Reference documentation for deal.II version Git 24041777c5 2021-12-02 20:43:25 -0700
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mapping_q.h
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15 
16 #ifndef dealii_mapping_q_h
17 #define dealii_mapping_q_h
18 
19 
20 #include <deal.II/base/config.h>
21 
25 #include <deal.II/base/table.h>
27 
28 #include <deal.II/fe/mapping.h>
29 
31 
34 
35 #include <array>
36 #include <cmath>
37 
39 
40 template <int, int>
41 class MappingQ;
42 
43 template <int, int>
45 
46 
49 
50 
111 template <int dim, int spacedim = dim>
112 class MappingQ : public Mapping<dim, spacedim>
113 {
114 public:
120  MappingQ(const unsigned int polynomial_degree);
121 
127  DEAL_II_DEPRECATED_EARLY
128  MappingQ(const unsigned int polynomial_degree,
129  const bool use_mapping_q_on_all_cells);
130 
134  MappingQ(const MappingQ<dim, spacedim> &mapping);
135 
136  // for documentation, see the Mapping base class
137  virtual std::unique_ptr<Mapping<dim, spacedim>>
138  clone() const override;
139 
144  unsigned int
145  get_degree() const;
146 
151  virtual bool
152  preserves_vertex_locations() const override;
153 
154  // for documentation, see the Mapping base class
155  virtual BoundingBox<spacedim>
157  &cell) const override;
158 
159  virtual bool
160  is_compatible_with(const ReferenceCell &reference_cell) const override;
161 
167  // for documentation, see the Mapping base class
168  virtual Point<spacedim>
170  const typename Triangulation<dim, spacedim>::cell_iterator &cell,
171  const Point<dim> &p) const override;
172 
173  // for documentation, see the Mapping base class
174  virtual Point<dim>
176  const typename Triangulation<dim, spacedim>::cell_iterator &cell,
177  const Point<spacedim> &p) const override;
178 
179  // for documentation, see the Mapping base class
180  virtual void
182  const typename Triangulation<dim, spacedim>::cell_iterator &cell,
183  const ArrayView<const Point<spacedim>> & real_points,
184  const ArrayView<Point<dim>> &unit_points) const override;
185 
195  // for documentation, see the Mapping base class
196  virtual void
197  transform(const ArrayView<const Tensor<1, dim>> & input,
198  const MappingKind kind,
199  const typename Mapping<dim, spacedim>::InternalDataBase &internal,
200  const ArrayView<Tensor<1, spacedim>> &output) const override;
201 
202  // for documentation, see the Mapping base class
203  virtual void
205  const MappingKind kind,
206  const typename Mapping<dim, spacedim>::InternalDataBase &internal,
207  const ArrayView<Tensor<2, spacedim>> &output) const override;
208 
209  // for documentation, see the Mapping base class
210  virtual void
211  transform(const ArrayView<const Tensor<2, dim>> & input,
212  const MappingKind kind,
213  const typename Mapping<dim, spacedim>::InternalDataBase &internal,
214  const ArrayView<Tensor<2, spacedim>> &output) const override;
215 
216  // for documentation, see the Mapping base class
217  virtual void
219  const MappingKind kind,
220  const typename Mapping<dim, spacedim>::InternalDataBase &internal,
221  const ArrayView<Tensor<3, spacedim>> &output) const override;
222 
223  // for documentation, see the Mapping base class
224  virtual void
225  transform(const ArrayView<const Tensor<3, dim>> & input,
226  const MappingKind kind,
227  const typename Mapping<dim, spacedim>::InternalDataBase &internal,
228  const ArrayView<Tensor<3, spacedim>> &output) const override;
229 
251  void
253  const typename Triangulation<dim, spacedim>::cell_iterator &cell,
254  const ArrayView<const Point<dim>> & unit_points,
255  const UpdateFlags update_flags,
257  &output_data) const;
258 
275  class InternalData : public Mapping<dim, spacedim>::InternalDataBase
276  {
277  public:
282  InternalData(const unsigned int polynomial_degree);
283 
292  void
293  initialize(const UpdateFlags update_flags,
294  const Quadrature<dim> &quadrature,
295  const unsigned int n_original_q_points);
296 
302  void
303  initialize_face(const UpdateFlags update_flags,
304  const Quadrature<dim> &quadrature,
305  const unsigned int n_original_q_points);
306 
322  void
323  compute_shape_function_values(const std::vector<Point<dim>> &unit_points);
324 
329  const double &
330  shape(const unsigned int qpoint, const unsigned int shape_nr) const;
331 
335  double &
