 |
Reference documentation for deal.II version 9.2.0
|
|
Reference documentation for deal.II version 9.2.0
|
#include <deal.II/fe/fe_dgq.h>
Public Member Functions | |
| FE_DGQHermite (const unsigned int degree) | |
| virtual std::string | get_name () const override |
| virtual std::unique_ptr< FiniteElement< dim, spacedim > > | clone () const override |
 Public Member Functions inherited from FE_DGQ< dim, dim > | |
| FE_DGQ (const unsigned int p) | |
| virtual std::string | get_name () const override |
| virtual void | get_interpolation_matrix (const FiniteElement< dim, spacedim > &source, FullMatrix< double > &matrix) const override |
| virtual void | get_face_interpolation_matrix (const FiniteElement< dim, spacedim > &source, FullMatrix< double > &matrix) const override |
| virtual void | get_subface_interpolation_matrix (const FiniteElement< dim, spacedim > &source, const unsigned int subface, FullMatrix< double > &matrix) const override |
| virtual const FullMatrix< double > & | get_restriction_matrix (const unsigned int child, const RefinementCase< dim > &refinement_case=RefinementCase< dim >::isotropic_refinement) const override |
| virtual const FullMatrix< double > & | get_prolongation_matrix (const unsigned int child, const RefinementCase< dim > &refinement_case=RefinementCase< dim >::isotropic_refinement) const override |
| virtual bool | has_support_on_face (const unsigned int shape_index, const unsigned int face_index) const override |
| virtual std::pair< Table< 2, bool >, std::vector< unsigned int > > | get_constant_modes () const override |
| virtual void | convert_generalized_support_point_values_to_dof_values (const std::vector< Vector< double >> &support_point_values, std::vector< double > &nodal_values) const override |
| virtual std::unique_ptr< FiniteElement< dim, spacedim > > | clone () const override |
| virtual std::vector< std::pair< unsigned int, unsigned int > > | hp_vertex_dof_identities (const FiniteElement< dim, spacedim > &fe_other) const override |
| virtual std::vector< std::pair< unsigned int, unsigned int > > | hp_line_dof_identities (const FiniteElement< dim, spacedim > &fe_other) const override |
| virtual std::vector< std::pair< unsigned int, unsigned int > > | hp_quad_dof_identities (const FiniteElement< dim, spacedim > &fe_other) const override |
| virtual bool | hp_constraints_are_implemented () const override |
| virtual FiniteElementDomination::Domination | compare_for_domination (const FiniteElement< dim, spacedim > &fe_other, const unsigned int codim=0) const override final |
| Public Member Functions inherited from FE_Poly< TensorProductPolynomials< dim >, dim, spacedim > | |
| FE_Poly (const TensorProductPolynomials< dim > &poly_space, const FiniteElementData< dim > &fe_data, const std::vector< bool > &restriction_is_additive_flags, const std::vector< ComponentMask > &nonzero_components) | |
| unsigned int | get_degree () const |
| virtual UpdateFlags | requires_update_flags (const UpdateFlags update_flags) const override |
| std::vector< unsigned int > | get_poly_space_numbering () const |
| std::vector< unsigned int > | get_poly_space_numbering_inverse () const |
| virtual double | shape_value (const unsigned int i, const Point< dim > &p) const override |
| virtual double | shape_value_component (const unsigned int i, const Point< dim > &p, const unsigned int component) const override |
| virtual Tensor< 1, dim > | shape_grad (const unsigned int i, const Point< dim > &p) const override |
| virtual Tensor< 1, dim > | shape_grad_component (const unsigned int i, const Point< dim > &p, const unsigned int component) const override |
| virtual Tensor< 2, dim > | shape_grad_grad (const unsigned int i, const Point< dim > &p) const override |
| virtual Tensor< 2, dim > | shape_grad_grad_component (const unsigned int i, const Point< dim > &p, const unsigned int component) const override |
