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

Inheritance diagram for FE_TraceQ< dim, spacedim >:

Public Member Functions
	FE_TraceQ (unsigned int p)

virtual std::string	get_name () const override

virtual std::unique_ptr< FiniteElement< dim, spacedim > >	clone () 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 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 bool	hp_constraints_are_implemented () 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 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_PolyFace< TensorProductPolynomials< dim - 1 >, dim, spacedim >
	FE_PolyFace (const TensorProductPolynomials< dim - 1 > &poly_space, const FiniteElementData< dim > &fe_data, const std::vector< bool > &restriction_is_additive_flags)

unsigned int	get_degree () const

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

virtual bool	operator== (const FiniteElement< dim, spacedim > &fe) const

bool	operator!= (const FiniteElement< dim, spacedim > &) const

virtual std::size_t	memory_consumption () const

virtual double	shape_value (const unsigned int i, const Point< dim > &p) const

virtual double	shape_value_component (const unsigned int i, const Point< dim > &p, const unsigned int component) const

virtual Tensor< 1, dim >	shape_grad (const unsigned int i, const Point< dim > &p) const

virtual Tensor< 1, dim >	shape_grad_component (const unsigned int i, const Point< dim > &p, const unsigned int component) const

virtual Tensor< 2, dim >	shape_grad_grad (const unsigned int i, const Point< dim > &p) const

virtual Tensor< 2, dim >	shape_grad_grad_component (const unsigned int i, const Point< dim > &p, const unsigned int component) const

virtual Tensor< 3, dim >	shape_3rd_derivative (const unsigned int i, const Point< dim > &p) const

virtual Tensor< 3, dim >	shape_3rd_derivative_component (const unsigned int i, const Point< dim > &p, const unsigned int component) const

virtual Tensor< 4, dim >	shape_4th_derivative (const unsigned int i, const Point< dim > &p) const

virtual Tensor< 4, dim >	shape_4th_derivative_component (const unsigned int i, const Point< dim > &p, const unsigned int component) const

virtual const FullMatrix< double > &	get_restriction_matrix (const unsigned int child, const RefinementCase< dim > &refinement_case=RefinementCase< dim >::isotropic_refinement) const

virtual const FullMatrix< double > &	get_prolongation_matrix (const unsigned int child, const RefinementCase< dim > &refinement_case=RefinementCase< dim >::isotropic_refinement) 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 void	get_interpolation_matrix (const FiniteElement< dim, spacedim > &source, FullMatrix< double > &matrix) const

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

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

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

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

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

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

const std::vector< Point< dim - 1 > > &	get_generalized_face_support_points () const

bool	has_generalized_face_support_points () const

GeometryPrimitive	get_associated_geometry_primitive (const unsigned int cell_dof_index) 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

Static Private Member Functions
static std::vector< unsigned int >	get_dpo_vector (const unsigned int deg)

Private Attributes
FE_Q< dim, spacedim >	fe_q

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 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 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_PolyFace< TensorProductPolynomials< dim - 1 >, dim, spacedim >
TensorProductPolynomials< dim - 1 >	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<int dim, int spacedim = dim>
class FE_TraceQ< dim, spacedim >

A finite element, which is the trace of FE_Q elements, that is a tensor product of polynomials on the faces, undefined in the interior of the cells and continuous. The basis functions on the faces are formed by a tensor product of 1D Lagrange polynomials with equidistant points up to degree 2 and Gauss-Lobatto points starting from degree 3.

This finite element is the trace space of FE_Q on the faces.

Note: Since these are only finite elements on faces, only FEFaceValues and FESubfaceValues will be able to extract reasonable values from any face polynomial. In order to make the use of FESystem simpler, FEValues objects will not fail using this finite element space, but all shape function values extracted will equal to zero.

Definition at line 46 of file fe_trace.h.

Constructor & Destructor Documentation

◆ FE_TraceQ()

template<int dim, int spacedim>

FE_TraceQ< dim, spacedim >::FE_TraceQ ( unsigned int p )

Constructor for tensor product polynomials of degree p. The shape functions created using this constructor correspond to Legendre polynomials in each coordinate direction.

Definition at line 38 of file fe_trace.cc.

