
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 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 |
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 |
Private Types | |
| typedef std::pair< const FiniteElement< dim, spacedim > *, unsigned int > | ElementPair |
Private Member Functions | |
| void | initialize_unit_support_points () |
| void | initialize_unit_face_support_points () |
| void | initialize_quad_dof_index_permutation () |
| void | initialize () |
| 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 FiniteElementData< dim > &fe_data, const unsigned int N) |
| static FiniteElementData< dim > | multiply_dof_numbers (const FiniteElementData< dim > &fe1, const unsigned int N1, const FiniteElementData< dim > &fe2, const unsigned int N2) |
| static FiniteElementData< dim > | multiply_dof_numbers (const FiniteElementData< dim > &fe1, const unsigned int N1, const FiniteElementData< dim > &fe2, const unsigned int N2, const FiniteElementData< dim > &fe3, const unsigned int N3) |
| static FiniteElementData< dim > | multiply_dof_numbers (const FiniteElementData< dim > &fe1, const unsigned int N1, const FiniteElementData< dim > &fe2, const unsigned int N2, const FiniteElementData< dim > &fe3, const unsigned int N3, const FiniteElementData< dim > &fe4, const unsigned int N4) |
| static FiniteElementData< dim > | multiply_dof_numbers (const FiniteElementData< dim > &fe1, const unsigned int N1, const FiniteElementData< dim > &fe2, const unsigned int N2, const FiniteElementData< dim > &fe3, const unsigned int N3, const FiniteElementData< dim > &fe4, const unsigned int N4, const FiniteElementData< dim > &fe5, const unsigned int N5) |
| 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 > &fe, const unsigned int N) |
| static std::vector< bool > | compute_restriction_is_additive_flags (const FiniteElement< dim, spacedim > &fe1, const unsigned int N1, const FiniteElement< dim, spacedim > &fe2, const unsigned int N2) |
| static std::vector< bool > | compute_restriction_is_additive_flags (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) |
| static std::vector< bool > | compute_restriction_is_additive_flags (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) |
| static std::vector< bool > | compute_restriction_is_additive_flags (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) |
| 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 < std::vector< bool > > | compute_nonzero_components (const FiniteElement< dim, spacedim > &fe1, const unsigned int N1) |
| static std::vector < std::vector< bool > > | compute_nonzero_components (const FiniteElement< dim, spacedim > &fe1, const unsigned int N1, const FiniteElement< dim, spacedim > &fe2, const unsigned int N2) |
| static std::vector < std::vector< bool > > | compute_nonzero_components (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) |
| static std::vector < std::vector< bool > > | compute_nonzero_components (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) |
| static std::vector < std::vector< bool > > | compute_nonzero_components (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) |
| static std::vector < std::vector< bool > > | compute_nonzero_components (const std::vector< const FiniteElement< dim, spacedim > * > &fes, const std::vector< unsigned int > &multiplicities) |
Private Attributes | |
| std::vector< ElementPair > | base_elements |
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 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 of a FESystem object is simply the sum of all multiplicities of base elements.
For example, the FESystem for the Taylor-Hood element for the three-dimensional Stokes problem can be built using the code
FE_Q<3> u(2); FE_Q<3> p(1); FESystem<3> sys1(u,3, p,1);
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
FESystem<3> U(u,3); FESystem<3> sys2(U,1, p,1);
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 sam 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
FE_RaviartThomas<3> u(1); FE_DGQ<3> p(1); FESystem<3> sys3(u,1, p,1);
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 a 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.
Definition at line 150 of file fe_system.h.
typedef std::pair<const FiniteElement<dim,spacedim> *, unsigned int> FESystem< dim, spacedim >::ElementPair [private] |
Pairs of multiplicity and element type.