336  shape(const unsigned int qpoint, const unsigned int shape_nr);
337 
341  const Tensor<1, dim> &
342  derivative(const unsigned int qpoint, const unsigned int shape_nr) const;
343 
348  derivative(const unsigned int qpoint, const unsigned int shape_nr);
349 
353  const Tensor<2, dim> &
354  second_derivative(const unsigned int qpoint,
355  const unsigned int shape_nr) const;
356 
361  second_derivative(const unsigned int qpoint, const unsigned int shape_nr);
362 
366  const Tensor<3, dim> &
367  third_derivative(const unsigned int qpoint,
368  const unsigned int shape_nr) const;
369 
374  third_derivative(const unsigned int qpoint, const unsigned int shape_nr);
375 
379  const Tensor<4, dim> &
380  fourth_derivative(const unsigned int qpoint,
381  const unsigned int shape_nr) const;
382 
387  fourth_derivative(const unsigned int qpoint, const unsigned int shape_nr);
388 
392  virtual std::size_t
393  memory_consumption() const override;
394 
401 
408 
416 
424 
432 
446  std::array<std::vector<Tensor<1, dim>>,
449 
454  const unsigned int polynomial_degree;
455 
465  const unsigned int n_shape_functions;
466 
467  /*
468  * The default line support points. Is used in when the shape function
469  * values are computed.
470  *
471  * The number of quadrature points depends on the degree of this
472  * class, and it matches the number of degrees of freedom of an
473  * FE_Q<1>(this->degree).
474  */
476 
491  using VectorizedArrayType =
493  std::min<std::size_t>(VectorizedArray<double>::size(),
494  (dim <= 2 ? 2 : 4))>;
495 
502 
508 
514 
520 
526 
532 
537 
548 
557 
561  mutable std::vector<AlignedVector<Tensor<1, spacedim>>> aux;
562 
567  mutable std::vector<Point<spacedim>> mapping_support_points;
568 
574 
580  };
581 
582 protected:
583  // documentation can be found in Mapping::requires_update_flags()
584  virtual UpdateFlags
585  requires_update_flags(const UpdateFlags update_flags) const override;
586 
587  // documentation can be found in Mapping::get_data()
588  virtual std::unique_ptr<typename Mapping<dim, spacedim>::InternalDataBase>
589  get_data(const UpdateFlags, const Quadrature<dim> &quadrature) const override;
590 
592 
593  // documentation can be found in Mapping::get_face_data()
594  virtual std::unique_ptr<typename Mapping<dim, spacedim>::InternalDataBase>
595  get_face_data(const UpdateFlags flags,
596  const hp::QCollection<dim - 1> &quadrature) const override;
597 
598  // documentation can be found in Mapping::get_subface_data()
599  virtual std::unique_ptr<typename Mapping<dim, spacedim>::InternalDataBase>
600  get_subface_data(const UpdateFlags flags,
601  const Quadrature<dim - 1> &quadrature) const override;
602 
603  // documentation can be found in Mapping::fill_fe_values()
606  const typename Triangulation<dim, spacedim>::cell_iterator &cell,
607  const CellSimilarity::Similarity cell_similarity,
608  const Quadrature<dim> & quadrature,
609  const typename Mapping<dim, spacedim>::InternalDataBase & internal_data,
611  &output_data) const override;
612 
614 
615  // documentation can be found in Mapping::fill_fe_face_values()
616  virtual void
618  const typename Triangulation<dim, spacedim>::cell_iterator &cell,
619  const unsigned int face_no,
620  const hp::QCollection<dim - 1> & quadrature,
621  const typename Mapping<dim, spacedim>::InternalDataBase & internal_data,
623  &output_data) const override;
624 
625  // documentation can be found in Mapping::fill_fe_subface_values()
626  virtual void
628  const typename Triangulation<dim, spacedim>::cell_iterator &cell,
629  const unsigned int face_no,
630  const unsigned int subface_no,
631  const Quadrature<dim - 1> & quadrature,
632  const typename Mapping<dim, spacedim>::InternalDataBase & internal_data,
634  &output_data) const override;
635 
636  // documentation can be found in Mapping::fill_fe_immersed_surface_values()
637  virtual void
639  const typename Triangulation<dim, spacedim>::cell_iterator &cell,
641  const typename Mapping<dim, spacedim>::InternalDataBase & internal_data,
643  &output_data) const override;
644 
653  const unsigned int polynomial_degree;
654 
655  /*
656  * The default line support points. These are used when computing the
657  * location in real space of the support points on lines and quads, which
658  * are needed by the Manifold<dim,spacedim> class.
