Reference documentation for deal.II version 8.1.0
Public Member Functions | Private Member Functions | List of all members
FE_Q_Hierarchical< dim > Class Template Reference

#include <fe_q_hierarchical.h>

Inheritance diagram for FE_Q_Hierarchical< dim >:
[legend]

Public Member Functions

 FE_Q_Hierarchical (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
 
template<>
bool has_support_on_face (const unsigned int, const unsigned int) const
 
- Public Member Functions inherited from FE_Poly< TensorProductPolynomials< dim >, dim >
 FE_Poly (const TensorProductPolynomials< dim > &poly_space, const FiniteElementData< dim > &fe_data, const std::vector< bool > &restriction_is_additive_flags, const std::vector< ComponentMask > &nonzero_components)
 
unsigned int get_degree () const
 
std::vector< unsigned intget_poly_space_numbering () const
 
std::vector< unsigned intget_poly_space_numbering_inverse () 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
 
- 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 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
 
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
 
- 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

template<>
void initialize_unit_face_support_points ()
 
template<>
std::vector< unsigned intface_fe_q_hierarchical_to_hierarchic_numbering (const unsigned int)
 

Functions to support hp

const std::vector< unsigned intface_renumber
 
template<int dim1>
class FE_Q_Hierarchical
 
virtual bool hp_constraints_are_implemented () const
 
virtual std::vector< std::pair< unsigned int, unsigned int > > hp_vertex_dof_identities (const FiniteElement< dim > &fe_other) const
 
virtual void get_face_interpolation_matrix (const FiniteElement< dim > &source, FullMatrix< double > &matrix) const
 
virtual void get_subface_interpolation_matrix (const FiniteElement< dim > &source, const unsigned int subface, FullMatrix< double > &matrix) const
 
virtual FiniteElementDomination::Domination compare_for_face_domination (const FiniteElement< dim > &fe_other) const
 
virtual std::size_t memory_consumption () const
 
std::vector< unsigned intget_embedding_dofs (const unsigned int sub_degree) const
 
virtual FiniteElement< dim > * clone () const
 
static std::vector< unsigned intget_dpo_vector (const unsigned int degree)
 
static std::vector< unsigned inthierarchic_to_fe_q_hierarchical_numbering (const FiniteElementData< dim > &fe)
 
static std::vector< unsigned intface_fe_q_hierarchical_to_hierarchic_numbering (const unsigned int degree)
 
void build_dofs_cell (std::vector< FullMatrix< double > > &dofs_cell, std::vector< FullMatrix< double > > &dofs_subcell) const
 
void initialize_constraints (const std::vector< FullMatrix< double > > &dofs_subcell)
 
void initialize_embedding_and_restriction (const std::vector< FullMatrix< double > > &dofs_cell, const std::vector< FullMatrix< double > > &dofs_subcell)
 
void initialize_unit_support_points ()
 
void initialize_unit_face_support_points ()
 

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_Poly< TensorProductPolynomials< 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
 
virtual UpdateFlags update_once (const UpdateFlags flags) const
 
virtual UpdateFlags update_each (const UpdateFlags flags) 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_Poly< TensorProductPolynomials< dim >, dim >
TensorProductPolynomials< dim > poly_space
 
- 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_Q_Hierarchical< dim >

Implementation of Hierarchical finite elements Qp that yield the finite element space of continuous, piecewise polynomials of degree p. This class is realized using tensor product polynomials based on a hierarchical basis Hierarchical of the interval [0,1] which is suitable for building an hp tensor product finite element, if we assume that each element has a single degree.

There are not many differences between FE_Q_Hierarchical and FE_Q, except that we add a function embedding_dofs that takes a given integer q, between 1 and p, and returns the numbering of basis functions of the element of order q in basis of order p. This function is useful if one wants to make calculations using the hierarchical nature of these shape functions.

The unit support points now are reduced to 0, 1, and 0.5 in one dimension, and tensor products in higher dimensions. Thus, various interpolation functions will only work correctly for the linear case. Future work will involve writing projection–interpolation operators that can interpolate onto the higher order bubble functions.

The constructor of this class takes the degree p of this finite element.

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

Implementation

The constructor creates a TensorProductPolynomials object that includes the tensor product of Hierarchical polynomials of degree p. This TensorProductPolynomials object provides all values and derivatives of the shape functions.

Numbering of the degrees of freedom (DoFs)

The original ordering of the shape functions represented by the TensorProductPolynomials is a tensor product numbering. However, the shape functions on a cell are renumbered beginning with the shape functions whose support points are at the vertices, then on the line, on the quads, and finally (for 3d) on the hexes. To be explicit, these numberings are listed in the following:

Q1 elements

Q2 elements

Q3 elements

Q4 elements

Author
Brian Carnes, 2002, Ralf Hartmann 2004, 2005

Definition at line 236 of file fe_q_hierarchical.h.

Constructor & Destructor Documentation

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

Constructor for tensor product polynomials of degree p.

Member Function Documentation

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

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

Implements FiniteElement< dim, dim >.

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

Check for non-zero values on a face.

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

Implementation of the interface in FiniteElement

Reimplemented from FiniteElement< dim, dim >.

template<int dim>
virtual bool FE_Q_Hierarchical< 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".

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

Reimplemented from FiniteElement< dim, dim >.

