Reference documentation for deal.II version 9.2.0
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Classes | Public Member Functions | Protected Member Functions | Protected Attributes | List of all members
FE_PolyTensor< dim, spacedim > Class Template Reference
Finite elements » Base classes

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

Inheritance diagram for FE_PolyTensor< dim, spacedim >:
[legend]

Classes

class  InternalData
 

Public Member Functions

 FE_PolyTensor (const TensorPolynomialsBase< dim > &polynomials, const FiniteElementData< dim > &fe_data, const std::vector< bool > &restriction_is_additive_flags, const std::vector< ComponentMask > &nonzero_components)
 
 FE_PolyTensor (const FE_PolyTensor &fe)
 
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 double shape_value_component (const unsigned int i, const Point< dim > &p, const unsigned int component) const override
 
virtual Tensor< 1, dim > shape_grad (const unsigned int i, const Point< dim > &p) const override
 
virtual Tensor< 1, dim > shape_grad_component (const unsigned int i, const Point< dim > &p, const unsigned int component) const override
 
virtual Tensor< 2, dim > shape_grad_grad (const unsigned int i, const Point< dim > &p) const override
 
virtual Tensor< 2, dim > shape_grad_grad_component (const unsigned int i, const Point< dim > &p, const unsigned int component) 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 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 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 final
 
virtual FiniteElementDomination::Domination compare_for_domination (const FiniteElement< dim, spacedim > &fe_other, const unsigned int codim=0) const
 
virtual bool operator== (const FiniteElement< dim, spacedim > &fe) const
 
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
 

Protected Member Functions

bool single_mapping_kind () const
 
MappingKind get_mapping_kind (const unsigned int i) const
 
virtual std::unique_ptr< typename FiniteElement< dim, spacedim >::InternalDataBase > get_data (const UpdateFlags update_flags, const Mapping< dim, spacedim > &, const Quadrature< dim > &quadrature, ::internal::FEValuesImplementation::FiniteElementRelatedData< dim, spacedim > &) 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
 
- 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
 

Protected Attributes

std::vector< MappingKind > mapping_kind
 
const std::unique_ptr< const TensorPolynomialsBase< dim > > poly_space
 
FullMatrix< double > inverse_node_matrix
 
std::mutex cache_mutex
 
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
 
const bool cached_primitivity
 

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

Detailed Description

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

This class provides a unified framework for the implementation of FiniteElement classes based on tensor-valued polynomial spaces like PolynomialsBDM and PolynomialsRaviartThomas. In this, it is the tensor-valued equivalent of the FE_Poly class.

In essence, what this class requires is that a derived class describes to it a (vector-valued) polynomial space in which every polynomial has exactly dim vector components. The classes that provide such implementations are all derived from the TensorPolynomialsBase class, and an object of one of these derived types needs to be provided to the constructor of this class.

Deriving classes

This class is not a fully implemented FiniteElement class, but implements some common features of vector valued elements based on vector valued polynomial classes. What's missing here in particular is information on the topological location of the node values (i.e., whether a degree of freedom is logically at a vertex, edge, face, or the interior of a cell – information that determines the continuity properties of the associated shape functions across cell interfaces), and derived classes need to provide this information.

Similarly, in many cases, node functionals depend on the shape of the mesh cell, since they evaluate normal or tangential components on the faces. In order to allow for a set of transformations, the variable mapping_kind has been introduced. It needs be set in the constructor of a derived class.

Any derived class must decide on the polynomial space to use. This polynomial space should be implemented simply as a set of vector valued polynomials like PolynomialsBDM and PolynomialsRaviartThomas. In order to facilitate this implementation, which basis the polynomial space chooses is not of importance to the current class – as described next, this class handles the transformation from the basis chosen by the polynomial space template argument to the basis we want to use for finite element computations internally.

Determining the correct basis

In most cases, the basis used by the class that describes the polynomial space, \(\{\tilde\varphi_j(\hat{\mathbf x})\}\), does not match the one we want to use for the finite element description, \(\{\varphi_j(\hat{\mathbf x})\}\). Rather, we need to express the finite element shape functions as a linear combination of the basis provided by the polynomial space:

\begin{align*} \varphi_j = \sum_k c_{jk} \tilde\varphi_j. \end{align*}

These expansion coefficients \(c_{jk}\) are typically computed in the constructors of derived classes. To facilitate this, this class at first (unless told otherwise, see below), assumes that the shape functions should be exactly the ones provided by the polynomial space. In the constructor of the derived class, one then typically has code of the form

// Now compute the inverse node matrix, generating the correct
// basis functions from the raw ones. For a discussion of what
// exactly happens here, see FETools::compute_node_matrix.
const FullMatrix<double> M = FETools::compute_node_matrix(*this);
this->inverse_node_matrix.reinit(n_dofs, n_dofs);
this->inverse_node_matrix.invert(M);
// From now on, the shape functions provided by FiniteElement::shape_value
// and similar functions will be the correct ones, not
// the raw shape functions from the polynomial space anymore.

