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Reference documentation for deal.II version 8.1.0
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#include <fe_system.h>
Classes | |
class | InternalData |
Public Member Functions | |
FESystem (const FiniteElement< dim, spacedim > &fe, const unsigned int n_elements) | |
FESystem (const FiniteElement< dim, spacedim > &fe1, const unsigned int n1, const FiniteElement< dim, spacedim > &fe2, const unsigned int n2) | |
FESystem (const FiniteElement< dim, spacedim > &fe1, const unsigned int n1, const FiniteElement< dim, spacedim > &fe2, const unsigned int n2, const FiniteElement< dim, spacedim > &fe3, const unsigned int n3) | |
FESystem (const FiniteElement< dim, spacedim > &fe1, const unsigned int n1, const FiniteElement< dim, spacedim > &fe2, const unsigned int n2, const FiniteElement< dim, spacedim > &fe3, const unsigned int n3, const FiniteElement< dim, spacedim > &fe4, const unsigned int n4) | |
FESystem (const FiniteElement< dim, spacedim > &fe1, const unsigned int n1, const FiniteElement< dim, spacedim > &fe2, const unsigned int n2, const FiniteElement< dim, spacedim > &fe3, const unsigned int n3, const FiniteElement< dim, spacedim > &fe4, const unsigned int n4, const FiniteElement< dim, spacedim > &fe5, const unsigned int n5) | |
FESystem (const std::vector< const FiniteElement< dim, spacedim > * > &fes, const std::vector< unsigned int > &multiplicities) | |
virtual | ~FESystem () |
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 |
virtual void | get_interpolation_matrix (const FiniteElement< dim, spacedim > &source, FullMatrix< double > &matrix) const |
virtual const FiniteElement < dim, spacedim > & | base_element (const unsigned int index) 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 Point< dim > | unit_support_point (const unsigned int index) const |
virtual Point< dim-1 > | unit_face_support_point (const unsigned int index) const |
virtual std::size_t | memory_consumption () const |
Functions to support hp | |
virtual bool | hp_constraints_are_implemented () 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 |
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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) | |
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 |
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 |
const std::vector< Point< dim-1 > > & | get_unit_face_support_points () const |
bool | has_face_support_points () 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 UpdateFlags | update_once (const UpdateFlags flags) const |
virtual UpdateFlags | update_each (const UpdateFlags flags) const |
virtual FiniteElement< dim, spacedim > * | clone () const |
virtual Mapping< dim, spacedim > ::InternalDataBase * | get_data (const UpdateFlags update_flags, const Mapping< dim, spacedim > &mapping, const Quadrature< dim > &quadrature) const |
virtual Mapping< dim, spacedim > ::InternalDataBase * | get_face_data (const UpdateFlags update_flags, const Mapping< dim, spacedim > &mapping, const Quadrature< dim-1 > &quadrature) const |
virtual Mapping< dim, spacedim > ::InternalDataBase * | get_subface_data (const UpdateFlags update_flags, const Mapping< dim, spacedim > &mapping, const Quadrature< dim-1 > &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_data, typename Mapping< dim, spacedim >::InternalDataBase &fe_data, 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_data, typename Mapping< dim, spacedim >::InternalDataBase &fe_data, 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_data, typename Mapping< dim, spacedim >::InternalDataBase &fe_data, FEValuesData< dim, spacedim > &data) const |
template<int dim_1> | |
void | compute_fill (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, CellSimilarity::Similarity cell_similarity, typename Mapping< dim, spacedim >::InternalDataBase &mapping_data, typename Mapping< dim, spacedim >::InternalDataBase &fe_data, 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 | |
void | initialize_unit_support_points () |
void | initialize_unit_face_support_points () |
void | initialize_quad_dof_index_permutation () |
void | initialize (const std::vector< const FiniteElement< dim, spacedim > * > &fes, const std::vector< unsigned int > &multiplicities) |
void | build_cell_tables () |
void | build_face_tables () |
void | build_interface_constraints () |
template<int structdim> | |
std::vector< std::pair < unsigned int, unsigned int > > | hp_object_dof_identities (const FiniteElement< dim, spacedim > &fe_other) const |
