#include <deal.II/fe/fe_q_base.h>

Inheritance diagram for FE_Q_Base< PolynomialType, dim, spacedim >:

Classes
struct	Implementation

Public Member Functions
	FE_Q_Base (const PolynomialType &poly_space, const FiniteElementData< dim > &fe_data, const std::vector< bool > &restriction_is_additive_flags)

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 bool	has_support_on_face (const unsigned int shape_index, const unsigned int face_index) 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 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 override

virtual std::pair< Table< 2, bool >, std::vector< unsigned int > >	get_constant_modes () const override

Public Member Functions inherited from FE_Poly< PolynomialType, PolynomialType::dimension, PolynomialType::dimension >
	FE_Poly (const PolynomialType &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

virtual std::unique_ptr< FiniteElement< dim, spacedim > >	clone () const =0

virtual std::string	get_name () const =0

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 FiniteElementDomination::Domination	compare_for_face_domination (const FiniteElement< dim, spacedim > &fe_other) const final

virtual FiniteElementDomination::Domination	compare_for_domination (const FiniteElement< dim, spacedim > &fe_other, const unsigned int codim=0) const

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

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

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 void	convert_generalized_support_point_values_to_dof_values (const std::vector< Vector< double >> &support_point_values, std::vector< double > &nodal_values) 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

Functions to support hp
struct	FE_Q_Base< PolynomialType, dim, spacedim >::Implementation

Threads::Mutex	mutex

const unsigned int	q_degree

virtual bool	hp_constraints_are_implemented () 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

static ::ExceptionBase &	ExcFEQCannotHaveDegree0 ()

static std::vector< unsigned int >	get_dpo_vector (const unsigned int degree)

void	initialize (const std::vector< Point< 1 >> &support_points_1d)

void	initialize_constraints (const std::vector< Point< 1 >> &points)

void	initialize_unit_support_points (const std::vector< Point< 1 >> &points)

void	initialize_unit_face_support_points (const std::vector< Point< 1 >> &points)

void	initialize_quad_dof_index_permutation ()

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_Poly< PolynomialType, PolynomialType::dimension, PolynomialType::dimension >
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< PolynomialType, PolynomialType::dimension, PolynomialType::dimension >
PolynomialType	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

Detailed Description

template<class PolynomialType, int dim = PolynomialType::dimension, int spacedim = dim>
class FE_Q_Base< PolynomialType, dim, spacedim >

This class collects the basic methods used in FE_Q, FE_Q_DG0 and FE_Q_Bubbles. There is no public constructor for this class as it is not functional as a stand-alone. The completion of definitions is left to the derived classes.

Author: Wolfgang Bangerth, 1998, 2003; Guido Kanschat, 2001; Ralf Hartmann, 2001, 2004, 2005; Oliver Kayser-Herold, 2004; Katharina Kormann, 2008; Martin Kronbichler, 2008, 2013

Definition at line 44 of file fe_q_base.h.

Constructor & Destructor Documentation

◆ FE_Q_Base()

template<class PolynomialType , int dim, int spacedim>

FE_Q_Base< PolynomialType, dim, spacedim >::FE_Q_Base	(	const PolynomialType &	poly_space,
		const FiniteElementData< dim > &	fe_data,
		const std::vector< bool > &	restriction_is_additive_flags
	)

Constructor.

Definition at line 406 of file fe_q_base.cc.

Member Function Documentation

◆ get_interpolation_matrix()

template<class PolynomialType , int dim, int spacedim>

void FE_Q_Base< PolynomialType, dim, spacedim >::get_interpolation_matrix	(	const FiniteElement< dim, spacedim > &	source,
		FullMatrix< double > &	matrix
	)		const

overridevirtual

Return the matrix interpolating from the given finite element to the present one. The size of the matrix is then dofs_per_cell times source.dofs_per_cell.