| virtual Tensor< 3, dim > | shape_3rd_derivative (const unsigned int i, const Point< dim > &p) const override |
| virtual Tensor< 3, dim > | shape_3rd_derivative_component (const unsigned int i, const Point< dim > &p, const unsigned int component) const override |
| virtual Tensor< 4, dim > | shape_4th_derivative (const unsigned int i, const Point< dim > &p) const override |
| virtual Tensor< 4, dim > | shape_4th_derivative_component (const unsigned int i, const Point< dim > &p, const unsigned int component) const override |
| virtual std::size_t | memory_consumption () const override |
| Public Member Functions inherited from FiniteElement< dim, spacedim > | |
| FiniteElement (const FiniteElementData< dim > &fe_data, const std::vector< bool > &restriction_is_additive_flags, const std::vector< ComponentMask > &nonzero_components) | |
| FiniteElement (FiniteElement< dim, spacedim > &&)=default | |
| FiniteElement (const FiniteElement< dim, spacedim > &)=default | |
| virtual | ~FiniteElement () override=default |
| std::pair< std::unique_ptr< FiniteElement< dim, spacedim > >, unsigned int > | operator^ (const unsigned int multiplicity) const |
| const FiniteElement< dim, spacedim > & | operator[] (const unsigned int fe_index) const |
| bool | prolongation_is_implemented () const |
| bool | isotropic_prolongation_is_implemented () const |
| bool | restriction_is_implemented () const |
| bool | isotropic_restriction_is_implemented () const |
| bool | restriction_is_additive (const unsigned int index) const |
| const FullMatrix< double > & | constraints (const ::internal::SubfaceCase< dim > &subface_case=::internal::SubfaceCase< dim >::case_isotropic) const |
| bool | constraints_are_implemented (const ::internal::SubfaceCase< dim > &subface_case=::internal::SubfaceCase< dim >::case_isotropic) const |
| virtual bool | hp_constraints_are_implemented () const |
| virtual FiniteElementDomination::Domination | compare_for_face_domination (const FiniteElement< dim, spacedim > &fe_other) const final |
| virtual bool | operator== (const FiniteElement< dim, spacedim > &fe) const |
| bool | operator!= (const FiniteElement< dim, spacedim > &) const |
| std::pair< unsigned int, unsigned int > | system_to_component_index (const unsigned int index) const |
| unsigned int | component_to_system_index (const unsigned int component, const unsigned int index) const |
| std::pair< unsigned int, unsigned int > | face_system_to_component_index (const unsigned int index) const |
| unsigned int | adjust_quad_dof_index_for_face_orientation (const unsigned int index, const bool face_orientation, const bool face_flip, const bool face_rotation) const |
| 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 |
| unsigned int | adjust_line_dof_index_for_line_orientation (const unsigned int index, const bool line_orientation) const |
| const ComponentMask & | get_nonzero_components (const unsigned int i) const |
| unsigned int | n_nonzero_components (const unsigned int i) const |
| bool | is_primitive () const |
| bool | is_primitive (const unsigned int i) const |
| unsigned int | n_base_elements () const |
| virtual const FiniteElement< dim, spacedim > & | base_element (const unsigned int index) const |
| unsigned int | element_multiplicity (const unsigned int index) const |
| const FiniteElement< dim, spacedim > & | get_sub_fe (const ComponentMask &mask) const |
| virtual const FiniteElement< dim, spacedim > & | get_sub_fe (const unsigned int first_component, const unsigned int n_selected_components) const |
| std::pair< std::pair< unsigned int, unsigned int >, unsigned int > | system_to_base_index (const unsigned int index) const |
| std::pair< std::pair< unsigned int, unsigned int >, unsigned int > | face_system_to_base_index (const unsigned int index) const |
