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Reference documentation for deal.II version 8.1.0
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#include <fe_q_dg0.h>
Public Member Functions | |
FE_Q_DG0 (const unsigned int p) | |
FE_Q_DG0 (const Quadrature< 1 > &points) | |
virtual std::string | get_name () 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 |
virtual void | get_interpolation_matrix (const FiniteElement< dim, spacedim > &source, FullMatrix< double > &matrix) const |
virtual bool | has_support_on_face (const unsigned int shape_index, const unsigned int face_index) const |
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FE_Q_Base (const TensorProductPolynomialsConst< dim > &poly_space, const FiniteElementData< dim > &fe_data, const std::vector< bool > &restriction_is_additive_flags) | |
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 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 TensorProductPolynomialsConst< 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) | |
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.") | |
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 |
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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) |
Static Private Member Functions | |
static std::vector< bool > | get_riaf_vector (const unsigned int degree) |
static std::vector< unsigned int > | get_dpo_vector (const unsigned int degree) |
Implementation of a scalar Lagrange finite element Qp+DG0
that yields the finite element space of continuous, piecewise polynomials of degree p
in each coordinate direction plus the space of locally constant functions. 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.
For more information regarding this element see: Boffi, D., et al. "Local Mass Conservation of Stokes Finite Elements." Journal of Scientific Computing (2012): 1-18.
The constructor creates a TensorProductPolynomials object that includes the tensor product of LagrangeEquidistant
polynomials of degree p
plus the locally constant function. This TensorProductPolynomialsConst
object provides all values and derivatives of the shape functions. In case a quadrature rule is given, the constructor creates a TensorProductPolynomialsConst object that includes the tensor product of Lagrange
polynomials with the support points from points
and a locally constant function.
Furthermore the constructor fills the interface_constrains
, the prolongation
(embedding) and the restriction
matrices.
The original ordering of the shape functions represented by the TensorProductPolynomialsConst 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. Finally there is a support point for the discontinuous shape function in the middle of the cell. To be explicit, these numberings are listed in the following:
1D case:
* 0---2---1 *
2D case:
* 2-------3 * | | * | 5 | * | | * 0-------1 *
3D case:
* 6-------7 6-------7 * /| | / /| * / | | / / | * / | | / / | * 4 | 8 | 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]
; [1/2, 1/2, 1/2]
; 1D case:
* 0---2---1 *
Index 3 has the same coordinates as index 2
2D case:
* 2---7---3 * | | * 4 8 5 * | | * 0---6---1 *
Index 9 has the same coordinates as index 2
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---8---1 * * *-------* *-------* * /| | / /| * / | 23 | / 25 / | * / | | / / | * * | | *-------* | * |20 *-------* | |21 * * | / / | 22 | / * | / 24 / | | / * |/ / | |/ * *-------* *-------* *
The center vertices have number 26 and 27.
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]
; [1/2, 1/2, 1/2]
; 1D case:
* 0--2-4-3--1 *
* 2--10-11-3 * | | * 5 14 15 7 * | 16 | * 4 12 13 6 * | | * 0--8--9--1 *
1D case:
* 0--2--3--4--1 *
Index 5 has the same coordinates as index 3
* 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 *Index 21 has the same coordinates as index 20
Definition at line 238 of file fe_q_dg0.h.
Constructor for tensor product polynomials of degree p
plus locally constant functions.
FE_Q_DG0< dim, spacedim >::FE_Q_DG0 | ( | const Quadrature< 1 > & | points | ) |
Constructor for tensor product polynomials with support points points
plus locally constant functions 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.
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virtual |
Return a string that uniquely identifies a finite element. This class returns FE_Q_DG0<dim>(degree)
, with dim
and degree
replaced by appropriate values.
Implements FiniteElement< dim, spacedim >.
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virtual |
Interpolate a set of scalar values, computed in the generalized support points.
Reimplemented from FiniteElement< dim, spacedim >.
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virtual |
Interpolate a set of vector values, computed in the generalized support points.
Since a finite element often only interpolates part of a vector, offset
is used to determine the first component of the vector to be interpolated. Maybe consider changing your data structures to use the next function.
Reimplemented from FiniteElement< dim, spacedim >.
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virtual |
Interpolate a set of vector values, computed in the generalized support points.
Reimplemented from FiniteElement< 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_Q_DG0
element. Otherwise, an exception of type FiniteElement<dim,spacedim>::ExcInterpolationNotImplemented is thrown.
Reimplemented from FE_Q_Base< TensorProductPolynomialsConst< dim >, 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 FE_Q_Base< TensorProductPolynomialsConst< dim >, 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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staticprivate |
Returns the restriction_is_additive flags. Only the last component is true.
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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
.