #include <memory>
36 #include <string>
37 #include <vector>
38 
39 
41 
42 // Forward declarations
43 #ifndef DOXYGEN
44 template <typename number>
45 class FullMatrix;
46 template <int dim>
47 class Quadrature;
48 template <int dim, int spacedim>
49 class FiniteElement;
50 template <int dim, int spacedim>
51 class DoFHandler;
52 template <int dim>
53 class FiniteElementData;
54 template <typename number>
55 class AffineConstraints;
56 #endif
57 
58 
61 
62 
75 namespace FETools
76 {
85  template <int dim, int spacedim = dim>
86  class FEFactoryBase : public Subscriptor
87  {
88  public:
92  virtual std::unique_ptr<FiniteElement<dim, spacedim>>
93  get(const unsigned int degree) const = 0;
94 
100  virtual std::unique_ptr<FiniteElement<dim, spacedim>>
101  get(const Quadrature<1> &quad) const = 0;
102 
106  virtual ~FEFactoryBase() override = default;
107  };
108 
118  template <class FE>
119  class FEFactory : public FEFactoryBase<FE::dimension, FE::space_dimension>
120  {
121  public:
125  virtual std::unique_ptr<FiniteElement<FE::dimension, FE::space_dimension>>
126  get(const unsigned int degree) const override;
127 
132  virtual std::unique_ptr<FiniteElement<FE::dimension, FE::space_dimension>>
133  get(const Quadrature<1> &quad) const override;
134  };
135 
151  template <int dim, int spacedim>
152  void
154  std::vector<unsigned int> & renumbering,
155  std::vector<std::vector<unsigned int>> &start_indices);
156 
172  template <int dim, int spacedim>
173  void
175  std::vector<types::global_dof_index> &renumbering,
176  std::vector<types::global_dof_index> &block_data,
177  bool return_start_indices = true);
178 
192  template <int dim, typename number, int spacedim>
193  void
195  const FiniteElement<dim, spacedim> &fe2,
196  FullMatrix<number> &interpolation_matrix);
197 
209  template <int dim, typename number, int spacedim>
210  void
212  const FiniteElement<dim, spacedim> &fe2,
213  FullMatrix<number> &interpolation_matrix);
214 
226  template <int dim, typename number, int spacedim>
227  void
229  const FiniteElement<dim, spacedim> &fe2,
230  FullMatrix<number> &difference_matrix);
231 
235  template <int dim, typename number, int spacedim>
236  void
238  const FiniteElement<dim, spacedim> &fe2,
240 
309  template <int dim, int spacedim>
312 
351  template <int dim, typename number, int spacedim>
352  void
354  const FiniteElement<dim, spacedim> & fe,
355  std::vector<std::vector<FullMatrix<number>>> &matrices,
356  const bool isotropic_only = false,
357  const double threshold = 1.e-12);
358 
380  template <int dim, typename number, int spacedim>
381  void
385  const unsigned int face_coarse,
386  const unsigned int face_fine,
387  const double threshold = 1.e-12);
388 
420  template <int dim, typename number, int spacedim>
421  void
423  const FiniteElement<dim, spacedim> & fe,
424  std::vector<std::vector<FullMatrix<number>>> &matrices,
425  const bool isotropic_only = false);
426 
512  template <int dim, int spacedim>
513  void
516  const Quadrature<dim> & lhs_quadrature,
517  const Quadrature<dim> & rhs_quadrature,
518  FullMatrix<double> & X);
519 
527  template <int dim, int spacedim>
528  void
531  const Quadrature<dim> & quadrature,
532  FullMatrix<double> & I_q);
533 
547  template <int dim>
548  void
550  const FullMatrix<double> & projection_matrix,
551  const std::vector<Tensor<1, dim>> &vector_of_tensors_at_qp,
552  std::vector<Tensor<1, dim>> & vector_of_tensors_at_nodes);
553 
554 
555 
559  template <int dim>
560  void
562  const FullMatrix<double> & projection_matrix,
563  const std::vector<SymmetricTensor<2, dim>> &vector_of_tensors_at_qp,
564  std::vector<SymmetricTensor<2, dim>> & vector_of_tensors_at_nodes);
565 
566 
567 
577  template <int dim, int spacedim>