Static Private Member Functions | |
static FiniteElementData< dim > | multiply_dof_numbers (const FiniteElement< dim, spacedim > *fe1, const unsigned int N1, const FiniteElement< dim, spacedim > *fe2=NULL, const unsigned int N2=0, const FiniteElement< dim, spacedim > *fe3=NULL, const unsigned int N3=0, const FiniteElement< dim, spacedim > *fe4=NULL, const unsigned int N4=0, const FiniteElement< dim, spacedim > *fe5=NULL, const unsigned int N5=0) |
static FiniteElementData< dim > | multiply_dof_numbers (const std::vector< const FiniteElement< dim, spacedim > * > &fes, const std::vector< unsigned int > &multiplicities) |
static std::vector< bool > | compute_restriction_is_additive_flags (const FiniteElement< dim, spacedim > *fe1, const unsigned int N1, const FiniteElement< dim, spacedim > *fe2=NULL, const unsigned int N2=0, const FiniteElement< dim, spacedim > *fe3=NULL, const unsigned int N3=0, const FiniteElement< dim, spacedim > *fe4=NULL, const unsigned int N4=0, const FiniteElement< dim, spacedim > *fe5=NULL, const unsigned int N5=0) |
static std::vector< bool > | compute_restriction_is_additive_flags (const std::vector< const FiniteElement< dim, spacedim > * > &fes, const std::vector< unsigned int > &multiplicities) |
static std::vector< ComponentMask > | compute_nonzero_components (const FiniteElement< dim, spacedim > *fe1, const unsigned int N1, const FiniteElement< dim, spacedim > *fe2=NULL, const unsigned int N2=0, const FiniteElement< dim, spacedim > *fe3=NULL, const unsigned int N3=0, const FiniteElement< dim, spacedim > *fe4=NULL, const unsigned int N4=0, const FiniteElement< dim, spacedim > *fe5=NULL, const unsigned int N5=0) |
static std::vector< ComponentMask > | compute_nonzero_components (const std::vector< const FiniteElement< dim, spacedim > * > &fes, const std::vector< unsigned int > &multiplicities) |
Private Attributes | |
std::vector< std::pair < std_cxx1x::shared_ptr< const FiniteElement< dim, spacedim > >, unsigned int > > | base_elements |
Threads::Mutex | mutex |
Static Private Attributes | |
static const unsigned int | invalid_face_number = numbers::invalid_unsigned_int |
This class provides an interface to group several elements together into one. To the outside world, the resulting object looks just like a usual finite element object, which is composed of several other finite elements that are possibly of different type. The result is then a vector-valued finite element. Vector valued elements are discussed in a number of tutorial programs, for example step-8, step-20, step-21, and in particular in the Handling vector valued problems module.
An FESystem, except in the most trivial case, produces a vector-valued finite element with several components. The number of components n_components() corresponds to the dimension of the solution function in the PDE system, and correspondingly also to the number of equations your PDE system has. For example, the mixed Laplace system covered in step-20 has components in
space dimensions: the scalar pressure and the
components of the velocity vector. Similarly, the elasticity equation covered in step-8 has
components in
space dimensions. In general, the number of components of a FESystem element is the accumulated number of components of all base elements times their multiplicities. A bit more on components is also given in the glossary entry on components.
While the concept of components is important from the viewpoint of a partial differential equation, the finite element side looks a bit different Since not only FESystem, but also vector-valued elements like FE_RaviartThomas, have several components. The concept needed here is a block. Each block encompasses the set of degrees of freedom associated with a single base element of an FESystem, where base elements with multiplicities count multiple times. These blocks are usually addressed using the information in DoFHandler::block_info(). The number of blocks of a FESystem object is simply the sum of all multiplicities of base elements and is given by n_blocks().
For example, the FESystem for the Taylor-Hood element for the three-dimensional Stokes problem can be built using the code
This example creates an FESystem sys1
with four components, three for the velocity components and one for the pressure, and also four blocks with the degrees of freedom of each of the velocity components and the pressure in a separate block each. The number of blocks is four since the first base element is repeated three times.