The FETools::compute_node_matrix() function explains in more detail what exactly it computes, and how; in any case, the result is that inverse_node_matrix now contains the expansion coefficients \(c_{jk}\), and the fact that this block of code now sets the matrix to a non-zero size indicates to the functions of the current class that it should from then on use the expanded basis, \(\{\varphi_j(\hat{\mathbf x})\}\), and no longer the original, "raw" basis \(\{\tilde\varphi_j(\hat{\mathbf x})\}\) when asked for values or derivatives of shape functions.

In order for this scheme to work, it is important to ensure that the size of the inverse_node_matrix be zero at the time when FETools::compute_node_matrix() is called; thus, the call to this function cannot be inlined into the last line – the result of the call really does need to be stored in the temporary object M.

Setting the transformation

In most cases, vector valued basis functions must be transformed when mapped from the reference cell to the actual grid cell. These transformations can be selected from the set MappingKind and stored in mapping_kind. Therefore, each constructor should contain a line like:

this->mapping_kind = {mapping_none};

(in case no mapping is required) or using whatever value among the ones defined in MappingKind is appropriate for the element you are implementing. If each shape function may be mapped by different mappings, then mapping_kind may be a vector with the same number of elements as there are shape functions.

See also
TensorPolynomialsBase
Author
Guido Kanschat
Date
2005

Definition at line 143 of file fe_poly_tensor.h.

Constructor & Destructor Documentation

◆ FE_PolyTensor() [1/2]

template<int dim, int spacedim>
FE_PolyTensor< dim, spacedim >::FE_PolyTensor ( const TensorPolynomialsBase< dim > &  polynomials,
const FiniteElementData< dim > &  fe_data,
const std::vector< bool > &  restriction_is_additive_flags,
const std::vector< ComponentMask > &  nonzero_components 
)

Constructor. This constructor does a deep copy of the polynomials object via the TensorPolynomialsBase::clone() function and stores a pointer to the copy. As a consequence, the calling site can simply pass a temporary object as the first argument.

Definition at line 170 of file fe_poly_tensor.cc.

◆ FE_PolyTensor() [2/2]

template<int dim, int spacedim>
FE_PolyTensor< dim, spacedim >::FE_PolyTensor ( const FE_PolyTensor< dim, spacedim > &  fe)

Copy constructor.

Definition at line 196 of file fe_poly_tensor.cc.

Member Function Documentation

◆ requires_update_flags()

template<int dim, int spacedim>
UpdateFlags FE_PolyTensor< 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 2188 of file fe_poly_tensor.cc.

◆ shape_value()

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

Compute the (scalar) value of shape function i at the given quadrature point p. Since the elements represented by this class are vector valued, there is no such scalar value and the function therefore throws an exception.

Reimplemented from FiniteElement< dim, dim >.

Definition at line 229 of file fe_poly_tensor.cc.

◆ shape_value_component()

template<int dim, int spacedim>
double FE_PolyTensor< dim, spacedim >::shape_value_component ( const unsigned int  i,
const Point< dim > &  p,
const unsigned int  component 
) const
overridevirtual

Just like for shape_value(), but this function will be called when the shape function has more than one non-zero vector component. In that case, this function should return the value of the component-th vector component of the ith shape function at point p.

Reimplemented from FiniteElement< dim, dim >.

Definition at line 241 of file fe_poly_tensor.cc.

◆ shape_grad()

template<int dim, int spacedim>
Tensor< 1, dim > FE_PolyTensor< dim, spacedim >::shape_grad ( const unsigned int  i,
const Point< dim > &  p 
) const
overridevirtual

Compute the gradient of (scalar) shape function i at the given quadrature point p. Since the elements represented by this class are vector valued, there is no such scalar value and the function therefore throws an exception.

Reimplemented from FiniteElement< dim, dim >.

Definition at line 275 of file fe_poly_tensor.cc.

◆ shape_grad_component()

template<int dim, int spacedim>
Tensor< 1, dim > FE_PolyTensor< dim, spacedim >::shape_grad_component ( const unsigned int  i,
const Point< dim > &  p,
const unsigned int  component 
) const
overridevirtual

Just like for shape_grad(), but this function will be called when the shape function has more than one non-zero vector component. In that case, this function should return the gradient of the component-th vector component of the ith shape function at point p.

Reimplemented from FiniteElement< dim, dim >.

Definition at line 286 of file fe_poly_tensor.cc.