578  void
581  const Quadrature<dim - 1> & lhs_quadrature,
582  const Quadrature<dim - 1> & rhs_quadrature,
584  const unsigned int face,
585  FullMatrix<double> & X);
586 
587 
588 
604  template <int dim, int spacedim, typename number>
605  void
607  const FiniteElement<dim, spacedim> &finite_element,
608  const std::vector<Vector<number>> & support_point_values,
609  std::vector<number> & dof_values);
610 
611 
612 
614 
647  template <int dim, int spacedim, class InVector, class OutVector>
648  void
650  const InVector & u1,
651  const DoFHandler<dim, spacedim> &dof2,
652  OutVector & u2);
653 
670  template <int dim, int spacedim, class InVector, class OutVector>
671  void
672  interpolate(
673  const DoFHandler<dim, spacedim> & dof1,
674  const InVector & u1,
675  const DoFHandler<dim, spacedim> & dof2,
677  OutVector & u2);
678 
692  template <int dim, class InVector, class OutVector, int spacedim>
693  void
695  const InVector & u1,
696  const FiniteElement<dim, spacedim> &fe2,
697  OutVector & u1_interpolated);
698 
711  template <int dim, class InVector, class OutVector, int spacedim>
712  void
714  const DoFHandler<dim, spacedim> & dof1,
716  const InVector & u1,
717  const DoFHandler<dim, spacedim> & dof2,
719  OutVector & u1_interpolated);
720 
730  template <int dim, class InVector, class OutVector, int spacedim>
731  void
733  const InVector & z1,
734  const FiniteElement<dim, spacedim> &fe2,
735  OutVector & z1_difference);
736 
749  template <int dim, class InVector, class OutVector, int spacedim>
750  void
752  const DoFHandler<dim, spacedim> & dof1,
754  const InVector & z1,
755  const DoFHandler<dim, spacedim> & dof2,
757  OutVector & z1_difference);
758 
759 
760 
769  template <int dim, class InVector, class OutVector, int spacedim>
770  void
772  const InVector & u1,
773  const DoFHandler<dim, spacedim> &dof2,
774  OutVector & u2);
775 
836  template <int dim, class InVector, class OutVector, int spacedim>
837  void
839  const InVector & z1,
840  const DoFHandler<dim, spacedim> &dof2,
841  OutVector & z2);
842 
855  template <int dim, class InVector, class OutVector, int spacedim>
856  void
857  extrapolate(
858  const DoFHandler<dim, spacedim> & dof1,
859  const InVector & z1,
860  const DoFHandler<dim, spacedim> & dof2,
862  OutVector & z2);
863 
865 
879  template <int dim>
880  std::vector<unsigned int>
881  hierarchic_to_lexicographic_numbering(unsigned int degree);
882 
889  template <int dim>
890  std::vector<unsigned int>
891  lexicographic_to_hierarchic_numbering(unsigned int degree);
892 
966  namespace Compositing
967  {
984  template <int dim, int spacedim>
987  const std::vector<const FiniteElement<dim, spacedim> *> &fes,
988  const std::vector<unsigned int> & multiplicities,
989  const bool do_tensor_product = true);
990 
996  template <int dim, int spacedim>
999  const std::initializer_list<
1000  std::pair<std::unique_ptr<FiniteElement<dim, spacedim>>, unsigned int>>
1001  &fe_systems);
1002 
1006  template <int dim, int spacedim>
1009  const unsigned int N1,
1010  const FiniteElement<dim, spacedim> *fe2 = nullptr,
1011  const unsigned int N2 = 0,
1012  const FiniteElement<dim, spacedim> *fe3 = nullptr,
1013  const unsigned int N3 = 0,
1014  const FiniteElement<dim, spacedim> *fe4 = nullptr,
1015  const unsigned int N4 = 0,
1016  const FiniteElement<dim, spacedim> *fe5 = nullptr,
1017  const unsigned int N5 = 0);
1018 
1031  template <int dim, int spacedim>
1032  std::vector<bool>
1034  const std::vector<const FiniteElement<dim, spacedim> *> &fes,
1035  const std::vector<unsigned int> & multiplicities);
1036 
1042  template <int dim, int spacedim>
1043  std::vector<bool>
1045  const std::initializer_list<
