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

Inheritance diagram for FE_RaviartThomasNodal< dim >:

Public Member Functions
	FE_RaviartThomasNodal (const unsigned int p)

virtual std::string	get_name () const

virtual FiniteElement< dim > *	clone () const

virtual void	interpolate (std::vector< double > &local_dofs, const std::vector< double > &values) const

virtual void	interpolate (std::vector< double > &local_dofs, const std::vector< Vector< double > > &values, unsigned int offset=0) const

virtual void	interpolate (std::vector< double > &local_dofs, const VectorSlice< const std::vector< std::vector< double > > > &values) const

virtual bool	hp_constraints_are_implemented () const

Public Member Functions inherited from FE_PolyTensor< PolynomialsRaviartThomas< dim >, dim >
	FE_PolyTensor (const unsigned int degree, const FiniteElementData< dim > &fe_data, const std::vector< bool > &restriction_is_additive_flags, const std::vector< ComponentMask > &nonzero_components)

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

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

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

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)

virtual	~FiniteElement ()

const FiniteElement< dim, spacedim > &	operator[] (const unsigned int fe_index) const

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

virtual std::size_t	memory_consumption () const

	DeclException1 (ExcShapeFunctionNotPrimitive, int,<< "The shape function with index "<< arg1<< " is not primitive, i.e. it is vector-valued and "<< "has more than one non-zero vector component. This "<< "function cannot be called for these shape functions. "<< "Maybe you want to use the same function with the "<< "_component suffix?")

	DeclException0 (ExcFENotPrimitive)

	DeclException0 (ExcInterpolationNotImplemented)

	DeclExceptionMsg (ExcUnitShapeValuesDoNotExist, "You are trying to access the values or derivatives of shape functions " "on the reference cell of an element that does not define its shape " "functions through mapping from the reference cell. Consequently, " "you cannot ask for shape function values or derivatives on the " "reference cell.")

	DeclExceptionMsg (ExcFEHasNoSupportPoints, "You are trying to access the support points of a finite " "element that either has no support points at all, or for " "which the corresponding tables have not been implemented.")

	DeclExceptionMsg (ExcEmbeddingVoid, "You are trying to access the matrices that describe how " "to embed a finite element function on one cell into the " "finite element space on one of its children (i.e., the " "'embedding' or 'prolongation' matrices). However, the " "current finite element can either not define this sort of " "operation, or it has not yet been implemented.")

	DeclExceptionMsg (ExcProjectionVoid, "You are trying to access the matrices that describe how " "to restrict a finite element function from the children " "of one cell to the finite element space defined on their " "parent (i.e., the 'restriction' or 'projection' matrices). " "However, the current finite element can either not define " "this sort of operation, or it has not yet been " "implemented.")

	DeclException2 (ExcWrongInterfaceMatrixSize, int, int,<< "The interface matrix has a size of "<< arg1<< "x"<< arg2<< ", which is not reasonable for the current element " "in the present dimension.")

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

virtual void	get_subface_interpolation_matrix (const FiniteElement< dim, spacedim > &source, const unsigned int subface, 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

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 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

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

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 &)

virtual	~Subscriptor ()

Subscriptor &	operator= (const Subscriptor &)

void	subscribe (const char *identifier=0) const

void	unsubscribe (const char *identifier=0) const

unsigned int	n_subscriptions () const

void	list_subscribers () const

	DeclException3 (ExcInUse, int, char *, std::string &,<< "Object of class "<< arg2<< " is still used by "<< arg1<< " other objects."<< "\"<< "(Additional information: "<< arg3<< ")\"<< "See the entry in the Frequently Asked Questions of "<< "deal.II (linked to from http://www.dealii.org/) for "<< "a lot more information on what this error means and "<< "how to fix programs in which it happens.")

	DeclException2 (ExcNoSubscriber, char , char ,<< "No subscriber with identifier <"<< arg2<< "> subscribes to this object of class "<< arg1<< ". Consequently, it cannot be unsubscribed.")

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

bool	is_primitive () const

unsigned int	tensor_degree () const

bool	conforms (const Conformity) const

bool	operator== (const FiniteElementData &) const

Private Member Functions
virtual bool	has_support_on_face (const unsigned int shape_index, const unsigned int face_index) const

void	initialize_support_points (const unsigned int rt_degree)

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

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

Additional Inherited Members
Public Types inherited from FiniteElementData< dim >
enum	Conformity { unknown = 0x00, L2 = 0x01, Hcurl = 0x02, Hdiv = 0x04, H1 = Hcurl \| Hdiv, H2 = 0x0e }

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 InternalDataBase *	get_data (const UpdateFlags update_flags, const Mapping< dim, spacedim > &mapping, const Quadrature< dim > &quadrature, ::internal::FEValues::FiniteElementRelatedData< dim, spacedim > &output_data) const=0

virtual InternalDataBase *	get_face_data (const UpdateFlags update_flags, const Mapping< dim, spacedim > &mapping, const Quadrature< dim-1 > &quadrature, ::internal::FEValues::FiniteElementRelatedData< dim, spacedim > &output_data) const

virtual InternalDataBase *	get_subface_data (const UpdateFlags update_flags, const Mapping< dim, spacedim > &mapping, const Quadrature< dim-1 > &quadrature, ::internal::FEValues::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::FEValues::MappingRelatedData< dim, spacedim > &mapping_data, const InternalDataBase &fe_internal, ::internal::FEValues::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::FEValues::MappingRelatedData< dim, spacedim > &mapping_data, const InternalDataBase &fe_internal, ::internal::FEValues::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::FEValues::MappingRelatedData< dim, spacedim > &mapping_data, const InternalDataBase &fe_internal, ::internal::FEValues::FiniteElementRelatedData< dim, spacedim > &output_data) const=0

Protected Member Functions inherited from FiniteElementData< dim >
void	set_primitivity (const bool value)

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 FE_PolyTensor< PolynomialsRaviartThomas< dim >, dim >
MappingType	mapping_type

PolynomialsRaviartThomas< dim >	poly_space

FullMatrix< double >	inverse_node_matrix

Point< dim >	cached_point

std::vector< Tensor< 1, dim > >	cached_values

std::vector< Tensor< 2, dim > >	cached_grads

std::vector< Tensor< 3, dim > >	cached_grad_grads

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

Detailed Description

template<int dim>
class FE_RaviartThomasNodal< dim >

The Raviart-Thomas elements with node functionals defined as point values in Gauss points.