On the other hand, a Taylor-Hood element can also be constructed using
The FESystem sys2
created here has the same four components, but the degrees of freedom are distributed into only two blocks. The first block has all velocity degrees of freedom from U
, while the second block contains the pressure degrees of freedom. Note that while U
itself has 3 blocks, the FESystem sys2
does not attempt to split U
into its base elements but considers it a block of its own. By blocking all velocities into one system first as in sys2
, we achieve the same block structure that would be generated if instead of using a element for the velocities we had used vector-valued base elements, for instance like using a mixed discretization of Darcy's law using
This example also produces a system with four components, but only two blocks.
In most cases, the composed element behaves as if it were a usual element. It just has more degrees of freedom than most of the "common" elements. However the underlying structure is visible in the restriction, prolongation and interface constraint matrices, which do not couple the degrees of freedom of the base elements. E.g. the continuity requirement is imposed for the shape functions of the subobjects separately; no requirement exist between shape functions of different subobjects, i.e. in the above example: on a hanging node, the respective value of the u
velocity is only coupled to u
at the vertices and the line on the larger cell next to this vertex, but there is no interaction with v
and w
of this or the other cell.
The overall numbering of degrees of freedom is as follows: for each subobject (vertex, line, quad, or hex), the degrees of freedom are numbered such that we run over all subelements first, before turning for the next dof on this subobject or for the next subobject. For example, for an element of three components in one space dimension, the first two components being cubic lagrange elements and the third being a quadratic lagrange element, the ordering for the system s=(u,v,p)
is:
u0, v0, p0 = s0, s1, s2
u1, v1, p1 = s3, s4, s5
u2, u3 = s4, s5
v2, v3 = s6, s7
. p2 = s8
. That said, you should not rely on this numbering in your application as these internals might change in future. Rather use the functions system_to_component_index() and component_to_system_index().
For more information on the template parameter spacedim
see the documentation of Triangulation.
FESystem< dim, spacedim >::FESystem | ( | const FiniteElement< dim, spacedim > & | fe, |
const unsigned int | n_elements | ||
) |
Constructor. Take a finite element type and the number of elements you want to group together using this class.
In fact, the object fe
is not used, apart from getting the number of dofs per vertex, line, etc for that finite element class. The objects creates its own copy of the finite element object at construction time (but after the initialization of the base class FiniteElement
, which is why we need a valid finite element object passed to the constructor).
Obviously, the template finite element class needs to be of the same dimension as is this object.
FESystem< dim, spacedim >::FESystem | ( | const FiniteElement< dim, spacedim > & | fe1, |
const unsigned int | n1, | ||
const FiniteElement< dim, spacedim > & | fe2, | ||
const unsigned int | n2 | ||
) |
Constructor for mixed discretizations with two base elements.
See the other constructor.
FESystem< dim, spacedim >::FESystem | ( | const FiniteElement< dim, spacedim > & | fe1, |
const unsigned int | n1, | ||
const FiniteElement< dim, spacedim > & | fe2, | ||
const unsigned int | n2, | ||
const FiniteElement< dim, spacedim > & | fe3, | ||
const unsigned int | n3 | ||
) |
Constructor for mixed discretizations with three base elements.
See the other constructor.
FESystem< dim, spacedim >::FESystem | ( | const FiniteElement< dim, spacedim > & | fe1, |
const unsigned int | n1, | ||
const FiniteElement< dim, spacedim > & | fe2, | ||
const unsigned int | n2, | ||
const FiniteElement< dim, spacedim > & | fe3, | ||
const unsigned int | n3, | ||
const FiniteElement< dim, spacedim > & | fe4, | ||
const unsigned int | n4 | ||
) |
Constructor for mixed discretizations with four base elements.
See the other constructor.
FESystem< dim, spacedim >::FESystem | ( | const FiniteElement< dim, spacedim > & | fe1, |
const unsigned int | n1, | ||
const FiniteElement< dim, spacedim > & | fe2, | ||
const unsigned int | n2, | ||
const FiniteElement< dim, spacedim > & | fe3, | ||
const unsigned int | n3, | ||
const FiniteElement< dim, spacedim > & | fe4, | ||
const unsigned int | n4, | ||
const FiniteElement< dim, spacedim > & | fe5, | ||
const unsigned int | n5 | ||
) |
Constructor for mixed discretizations with five base elements.