Definition at line 798 of file fe_system.h.
| 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 std::string FESystem< dim, spacedim >::get_name | ( | ) | const [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 double FESystem< dim, spacedim >::shape_value | ( | const unsigned int | i, |
| const Point< dim > & | p | ||
| ) | const [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 double FESystem< dim, spacedim >::shape_value_component | ( | const unsigned int | i, |
| const Point< dim > & | p, | ||
| const unsigned int | component | ||
| ) | const [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 Tensor<1,dim> FESystem< dim, spacedim >::shape_grad | ( | const unsigned int | i, |
| const Point< dim > & | p | ||
| ) | const [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 Tensor<1,dim> FESystem< dim, spacedim >::shape_grad_component | ( | const unsigned int | i, |
| const Point< dim > & | p, | ||
| const unsigned int | component | ||
| ) | const [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 Tensor<2,dim> FESystem< dim, spacedim >::shape_grad_grad | ( | const unsigned int | i, |
| const Point< dim > & | p | ||
| ) | const [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 Tensor<2,dim> FESystem< dim, spacedim >::shape_grad_grad_component | ( | const unsigned int | i, |
| const Point< dim > & | p, | ||
| const unsigned int | component | ||
| ) | const [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 void FESystem< dim, spacedim >::get_interpolation_matrix | ( | const FiniteElement< dim, spacedim > & | source, |
| FullMatrix< double > & | matrix | ||
| ) | const [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 const FiniteElement<dim,spacedim>& FESystem< dim, spacedim >::base_element | ( | const unsigned int | index ) | const [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 bool FESystem< dim, spacedim >::has_support_on_face | ( | const unsigned int | shape_index, |
| const unsigned int | face_index | ||
| ) | const [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 Point<dim> FESystem< dim, spacedim >::unit_support_point | ( | const unsigned int | index ) | const [virtual] |
Implementation of the respective function in the base class.
Reimplemented from FiniteElement< dim, spacedim >.
| virtual Point<dim-1> FESystem< dim, spacedim >::unit_face_support_point | ( | const unsigned int | index ) | const [virtual] |
Implementation of the respective function in the base class.
Reimplemented from FiniteElement< dim, spacedim >.
| virtual bool FESystem< dim, spacedim >::hp_constraints_are_implemented | ( | ) | const [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 void FESystem< dim, spacedim >::get_face_interpolation_matrix | ( | const FiniteElement< dim, spacedim > & | source, |
| FullMatrix< double > & | matrix | ||
| ) | const [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 void FESystem< dim, spacedim >::get_subface_interpolation_matrix | ( | const FiniteElement< dim, spacedim > & | source, |
| const unsigned int | subface, | ||
| FullMatrix< double > & | matrix | ||
| ) | const [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 std::vector<std::pair<unsigned int, unsigned int> > FESystem< dim, spacedim >::hp_vertex_dof_identities | ( | const FiniteElement< dim, spacedim > & | fe_other ) | const [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, and returns a list of pairs of global dof indices in identities. 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 std::vector<std::pair<unsigned int, unsigned int> > FESystem< dim, spacedim >::hp_line_dof_identities | ( | const FiniteElement< dim, spacedim > & | fe_other ) | const [virtual] |
Same as hp_vertex_dof_indices(), except that the function treats degrees of freedom on lines.
Reimplemented from FiniteElement< dim, spacedim >.
| virtual std::vector<std::pair<unsigned int, unsigned int> > FESystem< dim, spacedim >::hp_quad_dof_identities | ( | const FiniteElement< dim, spacedim > & | fe_other ) | const [virtual] |
Same as hp_vertex_dof_indices(), except that the function treats degrees of freedom on quads.
Reimplemented from FiniteElement< dim, spacedim >.
| virtual FiniteElementDomination::Domination FESystem< dim, spacedim >::compare_for_face_domination | ( | const FiniteElement< dim, spacedim > & | fe_other ) | const [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 std::size_t FESystem< dim, spacedim >::memory_consumption | ( | ) | const [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 >.
| virtual UpdateFlags FESystem< dim, spacedim >::update_once | ( | const UpdateFlags | flags ) | const [protected, virtual] |
Compute flags for initial update only.
Implements FiniteElement< dim, spacedim >.
| virtual UpdateFlags FESystem< dim, spacedim >::update_each | ( | const UpdateFlags | flags ) | const [protected, virtual] |
Compute flags for update on each cell.
Implements FiniteElement< dim, spacedim >.
| virtual FiniteElement<dim,spacedim>* FESystem< dim, spacedim >::clone | ( | ) | const [protected, virtual] |
clone function instead of a copy constructor.
This function is needed by the constructors of FESystem.