◆ shape_grad_grad()

template<int dim, int spacedim>
Tensor< 2, dim > FE_PolyTensor< dim, spacedim >::shape_grad_grad ( const unsigned int  i,
const Point< dim > &  p 
) const
overridevirtual

Compute the Hessian of (scalar) shape function i at the given quadrature point p. Since the elements represented by this class are vector valued, there is no such scalar value and the function therefore throws an exception.

Reimplemented from FiniteElement< dim, dim >.

Definition at line 321 of file fe_poly_tensor.cc.

◆ shape_grad_grad_component()

template<int dim, int spacedim>
Tensor< 2, dim > FE_PolyTensor< dim, spacedim >::shape_grad_grad_component ( const unsigned int  i,
const Point< dim > &  p,
const unsigned int  component 
) const
overridevirtual

Just like for shape_grad_grad(), but this function will be called when the shape function has more than one non-zero vector component. In that case, this function should return the gradient of the component-th vector component of the ith shape function at point p.

Reimplemented from FiniteElement< dim, dim >.

Definition at line 332 of file fe_poly_tensor.cc.

◆ single_mapping_kind()

template<int dim, int spacedim>
bool FE_PolyTensor< dim, spacedim >::single_mapping_kind
protected

Returns a boolean that is true when the finite element uses a single mapping and false when the finite element uses multiple mappings.

Definition at line 207 of file fe_poly_tensor.cc.

◆ get_mapping_kind()

template<int dim, int spacedim>
MappingKind FE_PolyTensor< dim, spacedim >::get_mapping_kind ( const unsigned int  i) const
protected

Returns MappingKind i for the finite element.

Definition at line 216 of file fe_poly_tensor.cc.

◆ get_data()

template<int dim, int spacedim = dim>
virtual std::unique_ptr< typename FiniteElement<dim, spacedim>::InternalDataBase> FE_PolyTensor< 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
inlineoverrideprotectedvirtual

Create an internal data object and return a pointer to it of which the caller of this function then assumes ownership. This object will then be passed to the FiniteElement::fill_fe_values() every time the finite element shape functions and their derivatives are evaluated on a concrete cell. The object created here is therefore used by derived classes as a place for scratch objects that are used in evaluating shape functions, as well as to store information that can be pre-computed once and re-used on every cell (e.g., for evaluating the values and gradients of shape functions on the reference cell, for later re-use when transforming these values to a concrete cell).

This function is the first one called in the process of initializing a FEValues object for a given mapping and finite element object. The returned object will later be passed to FiniteElement::fill_fe_values() for a concrete cell, which will itself place its output into an object of type internal::FEValuesImplementation::FiniteElementRelatedData. Since there may be data that can already be computed in its final form on the reference cell, this function also receives a reference to the internal::FEValuesImplementation::FiniteElementRelatedData object as its last argument. This output argument is guaranteed to always be the same one when used with the InternalDataBase object returned by this function. In other words, the subdivision of scratch data and final data in the returned object and the output_data object is as follows: If data can be pre- computed on the reference cell in the exact form in which it will later be needed on a concrete cell, then this function should already emplace it in the output_data object. An example are the values of shape functions at quadrature points for the usual Lagrange elements which on a concrete cell are identical to the ones on the reference cell. On the other hand, if some data can be pre-computed to make computations on a concrete cell cheaper, then it should be put into the returned object for later re-use in a derive class's implementation of FiniteElement::fill_fe_values(). An example are the gradients of shape functions on the reference cell for Lagrange elements: to compute the gradients of the shape functions on a concrete cell, one has to multiply the gradients on the reference cell by the inverse of the Jacobian of the mapping; consequently, we cannot already compute the gradients on a concrete cell at the time the current function is called, but we can at least pre-compute the gradients on the reference cell, and store it in the object returned.

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 the documentation of the InternalDataBase class.

Parameters
[in]update_flagsA set of UpdateFlags values that describe what kind of information the FEValues object requests the finite element to compute. This set of flags may also include information that the finite element can not compute, e.g., flags that pertain to data produced by the mapping. An implementation of this function needs to set up all data fields in the returned object that are necessary to produce the finite- element related data specified by these flags, and may already pre- compute part of this information as discussed above. Elements may want to store these update flags (or a subset of these flags) in InternalDataBase::update_each so they know at the time when FiniteElement::fill_fe_values() is called what they are supposed to compute
[in]mappingA reference to the mapping used for computing values and derivatives of shape functions.
[in]quadratureA reference to the object that describes where the shape functions should be evaluated.
[out]output_dataA reference to the object that FEValues will use in conjunction with the object returned here and where an implementation of FiniteElement::fill_fe_values() will place the requested information. This allows the current function to already pre-compute pieces of information that can be computed on the reference cell, as discussed above. FEValues guarantees that this output object and the object returned by the current function will always be used together.
Returns
A pointer to an object of a type derived from InternalDataBase and that derived classes can use to store scratch data that can be pre- computed, or for scratch arrays that then only need to be allocated once. The calling site assumes ownership of this object and will delete it when it is no longer necessary.

