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

Inheritance diagram for FE_Nothing< dim, spacedim >:

Public Member Functions
	FE_Nothing (const unsigned int n_components=1, const bool dominate=false)

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

virtual std::string	get_name () const override

virtual UpdateFlags	requires_update_flags (const UpdateFlags update_flags) const override

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

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

virtual std::unique_ptr< typename FiniteElement< dim, spacedim >::InternalDataBase >	get_data (const UpdateFlags update_flags, const Mapping< dim, spacedim > &mapping, const Quadrature< dim > &quadrature, ::internal::FEValuesImplementation::FiniteElementRelatedData< dim, spacedim > &output_data) const override

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

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 void	get_interpolation_matrix (const FiniteElement< dim, spacedim > &source_fe, FullMatrix< double > &interpolation_matrix) const override

virtual void	get_face_interpolation_matrix (const FiniteElement< dim, spacedim > &source_fe, FullMatrix< double > &interpolation_matrix) const override

virtual void	get_subface_interpolation_matrix (const FiniteElement< dim, spacedim > &source_fe, const unsigned int index, FullMatrix< double > &interpolation_matrix) const override

bool	is_dominating () const

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

Public Member Functions inherited from FiniteElement< dim, dim >
	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

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

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

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 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

Private Attributes
const bool	dominate

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, dim >
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, dim >
static const unsigned int	space_dimension

Static Public Attributes inherited from FiniteElementData< dim >
static const unsigned int	dimension = dim

Protected Member Functions inherited from FiniteElement< dim, dim >
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, dim >
static std::vector< unsigned int >	compute_n_nonzero_components (const std::vector< ComponentMask > &nonzero_components)

Protected Attributes inherited from FiniteElement< dim, dim >
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_Nothing< dim, spacedim >

Definition of a finite element space with zero degrees of freedom and that, consequently, can only represent a single function: the zero function. This class is useful (in the context of an hp method) to represent empty cells in the triangulation on which no degrees of freedom should be allocated, or to describe a field that is extended by zero to a part of the domain where we don't need it. Thus a triangulation may be divided into two regions: an active region where normal elements are used, and an inactive region where FE_Nothing elements are used. The hp::DoFHandler will therefore assign no degrees of freedom to the FE_Nothing cells, and this subregion is therefore implicitly deleted from the computation. step-10 and step-46 show use cases for this element. An interesting application for this element is also presented in the paper A. Cangiani, J. Chapman, E. Georgoulis, M. Jensen: Implementation of the Continuous-Discontinuous Galerkin Finite Element Method, arXiv:1201.2878v1 [math.NA], 2012 (see http://arxiv.org/abs/1201.2878).

Note that some care must be taken that the resulting mesh topology continues to make sense when FE_Nothing elements are introduced. This is particularly true when dealing with hanging node constraints, because the library makes some basic assumptions about the nature of those constraints. The following geometries are acceptable:

+---------+----+----+
|         | 0  |    |
|    1    +----+----+
|         | 0  |    |
+---------+----+----+

+---------+----+----+
|         | 1  |    |
|    0    +----+----+
|         | 1  |    |
+---------+----+----+

Here, 0 denotes an FE_Nothing cell, and 1 denotes some other element type. The library has no difficulty computing the necessary hanging node constraints in these cases (i.e. no constraint). However, the following geometry is NOT acceptable (at least in the current implementation):

+---------+----+----+
|         | 0  |    |
|    1    +----+----+
|         | 1  |    |
+---------+----+----+

The distinction lies in the mixed nature of the child faces, a case we have not implemented as of yet.

Author: Joshua White, Wolfgang Bangerth

Definition at line 83 of file fe_nothing.h.

Constructor & Destructor Documentation

◆ FE_Nothing()

template<int dim, int spacedim>

FE_Nothing< dim, spacedim >::FE_Nothing	(	const unsigned int	n_components = `1`,
		const bool	dominate = `false`
	)

Constructor. First argument denotes the number of components to give this finite element (default = 1).

Second argument decides whether FE_Nothing will dominate any other FE in compare_for_domination() (default = false). Therefore at interfaces where, for example, a Q1 meets an FE_Nothing, we will force the traces of the two functions to be the same. Because the FE_Nothing encodes a space that is zero everywhere, this means that the Q1 field will be forced to become zero at this interface.