See the other constructor.
FESystem< dim, spacedim >::FESystem | ( | const std::vector< const FiniteElement< dim, spacedim > * > & | fes, |
const std::vector< unsigned int > & | multiplicities | ||
) |
Same as above but for any number of base elements. Pointers to the base elements and their multiplicities are passed as vectors to this constructor. The length of these vectors is assumed to be equal.
Destructor.
|
virtual |
Return a string that uniquely identifies a finite element. This element returns a string that is composed of the strings name1
...nameN
returned by the basis elements. From these, we create a sequence FESystem<dim>[name1^m1-name2^m2-...-nameN^mN]
, where mi
are the multiplicities of the basis elements. If a multiplicity is equal to one, then the superscript is omitted.
Implements FiniteElement< dim, spacedim >.
|
virtual |
Return the value of the ith
shape function at the point p
. p
is a point on the reference element. Since this finite element is always vector-valued, we return the value of the only non-zero component of the vector value of this shape function. If the shape function has more than one non-zero component (which we refer to with the term non-primitive), then throw an exception of type ExcShapeFunctionNotPrimitive
.
An ExcUnitShapeValuesDoNotExist
is thrown if the shape values of the FiniteElement
(corresponding to the ith
shape function) depend on the shape of the cell in real space.
Reimplemented from FiniteElement< dim, spacedim >.
|
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 vector valued in general, it relays the computation of these values to the base elements.
Reimplemented from FiniteElement< dim, spacedim >.
|
virtual |
Return the gradient of the ith
shape function at the point p
. p
is a point on the reference element, and likewise the gradient is the gradient on the unit cell with respect to unit cell coordinates. Since this finite element is always vector-valued, we return the value of the only non-zero component of the vector value of this shape function. If the shape function has more than one non-zero component (which we refer to with the term non-primitive), then throw an exception of type ExcShapeFunctionNotPrimitive
.
An ExcUnitShapeValuesDoNotExist
is thrown if the shape values of the FiniteElement
(corresponding to the ith
shape function) depend on the shape of the cell in real space.
Reimplemented from FiniteElement< dim, spacedim >.
|
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 vector valued in general, it relays the computation of these values to the base elements.
Reimplemented from FiniteElement< dim, spacedim >.
|
virtual |
Return the tensor of second derivatives of the ith
shape function at point p
on the unit cell. The derivatives are derivatives on the unit cell with respect to unit cell coordinates. Since this finite element is always vector-valued, we return the value of the only non-zero component of the vector value of this shape function. If the shape function has more than one non-zero component (which we refer to with the term non-primitive), then throw an exception of type ExcShapeFunctionNotPrimitive
.
An ExcUnitShapeValuesDoNotExist
is thrown if the shape values of the FiniteElement
(corresponding to the ith
shape function) depend on the shape of the cell in real space.
Reimplemented from FiniteElement< dim, spacedim >.
|
virtual |
Return the second derivatives 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 vector valued in general, it relays the computation of these values to the base elements.
Reimplemented from FiniteElement< dim, spacedim >.
|
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 available if source and destination element are both FESystem
elements, have the same number of base elements with same element multiplicity, and if these base elements also implement their get_interpolation_matrix
functions. Otherwise, an exception of type FiniteElement<dim,spacedim>::ExcInterpolationNotImplemented is thrown.
Reimplemented from FiniteElement< dim, spacedim >.
|
virtual |
Access to a composing element. The index needs to be smaller than the number of base elements. Note that the number of base elements may in turn be smaller than the number of components of the system element, if the multiplicities are greater than one.
Reimplemented from FiniteElement< dim, spacedim >.
|
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 >.
|
virtual |
Projection from a fine grid space onto a coarse grid space. Overrides the respective method in FiniteElement, implementing lazy evaluation (initialize when requested).
If this projection operator is associated with a matrix P
, then the restriction of this matrix P_i
to a single child cell is returned here.
The matrix P
is the concatenation or the sum of the cell matrices P_i
, depending on the restriction_is_additive_flags. This distinguishes interpolation (concatenation) and projection with respect to scalar products (summation).