Description of node values

For this Raviart-Thomas element, the node values are not cell and face moments with respect to certain polynomials, but the values in quadrature points. Following the general scheme for numbering degrees of freedom, the node values on edges are first, edge by edge, according to the natural ordering of the edges of a cell. The interior degrees of freedom are last.

For an RT-element of degree k, we choose (k+1)^d-1 Gauss points on each face. These points are ordered lexicographically with respect to the orientation of the face. This way, the normal component which is in Q_k is uniquely determined. Furthermore, since this Gauss-formula is exact on Q_2k+1, these node values correspond to the exact integration of the moments of the RT-space.

In the interior of the cells, the moments are with respect to an anisotropic Q_k space, where the test functions are one degree lower in the direction corresponding to the vector component under consideration. This is emulated by using an anisotropic Gauss formula for integration.

Todo:: The current implementation is for Cartesian meshes only. You must use MappingCartesian.

Todo:: Even if this element is implemented for two and three space dimensions, the definition of the node values relies on consistently oriented faces in 3D. Therefore, care should be taken on complicated meshes.

Note: The degree stored in the member variable FiniteElementData<dim>::degree is higher by one than the constructor argument!

Author: Guido Kanschat, 2005, Zhu Liang, 2008

Definition at line 246 of file fe_raviart_thomas.h.

Constructor & Destructor Documentation

§ FE_RaviartThomasNodal()

template<int dim>

FE_RaviartThomasNodal< dim >::FE_RaviartThomasNodal ( const unsigned int p )

Constructor for the Raviart-Thomas element of degree p.

Definition at line 36 of file fe_raviart_thomas_nodal.cc.

Member Function Documentation

§ get_name()

template<int dim>

std::string FE_RaviartThomasNodal< dim >::get_name ( ) const

virtual

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

Implements FiniteElement< dim, dim >.

Definition at line 108 of file fe_raviart_thomas_nodal.cc.

§ clone()

template<int dim>

FiniteElement< dim > * FE_RaviartThomasNodal< dim >::clone ( ) const

virtual

A sort of virtual copy constructor. 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, dim >.

Definition at line 130 of file fe_raviart_thomas_nodal.cc.

§ interpolate() [1/3]

template<int dim>

void FE_RaviartThomasNodal< dim >::interpolate	(	std::vector< double > &	local_dofs,
		const std::vector< double > &	values
	)		const

virtual

Interpolate a set of scalar values, computed in the generalized support points.

Note: This function is implemented in FiniteElement for the case that the element has support points. In this case, the resulting coefficients are just the values in the support points. All other elements must reimplement it.

Reimplemented from FiniteElement< dim, dim >.

Definition at line 292 of file fe_raviart_thomas_nodal.cc.

§ interpolate() [2/3]

template<int dim>

void FE_RaviartThomasNodal< dim >::interpolate	(	std::vector< double > &	local_dofs,
		const std::vector< Vector< double > > &	values,
		unsigned int	offset = `0`
	)		const

virtual

Interpolate a set of vector values, computed in the generalized support points.

Since a finite element often only interpolates part of a vector, offset is used to determine the first component of the vector to be interpolated. Maybe consider changing your data structures to use the next function.

Reimplemented from FiniteElement< dim, dim >.

Definition at line 302 of file fe_raviart_thomas_nodal.cc.

§ interpolate() [3/3]

template<int dim>

void FE_RaviartThomasNodal< dim >::interpolate	(	std::vector< double > &	local_dofs,
		const VectorSlice< const std::vector< std::vector< double > > > &	values
	)		const

virtual

Interpolate a set of vector values, computed in the generalized support points.

Reimplemented from FiniteElement< dim, dim >.

Definition at line 350 of file fe_raviart_thomas_nodal.cc.

§ hp_constraints_are_implemented()

template<int dim>

bool FE_RaviartThomasNodal< dim >::hp_constraints_are_implemented ( ) const

virtual

Return whether this element implements its hanging node constraints in the new way, which has to be used to make elements "hp compatible". That means, the element properly implements the get_face_interpolation_matrix and get_subface_interpolation_matrix methods. Therefore the return value also indicates whether a call to the get_face_interpolation_matrix() method and the get_subface_interpolation_matrix() method will generate an error or not.

Currently the main purpose of this function is to allow the make_hanging_node_constraints method to decide whether the new procedures, which are supposed to work in the hp framework can be used, or if the old well verified but not hp capable functions should be used. Once the transition to the new scheme for computing the interface constraints is complete, this function will be superfluous and will probably go away.

Derived classes should implement this function accordingly. The default assumption is that a finite element does not provide hp capable face interpolation, and the default implementation therefore returns false.

Reimplemented from FiniteElement< dim, dim >.

Definition at line 397 of file fe_raviart_thomas_nodal.cc.

§ get_dpo_vector()

template<int dim>

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

staticprivate

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 208 of file fe_raviart_thomas_nodal.cc.