Member Function Documentation

◆ get_name()

template<int dim, int spacedim>

std::string FE_TraceQ< dim, spacedim >::get_name ( ) const

overridevirtual

Return a string that uniquely identifies a finite element. This class returns FE_DGQ<dim>(degree), with dim and degree replaced by appropriate values.

Implements FiniteElement< dim, spacedim >.

Definition at line 84 of file fe_trace.cc.

◆ clone()

template<int dim, int spacedim>

std::unique_ptr< FiniteElement< dim, spacedim > > FE_TraceQ< dim, spacedim >::clone ( ) const

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 >.

Definition at line 75 of file fe_trace.cc.

◆ convert_generalized_support_point_values_to_dof_values()

template<int dim, int spacedim>

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

overridevirtual

Implementation of the corresponding function in the FiniteElement class. Since the current element is interpolatory, the nodal values are exactly the support point values. Furthermore, since the current element is scalar, the support point values need to be vectors of length 1.

Reimplemented from FiniteElement< dim, spacedim >.

Definition at line 134 of file fe_trace.cc.

◆ has_support_on_face()

template<int dim, int spacedim>

bool FE_TraceQ< 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 >.

Definition at line 101 of file fe_trace.cc.

◆ get_constant_modes()

template<int dim, int spacedim>

std::pair< Table< 2, bool >, std::vector< unsigned int > > FE_TraceQ< dim, spacedim >::get_constant_modes ( ) const

overridevirtual

Return a list of constant modes of the element. For this element, it simply returns one row with all entries set to true.

Reimplemented from FiniteElement< dim, spacedim >.

Definition at line 122 of file fe_trace.cc.

◆ hp_constraints_are_implemented()

template<int dim, int spacedim>

bool FE_TraceQ< dim, spacedim >::hp_constraints_are_implemented ( ) const

overridevirtual

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

Reimplemented from FiniteElement< dim, spacedim >.

Definition at line 172 of file fe_trace.cc.

◆ get_face_interpolation_matrix()

template<int dim, int spacedim>

void FE_TraceQ< 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. This element 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 >.

Definition at line 219 of file fe_trace.cc.

◆ get_subface_interpolation_matrix()

template<int dim, int spacedim>

void FE_TraceQ< 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. This element 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 >.

Definition at line 232 of file fe_trace.cc.

◆ compare_for_domination()

template<int dim, int spacedim>

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

finaloverridevirtual

Return whether this element dominates another one given as argument fe_other, whether it is the other way around, whether neither dominates, or if either could dominate. The codim parameter describes the codimension of the investigated subspace and specifies that it is subject to this comparison. For example, if codim==0 then this function compares which element dominates at the cell level. If codim==1, then the elements are compared at faces, i.e., the comparison happens between the function spaces of the two finite elements as restricted to a face. Larger values of codim work correspondingly.

For a definition of domination, see FiniteElementDomination::Domination and in particular the hp paper.

Reimplemented from FiniteElement< dim, spacedim >.

Definition at line 180 of file fe_trace.cc.

◆ get_dpo_vector()

template<int dim, int spacedim>

std::vector< unsigned int > FE_TraceQ< dim, spacedim >::get_dpo_vector ( const unsigned int deg )

staticprivate

Return vector with dofs per vertex, line, quad, hex.

Definition at line 154 of file fe_trace.cc.

Member Data Documentation

◆ fe_q

template<int dim, int spacedim = dim>

FE_Q<dim, spacedim> FE_TraceQ< dim, spacedim >::fe_q

private

Store a copy of FE_Q for delegating the hp-constraints functionality.

Definition at line 138 of file fe_trace.h.

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

deal.II/fe/fe_trace.h
source/fe/fe_trace.cc

Public Member Functions

Static Private Member Functions

Private Attributes

Additional Inherited Members

Detailed Description

template<int dim, int spacedim = dim> class FE_TraceQ< dim, spacedim >

Constructor & Destructor Documentation

◆ FE_TraceQ()

Member Function Documentation

◆ get_name()

◆ clone()

◆ convert_generalized_support_point_values_to_dof_values()

◆ has_support_on_face()

◆ get_constant_modes()

◆ hp_constraints_are_implemented()

◆ get_face_interpolation_matrix()

◆ get_subface_interpolation_matrix()

◆ compare_for_domination()

◆ get_dpo_vector()

Member Data Documentation

◆ fe_q

template<int dim, int spacedim = dim>
class FE_TraceQ< dim, spacedim >