1046  std::pair<std::unique_ptr<FiniteElement<dim, spacedim>>, unsigned int>>
1047  &fe_systems);
1048 
1063  template <int dim, int spacedim>
1064  std::vector<bool>
1066  const FiniteElement<dim, spacedim> *fe1,
1067  const unsigned int N1,
1068  const FiniteElement<dim, spacedim> *fe2 = nullptr,
1069  const unsigned int N2 = 0,
1070  const FiniteElement<dim, spacedim> *fe3 = nullptr,
1071  const unsigned int N3 = 0,
1072  const FiniteElement<dim, spacedim> *fe4 = nullptr,
1073  const unsigned int N4 = 0,
1074  const FiniteElement<dim, spacedim> *fe5 = nullptr,
1075  const unsigned int N5 = 0);
1076 
1077 
1094  template <int dim, int spacedim>
1095  std::vector<ComponentMask>
1097  const std::vector<const FiniteElement<dim, spacedim> *> &fes,
1098  const std::vector<unsigned int> & multiplicities,
1099  const bool do_tensor_product = true);
1100 
1106  template <int dim, int spacedim>
1107  std::vector<ComponentMask>
1109  const std::initializer_list<
1110  std::pair<std::unique_ptr<FiniteElement<dim, spacedim>>, unsigned int>>
1111  &fe_systems);
1112 
1131  template <int dim, int spacedim>
1132  std::vector<ComponentMask>
1134  const FiniteElement<dim, spacedim> *fe1,
1135  const unsigned int N1,
1136  const FiniteElement<dim, spacedim> *fe2 = nullptr,
1137  const unsigned int N2 = 0,
1138  const FiniteElement<dim, spacedim> *fe3 = nullptr,
1139  const unsigned int N3 = 0,
1140  const FiniteElement<dim, spacedim> *fe4 = nullptr,
1141  const unsigned int N4 = 0,
1142  const FiniteElement<dim, spacedim> *fe5 = nullptr,
1143  const unsigned int N5 = 0,
1144  const bool do_tensor_product = true);
1145 
1162  template <int dim, int spacedim>
1163  void
1165  std::vector<std::pair<std::pair<unsigned int, unsigned int>,
1166  unsigned int>> &system_to_base_table,
1167  std::vector<std::pair<unsigned int, unsigned int>>
1168  & system_to_component_table,
1169  std::vector<std::pair<std::pair<unsigned int, unsigned int>,
1170  unsigned int>> &component_to_base_table,
1171  const FiniteElement<dim, spacedim> & finite_element,
1172  const bool do_tensor_product = true);
1173 
1189  template <int dim, int spacedim>
1190  void
1192  std::vector<std::pair<std::pair<unsigned int, unsigned int>,
1193  unsigned int>> &face_system_to_base_table,
1194  std::vector<std::pair<unsigned int, unsigned int>>
1195  & face_system_to_component_table,
1196  const FiniteElement<dim, spacedim> &finite_element,
1197  const bool do_tensor_product = true,
1198  const unsigned int face_no = 0 /*TODO*/);
1199 
1200  } // namespace Compositing
1201 
1202 
1236  template <int dim, int spacedim = dim>
1237  std::unique_ptr<FiniteElement<dim, spacedim>>
1238  get_fe_by_name(const std::string &name);
1239 
1282  template <int dim, int spacedim>
1283  void
1284  add_fe_name(const std::string & name,
1285  const FEFactoryBase<dim, spacedim> *factory);
1286 
1297  std::string,
1298  << "Can't re-generate a finite element from the string '"
1299  << arg1 << "'.");
1300 
1313  char,
1314  int,
1315  << "The dimension " << arg1
1316  << " in the finite element string must match "
1317  << "the space dimension " << arg2 << ".");
1318 
1325 
1339 
1347  "You are using continuous elements on a grid with "
1348  "hanging nodes but without providing hanging node "
1349  "constraints. Use the respective function with "
1350  "additional AffineConstraints argument(s), instead.");
1363  int,
1364  int,
1365  int,
1366  int,
1367  << "This is a " << arg1 << "x" << arg2 << " matrix, "
1368  << "but should be a " << arg3 << "x" << arg4 << " matrix.");
1369 
1376  double,
1377  << "Least squares fit leaves a gap of " << arg1);
1378 
1385  int,
1386  int,
1387  << arg1 << " must be greater than " << arg2);
1388 } // namespace FETools
1389 
1390 
1391 #ifndef DOXYGEN
1392 