659  *
660  * The number of points depends on the degree of this class, and it matches
661  * the number of degrees of freedom of an FE_Q<1>(this->degree).
662  */
663  const std::vector<Point<1>> line_support_points;
664 
665  /*
666  * The one-dimensional polynomials defined as Lagrange polynomials from the
667  * line support points. These are used for point evaluations and match the
668  * polynomial space of an FE_Q<1>(this->degree).
669  */
670  const std::vector<Polynomials::Polynomial<double>> polynomials_1d;
671 
672  /*
673  * The numbering from the lexicographic to the hierarchical ordering used
674  * when expanding the tensor product with the mapping support points (which
675  * come in hierarchical numbers).
676  */
677  const std::vector<unsigned int> renumber_lexicographic_to_hierarchic;
678 
679  /*
680  * The support points in reference coordinates. These are used for
681  * constructing approximations of the output of
682  * compute_mapping_support_points() when evaluating the mapping on the fly,
683  * rather than going through the FEValues interface provided by
684  * InternalData.
685  *
686  * The number of points depends on the degree of this class, and it matches
687  * the number of degrees of freedom of an FE_Q<dim>(this->degree).
688  */
689  const std::vector<Point<dim>> unit_cell_support_points;
690 
710  const std::vector<Table<2, double>>
712 
726 
756  virtual std::vector<Point<spacedim>>
758  const typename Triangulation<dim, spacedim>::cell_iterator &cell) const;
759 
764  Point<dim>
766  const typename Triangulation<dim, spacedim>::cell_iterator &cell,
767  const Point<spacedim> & p,
768  const Point<dim> &initial_p_unit) const;
769 
783  virtual void
785  const typename Triangulation<dim, spacedim>::cell_iterator &cell,
786  std::vector<Point<spacedim>> & a) const;
787 
802  virtual void
804  const typename Triangulation<dim, spacedim>::cell_iterator &cell,
805  std::vector<Point<spacedim>> & a) const;
806 
807  // Make MappingQCache a friend since it needs to call the
808  // compute_mapping_support_points() function.
809  template <int, int>
810  friend class MappingQCache;
811 };
812 
813 
814 
820 template <int dim, int spacedim = dim>
822 
826 /*----------------------------------------------------------------------*/
827 
828 #ifndef DOXYGEN
829 
830 template <int dim, int spacedim>
831 inline const double &
832 MappingQ<dim, spacedim>::InternalData::shape(const unsigned int qpoint,
833  const unsigned int shape_nr) const
834 {
835  AssertIndexRange(qpoint * n_shape_functions + shape_nr, shape_values.size());
836  return shape_values[qpoint * n_shape_functions + shape_nr];
837 }
838 
839 
840 
841 template <int dim, int spacedim>
842 inline double &
843 MappingQ<dim, spacedim>::InternalData::shape(const unsigned int qpoint,
844  const unsigned int shape_nr)
845 {
846  AssertIndexRange(qpoint * n_shape_functions + shape_nr, shape_values.size());
847  return shape_values[qpoint * n_shape_functions + shape_nr];
848 }
849 
850 
851 template <int dim, int spacedim>
852 inline const Tensor<1, dim> &
854  const unsigned int qpoint,
855  const unsigned int shape_nr) const
856 {
857  AssertIndexRange(qpoint * n_shape_functions + shape_nr,