Definition at line 25 of file fe_nothing.cc.

Member Function Documentation

◆ clone()

template<int dim, int spacedim>

std::unique_ptr< FiniteElement< dim, spacedim > > FE_Nothing< dim, spacedim >::clone

overridevirtual

Definition at line 46 of file fe_nothing.cc.

◆ get_name()

template<int dim, int spacedim>

std::string FE_Nothing< dim, spacedim >::get_name

overridevirtual

Return a string that uniquely identifies a finite element. In this case it is FE_Nothing<dim>.

Definition at line 55 of file fe_nothing.cc.

◆ requires_update_flags()

template<int dim, int spacedim>

UpdateFlags FE_Nothing< dim, spacedim >::requires_update_flags ( const UpdateFlags update_flags ) const

overridevirtual

Given a set of update flags, compute which other quantities also need to be computed in order to satisfy the request by the given flags. Then return the combination of the original set of flags and those just computed.

As an example, if update_flags contains update_gradients a finite element class will typically require the computation of the inverse of the Jacobian matrix in order to rotate the gradient of shape functions on the reference cell to the real cell. It would then return not just update_gradients, but also update_covariant_transformation, the flag that makes the mapping class produce the inverse of the Jacobian matrix.

An extensive discussion of the interaction between this function and FEValues can be found in the How Mapping, FiniteElement, and FEValues work together documentation module.

See also: UpdateFlags

Implements FiniteElement< dim, dim >.

Definition at line 75 of file fe_nothing.cc.

◆ shape_value()

template<int dim, int spacedim>

double FE_Nothing< dim, spacedim >::shape_value	(	const unsigned int	i,
		const Point< dim > &	p
	)		const

overridevirtual

Return the value of the ith shape function at the point p. p is a point on the reference element. Because the current element has no degrees of freedom, this function should obviously not be called in practice. All this function really does, therefore, is trigger an exception.

Reimplemented from FiniteElement< dim, dim >.

Definition at line 84 of file fe_nothing.cc.

◆ fill_fe_values()

template<int dim, int spacedim>

void FE_Nothing< dim, spacedim >::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

overridevirtual

Definition at line 114 of file fe_nothing.cc.

◆ fill_fe_face_values()

template<int dim, int spacedim>

void FE_Nothing< dim, spacedim >::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

overridevirtual

Definition at line 135 of file fe_nothing.cc.

◆ fill_fe_subface_values()

template<int dim, int spacedim>

void FE_Nothing< dim, spacedim >::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

overridevirtual

Definition at line 156 of file fe_nothing.cc.

◆ get_data()

template<int dim, int spacedim>

std::unique_ptr< typename FiniteElement< dim, spacedim >::InternalDataBase > FE_Nothing< dim, spacedim >::get_data	(	const UpdateFlags	update_flags,
		const Mapping< dim, spacedim > &	mapping,
		const Quadrature< dim > &	quadrature,
		::internal::FEValuesImplementation::FiniteElementRelatedData< dim, spacedim > &	output_data
	)		const

overridevirtual

Prepare internal data structures and fill in values independent of the cell. Returns a pointer to an object of which the caller of this function then has to assume ownership (which includes destruction when it is no more needed).

In the current case, this function just returns a default pointer, since no meaningful data exists for this element.

Implements FiniteElement< dim, dim >.

Definition at line 95 of file fe_nothing.cc.

◆ compare_for_domination()

template<int dim, int spacedim>

FiniteElementDomination::Domination FE_Nothing< 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.

In the current case, this element is assumed to dominate if the second argument in the constructor dominate is true. When this argument is false and fe_other is also of type FE_Nothing(), either element can dominate. Otherwise there are no_requirements.

Reimplemented from FiniteElement< dim, dim >.

Definition at line 209 of file fe_nothing.cc.

◆ hp_vertex_dof_identities()

template<int dim, int spacedim>

std::vector< std::pair< unsigned int, unsigned int > > FE_Nothing< 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, dim >.

Definition at line 230 of file fe_nothing.cc.