Implements FiniteElement< dim, spacedim >.
| virtual Mapping<dim,spacedim>::InternalDataBase* FESystem< dim, spacedim >::get_data | ( | const UpdateFlags | flags, |
| const Mapping< dim, spacedim > & | mapping, | ||
| const Quadrature< dim > & | quadrature | ||
| ) | const [protected, virtual] |
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 >.
| virtual Mapping<dim,spacedim>::InternalDataBase* FESystem< dim, spacedim >::get_face_data | ( | const UpdateFlags | flags, |
| const Mapping< dim, spacedim > & | mapping, | ||
| const Quadrature< dim-1 > & | quadrature | ||
| ) | const [protected, virtual] |
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 >.
| virtual Mapping<dim,spacedim>::InternalDataBase* FESystem< dim, spacedim >::get_subface_data | ( | const UpdateFlags | flags, |
| const Mapping< dim, spacedim > & | mapping, | ||
| const Quadrature< dim-1 > & | quadrature | ||
| ) | const [protected, virtual] |
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 >.
| virtual void FESystem< dim, spacedim >::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 [protected, virtual] |
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 >.
| virtual void FESystem< dim, spacedim >::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 [protected, virtual] |
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 >.
| virtual void FESystem< dim, spacedim >::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 [protected, virtual] |
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 >.
| void FESystem< dim, spacedim >::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 [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.
| void FESystem< dim, spacedim >::initialize_unit_support_points | ( | ) | [private] |
Initialize the unit_support_points field of the FiniteElement class. Called from the constructor.
| void FESystem< dim, spacedim >::initialize_unit_face_support_points | ( | ) | [private] |
Initialize the unit_face_support_points field of the FiniteElement class. Called from the constructor.
| void FESystem< dim, spacedim >::initialize_quad_dof_index_permutation | ( | ) | [private] |
Initialize the adjust_quad_dof_index_for_face_orientation_table field of the FiniteElement class. Called from the constructor.
| static FiniteElementData<dim> FESystem< dim, spacedim >::multiply_dof_numbers | ( | const FiniteElementData< dim > & | fe_data, |
| const unsigned int | N | ||
| ) | [static, private] |
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.
| static FiniteElementData<dim> FESystem< dim, spacedim >::multiply_dof_numbers | ( | const FiniteElementData< dim > & | fe1, |
| const unsigned int | N1, | ||
| const FiniteElementData< dim > & | fe2, | ||
| const unsigned int | N2 | ||
| ) | [static, private] |
Same as above for mixed elements with two different sub-elements.
| static FiniteElementData<dim> FESystem< dim, spacedim >::multiply_dof_numbers | ( | const FiniteElementData< dim > & | fe1, |
| const unsigned int | N1, | ||
| const FiniteElementData< dim > & | fe2, | ||
| const unsigned int | N2, | ||
| const FiniteElementData< dim > & | fe3, | ||
| const unsigned int | N3 | ||
| ) | [static, private] |
Same as above for mixed elements with three different sub-elements.
| static FiniteElementData<dim> FESystem< dim, spacedim >::multiply_dof_numbers | ( | const FiniteElementData< dim > & | fe1, |
| const unsigned int | N1, | ||
| const FiniteElementData< dim > & | fe2, | ||
| const unsigned int | N2, | ||
| const FiniteElementData< dim > & | fe3, | ||
| const unsigned int | N3, | ||
| const FiniteElementData< dim > & | fe4, | ||
| const unsigned int | N4 | ||
| ) | [static, private] |
with 4 different sub-elements
| static FiniteElementData<dim> FESystem< dim, spacedim >::multiply_dof_numbers | ( | const FiniteElementData< dim > & | fe1, |
| const unsigned int | N1, | ||
| const FiniteElementData< dim > & | fe2, | ||
| const unsigned int | N2, | ||
| const FiniteElementData< dim > & | fe3, | ||
| const unsigned int | N3, | ||
| const FiniteElementData< dim > & | fe4, | ||
| const unsigned int | N4, | ||
| const FiniteElementData< dim > & | fe5, | ||
| const unsigned int | N5 | ||
| ) | [static, private] |
and with 5 different sub-elements
| static FiniteElementData<dim> FESystem< dim, spacedim >::multiply_dof_numbers | ( | const std::vector< const FiniteElement< dim, spacedim > * > & | fes, |
| const std::vector< unsigned int > & | multiplicities | ||
| ) | [static, private] |
Same as above but for any number of sub-elements.