859  return shape_derivatives[qpoint * n_shape_functions + shape_nr];
860 }
861 
862 
863 
864 template <int dim, int spacedim>
865 inline Tensor<1, dim> &
866 MappingQ<dim, spacedim>::InternalData::derivative(const unsigned int qpoint,
867  const unsigned int shape_nr)
868 {
869  AssertIndexRange(qpoint * n_shape_functions + shape_nr,
871  return shape_derivatives[qpoint * n_shape_functions + shape_nr];
872 }
873 
874 
875 template <int dim, int spacedim>
876 inline const Tensor<2, dim> &
878  const unsigned int qpoint,
879  const unsigned int shape_nr) const
880 {
881  AssertIndexRange(qpoint * n_shape_functions + shape_nr,
883  return shape_second_derivatives[qpoint * n_shape_functions + shape_nr];
884 }
885 
886 
887 template <int dim, int spacedim>
888 inline Tensor<2, dim> &
890  const unsigned int qpoint,
891  const unsigned int shape_nr)
892 {
893  AssertIndexRange(qpoint * n_shape_functions + shape_nr,
895  return shape_second_derivatives[qpoint * n_shape_functions + shape_nr];
896 }
897 
898 template <int dim, int spacedim>
899 inline const Tensor<3, dim> &
901  const unsigned int qpoint,
902  const unsigned int shape_nr) const
903 {
904  AssertIndexRange(qpoint * n_shape_functions + shape_nr,
906  return shape_third_derivatives[qpoint * n_shape_functions + shape_nr];
907 }
908 
909 
910 template <int dim, int spacedim>
911 inline Tensor<3, dim> &
913  const unsigned int qpoint,
914  const unsigned int shape_nr)
915 {
916  AssertIndexRange(qpoint * n_shape_functions + shape_nr,
918  return shape_third_derivatives[qpoint * n_shape_functions + shape_nr];
919 }
920 
921 
922 template <int dim, int spacedim>
923 inline const Tensor<4, dim> &
925  const unsigned int qpoint,
926  const unsigned int shape_nr) const
927 {
928  AssertIndexRange(qpoint * n_shape_functions + shape_nr,
930  return shape_fourth_derivatives[qpoint * n_shape_functions + shape_nr];
931 }
932 
933 
934 template <int dim, int spacedim>
935 inline Tensor<4, dim> &
937  const unsigned int qpoint,
938  const unsigned int shape_nr)
939 {
940  AssertIndexRange(qpoint * n_shape_functions + shape_nr,
942  return shape_fourth_derivatives[qpoint * n_shape_functions + shape_nr];
943 }
944 
945 
946 
947 template <int dim, int spacedim>
948 inline bool
950 {
951  return true;
952 }
953 
954 #endif // DOXYGEN
955 
956 /* -------------- declaration of explicit specializations ------------- */
957 
958 
960 
961 #endif
const unsigned int polynomial_degree
Definition: mapping_q.h:454
unsigned int get_degree() const
Definition: mapping_q.cc:444
const std::vector< Point< dim > > unit_cell_support_points
Definition: mapping_q.h:689
AlignedVector< Tensor< 4, dim > > shape_fourth_derivatives
Definition: mapping_q.h:431
AlignedVector< VectorizedArrayType > gradients_quad
Definition: mapping_q.h:525
virtual std::size_t memory_consumption() const override
Definition: mapping_q.cc:64
virtual void transform_points_real_to_unit_cell(const typename Triangulation< dim, spacedim >::cell_iterator &cell, const ArrayView< const Point< spacedim >> &real_points, const ArrayView< Point< dim >> &unit_points) const override
Definition: mapping_q.cc:752
void compute_shape_function_values(const std::vector< Point< dim >> &unit_points)
Definition: mapping_q.cc:271
