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Reference documentation for deal.II version 8.1.0
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#include <fe_dgp_nonparametric.h>
Classes | |
class | InternalData |
struct | Matrices |
Public Member Functions | |
FE_DGPNonparametric (const unsigned int k) | |
virtual std::string | get_name () 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 |
unsigned int | get_degree () 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 bool | has_support_on_face (const unsigned int shape_index, const unsigned int face_index) const |
virtual std::size_t | memory_consumption () const |
Functions to support hp | |
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 bool | hp_constraints_are_implemented () const |
virtual FiniteElementDomination::Domination | compare_for_face_domination (const FiniteElement< dim, spacedim > &fe_other) const |
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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 |
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 |
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 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 |
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 |
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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.\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) |
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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 BlockIndices & | block_indices () const |
bool | is_primitive () const |
unsigned int | tensor_degree () const |
bool | conforms (const Conformity) const |
bool | operator== (const FiniteElementData &) const |
Protected Member Functions | |
virtual FiniteElement< dim, spacedim > * | clone () const |
virtual Mapping< dim, spacedim > ::InternalDataBase * | get_data (const UpdateFlags, const Mapping< dim, spacedim > &mapping, const Quadrature< dim > &quadrature) const |
virtual void | fill_fe_values (const Mapping< dim, spacedim > &mapping, const typename Triangulation< dim, spacedim >::cell_iterator &cell, const Quadrature< dim > &quadrature, typename Mapping< dim, spacedim >::InternalDataBase &mapping_internal, typename Mapping< dim, spacedim >::InternalDataBase &fe_internal, FEValuesData< dim, spacedim > &data, CellSimilarity::Similarity &cell_similarity) const |
virtual void | fill_fe_face_values (const Mapping< dim, spacedim > &mapping, const typename Triangulation< dim, spacedim >::cell_iterator &cell, const unsigned int face_no, const Quadrature< dim-1 > &quadrature, typename Mapping< dim, spacedim >::InternalDataBase &mapping_internal, typename Mapping< dim, spacedim >::InternalDataBase &fe_internal, FEValuesData< dim, spacedim > &data) const |
virtual void | fill_fe_subface_values (const Mapping< dim, spacedim > &mapping, const typename Triangulation< dim, spacedim >::cell_iterator &cell, const unsigned int face_no, const unsigned int sub_no, const Quadrature< dim-1 > &quadrature, typename Mapping< dim, spacedim >::InternalDataBase &mapping_internal, typename Mapping< dim, spacedim >::InternalDataBase &fe_internal, FEValuesData< dim, spacedim > &data) const |
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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 |
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void | set_primitivity (const bool value) |
Private Member Functions | |
virtual UpdateFlags | update_once (const UpdateFlags flags) const |
virtual UpdateFlags | update_each (const UpdateFlags flags) const |
Static Private Member Functions | |
static std::vector< unsigned int > | get_dpo_vector (const unsigned int degree) |
Private Attributes | |
const unsigned int | degree |
const PolynomialSpace< dim > | polynomial_space |
Friends | |
template<int , int > | |
class | FE_DGPNonparametric |
template<int , int > | |
class | MappingQ |
Discontinuous finite elements evaluated at the mapped quadrature points.
Warning: this class does not work properly, yet. Don't use it!
This finite element implements complete polynomial spaces, that is, -dimensional polynomials of order
.
The polynomials are not mapped. Therefore, they are constant, linear, quadratic, etc. on any grid cell.
Since the polynomials are evaluated at the quadrature points of the actual grid cell, no grid transfer and interpolation matrices are available.
The purpose of this class is experimental, therefore the implementation will remain incomplete.
Besides, this class is not implemented for the codimension one case (spacedim != dim
).
Definition at line 58 of file fe_dgp_nonparametric.h.
FE_DGPNonparametric< dim, spacedim >::FE_DGPNonparametric | ( | const unsigned int | k | ) |
Constructor for tensor product polynomials of degree k
.
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virtual |
Return a string that uniquely identifies a finite element. This class returns FE_DGPNonparametric<dim>(degree)
, with dim
and degree
replaced by appropriate values.
Implements FiniteElement< dim, spacedim >.
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virtual |
Return the value of the ith
shape function at the point p
. See the FiniteElement base class for more information about the semantics of this function.
Reimplemented from FiniteElement< dim, spacedim >.
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virtual |
Return the value of the componentth
vector component of the ith
shape function at the point p
. See the FiniteElement base class for more information about the semantics of this function.