| static std::vector<bool> FESystem< dim, spacedim >::compute_restriction_is_additive_flags | ( | const FiniteElement< dim, spacedim > & | fe, |
| const unsigned int | N | ||
| ) | [static, private] |
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.
| static std::vector<bool> FESystem< dim, spacedim >::compute_restriction_is_additive_flags | ( | const FiniteElement< dim, spacedim > & | fe1, |
| const unsigned int | N1, | ||
| const FiniteElement< dim, spacedim > & | fe2, | ||
| const unsigned int | N2 | ||
| ) | [static, private] |
Same as above for mixed elements with two different sub-elements.
| static std::vector<bool> FESystem< dim, spacedim >::compute_restriction_is_additive_flags | ( | 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 | ||
| ) | [static, private] |
Same as above for mixed elements with three different sub-elements.
| static std::vector<bool> FESystem< dim, spacedim >::compute_restriction_is_additive_flags | ( | 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 | ||
| ) | [static, private] |
with four different sub-elements
| static std::vector<bool> FESystem< dim, spacedim >::compute_restriction_is_additive_flags | ( | 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 | ||
| ) | [static, private] |
and with five different sub-elements
| static std::vector<bool> FESystem< dim, spacedim >::compute_restriction_is_additive_flags | ( | const std::vector< const FiniteElement< dim, spacedim > * > & | fes, |
| const std::vector< unsigned int > & | multiplicities | ||
| ) | [static, private] |
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.
| static std::vector<std::vector<bool> > FESystem< dim, spacedim >::compute_nonzero_components | ( | const FiniteElement< dim, spacedim > & | fe1, |
| const unsigned int | N1 | ||
| ) | [static, private] |
Compute the non-zero vector components of a composed finite element.
| static std::vector<std::vector<bool> > FESystem< dim, spacedim >::compute_nonzero_components | ( | const FiniteElement< dim, spacedim > & | fe1, |
| const unsigned int | N1, | ||
| const FiniteElement< dim, spacedim > & | fe2, | ||
| const unsigned int | N2 | ||
| ) | [static, private] |
Compute the non-zero vector components of a composed finite element.
| static std::vector<std::vector<bool> > FESystem< dim, spacedim >::compute_nonzero_components | ( | 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 | ||
| ) | [static, private] |
Compute the non-zero vector components of a composed finite element.
| static std::vector<std::vector<bool> > FESystem< dim, spacedim >::compute_nonzero_components | ( | 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 | ||
| ) | [static, private] |
Compute the non-zero vector components of a composed finite element.
| static std::vector<std::vector<bool> > FESystem< dim, spacedim >::compute_nonzero_components | ( | 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 | ||
| ) | [static, private] |
With 5 elements.
| static std::vector<std::vector<bool> > FESystem< dim, spacedim >::compute_nonzero_components | ( | const std::vector< const FiniteElement< dim, spacedim > * > & | fes, |
| const std::vector< unsigned int > & | multiplicities | ||
| ) | [static, private] |
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.
| void FESystem< dim, spacedim >::initialize | ( | ) | [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.
| void FESystem< dim, spacedim >::build_cell_tables | ( | ) | [private] |
Used by initialize.
| void FESystem< dim, spacedim >::build_face_tables | ( | ) | [private] |
Used by initialize.
| void FESystem< dim, spacedim >::build_interface_constraints | ( | ) | [private] |
Used by initialize.
| std::vector<std::pair<unsigned int, unsigned int> > FESystem< dim, spacedim >::hp_object_dof_identities | ( | const FiniteElement< dim, spacedim > & | fe_other ) | const [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.
const unsigned int FESystem< dim, spacedim >::invalid_face_number = numbers::invalid_unsigned_int [static, private] |
Value to indicate that a given face or subface number is invalid.
Definition at line 792 of file fe_system.h.
std::vector<ElementPair> FESystem< dim, spacedim >::base_elements [private] |
Pointer to underlying finite element classes.
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.
Definition at line 811 of file fe_system.h.
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