Row and column indices are related to coarse grid and fine grid spaces, respectively, consistent with the definition of the associated operator.
If projection matrices are not implemented in the derived finite element class, this function aborts with ExcProjectionVoid. You can check whether this is the case by calling the restriction_is_implemented() or the isotropic_restriction_is_implemented() function.
Reimplemented from FiniteElement< dim, spacedim >.
|
virtual |
Embedding matrix between grids. Overrides the respective method in FiniteElement, implementing lazy evaluation (initialize when queried).
The identity operator from a coarse grid space into a fine grid space is associated with a matrix P
. The restriction of this matrix P_i
to a single child cell is returned here.
The matrix P
is the concatenation, not the sum of the cell matrices P_i
. That is, if the same non-zero entry j,k
exists in in two different child matrices P_i
, the value should be the same in both matrices and it is copied into the matrix P
only once.
Row and column indices are related to fine grid and coarse grid spaces, respectively, consistent with the definition of the associated operator.
These matrices are used by routines assembling the prolongation matrix for multi-level methods. Upon assembling the transfer matrix between cells using this matrix array, zero elements in the prolongation matrix are discarded and will not fill up the transfer matrix.
If projection matrices are not implemented in the derived finite element class, this function aborts with ExcEmbeddingVoid. You can check whether this is the case by calling the prolongation_is_implemented() or the isotropic_prolongation_is_implemented() function.
Reimplemented from FiniteElement< dim, spacedim >.
|
virtual |
Given an index in the natural ordering of indices on a face, return the index of the same degree of freedom on the cell.
To explain the concept, consider the case where we would like to know whether a degree of freedom on a face, for example as part of an FESystem element, is primitive. Unfortunately, the is_primitive() function in the FiniteElement class takes a cell index, so we would need to find the cell index of the shape function that corresponds to the present face index. This function does that.
Code implementing this would then look like this:
The function takes additional arguments that account for the fact that actual faces can be in their standard ordering with respect to the cell under consideration, or can be flipped, oriented, etc.
face_dof_index | The index of the degree of freedom on a face. This index must be between zero and dofs_per_face. |
face | The number of the face this degree of freedom lives on. This number must be between zero and GeometryInfo::faces_per_cell. |
face_orientation | One part of the description of the orientation of the face. See GlossFaceOrientation . |
face_flip | One part of the description of the orientation of the face. See GlossFaceOrientation . |
face_rotation | One part of the description of the orientation of the face. See GlossFaceOrientation . |
Reimplemented from FiniteElement< dim, spacedim >.
|
virtual |
Implementation of the respective function in the base class.
Reimplemented from FiniteElement< dim, spacedim >.
|
virtual |
Implementation of the respective function in the base class.
Reimplemented from FiniteElement< dim, spacedim >.
|
virtual |
Return whether this element implements its hanging node constraints in the new way, which has to be used to make elements "hp compatible".
This function returns true
iff all its base elements return true
for this function.
Reimplemented from FiniteElement< dim, spacedim >.
|
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
.
Base elements of this element 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, which will get propagated out from this element.
Reimplemented from FiniteElement< dim, spacedim >.
|
virtual |
Return the matrix interpolating from a face of of one element to the subface of the neighboring element. The size of the matrix is then source.dofs_per_face
times this->dofs_per_face
.
Base elements of this element 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, which will get propagated out from this element.
Reimplemented from FiniteElement< dim, spacedim >.
|
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.
Reimplemented from FiniteElement< dim, spacedim >.
|
virtual |
Same as hp_vertex_dof_indices(), except that the function treats degrees of freedom on lines.
Reimplemented from FiniteElement< dim, spacedim >.
|
virtual |
Same as hp_vertex_dof_indices(), except that the function treats degrees of freedom on quads.
Reimplemented from FiniteElement< dim, spacedim >.
|
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 >.
|
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 >.
|
protectedvirtual |
Compute flags for initial update only.
Implements FiniteElement< dim, spacedim >.
|
protectedvirtual |
Compute flags for update on each cell.
