FESystem< dim, spacedim > Class Template Reference
[Base classesFinite element space descriptionsHandling vector valued problems]

Inheritance diagram for FESystem< dim, spacedim >:
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List of all members.

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)
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 unsigned int n_base_elements () const
virtual unsigned int element_multiplicity (const unsigned int index) 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 unsigned int memory_consumption () const
template<>
void initialize_unit_face_support_points ()
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 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, enum 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, enum 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 std::vector< boolcompute_restriction_is_additive_flags (const FiniteElement< dim, spacedim > &fe, const unsigned int N)
static std::vector< boolcompute_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< boolcompute_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< boolcompute_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 std::vector< const FiniteElement< dim, spacedim > * > &fes, const std::vector< unsigned int > &multiplicities)

Private Attributes

std::vector< ElementPairbase_elements

Static Private Attributes

static const unsigned int invalid_face_number = numbers::invalid_unsigned_int

Detailed Description

template<int dim, int spacedim = dim>
class FESystem< dim, spacedim >

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.

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:

Do 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, instead.

In the most cases, the composed element behaves as if it were a usual element with more degrees of freedom. However the underlying structure is visible in the restriction, prolongation and interface constraint matrices, which do not couple the degrees of freedom of the subobject. 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, there is no interaction with v and w of this or the other cell.

The number of components of such a system element is the accumulated number of components of all base elements times their multiplicity. The number of blocks of the system is simply the sum of all multiplicities.

For more information on the template parameter spacedim see the documentation of Triangulation.

Author:
Wolfgang Bangerth, Guido Kanschat, 1999, 2002, 2003, 2006, Ralf Hartmann 2001.

Member Typedef Documentation

template<int dim, int spacedim = dim>
typedef std::pair<const FiniteElement<dim,spacedim> *, unsigned int> FESystem< dim, spacedim >::ElementPair [private]

Pairs of multiplicity and element type.


Constructor & Destructor Documentation

template<int dim, int spacedim = dim>
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.

template<int dim, int spacedim = dim>
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.

template<int dim, int spacedim = dim>
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.

template<int dim, int spacedim = dim>
virtual FESystem< dim, spacedim >::~FESystem (  )  [virtual]

Destructor.


Member Function Documentation

template<int dim, int spacedim = dim>
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 >.

template<int dim, int spacedim = dim>
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 >.

template<int dim, int spacedim = dim>
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 >.

template<int dim, int spacedim = dim>
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 >.

template<int dim, int spacedim = dim>
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 >.

template<int dim, int spacedim = dim>
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 >.

template<int dim, int spacedim = dim>
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 >.

template<int dim, int spacedim = dim>
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.

template<int dim, int spacedim = dim>
virtual unsigned int FESystem< dim, spacedim >::n_base_elements (  )  const [virtual]

Number of different base elements of this object.

Since these objects can have multiplicity and subobjects themselves, this may be smaller than the total number of finite elements composed into this structure.

Implements FiniteElement< dim, spacedim >.

template<int dim, int spacedim = dim>
virtual unsigned int FESystem< dim, spacedim >::element_multiplicity ( const unsigned int  index  )  const [virtual]

How often is a composing element used.

Implements FiniteElement< dim, spacedim >.

template<int dim, int spacedim = dim>
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.

Implements FiniteElement< dim, spacedim >.

template<int dim, int spacedim = dim>
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 >.

template<int dim, int spacedim = dim>
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 >.

template<int dim, int spacedim = dim>
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 >.

template<int dim, int spacedim = dim>
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 >.

template<int dim, int spacedim = dim>
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.

template<int dim, int spacedim = dim>
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.

template<int dim, int spacedim = dim>
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.

template<int dim, int spacedim = dim>
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.

template<int dim, int spacedim = dim>
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.

template<int dim, int spacedim = dim>
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.

template<int dim, int spacedim = dim>
virtual unsigned int 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 >.

template<int dim, int spacedim = dim>
virtual UpdateFlags FESystem< dim, spacedim >::update_once ( const UpdateFlags  flags  )  const [protected, virtual]

Compute flags for initial update only.

Implements FiniteElement< dim, spacedim >.

template<int dim, int spacedim = dim>
virtual UpdateFlags FESystem< dim, spacedim >::update_each ( const UpdateFlags  flags  )  const [protected, virtual]

Compute flags for update on each cell.

Implements FiniteElement< dim, spacedim >.

template<int dim, int spacedim = dim>
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 >.

template<int dim, int spacedim = dim>
virtual Mapping<dim,spacedim>::InternalDataBase* FESystem< dim, spacedim >::get_data ( const UpdateFlags  update_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.

Implements FiniteElement< dim, spacedim >.

template<int dim, int spacedim = dim>
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,
enum 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 >.

template<int dim, int spacedim = dim>
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 >.

template<int dim, int spacedim = dim>
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 >.

template<int dim, int spacedim = dim>
template<int dim_1>
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,
enum CellSimilarity::Similarity  cell_similarity,
typename Mapping< dim, spacedim >::InternalDataBase mapping_data,
typename Mapping< dim, spacedim >::InternalDataBase fe_data,
FEValuesData< dim, spacedim > &  data 
) const [inline, 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.

template<int dim, int spacedim = dim>
void FESystem< dim, spacedim >::initialize_unit_support_points (  )  [private]

Initialize the unit_support_points field of the FiniteElement class. Called from the constructor.

template<int dim, int spacedim = dim>
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.

template<int dim, int spacedim = dim>
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.

template<int dim, int spacedim = dim>
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.

template<int dim, int spacedim = dim>
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.

template<int dim, int spacedim = dim>
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.

template<int dim, int spacedim = dim>
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.

template<int dim, int spacedim = dim>
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.

template<int dim, int spacedim = dim>
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.

template<int dim, int spacedim = dim>
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.

template<int dim, int spacedim = dim>
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.

template<int dim, int spacedim = dim>
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.

template<int dim, int spacedim = dim>
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.

template<int dim, int spacedim = dim>
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.

template<int dim, int spacedim = dim>
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.

template<int dim, int spacedim = dim>
void FESystem< dim, spacedim >::build_cell_tables (  )  [private]

Used by initialize.

template<int dim, int spacedim = dim>
void FESystem< dim, spacedim >::build_face_tables (  )  [private]

Used by initialize.

template<int dim, int spacedim = dim>
void FESystem< dim, spacedim >::build_interface_constraints (  )  [private]

Used by initialize.

template<int dim, int spacedim = dim>
template<int structdim>
std::vector<std::pair<unsigned int, unsigned int> > FESystem< dim, spacedim >::hp_object_dof_identities ( const FiniteElement< dim, spacedim > &  fe_other  )  const [inline, 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.

template<>
void FESystem< 1 >::initialize_unit_face_support_points (  )  [inline]

Member Data Documentation

template<int dim, int spacedim = dim>
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.

template<int dim, int spacedim = dim>
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.


The documentation for this class was generated from the following file:

deal.II documentation generated on Mon Nov 23 22:57:42 2009 by doxygen 1.6.1