These matrices are only available if the source element is also a FE_Q element. Otherwise, an exception of type FiniteElement<dim,spacedim>::ExcInterpolationNotImplemented is thrown.

Reimplemented from FiniteElement< dim, spacedim >.

Reimplemented in FE_Q_DG0< dim, spacedim >, FE_Q_Bubbles< dim, spacedim >, and FE_Bernstein< dim, spacedim >.

Definition at line 471 of file fe_q_base.cc.

◆ get_face_interpolation_matrix()

template<class PolynomialType , int dim, int spacedim>

void FE_Q_Base< PolynomialType, dim, spacedim >::get_face_interpolation_matrix	(	const FiniteElement< dim, spacedim > &	source,
		FullMatrix< double > &	matrix
	)		const

overridevirtual

Return the matrix interpolating from a face of one element to the face of the neighboring element. The size of the matrix is then source.dofs_per_face times this->dofs_per_face. The FE_Q element family only provides interpolation matrices for elements of the same type and FE_Nothing. For all other elements, an exception of type FiniteElement<dim,spacedim>::ExcInterpolationNotImplemented is thrown.

Reimplemented from FiniteElement< dim, spacedim >.

Reimplemented in FE_Bernstein< dim, spacedim >.

Definition at line 569 of file fe_q_base.cc.

◆ get_subface_interpolation_matrix()

template<class PolynomialType , int dim, int spacedim>

void FE_Q_Base< PolynomialType, dim, spacedim >::get_subface_interpolation_matrix	(	const FiniteElement< dim, spacedim > &	source,
		const unsigned int	subface,
		FullMatrix< double > &	matrix
	)		const

overridevirtual

Return the matrix interpolating from a face of one element to the face of the neighboring element. The size of the matrix is then source.dofs_per_face times this->dofs_per_face. The FE_Q element family only provides interpolation matrices for elements of the same type and FE_Nothing. For all other elements, an exception of type FiniteElement<dim,spacedim>::ExcInterpolationNotImplemented is thrown.

Reimplemented from FiniteElement< dim, spacedim >.

Reimplemented in FE_Bernstein< dim, spacedim >.

Definition at line 583 of file fe_q_base.cc.

◆ has_support_on_face()

template<class PolynomialType , int dim, int spacedim>

bool FE_Q_Base< PolynomialType, dim, spacedim >::has_support_on_face	(	const unsigned int	shape_index,
		const unsigned int	face_index
	)		const

overridevirtual

This function returns true, if the shape function shape_index has non-zero function values somewhere on the face face_index.

Reimplemented from FiniteElement< dim, spacedim >.

Reimplemented in FE_Q_DG0< dim, spacedim >, and FE_Q_Bubbles< dim, spacedim >.

Definition at line 1479 of file fe_q_base.cc.

◆ get_restriction_matrix()

template<class PolynomialType , int dim, int spacedim>

const FullMatrix< double > & FE_Q_Base< PolynomialType, dim, spacedim >::get_restriction_matrix	(	const unsigned int	child,
		const RefinementCase< dim > &	refinement_case = `RefinementCase<dim>::isotropic_refinement`
	)		const

overridevirtual

Projection from a fine grid space onto a coarse grid space. Overrides the respective method in FiniteElement, implementing lazy evaluation (initialize when requested).

If this projection operator is associated with a matrix P, then the restriction of this matrix P_i to a single child cell is returned here.

The matrix P is the concatenation or the sum of the cell matrices P_i, depending on the restriction_is_additive_flags. This distinguishes interpolation (concatenation) and projection with respect to scalar products (summation).

Row and column indices are related to coarse grid and fine grid spaces, respectively, consistent with the definition of the associated operator.

If projection matrices are not implemented in the derived finite element class, this function aborts with ExcProjectionVoid. You can check whether this is the case by calling the restriction_is_implemented() or the isotropic_restriction_is_implemented() function.

Reimplemented from FiniteElement< dim, spacedim >.

