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Reference documentation for deal.II version 8.1.0
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#include <fe_q.h>
Public Member Functions | |
FE_Q (const unsigned int p) | |
FE_Q (const Quadrature< 1 > &points) | |
FE_Q (const unsigned int subdivisions_per_dimension, const unsigned int base_degree) | |
virtual std::string | get_name () const |
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FE_Q_Base (const TensorProductPolynomials< dim > &poly_space, const FiniteElementData< dim > &fe_data, const std::vector< bool > &restriction_is_additive_flags) | |
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 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 |
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 |
virtual bool | hp_constraints_are_implemented () 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 |
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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 |
virtual std::size_t | memory_consumption () 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) | |
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 |
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 |
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void | initialize (const std::vector< Point< 1 > > &support_points_1d) |
void | initialize_constraints (const std::vector< Point< 1 > > &points) |
void | initialize_unit_support_points (const std::vector< Point< 1 > > &points) |
void | initialize_unit_face_support_points (const std::vector< Point< 1 > > &points) |
void | initialize_quad_dof_index_permutation () |
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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) |
Implementation of a scalar Lagrange finite element Qp
that yields the finite element space of continuous, piecewise polynomials of degree p
in each coordinate direction. This class is realized using tensor product polynomials based on equidistant or given support points.
The standard constructor of this class takes the degree p
of this finite element. Alternatively, it can take a quadrature formula points
defining the support points of the Lagrange interpolation in one coordinate direction.
For more information about the spacedim
template parameter check the documentation of FiniteElement or the one of Triangulation.
The constructor creates a TensorProductPolynomials object that includes the tensor product of LagrangeEquidistant
polynomials of degree p
. This TensorProductPolynomials
object provides all values and derivatives of the shape functions. In case a quadrature rule is given, the constructor creates a TensorProductPolynomials object that includes the tensor product of Lagrange
polynomials with the support points from points
.
Furthermore the constructor fills the interface_constraints
, the prolongation
(embedding) and the restriction
matrices. These are implemented only up to a certain degree and may not be available for very high polynomial degree.
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:
1D case:
* 0-------1 *
2D case:
* 2-------3 * | | * | | * | | * 0-------1 *
3D case:
* 6-------7 6-------7 * /| | / /| * / | | / / | * / | | / / | * 4 | | 4-------5 | * | 2-------3 | | 3 * | / / | | / * | / / | | / * |/ / | |/ * 0-------1 0-------1 *
The respective coordinate values of the support points of the degrees of freedom are as follows:
[0, 0, 0]
; [1, 0, 0]
; [0, 1, 0]
; [1, 1, 0]
; [0, 0, 1]
; [1, 0, 1]
; [0, 1, 1]
; [1, 1, 1]
; 1D case:
* 0---2---1 *
2D case:
* 2---7---3 * | | * 4 8 5 * | | * 0---6---1 *
3D case:
* 6--15---7 6--15---7 * /| | / /| * 12 | 19 12 1319 * / 18 | / / | * 4 | | 4---14--5 | * | 2---11--3 | | 3 * | / / | 17 / * 16 8 9 16 | 9 * |/ / | |/ * 0---10--1 0---10--1 * * *-------* *-------* * /| | / /| * / | 23 | / 25 / | * / | | / / | * * | | *-------* | * |20 *-------* | |21 * * | / / | 22 | / * | / 24 / | | / * |/ / | |/ * *-------* *-------* *
The center vertex has number 26.
The respective coordinate values of the support points of the degrees of freedom are as follows:
[0, 0, 0]
; [1, 0, 0]
; [0, 1, 0]
; [1, 1, 0]
; [0, 0, 1]
; [1, 0, 1]
; [0, 1, 1]
; [1, 1, 1]
; [0, 1/2, 0]
; [1, 1/2, 0]
; [1/2, 0, 0]
; [1/2, 1, 0]
; [0, 1/2, 1]
; [1, 1/2, 1]
; [1/2, 0, 1]
; [1/2, 1, 1]
; [0, 0, 1/2]
; [1, 0, 1/2]
; [0, 1, 1/2]
; [1, 1, 1/2]
; [0, 1/2, 1/2]
; [1, 1/2, 1/2]
; [1/2, 0, 1/2]
; [1/2, 1, 1/2]
; [1/2, 1/2, 0]
; [1/2, 1/2, 1]
; [1/2, 1/2, 1/2]
; 1D case:
* 0--2--3--1 *
* 2--10-11-3 * | | * 5 14 15 7 * | | * 4 12 13 6 * | | * 0--8--9--1 *
1D case:
* 0--2--3--4--1 *
* 2--13-14-15-3 * | | * 6 22 23 24 9 * | | * 5 19 20 21 8 * | | * 4 16 17 18 7 * | | * 0--10-11-12-1 *
Constructor for tensor product polynomials of degree p
.
FE_Q< dim, spacedim >::FE_Q | ( | const Quadrature< 1 > & | points | ) |
Constructor for tensor product polynomials with support points points
based on a one-dimensional quadrature formula. The degree of the finite element is points.size()-1
. Note that the first point has to be 0 and the last one 1. If FE_Q<dim>(QGaussLobatto<1>(fe_degree+1))
is specified, so-called Gauss-Lobatto elements are obtained which can give a diagonal mass matrix if combined with Gauss-Lobatto quadrature on the same points. Their use is shown in step-48.
FE_Q< dim, spacedim >::FE_Q | ( | const unsigned int | subdivisions_per_dimension, |
const unsigned int | base_degree | ||
) |
Constructs a FE_Q_isoQ1 element. That element shares large parts of code with FE_Q so most of the construction work is done in this routine, whereas the public constructor is in the class FE_Q_isoQ1.
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virtual |
Return a string that uniquely identifies a finite element. This class returns FE_Q<dim>(degree)
, with dim
and degree
replaced by appropriate values.
Implements 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 >.