◆ hp_line_dof_identities()

template<int dim, int spacedim>

std::vector< std::pair< unsigned int, unsigned int > > FE_Nothing< 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, dim >.

Definition at line 243 of file fe_nothing.cc.

◆ hp_quad_dof_identities()

template<int dim, int spacedim>

std::vector< std::pair< unsigned int, unsigned int > > FE_Nothing< 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, dim >.

Definition at line 256 of file fe_nothing.cc.

◆ hp_constraints_are_implemented()

template<int dim, int spacedim>

bool FE_Nothing< dim, spacedim >::hp_constraints_are_implemented

overridevirtual

Definition at line 269 of file fe_nothing.cc.

◆ get_interpolation_matrix()

template<int dim, int spacedim>

void FE_Nothing< dim, spacedim >::get_interpolation_matrix	(	const FiniteElement< dim, spacedim > &	source_fe,
		FullMatrix< double > &	interpolation_matrix
	)		const

overridevirtual

Return the matrix interpolating from the given finite element to the present one. Since the current finite element has no degrees of freedom, the interpolation matrix is necessarily empty.

Reimplemented from FiniteElement< dim, dim >.

Definition at line 278 of file fe_nothing.cc.

◆ get_face_interpolation_matrix()

template<int dim, int spacedim>

void FE_Nothing< dim, spacedim >::get_face_interpolation_matrix	(	const FiniteElement< dim, spacedim > &	source_fe,
		FullMatrix< double > &	interpolation_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.

Since the current finite element has no degrees of freedom, the interpolation matrix is necessarily empty.

Reimplemented from FiniteElement< dim, dim >.

Definition at line 296 of file fe_nothing.cc.

◆ get_subface_interpolation_matrix()

template<int dim, int spacedim>

void FE_Nothing< dim, spacedim >::get_subface_interpolation_matrix	(	const FiniteElement< dim, spacedim > &	source_fe,
		const unsigned int	index,
		FullMatrix< double > &	interpolation_matrix
	)		const

overridevirtual

Return the matrix interpolating from a face of one element to the subface of the neighboring element. The size of the matrix is then source.dofs_per_face times this->dofs_per_face.

Since the current finite element has no degrees of freedom, the interpolation matrix is necessarily empty.

Reimplemented from FiniteElement< dim, dim >.

Definition at line 313 of file fe_nothing.cc.

◆ is_dominating()

template<int dim, int spacedim>

bool FE_Nothing< dim, spacedim >::is_dominating

Returns: true if the FE dominates any other.

Definition at line 178 of file fe_nothing.cc.

◆ operator==()

template<int dim, int spacedim>

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

overridevirtual

Comparison operator. In addition to the fields already checked by FiniteElement::operator==(), this operator also checks for equality of the arguments passed to the constructors of the current object as well as the object against which the comparison is done (which for this purpose obviously also needs to be of type FE_Nothing).

Reimplemented from FiniteElement< dim, dim >.

Definition at line 188 of file fe_nothing.cc.

Member Data Documentation

◆ dominate

template<int dim, int spacedim = dim>

const bool FE_Nothing< dim, spacedim >::dominate

private

If true, this element will dominate any other apart from itself in compare_for_domination(). This is because a space that only contains the zero function is definitely smaller (and consequently dominant) when compared to any other finite element space.

Definition at line 280 of file fe_nothing.h.

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

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

Public Member Functions

Private Attributes

Additional Inherited Members

Detailed Description

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

Constructor & Destructor Documentation

◆ FE_Nothing()

Member Function Documentation

◆ clone()

◆ get_name()

◆ requires_update_flags()

◆ shape_value()

◆ fill_fe_values()

◆ fill_fe_face_values()

◆ fill_fe_subface_values()

◆ get_data()

◆ compare_for_domination()

◆ hp_vertex_dof_identities()

◆ hp_line_dof_identities()

◆ hp_quad_dof_identities()

◆ hp_constraints_are_implemented()

◆ get_interpolation_matrix()

◆ get_face_interpolation_matrix()

◆ get_subface_interpolation_matrix()

◆ is_dominating()

◆ operator==()

Member Data Documentation

◆ dominate

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