| types::global_dof_index | first_block_of_base (const unsigned int b) const |
| std::pair< unsigned int, unsigned int > | component_to_base_index (const unsigned int component) const |
| std::pair< unsigned int, unsigned int > | block_to_base_index (const unsigned int block) const |
| std::pair< unsigned int, types::global_dof_index > | system_to_block_index (const unsigned int component) const |
| unsigned int | component_to_block_index (const unsigned int component) const |
| ComponentMask | component_mask (const FEValuesExtractors::Scalar &scalar) const |
| ComponentMask | component_mask (const FEValuesExtractors::Vector &vector) const |
| ComponentMask | component_mask (const FEValuesExtractors::SymmetricTensor< 2 > &sym_tensor) const |
| ComponentMask | component_mask (const BlockMask &block_mask) const |
| BlockMask | block_mask (const FEValuesExtractors::Scalar &scalar) const |
| BlockMask | block_mask (const FEValuesExtractors::Vector &vector) const |
| BlockMask | block_mask (const FEValuesExtractors::SymmetricTensor< 2 > &sym_tensor) const |
| BlockMask | block_mask (const ComponentMask &component_mask) const |
| virtual std::pair< Table< 2, bool >, std::vector< unsigned int > > | get_constant_modes () const |
| const std::vector< Point< dim > > & | get_unit_support_points () const |
| bool | has_support_points () const |
| virtual Point< dim > | unit_support_point (const unsigned int index) const |
| const std::vector< Point< dim - 1 > > & | get_unit_face_support_points () const |
| bool | has_face_support_points () const |
| virtual Point< dim - 1 > | unit_face_support_point (const unsigned int index) const |
| const std::vector< Point< dim > > & | get_generalized_support_points () const |
| bool | has_generalized_support_points () const |
| GeometryPrimitive | get_associated_geometry_primitive (const unsigned int cell_dof_index) const |
| virtual std::size_t | memory_consumption () const |
| Public Member Functions inherited from Subscriptor | |
| Subscriptor () | |
| Subscriptor (const Subscriptor &) | |
| Subscriptor (Subscriptor &&) noexcept | |
| virtual | ~Subscriptor () |
| Subscriptor & | operator= (const Subscriptor &) |
| Subscriptor & | operator= (Subscriptor &&) noexcept |
| void | subscribe (std::atomic< bool > *const validity, const std::string &identifier="") const |
| void | unsubscribe (std::atomic< bool > *const validity, const std::string &identifier="") const |
| unsigned int | n_subscriptions () const |
| template<typename StreamType > | |
| void | list_subscribers (StreamType &stream) const |
| void | list_subscribers () const |
| template<class Archive > | |
| void | serialize (Archive &ar, const unsigned int version) |
| Public Member Functions inherited from FiniteElementData< dim > | |
| FiniteElementData (const std::vector< unsigned int > &dofs_per_object, const unsigned int n_components, const unsigned int degree, const Conformity conformity=unknown, const BlockIndices &block_indices=BlockIndices()) | |
| unsigned int | n_dofs_per_vertex () const |
| unsigned int | n_dofs_per_line () const |
| unsigned int | n_dofs_per_quad () const |
| unsigned int | n_dofs_per_hex () const |
| unsigned int | n_dofs_per_face () const |
| unsigned int | n_dofs_per_cell () const |
| template<int structdim> | |
| unsigned int | n_dofs_per_object () const |
| unsigned int | n_components () const |
| unsigned int | n_blocks () const |
| const BlockIndices & | block_indices () const |
| unsigned int | tensor_degree () const |
| bool | conforms (const Conformity) const |
| bool | operator== (const FiniteElementData &) const |
Additional Inherited Members | |
| Public Types inherited from FiniteElementData< dim > | |
| enum | Conformity { unknown = 0x00, L2 = 0x01, Hcurl = 0x02, Hdiv = 0x04, H1 = Hcurl | Hdiv, H2 = 0x0e } |