Reimplemented in FE_Bernstein< dim, spacedim >, and FE_Q_Bubbles< dim, spacedim >.

Definition at line 1337 of file fe_q_base.cc.

◆ get_prolongation_matrix()

template<class PolynomialType , int dim, int spacedim>

const FullMatrix< double > & FE_Q_Base< PolynomialType, dim, spacedim >::get_prolongation_matrix	(	const unsigned int	child,
		const RefinementCase< dim > &	refinement_case = `RefinementCase<dim>::isotropic_refinement`
	)		const

overridevirtual

Embedding matrix between grids. Overrides the respective method in FiniteElement, implementing lazy evaluation (initialize when queried).

The identity operator from a coarse grid space into a fine grid space is associated with a matrix P. The restriction of this matrix P_i to a single child cell is returned here.

The matrix P is the concatenation, not the sum of the cell matrices P_i. That is, if the same non-zero entry j,k exists in two different child matrices P_i, the value should be the same in both matrices and it is copied into the matrix P only once.

Row and column indices are related to fine grid and coarse grid spaces, respectively, consistent with the definition of the associated operator.

These matrices are used by routines assembling the prolongation matrix for multi-level methods. Upon assembling the transfer matrix between cells using this matrix array, zero elements in the prolongation matrix are discarded and will not fill up the transfer matrix.

If projection matrices are not implemented in the derived finite element class, this function aborts with ExcEmbeddingVoid. You can check whether this is the case by calling the prolongation_is_implemented() or the isotropic_prolongation_is_implemented() function.

Reimplemented from FiniteElement< dim, spacedim >.

Reimplemented in FE_Bernstein< dim, spacedim >, and FE_Q_Bubbles< dim, spacedim >.

Definition at line 1140 of file fe_q_base.cc.

◆ face_to_cell_index()

template<class PolynomialType , int dim, int spacedim>

unsigned int FE_Q_Base< PolynomialType, dim, spacedim >::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

overridevirtual

Given an index in the natural ordering of indices on a face, return the index of the same degree of freedom on the cell.

To explain the concept, consider the case where we would like to know whether a degree of freedom on a face, for example as part of an FESystem element, is primitive. Unfortunately, the is_primitive() function in the FiniteElement class takes a cell index, so we would need to find the cell index of the shape function that corresponds to the present face index. This function does that.

Code implementing this would then look like this:

for (i=0; i<dofs_per_face; ++i)
 if (fe.is_primitive(fe.face_to_cell_index(i, some_face_no)))
  ... do whatever

The function takes additional arguments that account for the fact that actual faces can be in their standard ordering with respect to the cell under consideration, or can be flipped, oriented, etc.

Parameters

face_dof_index	The index of the degree of freedom on a face. This index must be between zero and dofs_per_face.
face	The number of the face this degree of freedom lives on. This number must be between zero and GeometryInfo::faces_per_cell.
face_orientation	One part of the description of the orientation of the face. See GlossFaceOrientation.
face_flip	One part of the description of the orientation of the face. See GlossFaceOrientation.
face_rotation	One part of the description of the orientation of the face. See GlossFaceOrientation.

Returns: The index of this degree of freedom within the set of degrees of freedom on the entire cell. The returned value will be between zero and dofs_per_cell.

Reimplemented from FiniteElement< dim, spacedim >.

Definition at line 1001 of file fe_q_base.cc.

◆ get_constant_modes()

template<typename PolynomialType , int dim, int spacedim>

std::pair< Table< 2, bool >, std::vector< unsigned int > > FE_Q_Base< PolynomialType, dim, spacedim >::get_constant_modes

overridevirtual

Return a list of constant modes of the element. For this element, the list consists of true arguments for all components.

Reimplemented from FiniteElement< dim, spacedim >.

Definition at line 1579 of file fe_q_base.cc.