1393 namespace FETools
1394 {
1395  template <class FE>
1396  std::unique_ptr<FiniteElement<FE::dimension, FE::space_dimension>>
1397  FEFactory<FE>::get(const unsigned int degree) const
1398  {
1399  return std::make_unique<FE>(degree);
1400  }
1401 
1402  namespace Compositing
1403  {
1404  template <int dim, int spacedim>
1405  std::vector<bool>
1407  const std::initializer_list<
1408  std::pair<std::unique_ptr<FiniteElement<dim, spacedim>>, unsigned int>>
1409  &fe_systems)
1410  {
1411  std::vector<const FiniteElement<dim, spacedim> *> fes;
1412  std::vector<unsigned int> multiplicities;
1413 
1414  const auto extract =
1415  [&fes, &multiplicities](
1416  const std::pair<std::unique_ptr<FiniteElement<dim, spacedim>>,
1417  unsigned int> &fe_system) {
1418  fes.push_back(fe_system.first.get());
1419  multiplicities.push_back(fe_system.second);
1420  };
1421 
1422  for (const auto &p : fe_systems)
1423  extract(p);
1424 
1425  return compute_restriction_is_additive_flags(fes, multiplicities);
1426  }
1427 
1428 
1429 
1430  template <int dim, int spacedim>
1433  const std::initializer_list<
1434  std::pair<std::unique_ptr<FiniteElement<dim, spacedim>>, unsigned int>>
1435  &fe_systems)
1436  {
1437  std::vector<const FiniteElement<dim, spacedim> *> fes;
1438  std::vector<unsigned int> multiplicities;
1439 
1440  const auto extract =
1441  [&fes, &multiplicities](
1442  const std::pair<std::unique_ptr<FiniteElement<dim, spacedim>>,
1443  unsigned int> &fe_system) {
1444  fes.push_back(fe_system.first.get());
1445  multiplicities.push_back(fe_system.second);
1446  };
1447 
1448  for (const auto &p : fe_systems)
1449  extract(p);
1450 
1451  return multiply_dof_numbers(fes, multiplicities, true);
1452  }
1453 
1454 
1455 
1456  template <int dim, int spacedim>
1457  std::vector<ComponentMask>
1459  const std::initializer_list<
1460  std::pair<std::unique_ptr<FiniteElement<dim, spacedim>>, unsigned int>>
1461  &fe_systems)
1462  {
1463  std::vector<const FiniteElement<dim, spacedim> *> fes;
1464  std::vector<unsigned int> multiplicities;
1465 
1466  const auto extract =
1467  [&fes, &multiplicities](
1468  const std::pair<std::unique_ptr<FiniteElement<dim, spacedim>>,
1469  unsigned int> &fe_system) {
1470  fes.push_back(fe_system.first.get());
1471  multiplicities.push_back(fe_system.second);
1472  };
1473 
1474  for (const auto &p : fe_systems)
1475  extract(p);
1476 
1477  return compute_nonzero_components(fes, multiplicities, true);
1478  }
1479  } // namespace Compositing
1480 } // namespace FETools
1481 
1482 #endif
1483 
1487 
1488 #endif /* dealii_fe_tools_H */
void project_dg(const DoFHandler< dim, spacedim > &dof1, const InVector &u1, const DoFHandler< dim, spacedim > &dof2, OutVector &u2)
static ::ExceptionBase & ExcLeastSquaresError(double arg1)
std::vector< ComponentMask > compute_nonzero_components(const FiniteElement< dim, spacedim > *fe1, const unsigned int N1, const FiniteElement< dim, spacedim > *fe2=nullptr, const unsigned int N2=0, const FiniteElement< dim, spacedim > *fe3=nullptr, const unsigned int N3=0, const FiniteElement< dim, spacedim > *fe4=nullptr, const unsigned int N4=0, const FiniteElement< dim, spacedim > *fe5=nullptr, const unsigned int N5=0, const bool do_tensor_product=true)
void compute_interpolation_to_quadrature_points_matrix(const FiniteElement< dim, spacedim > &fe, const Quadrature< dim > &quadrature, FullMatrix< double > &I_q)
#define DeclException2(Exception2, type1, type2, outsequence)
Definition: exceptions.h:532
static ::ExceptionBase & ExcGridNotRefinedAtLeastOnce()
std::unique_ptr< FiniteElement< dim, spacedim > > get_fe_by_name(const std::string &name)
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)
Contents is actually a matrix.