| Static Public Member Functions inherited from FiniteElement< dim, spacedim > | |
| static ::ExceptionBase & | ExcShapeFunctionNotPrimitive (int arg1) |
| static ::ExceptionBase & | ExcFENotPrimitive () |
| static ::ExceptionBase & | ExcUnitShapeValuesDoNotExist () |
| static ::ExceptionBase & | ExcFEHasNoSupportPoints () |
| static ::ExceptionBase & | ExcEmbeddingVoid () |
| static ::ExceptionBase & | ExcProjectionVoid () |
| static ::ExceptionBase & | ExcWrongInterfaceMatrixSize (int arg1, int arg2) |
| static ::ExceptionBase & | ExcInterpolationNotImplemented () |
| Static Public Member Functions inherited from Subscriptor | |
| static ::ExceptionBase & | ExcInUse (int arg1, std::string arg2, std::string arg3) |
| static ::ExceptionBase & | ExcNoSubscriber (std::string arg1, std::string arg2) |
| Public Attributes inherited from FiniteElementData< dim > | |
| const unsigned int | dofs_per_vertex |
| const unsigned int | dofs_per_line |
| const unsigned int | dofs_per_quad |
| const unsigned int | dofs_per_hex |
| const unsigned int | first_line_index |
| const unsigned int | first_quad_index |
| const unsigned int | first_hex_index |
| const unsigned int | first_face_line_index |
| const unsigned int | first_face_quad_index |
| const unsigned int | dofs_per_face |
| const unsigned int | dofs_per_cell |
| const unsigned int | components |
| const unsigned int | degree |
| const Conformity | conforming_space |
| const BlockIndices | block_indices_data |
| Static Public Attributes inherited from FiniteElement< dim, spacedim > | |
| static const unsigned int | space_dimension = spacedim |
| Static Public Attributes inherited from FiniteElementData< dim > | |
| static const unsigned int | dimension = dim |
| Protected Member Functions inherited from FE_DGQ< dim, dim > | |
| FE_DGQ (const std::vector< Polynomials::Polynomial< double >> &polynomials) | |
| Protected Member Functions inherited from FE_Poly< TensorProductPolynomials< dim >, dim, spacedim > | |
| virtual std::unique_ptr< typename FiniteElement< dim, spacedim >::InternalDataBase > | get_data (const UpdateFlags update_flags, const Mapping< dim, spacedim > &, const Quadrature< dim > &quadrature, ::internal::FEValuesImplementation::FiniteElementRelatedData< dim, spacedim > &output_data) const override |
| virtual void | fill_fe_values (const typename Triangulation< dim, spacedim >::cell_iterator &cell, const CellSimilarity::Similarity cell_similarity, const Quadrature< dim > &quadrature, const Mapping< dim, spacedim > &mapping, const typename Mapping< dim, spacedim >::InternalDataBase &mapping_internal, const ::internal::FEValuesImplementation::MappingRelatedData< dim, spacedim > &mapping_data, const typename FiniteElement< dim, spacedim >::InternalDataBase &fe_internal, ::internal::FEValuesImplementation::FiniteElementRelatedData< dim, spacedim > &output_data) const override |
| void | fill_fe_values (const Triangulation< 1, 2 >::cell_iterator &, const CellSimilarity::Similarity cell_similarity, const Quadrature< 1 > &quadrature, const Mapping< 1, 2 > &mapping, const Mapping< 1, 2 >::InternalDataBase &mapping_internal, const ::internal::FEValuesImplementation::MappingRelatedData< 1, 2 > &mapping_data, const FiniteElement< 1, 2 >::InternalDataBase &fe_internal,::internal::FEValuesImplementation::FiniteElementRelatedData< 1, 2 > &output_data) const |
| void | fill_fe_values (const Triangulation< 2, 3 >::cell_iterator &, const CellSimilarity::Similarity cell_similarity, const Quadrature< 2 > &quadrature, const Mapping< 2, 3 > &mapping, const Mapping< 2, 3 >::InternalDataBase &mapping_internal, const ::internal::FEValuesImplementation::MappingRelatedData< 2, 3 > &mapping_data, const FiniteElement< 2, 3 >::InternalDataBase &fe_internal,::internal::FEValuesImplementation::FiniteElementRelatedData< 2, 3 > &output_data) const |