AlignedVector< DerivativeForm< 1, dim, spacedim > > contravariant
Definition: mapping_q.h:556
const double & shape(const unsigned int qpoint, const unsigned int shape_nr) const
MappingQ(const unsigned int polynomial_degree)
Definition: mapping_q.cc:362
InternalData(const unsigned int polynomial_degree)
Definition: mapping_q.cc:52
virtual std::unique_ptr< typename Mapping< dim, spacedim >::InternalDataBase > get_data(const UpdateFlags, const Quadrature< dim > &quadrature) const override
Definition: mapping_q.cc:890
std::array< std::vector< Tensor< 1, dim > >, GeometryInfo< dim >::faces_per_cell *(dim - 1)> unit_tangentials
Definition: mapping_q.h:448
AlignedVector< VectorizedArrayType > scratch
Definition: mapping_q.h:507
#define AssertIndexRange(index, range)
Definition: exceptions.h:1720
AlignedVector< double > volume_elements
Definition: mapping_q.h:579
virtual void add_quad_support_points(const typename Triangulation< dim, spacedim >::cell_iterator &cell, std::vector< Point< spacedim >> &a) const
Definition: mapping_q.cc:1802
virtual void transform(const ArrayView< const Tensor< 1, dim >> &input, const MappingKind kind, const typename Mapping< dim, spacedim >::InternalDataBase &internal, const ArrayView< Tensor< 1, spacedim >> &output) const override
Definition: mapping_q.cc:1498
MappingKind
Definition: mapping.h:71
const std::vector< unsigned int > renumber_lexicographic_to_hierarchic
Definition: mapping_q.h:677
void initialize_face(const UpdateFlags update_flags, const Quadrature< dim > &quadrature, const unsigned int n_original_q_points)
Definition: mapping_q.cc:215
std::vector< AlignedVector< Tensor< 1, spacedim > > > aux
Definition: mapping_q.h:561
internal::MatrixFreeFunctions::ShapeInfo< VectorizedArrayType > shape_info
Definition: mapping_q.h:501
virtual std::unique_ptr< typename Mapping< dim, spacedim >::InternalDataBase > get_face_data(const UpdateFlags flags, const hp::QCollection< dim - 1 > &quadrature) const override
Definition: mapping_q.cc:905
void initialize(const UpdateFlags update_flags, const Quadrature< dim > &quadrature, const unsigned int n_original_q_points)
Definition: mapping_q.cc:85
const Tensor< 3, dim > & third_derivative(const unsigned int qpoint, const unsigned int shape_nr) const
const unsigned int n_shape_functions
Definition: mapping_q.h:465
AlignedVector< double > shape_values
Definition: mapping_q.h:400
const Tensor< 2, dim > & second_derivative(const unsigned int qpoint, const unsigned int shape_nr) const
AlignedVector< VectorizedArrayType > values_dofs
Definition: mapping_q.h:513
const Tensor< 1, dim > & derivative(const unsigned int qpoint, const unsigned int shape_nr) const
virtual void fill_fe_face_values(const typename Triangulation< dim, spacedim >::cell_iterator &cell, const unsigned int face_no, const hp::QCollection< dim - 1 > &quadrature, const typename Mapping< dim, spacedim >::InternalDataBase &internal_data, ::internal::FEValuesImplementation::MappingRelatedData< dim, spacedim > &output_data) const override
Definition: mapping_q.cc:1165
UpdateFlags
const Table< 2, double > support_point_weights_cell
Definition: mapping_q.h:725
const std::vector< Point< 1 > > line_support_points
Definition: mapping_q.h:663
Abstract base class for mapping classes.