◆ hp_constraints_are_implemented()

template<class PolynomialType , int dim, int spacedim>

bool FE_Q_Base< PolynomialType, dim, spacedim >::hp_constraints_are_implemented

overridevirtual

Return whether this element implements its hanging node constraints in the new way, which has to be used to make elements "hp compatible".

For the FE_Q class the result is always true (independent of the degree of the element), as it implements the complete set of functions necessary for hp capability.

Reimplemented from FiniteElement< dim, spacedim >.

Definition at line 679 of file fe_q_base.cc.

◆ hp_vertex_dof_identities()

template<class PolynomialType , int dim, int spacedim>

std::vector< std::pair< unsigned int, unsigned int > > FE_Q_Base< PolynomialType, dim, spacedim >::hp_vertex_dof_identities ( const FiniteElement< dim, spacedim > & fe_other ) const

overridevirtual

If, on a vertex, several finite elements are active, the hp code first assigns the degrees of freedom of each of these FEs different global indices. It then calls this function to find out which of them should get identical values, and consequently can receive the same global DoF index. This function therefore returns a list of identities between DoFs of the present finite element object with the DoFs of fe_other, which is a reference to a finite element object representing one of the other finite elements active on this particular vertex. The function computes which of the degrees of freedom of the two finite element objects are equivalent, both numbered between zero and the corresponding value of dofs_per_vertex of the two finite elements. The first index of each pair denotes one of the vertex dofs of the present element, whereas the second is the corresponding index of the other finite element.

Reimplemented from FiniteElement< dim, spacedim >.

Reimplemented in FE_Bernstein< dim, spacedim >.

Definition at line 688 of file fe_q_base.cc.

◆ hp_line_dof_identities()

template<class PolynomialType , int dim, int spacedim>

std::vector< std::pair< unsigned int, unsigned int > > FE_Q_Base< PolynomialType, dim, spacedim >::hp_line_dof_identities ( const FiniteElement< dim, spacedim > & fe_other ) const

overridevirtual

Same as hp_vertex_dof_indices(), except that the function treats degrees of freedom on lines.

Reimplemented from FiniteElement< dim, spacedim >.

Reimplemented in FE_Bernstein< dim, spacedim >.

Definition at line 729 of file fe_q_base.cc.

◆ hp_quad_dof_identities()

template<class PolynomialType , int dim, int spacedim>

std::vector< std::pair< unsigned int, unsigned int > > FE_Q_Base< PolynomialType, dim, spacedim >::hp_quad_dof_identities ( const FiniteElement< dim, spacedim > & fe_other ) const

overridevirtual

Same as hp_vertex_dof_indices(), except that the function treats degrees of freedom on quads.

Reimplemented from FiniteElement< dim, spacedim >.

Reimplemented in FE_Bernstein< dim, spacedim >.

Definition at line 794 of file fe_q_base.cc.

◆ get_dpo_vector()

template<class PolynomialType , int dim, int spacedim>

std::vector< unsigned int > FE_Q_Base< PolynomialType, dim, spacedim >::get_dpo_vector ( const unsigned int degree )

staticprotected

Only for internal use. Its full name is get_dofs_per_object_vector function and it creates the dofs_per_object vector that is needed within the constructor to be passed to the constructor of FiniteElementData.

Definition at line 1115 of file fe_q_base.cc.

◆ initialize()

template<class PolynomialType , int dim, int spacedim>

void FE_Q_Base< PolynomialType, dim, spacedim >::initialize ( const std::vector< Point< 1 >> & support_points_1d )

protected

Perform the initialization of the element based on 1D support points, i.e., sets renumbering, initializes unit support points, initializes constraints as well as restriction and prolongation matrices.

Definition at line 425 of file fe_q_base.cc.

◆ initialize_constraints()

template<class PolynomialType , int dim, int spacedim>

void FE_Q_Base< PolynomialType, dim, spacedim >::initialize_constraints ( const std::vector< Point< 1 >> & points )

protected

Initialize the hanging node constraints matrices. Called from initialize().