| virtual void | fill_fe_face_values (const typename Triangulation< dim, spacedim >::cell_iterator &cell, const unsigned int face_no, const Quadrature< dim - 1 > &quadrature, const Mapping< dim, spacedim > &mapping, const typename Mapping< dim, spacedim >::InternalDataBase &mapping_internal, const ::internal::FEValuesImplementation::MappingRelatedData< dim, spacedim > &mapping_data, const typename FiniteElement< dim, spacedim >::InternalDataBase &fe_internal, ::internal::FEValuesImplementation::FiniteElementRelatedData< dim, spacedim > &output_data) const override |
| virtual void | fill_fe_subface_values (const typename Triangulation< dim, spacedim >::cell_iterator &cell, const unsigned int face_no, const unsigned int sub_no, const Quadrature< dim - 1 > &quadrature, const Mapping< dim, spacedim > &mapping, const typename Mapping< dim, spacedim >::InternalDataBase &mapping_internal, const ::internal::FEValuesImplementation::MappingRelatedData< dim, spacedim > &mapping_data, const typename FiniteElement< dim, spacedim >::InternalDataBase &fe_internal, ::internal::FEValuesImplementation::FiniteElementRelatedData< dim, spacedim > &output_data) const override |
| void | correct_hessians (internal::FEValuesImplementation::FiniteElementRelatedData< dim, spacedim > &output_data, const internal::FEValuesImplementation::MappingRelatedData< dim, spacedim > &mapping_data, const unsigned int n_q_points) const |
| void | correct_third_derivatives (internal::FEValuesImplementation::FiniteElementRelatedData< dim, spacedim > &output_data, const internal::FEValuesImplementation::MappingRelatedData< dim, spacedim > &mapping_data, const unsigned int n_q_points) const |
| Protected Member Functions inherited from FiniteElement< dim, spacedim > | |
| void | reinit_restriction_and_prolongation_matrices (const bool isotropic_restriction_only=false, const bool isotropic_prolongation_only=false) |
| TableIndices< 2 > | interface_constraints_size () const |
| virtual std::unique_ptr< InternalDataBase > | get_face_data (const UpdateFlags update_flags, const Mapping< dim, spacedim > &mapping, const Quadrature< dim - 1 > &quadrature, ::internal::FEValuesImplementation::FiniteElementRelatedData< dim, spacedim > &output_data) const |
| virtual std::unique_ptr< InternalDataBase > | get_subface_data (const UpdateFlags update_flags, const Mapping< dim, spacedim > &mapping, const Quadrature< dim - 1 > &quadrature, ::internal::FEValuesImplementation::FiniteElementRelatedData< dim, spacedim > &output_data) const |
| virtual void | fill_fe_values (const typename Triangulation< dim, spacedim >::cell_iterator &cell, const CellSimilarity::Similarity cell_similarity, const Quadrature< dim > &quadrature, const Mapping< dim, spacedim > &mapping, const typename Mapping< dim, spacedim >::InternalDataBase &mapping_internal, const ::internal::FEValuesImplementation::MappingRelatedData< dim, spacedim > &mapping_data, const InternalDataBase &fe_internal, ::internal::FEValuesImplementation::FiniteElementRelatedData< dim, spacedim > &output_data) const =0 |
| virtual void | fill_fe_face_values (const typename Triangulation< dim, spacedim >::cell_iterator &cell, const unsigned int face_no, const Quadrature< dim - 1 > &quadrature, const Mapping< dim, spacedim > &mapping, const typename Mapping< dim, spacedim >::InternalDataBase &mapping_internal, const ::internal::FEValuesImplementation::MappingRelatedData< dim, spacedim > &mapping_data, const InternalDataBase &fe_internal, ::internal::FEValuesImplementation::FiniteElementRelatedData< dim, spacedim > &output_data) const =0 |