Definition: mapping.h:310
#define DEAL_II_NAMESPACE_CLOSE
Definition: config.h:404
const unsigned int polynomial_degree
Definition: mapping_q.h:653
const Tensor< 4, dim > & fourth_derivative(const unsigned int qpoint, const unsigned int shape_nr) const
AlignedVector< Tensor< 2, dim > > shape_second_derivatives
Definition: mapping_q.h:415
virtual BoundingBox< spacedim > get_bounding_box(const typename Triangulation< dim, spacedim >::cell_iterator &cell) const override
Definition: mapping_q.cc:1912
const std::vector< Polynomials::Polynomial< double > > polynomials_1d
Definition: mapping_q.h:670
QGaussLobatto< 1 > line_support_points
Definition: mapping_q.h:475
Triangulation< dim, spacedim >::cell_iterator cell_of_current_support_points
Definition: mapping_q.h:573
std::vector< Point< spacedim > > mapping_support_points
Definition: mapping_q.h:567
virtual void fill_fe_subface_values(const typename Triangulation< dim, spacedim >::cell_iterator &cell, const unsigned int face_no, const unsigned int subface_no, const Quadrature< dim - 1 > &quadrature, const typename Mapping< dim, spacedim >::InternalDataBase &internal_data, ::internal::FEValuesImplementation::MappingRelatedData< dim, spacedim > &output_data) const override
Definition: mapping_q.cc:1214
void reference_cell(Triangulation< dim, spacedim > &tria, const ReferenceCell &reference_cell)
virtual std::unique_ptr< typename Mapping< dim, spacedim >::InternalDataBase > get_subface_data(const UpdateFlags flags, const Quadrature< dim - 1 > &quadrature) const override
Definition: mapping_q.cc:926
virtual bool is_compatible_with(const ReferenceCell &reference_cell) const override
Definition: mapping_q.cc:1922
void fill_mapping_data_for_generic_points(const typename Triangulation< dim, spacedim >::cell_iterator &cell, const ArrayView< const Point< dim >> &unit_points, const UpdateFlags update_flags, ::internal::FEValuesImplementation::MappingRelatedData< dim, spacedim > &output_data) const
Definition: mapping_q.cc:1397
virtual std::vector< Point< spacedim > > compute_mapping_support_points(const typename Triangulation< dim, spacedim >::cell_iterator &cell) const
Definition: mapping_q.cc:1813
virtual Point< spacedim > transform_unit_to_real_cell(const typename Triangulation< dim, spacedim >::cell_iterator &cell, const Point< dim > &p) const override
Definition: mapping_q.cc:453
AlignedVector< VectorizedArrayType > hessians_quad
Definition: mapping_q.h:531
AlignedVector< Tensor< 3, dim > > shape_third_derivatives
Definition: mapping_q.h:423
virtual bool preserves_vertex_locations() const override
AlignedVector< VectorizedArrayType > values_quad
Definition: mapping_q.h:519
#define DEAL_II_NAMESPACE_OPEN
Definition: config.h:403
AlignedVector< Tensor< 1, dim > > shape_derivatives
Definition: mapping_q.h:407
const std::vector< Table< 2, double > > support_point_weights_perimeter_to_interior
Definition: mapping_q.h:711
size_type size() const
virtual void fill_fe_immersed_surface_values(const typename Triangulation< dim, spacedim >::cell_iterator &cell, const NonMatching::ImmersedSurfaceQuadrature< dim > &quadrature, const typename Mapping< dim, spacedim >::InternalDataBase &internal_data, ::internal::FEValuesImplementation::MappingRelatedData< dim, spacedim > &output_data) const override
Definition: mapping_q.cc:1264
Point< dim > transform_real_to_unit_cell_internal(const typename Triangulation< dim, spacedim >::cell_iterator &cell, const Point< spacedim > &p, const Point< dim > &initial_p_unit) const
Definition: mapping_q.cc:488
virtual std::unique_ptr< Mapping< dim, spacedim > > clone() const override
Definition: mapping_q.cc:435
virtual void add_line_support_points(const typename Triangulation< dim, spacedim >::cell_iterator &cell, std::vector< Point< spacedim >> &a) const
Definition: mapping_q.cc:1636
virtual UpdateFlags requires_update_flags(const UpdateFlags update_flags) const override
Definition: mapping_q.cc:834
virtual CellSimilarity::Similarity fill_fe_values(const typename Triangulation< dim, spacedim >::cell_iterator &cell, const CellSimilarity::Similarity cell_similarity, const Quadrature< dim > &quadrature, const typename Mapping< dim, spacedim >::InternalDataBase &internal_data, ::internal::FEValuesImplementation::MappingRelatedData< dim, spacedim > &output_data) const override
Definition: mapping_q.cc:945
virtual Point< dim > transform_real_to_unit_cell(const typename Triangulation< dim, spacedim >::cell_iterator &cell, const Point< spacedim > &p) const override
Definition: mapping_q.cc:631
AlignedVector< DerivativeForm< 1, dim, spacedim > > covariant
Definition: mapping_q.h:547