Definition at line 1130 of file fe_q_base.cc.

◆ initialize_unit_support_points()

template<class PolynomialType , int dim, int spacedim>

void FE_Q_Base< PolynomialType, dim, spacedim >::initialize_unit_support_points ( const std::vector< Point< 1 >> & points )

protected

Initialize the unit_support_points field of the FiniteElement class. Called from initialize().

Definition at line 870 of file fe_q_base.cc.

◆ initialize_unit_face_support_points()

template<class PolynomialType , int dim, int spacedim>

void FE_Q_Base< PolynomialType, dim, spacedim >::initialize_unit_face_support_points ( const std::vector< Point< 1 >> & points )

protected

Initialize the unit_face_support_points field of the FiniteElement class. Called from initialize().

Definition at line 895 of file fe_q_base.cc.

◆ initialize_quad_dof_index_permutation()

template<class PolynomialType , int dim, int spacedim>

void FE_Q_Base< PolynomialType, dim, spacedim >::initialize_quad_dof_index_permutation

protected

Initialize the adjust_quad_dof_index_for_face_orientation_table field of the FiniteElement class. Called from initialize().

Definition at line 929 of file fe_q_base.cc.

Friends And Related Function Documentation

◆ FE_Q_Base< PolynomialType, dim, spacedim >::Implementation

template<class PolynomialType , int dim = PolynomialType::dimension, int spacedim = dim>

friend struct FE_Q_Base< PolynomialType, dim, spacedim >::Implementation

friend

Definition at line 331 of file fe_q_base.h.

Member Data Documentation

◆ mutex

template<class PolynomialType , int dim = PolynomialType::dimension, int spacedim = dim>

Threads::Mutex FE_Q_Base< PolynomialType, dim, spacedim >::mutex

mutableprivate

Mutex for protecting initialization of restriction and embedding matrix.

Definition at line 340 of file fe_q_base.h.

◆ q_degree

template<class PolynomialType , int dim = PolynomialType::dimension, int spacedim = dim>

const unsigned int FE_Q_Base< PolynomialType, dim, spacedim >::q_degree

private

The highest polynomial degree of the underlying tensor product space without any enrichment. For FE_Q*(p) this is p. Note that enrichments may lead to a difference to degree.

Definition at line 347 of file fe_q_base.h.

The documentation for this class was generated from the following files:

include/deal.II/fe/fe_q_base.h
source/fe/fe_q_base.cc

Classes

Public Member Functions

Functions to support hp

Additional Inherited Members

Detailed Description

template<class PolynomialType, int dim = PolynomialType::dimension, int spacedim = dim> class FE_Q_Base< PolynomialType, dim, spacedim >

Constructor & Destructor Documentation

◆ FE_Q_Base()

Member Function Documentation

◆ get_interpolation_matrix()

◆ get_face_interpolation_matrix()

◆ get_subface_interpolation_matrix()

◆ has_support_on_face()

◆ get_restriction_matrix()

◆ get_prolongation_matrix()

◆ face_to_cell_index()

◆ get_constant_modes()

◆ hp_constraints_are_implemented()

◆ hp_vertex_dof_identities()

◆ hp_line_dof_identities()

◆ hp_quad_dof_identities()

◆ get_dpo_vector()

◆ initialize()

◆ initialize_constraints()

◆ initialize_unit_support_points()

◆ initialize_unit_face_support_points()

◆ initialize_quad_dof_index_permutation()

Friends And Related Function Documentation

◆ FE_Q_Base< PolynomialType, dim, spacedim >::Implementation

Member Data Documentation

◆ mutex

◆ q_degree

template<class PolynomialType, int dim = PolynomialType::dimension, int spacedim = dim>
class FE_Q_Base< PolynomialType, dim, spacedim >