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

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.

template<int dim>
virtual void FE_Q_Hierarchical< dim >::get_face_interpolation_matrix ( const FiniteElement< dim > &  source,
FullMatrix< double > &  matrix 
) const
virtual

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.

Derived elements will have to implement this function. They may only provide interpolation matrices for certain source finite elements, for example those from the same family. If they don't implement interpolation from a given element, then they must throw an exception of type FiniteElement<dim>::ExcInterpolationNotImplemented.

template<int dim>
virtual void FE_Q_Hierarchical< dim >::get_subface_interpolation_matrix ( const FiniteElement< dim > &  source,
const unsigned int  subface,
FullMatrix< double > &  matrix 
) const
virtual

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.

Derived elements will have to implement this function. They may only provide interpolation matrices for certain source finite elements, for example those from the same family. If they don't implement interpolation from a given element, then they must throw an exception of type ExcInterpolationNotImplemented.

template<int dim>
virtual FiniteElementDomination::Domination FE_Q_Hierarchical< dim >::compare_for_face_domination ( const FiniteElement< dim > &  fe_other) const
virtual

Return whether this element dominates the one given as argument when they meet at a common face, whether it is the other way around, whether neither dominates, or if either could dominate.

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

template<int dim>
virtual std::size_t FE_Q_Hierarchical< 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>
std::vector<unsigned int> FE_Q_Hierarchical< dim >::get_embedding_dofs ( const unsigned int  sub_degree) const

For a finite element of degree sub_degree < degree, we return a vector which maps the numbering on an FE of degree sub_degree into the numbering on this element.

template<int dim>
virtual FiniteElement<dim>* FE_Q_Hierarchical< dim >::clone ( ) const
protectedvirtual

clone function instead of a copy constructor.

This function is needed by the constructors of FESystem.

Implements FiniteElement< dim, dim >.

template<int dim>
static std::vector<unsigned int> FE_Q_Hierarchical< 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>
static std::vector<unsigned int> FE_Q_Hierarchical< dim >::hierarchic_to_fe_q_hierarchical_numbering ( const FiniteElementData< dim > &  fe)
staticprivate

The numbering of the degrees of freedom in continuous finite elements is hierarchic, i.e. in such a way that we first number the vertex dofs, in the order of the vertices as defined by the triangulation, then the line dofs in the order and respecting the direction of the lines, then the dofs on quads, etc.

The dofs associated with 1d hierarchical polynomials are ordered with the vertices first ( $phi_0(x)=1-x$ and $phi_1(x)=x$) and then the line dofs (the higher degree polynomials). The 2d and 3d hierarchical polynomials originate from the 1d hierarchical polynomials by tensor product. In the following, the resulting numbering of dofs will be denoted by fe_q_hierarchical numbering.

This function constructs a table which fe_q_hierarchical index each degree of freedom in the hierarchic numbering would have.

This function is anologous to the FETools::hierarchical_to_lexicographic_numbering() function. However, in contrast to the fe_q_hierarchical numbering defined above, the lexicographic numbering originates from the tensor products of consecutive numbered dofs (like for LagrangeEquidistant).

It is assumed that the size of the output argument already matches the correct size, which is equal to the number of degrees of freedom in the finite element.

template<int dim>
static std::vector<unsigned int> FE_Q_Hierarchical< dim >::face_fe_q_hierarchical_to_hierarchic_numbering ( const unsigned int  degree)
staticprivate

This is an analogon to the previous function, but working on faces.

template<int dim>
void FE_Q_Hierarchical< dim >::build_dofs_cell ( std::vector< FullMatrix< double > > &  dofs_cell,
std::vector< FullMatrix< double > > &  dofs_subcell 
) const
private

Initialize two auxiliary fields that will be used in setting up the various matrices in the constructor.

template<int dim>
void FE_Q_Hierarchical< dim >::initialize_constraints ( const std::vector< FullMatrix< double > > &  dofs_subcell)
private

Initialize the hanging node constraints matrices. Called from the constructor.

template<int dim>
void FE_Q_Hierarchical< dim >::initialize_embedding_and_restriction ( const std::vector< FullMatrix< double > > &  dofs_cell,
const std::vector< FullMatrix< double > > &  dofs_subcell 
)
private

Initialize the embedding matrices. Called from the constructor.

template<int dim>
void FE_Q_Hierarchical< dim >::initialize_unit_support_points ( )
private

Initialize the unit_support_points field of the FiniteElement class. Called from the constructor.

template<int dim>
void FE_Q_Hierarchical< dim >::initialize_unit_face_support_points ( )
private

Initialize the unit_face_support_points field of the FiniteElement class. Called from the constructor.

template<>
bool FE_Q_Hierarchical< 1 >::has_support_on_face ( const unsigned int  shape_index,
const unsigned int  face_index 
) const
virtual

Check for non-zero values on a face in order to optimize out matrix elements.

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

A default implementation is provided in this basis class which always returns true. This is the safe way to go.

Reimplemented from FiniteElement< dim, dim >.

Friends And Related Function Documentation

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

Allow access from other dimensions. We need this since we want to call the functions get_dpo_vector and lexicographic_to_hierarchic_numbering for the faces of the finite element of dimension dim+1.

Definition at line 531 of file fe_q_hierarchical.h.

Member Data Documentation

template<int dim>
const std::vector<unsigned int> FE_Q_Hierarchical< dim >::face_renumber
private

Mapping from lexicographic to shape function numbering on first face.

Definition at line 520 of file fe_q_hierarchical.h.


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