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Reference documentation for deal.II version 8.1.0
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#include <fe_dgq.h>
Public Member Functions | |
FE_DGQ (const unsigned int p) | |
virtual std::string | get_name () 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 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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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 int > | get_poly_space_numbering () const |
std::vector< unsigned int > | get_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 |
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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) | |
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.") | |
DeclException0 (ExcInterpolationNotImplemented) | |
DeclException0 (ExcBoundaryFaceUsed) | |
DeclException0 (ExcJacobiDeterminantHasWrongSign) | |
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 |
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 | |
FE_DGQ (const Quadrature< 1 > &points) | |
virtual FiniteElement< dim, spacedim > * | clone () const |
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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 |
virtual UpdateFlags | update_once (const UpdateFlags flags) const |
virtual UpdateFlags | update_each (const UpdateFlags flags) 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 | |
void | rotate_indices (std::vector< unsigned int > &indices, const char direction) const |
Static Private Member Functions | |
static std::vector< unsigned int > | get_dpo_vector (const unsigned int degree) |
Friends | |
template<int dim1, int spacedim1> | |
class | FE_DGQ |
template<int dim1, int spacedim1> | |
class | MappingQ |
Implementation of scalar, discontinuous tensor product elements based on equidistant support points.
This is a discontinuous finite element based on tensor products of Lagrangian polynomials. The shape functions are Lagrangian interpolants of an equidistant grid of points on the unit cell. The points are numbered in lexicographical order, with x running fastest, then y, then z (if these coordinates are present for a given space dimension at all). For example, these are the node orderings for FE_DGQ(1)
in 3d:
* 6-------7 6-------7 * /| | / /| * / | | / / | * / | | / / | * 4 | | 4-------5 | * | 2-------3 | | 3 * | / / | | / * | / / | | / * |/ / | |/ * 0-------1 0-------1 *
and FE_DGQ(2)
:
* 24--25--26 24--25--26 * /| | / /| * 21 | | 21 22 23 | * / 15 16 17 / / 17 * 18 | | 18--19--20 | * |12 6---7---8 | |14 8 * 9 / / 9 10 11 / * | 3 4 5 | | 5 * |/ / | |/ * 0---1---2 0---1---2 *
with node 13 being placed in the interior of the hex.
Note, however, that these are just the Lagrange interpolation points of the shape functions. Even though they may physically be on the surface of the cell, they are logically in the interior since there are no continuity requirements for these shape functions across cell boundaries. This class if partially implemented for the codimension one case (spacedim != dim
), since no passage of information between meshes of different refinement level is possible because the embedding and projection matrices are not computed in the class constructor.
Constructor for tensor product polynomials of degree p
. The shape functions created using this constructor correspond to Lagrange interpolation polynomials for equidistantly spaced support points in each coordinate direction.
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protected |
Constructor for tensor product polynomials based on Polynomials::Lagrange interpolation of the support points in the quadrature rule points
. The degree of these polynomials is points.size()-1
.
Note: The FE_DGQ::clone function does not work properly for FE with arbitrary nodes!
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virtual |
Return a string that uniquely identifies a finite element. This class returns FE_DGQ<dim>(degree)
, with dim
and degree
replaced by appropriate values.
Implements FiniteElement< dim, spacedim >.
Reimplemented in FE_DGQArbitraryNodes< dim, spacedim >.
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virtual |
Return the matrix interpolating from the given finite element to the present one. The size of the matrix is then dofs_per_cell
times source.dofs_per_cell
.
These matrices are only available if the source element is also a FE_DGQ
element. Otherwise, an exception of type FiniteElement<dim>::ExcInterpolationNotImplemented is thrown.
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>::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>::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_DGQ 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 >.
Reimplemented in FE_DGQArbitraryNodes< 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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private |
Compute renumbering for rotation of degrees of freedom.
Rotates a tensor product numbering of degrees of freedom by 90 degrees. It is used to compute the transfer matrices of the children by using only the matrix for the first child.
The direction parameter determines the type of rotation. It is one character of xXyYzZ
. The character determines the axis of rotation, case determines the direction. Lower case is counter-clockwise seen in direction of the axis.
Since rotation around the y-axis is not used, it is not implemented either.
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friend |