| virtual void | fill_fe_subface_values (const typename Triangulation< dim, spacedim >::cell_iterator &cell, const unsigned int face_no, const unsigned int sub_no, const Quadrature< dim - 1 > &quadrature, const Mapping< dim, spacedim > &mapping, const typename Mapping< dim, spacedim >::InternalDataBase &mapping_internal, const ::internal::FEValuesImplementation::MappingRelatedData< dim, spacedim > &mapping_data, const InternalDataBase &fe_internal, ::internal::FEValuesImplementation::FiniteElementRelatedData< dim, spacedim > &output_data) const =0 |
| Static Protected Member Functions inherited from FiniteElement< dim, spacedim > | |
| static std::vector< unsigned int > | compute_n_nonzero_components (const std::vector< ComponentMask > &nonzero_components) |
| Protected Attributes inherited from FE_Poly< TensorProductPolynomials< dim >, dim, spacedim > | |
| TensorProductPolynomials< dim > | poly_space |
| Protected Attributes inherited from FiniteElement< dim, spacedim > | |
| std::vector< std::vector< FullMatrix< double > > > | restriction |
| std::vector< std::vector< FullMatrix< double > > > | prolongation |
| FullMatrix< double > | interface_constraints |
| std::vector< Point< dim > > | unit_support_points |
| std::vector< Point< dim - 1 > > | unit_face_support_points |
| std::vector< Point< dim > > | generalized_support_points |
| std::vector< Point< dim - 1 > > | generalized_face_support_points |
| Table< 2, int > | adjust_quad_dof_index_for_face_orientation_table |
| std::vector< int > | adjust_line_dof_index_for_line_orientation_table |
| std::vector< std::pair< unsigned int, unsigned int > > | system_to_component_table |
| std::vector< std::pair< unsigned int, unsigned int > > | face_system_to_component_table |
| std::vector< std::pair< std::pair< unsigned int, unsigned int >, unsigned int > > | system_to_base_table |
| std::vector< std::pair< std::pair< unsigned int, unsigned int >, unsigned int > > | face_system_to_base_table |
| BlockIndices | base_to_block_indices |
| std::vector< std::pair< std::pair< unsigned int, unsigned int >, unsigned int > > | component_to_base_table |
| const std::vector< bool > | restriction_is_additive_flags |
| const std::vector< ComponentMask > | nonzero_components |
| const std::vector< unsigned int > | n_nonzero_components_table |
| const bool | cached_primitivity |
Implementation of scalar, discontinuous tensor product elements based on Hermite-like polynomials, described by the polynomial space Polynomials::HermiteLikeInterpolation. As opposed to the basic FE_DGQ element, these elements are not interpolatory and no support points are defined.
Note that Hermite polynomials are only available for degrees larger or equal to three, and thus the beneficial properties of Polynomials::HermiteLikeInterpolation with only two basis functions having a non-trivial value or derivative on a face per dimension is only present for higher degrees. To facilitate usage also for degrees zero to two, a usual Lagrange basis is constructed by this class.
See the base class documentation in FE_DGQ for details.
| FE_DGQHermite< dim, spacedim >::FE_DGQHermite | ( | const unsigned int | degree | ) |
Constructor for tensor product polynomials based on Polynomials::HermiteLikeInterpolation.
|
overridevirtual |
Return a string that uniquely identifies a finite element. This class returns FE_DGQHermite<dim>(degree), with dim and degree replaced by the values given by the template parameter and the argument passed to the constructor, respectively.
Implements FiniteElement< dim, spacedim >.
|
overridevirtual |
A sort of virtual copy constructor, this function returns a copy of the finite element object. Derived classes need to override the function here in this base class and return an object of the same type as the derived class.
Some places in the library, for example the constructors of FESystem as well as the hp::FECollection class, need to make copies of finite elements without knowing their exact type. They do so through this function.
Implements FiniteElement< dim, spacedim >.
1.8.17