Reference documentation for deal.II version 8.1.0
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FE_RaviartThomas< dim > Class Template Reference

#include <fe_raviart_thomas.h>

Inheritance diagram for FE_RaviartThomas< dim >:
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Classes

class  InternalData
 

Public Member Functions

 FE_RaviartThomas (const unsigned int p)
 
virtual std::string get_name () const
 
virtual bool has_support_on_face (const unsigned int shape_index, const unsigned int face_index) 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 std::size_t memory_consumption () const
 
virtual FiniteElement< dim > * clone () 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 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 UpdateFlags update_once (const UpdateFlags flags) const
 
virtual UpdateFlags update_each (const UpdateFlags flags) 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
 
 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 (ExcUnitShapeValuesDoNotExist)
 
 DeclException0 (ExcFEHasNoSupportPoints)
 
 DeclException0 (ExcEmbeddingVoid)
 
 DeclException0 (ExcProjectionVoid)
 
 DeclException0 (ExcConstraintsVoid)
 
 DeclException0 (ExcInterpolationNotImplemented)
 
 DeclException0 (ExcBoundaryFaceUsed)
 
 DeclException0 (ExcJacobiDeterminantHasWrongSign)
 
 DeclException2 (ExcWrongInterfaceMatrixSize, int, int,<< "The interface matrix has a size of "<< arg1<< "x"<< arg2<< ", which is not reasonable in the present dimension.")
 
 DeclException2 (ExcComponentIndexInvalid, int, int,<< "The component-index pair ("<< arg1<< ", "<< arg2<< ") is invalid, i.e. non-existent.")
 
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 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 intsystem_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 intface_system_to_component_index (const unsigned int index) 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_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 ComponentMaskget_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 intsystem_to_base_index (const unsigned int index) const
 
std::pair< std::pair< unsigned int, unsigned int >, unsigned intface_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 intcomponent_to_base_index (const unsigned int component) const
 
std::pair< unsigned int, unsigned intblock_to_base_index (const unsigned int block) const
 
std::pair< unsigned int, types::global_dof_indexsystem_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
 
- Public Member Functions inherited from Subscriptor
 Subscriptor ()
 
 Subscriptor (const Subscriptor &)
 
virtual ~Subscriptor ()
 
Subscriptoroperator= (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.\n"<< "(Additional information: "<< arg3<< ")\n"<< "Note the entry in the Frequently Asked Questions of "<< "deal.II (linked to from http://www.dealii.org/) for "<< "more information on what this error means.")
 
 DeclException2 (ExcNoSubscriber, char *, char *,<< "No subscriber with identifier \""<< arg2<< "\" did subscribe to this object of class "<< arg1)
 
template<class Archive >
void serialize (Archive &ar, const unsigned int version)
 
- Public Member Functions inherited from FiniteElementData< dim >
 FiniteElementData ()
 
 FiniteElementData (const std::vector< unsigned int > &dofs_per_object, const unsigned int n_components, const unsigned int degree, const Conformity conformity=unknown, const unsigned int n_blocks=numbers::invalid_unsigned_int)
 
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 BlockIndicesblock_indices () const
 
bool is_primitive () const
 
unsigned int tensor_degree () const
 
bool conforms (const Conformity) const
 
bool operator== (const FiniteElementData &) const
 

Private Member Functions

void initialize_support_points (const unsigned int rt_degree)
 
void initialize_restriction ()
 

Static Private Member Functions

static std::vector< unsigned intget_dpo_vector (const unsigned int degree)
 

Private Attributes

Table< 2, doubleboundary_weights
 
Table< 3, doubleinterior_weights
 

Friends

template<int dim1>
class FE_RaviartThomas
 

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
 
BlockIndices block_indices_data
 
- Static Public Attributes inherited from FiniteElementData< dim >
static const unsigned int dimension = dim
 
- Protected Member Functions inherited from FE_PolyTensor< PolynomialsRaviartThomas< dim >, dim >
virtual Mapping< dim, dim >::InternalDataBase * get_data (const UpdateFlags, const Mapping< dim, dim > &mapping, const Quadrature< dim > &quadrature) const
 
virtual void fill_fe_values (const Mapping< dim, dim > &mapping, const typename Triangulation< dim, dim >::cell_iterator &cell, const Quadrature< dim > &quadrature, typename Mapping< dim, dim >::InternalDataBase &mapping_internal, typename Mapping< dim, dim >::InternalDataBase &fe_internal, FEValuesData< dim, dim > &data, CellSimilarity::Similarity &cell_similarity) const
 
virtual void fill_fe_face_values (const Mapping< dim, dim > &mapping, const typename Triangulation< dim, dim >::cell_iterator &cell, const unsigned int face_no, const Quadrature< dim-1 > &quadrature, typename Mapping< dim, dim >::InternalDataBase &mapping_internal, typename Mapping< dim, dim >::InternalDataBase &fe_internal, FEValuesData< dim, dim > &data) const
 
virtual void fill_fe_subface_values (const Mapping< dim, dim > &mapping, const typename Triangulation< dim, dim >::cell_iterator &cell, const unsigned int face_no, const unsigned int sub_no, const Quadrature< dim-1 > &quadrature, typename Mapping< dim, dim >::InternalDataBase &mapping_internal, typename Mapping< dim, dim >::InternalDataBase &fe_internal, FEValuesData< dim, dim > &data) const
 
- 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
 
void compute_2nd (const Mapping< dim, spacedim > &mapping, const typename Triangulation< dim, spacedim >::cell_iterator &cell, const unsigned int offset, typename Mapping< dim, spacedim >::InternalDataBase &mapping_internal, InternalDataBase &fe_internal, FEValuesData< dim, spacedim > &data) const
 
- 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 intcompute_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< doubleinverse_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< doubleinterface_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, intadjust_quad_dof_index_for_face_orientation_table
 
std::vector< intadjust_line_dof_index_for_line_orientation_table
 

Detailed Description

template<int dim>
class FE_RaviartThomas< dim >

Implementation of Raviart-Thomas (RT) elements, conforming with the space Hdiv. These elements generate vector fields with normal components continuous between mesh cells.