Implements FiniteElement< dim, dim >.

Definition at line 240 of file fe_poly_tensor.h.

◆ fill_fe_values()

template<int dim, int spacedim>
void FE_PolyTensor< 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
overrideprotectedvirtual

Definition at line 370 of file fe_poly_tensor.cc.

◆ fill_fe_face_values()

template<int dim, int spacedim>
void FE_PolyTensor< 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
overrideprotectedvirtual

Definition at line 945 of file fe_poly_tensor.cc.

◆ fill_fe_subface_values()

template<int dim, int spacedim>
void FE_PolyTensor< 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
overrideprotectedvirtual

Definition at line 1570 of file fe_poly_tensor.cc.

Member Data Documentation

◆ mapping_kind

template<int dim, int spacedim = dim>
std::vector<MappingKind> FE_PolyTensor< dim, spacedim >::mapping_kind
protected

The mapping type to be used to map shape functions from the reference cell to the mesh cell. If this vector is length one, the same mapping will be applied to all shape functions. If the vector size is equal to the finite element dofs per cell, then each shape function will be mapped according to the corresponding entry in the vector.

Definition at line 220 of file fe_poly_tensor.h.

◆ poly_space

template<int dim, int spacedim = dim>
const std::unique_ptr<const TensorPolynomialsBase<dim> > FE_PolyTensor< dim, spacedim >::poly_space
protected

A copy of the object passed to the constructor that describes the polynomial space.

Definition at line 477 of file fe_poly_tensor.h.

◆ inverse_node_matrix

template<int dim, int spacedim = dim>
FullMatrix<double> FE_PolyTensor< dim, spacedim >::inverse_node_matrix
protected

The inverse of the matrix aij of node values Ni applied to polynomial pj. This matrix is used to convert polynomials in the "raw" basis provided in poly_space to the basis dual to the node functionals on the reference cell.

This object is not filled by FE_PolyTensor, but is a chance for a derived class to allow for reorganization of the basis functions. If it is left empty, the basis in poly_space is used.

Definition at line 490 of file fe_poly_tensor.h.

◆ cache_mutex

template<int dim, int spacedim = dim>
std::mutex FE_PolyTensor< dim, spacedim >::cache_mutex
mutableprotected

A mutex to be used to guard access to the variables below.

Definition at line 495 of file fe_poly_tensor.h.

◆ cached_point

template<int dim, int spacedim = dim>
Point<dim> FE_PolyTensor< dim, spacedim >::cached_point
mutableprotected

If a shape function is computed at a single point, we must compute all of them to apply inverse_node_matrix. In order to avoid too much overhead, we cache the point and the function values for the next evaluation.

Definition at line 502 of file fe_poly_tensor.h.

◆ cached_values

template<int dim, int spacedim = dim>
std::vector<Tensor<1, dim> > FE_PolyTensor< dim, spacedim >::cached_values
mutableprotected

Cached shape function values after call to shape_value_component().

Definition at line 507 of file fe_poly_tensor.h.

◆ cached_grads

template<int dim, int spacedim = dim>
std::vector<Tensor<2, dim> > FE_PolyTensor< dim, spacedim >::cached_grads
mutableprotected

Cached shape function gradients after call to shape_grad_component().

Definition at line 512 of file fe_poly_tensor.h.

◆ cached_grad_grads

template<int dim, int spacedim = dim>
std::vector<Tensor<3, dim> > FE_PolyTensor< dim, spacedim >::cached_grad_grads
mutableprotected

Cached second derivatives of shape functions after call to shape_grad_grad_component().

Definition at line 518 of file fe_poly_tensor.h.

The documentation for this class was generated from the following files:
TableBase::reinit
void reinit(const TableIndices< N > &new_size, const bool omit_default_initialization=false)
FE_PolyTensor::mapping_kind
std::vector< MappingKind > mapping_kind
Definition: fe_poly_tensor.h:220
FETools::compute_node_matrix
FullMatrix< double > compute_node_matrix(const FiniteElement< dim, spacedim > &fe)
FE_PolyTensor::inverse_node_matrix
FullMatrix< double > inverse_node_matrix
Definition: fe_poly_tensor.h:490
FullMatrix::invert
void invert(const FullMatrix< number2 > &M)
FullMatrix< double >
mapping_none
@ mapping_none
Definition: mapping.h:68
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