Implements FiniteElement< dim, spacedim >.
|
protectedvirtual |
clone
function instead of a copy constructor.
This function is needed by the constructors of FESystem
.
Implements FiniteElement< dim, spacedim >.
|
protectedvirtual |
Prepare internal data structures and fill in values independent of the cell. Returns a pointer to an object of which the caller of this function then has to assume ownership (which includes destruction when it is no more needed).
Implements FiniteElement< dim, spacedim >.
|
protectedvirtual |
Prepare internal data structure for transformation of faces and fill in values independent of the cell. Returns a pointer to an object of which the caller of this function then has to assume ownership (which includes destruction when it is no more needed).
Reimplemented from FiniteElement< dim, spacedim >.
|
protectedvirtual |
Prepare internal data structure for transformation of children of faces and fill in values independent of the cell. Returns a pointer to an object of which the caller of this function then has to assume ownership (which includes destruction when it is no more needed).
Reimplemented from FiniteElement< dim, spacedim >.
|
protectedvirtual |
Implementation of the same function in FiniteElement.
Passes on control to compute_fill
that does the work for all three fill_fe*_values
functions.
Implements FiniteElement< dim, spacedim >.
|
protectedvirtual |
Implementation of the same function in FiniteElement.
Passes on control to compute_fill
that does the work for all three fill_fe*_values
functions.
Implements FiniteElement< dim, spacedim >.
|
protectedvirtual |
Implementation of the same function in FiniteElement.
Passes on control to compute_fill
that does the work for all three fill_fe*_values
functions.
Implements FiniteElement< dim, spacedim >.
|
protected |
Do the work for the three fill_fe*_values
functions.
Calls (among other things) fill_fe_([sub]face)_values
of the base elements. Calls fill_fe_values
if face_no==invalid_face_no
and sub_no==invalid_face_no
; calls fill_fe_face_values
if face_no==invalid_face_no
and sub_no!=invalid_face_no
; and calls fill_fe_subface_values
if face_no!=invalid_face_no
and sub_no!=invalid_face_no
.
|
private |
Initialize the unit_support_points
field of the FiniteElement class. Called from the constructor.
|
private |
Initialize the unit_face_support_points
field of the FiniteElement class. Called from the constructor.
|
private |
Initialize the adjust_quad_dof_index_for_face_orientation_table
field of the FiniteElement class. Called from the constructor.
|
staticprivate |
Helper function used in the constructor: take a FiniteElementData
object and return an object of the same type with the number of degrees of freedom per vertex, line, etc. multiplied by n
. Don't touch the number of functions for the transformation from unit to real cell.
|
staticprivate |
Same as above but for any number of sub-elements.
|
staticprivate |
Helper function used in the constructor: takes a FiniteElement
object and returns an boolean vector including the restriction_is_additive_flags
of the mixed element consisting of N
elements of the sub-element fe
.
|
staticprivate |
Compute the named flags for a list of finite elements with multiplicities given in the second argument. This function is called from all the above functions.
|
staticprivate |
Compute the non-zero vector components of a composed finite element.
|
staticprivate |
Compute the nonzero components of a list of finite elements with multiplicities given in the second argument. This function is called from all the above functions.
|
private |
This function is simply singled out of the constructors since there are several of them. It sets up the index table for the system as well as restriction
and prolongation
matrices.
|
private |
Used by initialize
.
|
private |
Used by initialize
.
|
private |
Used by initialize
.
|
private |
A function that computes the hp_vertex_dof_identities(), hp_line_dof_identities(), or hp_quad_dof_identities(), depending on the value of the template parameter.
|
staticprivate |
Value to indicate that a given face or subface number is invalid.
Definition at line 686 of file fe_system.h.
|
private |
Pointers to underlying finite element objects.
This object contains a pointer to each contributing element of a mixed discretization and its multiplicity. It is created by the constructor and constant afterwards.
The pointers are managed as shared pointers. This ensures that we can use the copy constructor of this class without having to manage cloning the elements themselves. Since finite element objects do not contain any state, this also allows multiple copies of an FESystem object to share pointers to the underlying base finite elements. The last one of these copies around will then delete the pointer to the base elements.
Definition at line 704 of file fe_system.h.