Since this element is scalar, the returned value is the same as if the function without the _component
suffix were called, provided that the specified component is zero.
Reimplemented from FiniteElement< dim, spacedim >.
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virtual |
Return the gradient of the ith
shape function at the point p
. See the FiniteElement base class for more information about the semantics of this function.
Reimplemented from FiniteElement< dim, spacedim >.
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virtual |
Return the gradient of the componentth
vector component of the ith
shape function at the point p
. See the FiniteElement base class for more information about the semantics of this function.
Since this element is scalar, the returned value is the same as if the function without the _component
suffix were called, provided that the specified component is zero.
Reimplemented from FiniteElement< dim, spacedim >.
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virtual |
Return the tensor of second derivatives of the ith
shape function at point p
on the unit cell. See the FiniteElement base class for more information about the semantics of this function.
Reimplemented from FiniteElement< dim, spacedim >.
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virtual |
Return the second derivative of the componentth
vector component of the ith
shape function at the point p
. See the FiniteElement base class for more information about the semantics of this function.
Since this element is scalar, the returned value is the same as if the function without the _component
suffix were called, provided that the specified component is zero.
Reimplemented from FiniteElement< dim, spacedim >.
unsigned int FE_DGPNonparametric< dim, spacedim >::get_degree | ( | ) | const |
Return the polynomial degree of this finite element, i.e. the value passed to the constructor.
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virtual |
Return the matrix interpolating from a face of 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,spacedim>::ExcInterpolationNotImplemented.
Reimplemented from FiniteElement< dim, spacedim >.
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virtual |
Return the matrix interpolating from a face of 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,spacedim>::ExcInterpolationNotImplemented.
Reimplemented from FiniteElement< dim, spacedim >.
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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.
This being a discontinuous element, the set of such constraints is of course empty.
Reimplemented from FiniteElement< dim, spacedim >.
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virtual |
Same as hp_vertex_dof_indices(), except that the function treats degrees of freedom on lines.
This being a discontinuous element, the set of such constraints is of course empty.
Reimplemented from FiniteElement< dim, spacedim >.
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virtual |
Same as hp_vertex_dof_indices(), except that the function treats degrees of freedom on quads.
This being a discontinuous element, the set of such constraints is of course empty.
Reimplemented from FiniteElement< dim, spacedim >.
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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_DGPNonparametric class the result is always true (independent of the degree of the element), as it has no hanging nodes (being a discontinuous element).
Reimplemented from FiniteElement< dim, spacedim >.
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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.
Reimplemented from FiniteElement< dim, spacedim >.
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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, spacedim >.
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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, spacedim >.
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protectedvirtual |
clone
function instead of a copy constructor.
This function is needed by the constructors of FESystem
.
Implements FiniteElement< dim, spacedim >.
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protectedvirtual |
Prepare internal data structures and fill in values independent of the cell.
Implements FiniteElement< dim, spacedim >.
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protectedvirtual |
Implementation of the same function in FiniteElement.
Implements FiniteElement< dim, spacedim >.
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protectedvirtual |
Implementation of the same function in FiniteElement.
Implements FiniteElement< dim, spacedim >.
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protectedvirtual |
Implementation of the same function in FiniteElement.
Implements FiniteElement< dim, spacedim >.
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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
.
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privatevirtual |
Given a set of flags indicating what quantities are requested from a FEValues
object, return which of these can be precomputed once and for all. Often, the values of shape function at quadrature points can be precomputed, for example, in which case the return value of this function would be the logical and of the input flags
and update_values
.
For the present kind of finite element, this is exactly the case.
Implements FiniteElement< dim, spacedim >.
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privatevirtual |
This is the opposite to the above function: given a set of flags indicating what we want to know, return which of these need to be computed each time we visit a new cell.
If for the computation of one quantity something else is also required (for example, we often need the covariant transformation when gradients need to be computed), include this in the result as well.
Implements FiniteElement< dim, spacedim >.
Allow access from other dimensions.
Definition at line 553 of file fe_dgp_nonparametric.h.
Allows MappingQ
class to access to build_renumbering function.
Definition at line 560 of file fe_dgp_nonparametric.h.
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private |
Degree of the polynomials.
Definition at line 524 of file fe_dgp_nonparametric.h.
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private |
Pointer to an object representing the polynomial space used here.
Definition at line 531 of file fe_dgp_nonparametric.h.