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)
SymmetricTensor< 2, dim, Number > e(const Tensor< 2, dim, Number > &F)
std::vector< unsigned int > lexicographic_to_hierarchic_numbering(unsigned int degree)
std::vector< unsigned int > hierarchic_to_lexicographic_numbering(unsigned int degree)
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 interpolation_difference(const DoFHandler< dim, spacedim > &dof1, const InVector &z1, const FiniteElement< dim, spacedim > &fe2, OutVector &z1_difference)
FullMatrix< double > compute_node_matrix(const FiniteElement< dim, spacedim > &fe)
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 interpolate(const DoFHandler< dim, spacedim > &dof1, const InVector &u1, const DoFHandler< dim, spacedim > &dof2, OutVector &u2)
void extrapolate(const DoFHandler< dim, spacedim > &dof1, const InVector &z1, const DoFHandler< dim, spacedim > &dof2, OutVector &z2)
static ::ExceptionBase & ExcFENotPrimitive()
void get_projection_matrix(const FiniteElement< dim, spacedim > &fe1, const FiniteElement< dim, spacedim > &fe2, FullMatrix< number > &matrix)
virtual std::unique_ptr< FiniteElement< FE::dimension, FE::space_dimension > > get(const unsigned int degree) const override
static ::ExceptionBase & ExcMatrixDimensionMismatch(int arg1, int arg2, int arg3, int arg4)
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)
void compute_projection_matrices(const FiniteElement< dim, spacedim > &fe, std::vector< std::vector< FullMatrix< number >>> &matrices, const bool isotropic_only=false)
static ::ExceptionBase & ExcHangingNodesNotAllowed()
#define DeclException1(Exception1, type1, outsequence)
Definition: exceptions.h:509
void get_interpolation_matrix(const FiniteElement< dim, spacedim > &fe1, const FiniteElement< dim, spacedim > &fe2, FullMatrix< number > &interpolation_matrix)
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)
static ::ExceptionBase & ExcNotGreaterThan(int arg1, int arg2)
constexpr ReturnType< rank, T >::value_type & extract(T &t, const ArrayType &indices)
void back_interpolate(const DoFHandler< dim, spacedim > &dof1, const InVector &u1, const FiniteElement< dim, spacedim > &fe2, OutVector &u1_interpolated)
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)
#define DeclExceptionMsg(Exception, defaulttext)
Definition: exceptions.h:487
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)
#define DeclException0(Exception0)
Definition: exceptions.h:464
void get_back_interpolation_matrix(const FiniteElement< dim, spacedim > &fe1, const FiniteElement< dim, spacedim > &fe2, FullMatrix< number > &interpolation_matrix)
#define DEAL_II_NAMESPACE_CLOSE
Definition: config.h:401
static ::ExceptionBase & ExcInvalidFEDimension(char arg1, int arg2)
static ::ExceptionBase & ExcInvalidFE()
FiniteElementData< dim > multiply_dof_numbers(const FiniteElement< dim, spacedim > *fe1, const unsigned int N1, const FiniteElement< dim, spacedim > *fe2=nullptr, const unsigned int N2=0, const FiniteElement< dim, spacedim > *fe3=nullptr, const unsigned int N3=0, const FiniteElement< dim, spacedim > *fe4=nullptr, const unsigned int N4=0, const FiniteElement< dim, spacedim > *fe5=nullptr, const unsigned int N5=0)
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 add_fe_name(const std::string &name, const FEFactoryBase< dim, spacedim > *factory)
#define DEAL_II_NAMESPACE_OPEN
Definition: config.h:400
void get_interpolation_difference_matrix(const FiniteElement< dim, spacedim > &fe1, const FiniteElement< dim, spacedim > &fe2, FullMatrix< number > &difference_matrix)
#define DeclException4(Exception4, type1, type2, type3, type4, outsequence)
Definition: exceptions.h:578
void compute_component_wise(const FiniteElement< dim, spacedim > &fe, std::vector< unsigned int > &renumbering, std::vector< std::vector< unsigned int >> &start_indices)
virtual ~FEFactoryBase() override=default
static ::ExceptionBase & ExcInvalidFEName(std::string arg1)
typename ActiveSelector::active_cell_iterator active_cell_iterator
Definition: dof_handler.h:438
static ::ExceptionBase & ExcTriangulationMismatch()
std::vector< bool > compute_restriction_is_additive_flags(const FiniteElement< dim, spacedim > *fe1, const unsigned int N1, const FiniteElement< dim, spacedim > *fe2=nullptr, const unsigned int N2=0, const FiniteElement< dim, spacedim > *fe3=nullptr, const unsigned int N3=0, const FiniteElement< dim, spacedim > *fe4=nullptr, const unsigned int N4=0, const FiniteElement< dim, spacedim > *fe5=nullptr, const unsigned int N5=0)