We follow the usual definition of the degree of RT elements, which denotes the polynomial degree of the largest complete polynomial subspace contained in the RT space. Then, approximation order of the function itself is degree+1, as with usual polynomial spaces. The numbering so chosen implies the sequence

\[ Q_{k+1} \stackrel{\text{grad}}{\rightarrow} \text{Nedelec}_k \stackrel{\text{curl}}{\rightarrow} \text{RaviartThomas}_k \stackrel{\text{div}}{\rightarrow} DGQ_{k} \]

The lowest order element is consequently FE_RaviartThomas(0).

This class is not implemented for the codimension one case (spacedim != dim).

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.

Interpolation

The interpolation operators associated with the RT element are constructed such that interpolation and computing the divergence are commuting operations. We require this from interpolating arbitrary functions as well as the restriction matrices. It can be achieved by two interpolation schemes, the simplified one in FE_RaviartThomasNodal and the original one here:

Node values on edges/faces

On edges or faces, the node values are the moments of the normal component of the interpolated function with respect to the traces of the RT polynomials. Since the normal trace of the RT space of degree k on an edge/face is the space Qk, the moments are taken with respect to this space.

Interior node values

Higher order RT spaces have interior nodes. These are moments taken with respect to the gradient of functions in Qk on the cell (this space is the matching space for RTk in a mixed formulation).

Generalized support points

The node values above rely on integrals, which will be computed by quadrature rules themselves. The generalized support points are a set of points such that this quadrature can be performed with sufficient accuracy. The points needed are thode of QGaussk+1 on each face as well as QGaussk in the interior of the cell (or none for RT0).

Author
Guido Kanschat, 2005, based on previous Work by Wolfgang Bangerth

Definition at line 106 of file fe_raviart_thomas.h.

Constructor & Destructor Documentation

template<int dim>
FE_RaviartThomas< dim >::FE_RaviartThomas ( const unsigned int  p)

Constructor for the Raviart-Thomas element of degree p.

Member Function Documentation

template<int dim>
virtual std::string FE_RaviartThomas< dim >::get_name ( ) const
virtual

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

Implements FiniteElement< dim, dim >.

template<int dim>
virtual bool FE_RaviartThomas< dim >::has_support_on_face ( const unsigned int  shape_index,
const unsigned int  face_index 
) const
virtual

Check whether a shape function may be non-zero on a face.

Right now, this is only implemented for RT0 in 1D. Otherwise, returns always true.

Reimplemented from FiniteElement< dim, dim >.

template<int dim>
virtual void FE_RaviartThomas< 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 suport points. All other elements must reimplement it.

Reimplemented from FiniteElement< dim, dim >.

template<int dim>
virtual void FE_RaviartThomas< 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 >.

template<int dim>
virtual void FE_RaviartThomas< 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 >.

template<int dim>
virtual std::size_t FE_RaviartThomas< dim >::memory_consumption ( ) const
virtual

Determine an estimate for the memory consumption (in bytes) of this object.

This function is made virtual, since finite element objects are usually accessed through pointers to their base class, rather than the class itself.

Reimplemented from FiniteElement< dim, dim >.

template<int dim>
virtual FiniteElement<dim>* FE_RaviartThomas< 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 >.

template<int dim>
static std::vector<unsigned int> FE_RaviartThomas< 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.

template<int dim>
void FE_RaviartThomas< dim >::initialize_support_points ( const unsigned int  rt_degree)
private

Initialize the generalized_support_points field of the FiniteElement class and fill the tables with interpolation weights (boundary_weights and interior_weights). Called from the constructor.

template<int dim>
void FE_RaviartThomas< dim >::initialize_restriction ( )
private

Initialize the interpolation from functions on refined mesh cells onto the father cell. According to the philosophy of the Raviart-Thomas element, this restriction operator preserves the divergence of a function weakly.

Friends And Related Function Documentation

template<int dim>
template<int dim1>
friend class FE_RaviartThomas
friend

Allow access from other dimensions.

Definition at line 282 of file fe_raviart_thomas.h.

Member Data Documentation

template<int dim>
Table<2, double> FE_RaviartThomas< dim >::boundary_weights
private

These are the factors multiplied to a function in the generalized_face_support_points when computing the integration. They are organized such that there is one row for each generalized face support point and one column for each degree of freedom on the face.

See the glossary entry on generalized support points for more information.

Definition at line 264 of file fe_raviart_thomas.h.

template<int dim>
Table<3, double> FE_RaviartThomas< dim >::interior_weights
private

Precomputed factors for interpolation of interior degrees of freedom. The rationale for this Table is the same as for boundary_weights. Only, this table has a third coordinate for the space direction of the component evaluated.

Definition at line 276 of file fe_raviart_thomas.h.


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