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// $Id: fe_dgp_nonparametric.h 30036 2013-07-18 16:55:32Z maier $
//
// Copyright (C) 2002 - 2013 by the deal.II authors
//
// This file is part of the deal.II library.
//
// The deal.II library is free software; you can use it, redistribute
// it, and/or modify it under the terms of the GNU Lesser General
// Public License as published by the Free Software Foundation; either
// version 2.1 of the License, or (at your option) any later version.
// The full text of the license can be found in the file LICENSE at
// the top level of the deal.II distribution.
//
// ---------------------------------------------------------------------
#ifndef __deal2__fe_dgp_nonparametric_h
#define __deal2__fe_dgp_nonparametric_h
#include <deal.II/base/config.h>
#include <deal.II/base/polynomial.h>
#include <deal.II/base/polynomial_space.h>
#include <deal.II/fe/fe.h>
DEAL_II_NAMESPACE_OPEN
template <int dim> class PolynomialSpace;
template <int dim, int spacedim> class MappingQ;
/*!@addtogroup fe */
/*@{*/
/**
* Discontinuous finite elements evaluated at the mapped quadrature points.
*
* Warning: this class does not work properly, yet. Don't use it!
*
* This finite element implements complete polynomial spaces, that is,
* $d$-dimensional polynomials of order $k$.
*
* The polynomials are not mapped. Therefore, they are constant,
* linear, quadratic, etc. on any grid cell.
*
* Since the polynomials are evaluated at the quadrature points of the
* actual grid cell, no grid transfer and interpolation matrices are
* available.
*
* The purpose of this class is experimental, therefore the
* implementation will remain incomplete.
*
* Besides, this class is not implemented for the codimension one case
* (<tt>spacedim != dim</tt>).
*
* @author Guido Kanschat, 2002
*/
template <int dim, int spacedim=dim>
class FE_DGPNonparametric : public FiniteElement<dim,spacedim>
{
public:
/**
* Constructor for tensor product
* polynomials of degree @p k.
*/
FE_DGPNonparametric (const unsigned int k);
/**
* Return a string that uniquely
* identifies a finite
* element. This class returns
* <tt>FE_DGPNonparametric<dim>(degree)</tt>,
* with @p dim and @p degree
* replaced by appropriate
* values.
*/
virtual std::string get_name () const;
/**
* Return the value of the
* @p ith shape function at the
* point @p p. See the
* FiniteElement base
* class for more information
* about the semantics of this
* function.
*/
virtual double shape_value (const unsigned int i,
const Point<dim> &p) const;
/**
* Return the value of the
* @p componentth vector
* component of the @p ith shape
* function at the point
* @p p. See the
* FiniteElement base
* class for more information
* about the semantics of this
* function.
*
* Since this element is scalar,
* the returned value is the same
* as if the function without the
* @p _component suffix were
* called, provided that the
* specified component is zero.
*/
virtual double shape_value_component (const unsigned int i,
const Point<dim> &p,
const unsigned int component) const;
/**
* Return the gradient of the
* @p ith shape function at the
* point @p p. See the
* FiniteElement base
* class for more information
* about the semantics of this
* function.
*/
virtual Tensor<1,dim> shape_grad (const unsigned int i,
const Point<dim> &p) const;
/**
* Return the gradient of the
* @p componentth vector
* component of the @p ith shape
* function at the point
* @p p. See the
* FiniteElement base
* class for more information
* about the semantics of this
* function.
*
* Since this element is scalar,
* the returned value is the same
* as if the function without the
* @p _component suffix were
* called, provided that the
* specified component is zero.
*/
virtual Tensor<1,dim> shape_grad_component (const unsigned int i,
const Point<dim> &p,
const unsigned int component) const;
/**
* Return the tensor of second
* derivatives of the @p ith
* shape function at point @p p
* on the unit cell. See the
* FiniteElement base
* class for more information
* about the semantics of this
* function.
*/
virtual Tensor<2,dim> shape_grad_grad (const unsigned int i,
const Point<dim> &p) const;
/**
* Return the second derivative
* of the @p componentth vector
* component of the @p ith shape
* function at the point
* @p p. See the
* FiniteElement base
* class for more information
* about the semantics of this
* function.
*
* Since this element is scalar,
* the returned value is the same
* as if the function without the
* @p _component suffix were
* called, provided that the
* specified component is zero.
*/
virtual Tensor<2,dim> shape_grad_grad_component (const unsigned int i,
const Point<dim> &p,
const unsigned int component) const;
/**
* Return the polynomial degree
* of this finite element,
* i.e. the value passed to the
* constructor.
*/
unsigned int get_degree () const;
/**
* 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 <tt>source.dofs_per_face</tt> times
* <tt>this->dofs_per_face</tt>.
*
* Derived elements 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.
*/
virtual void
get_face_interpolation_matrix (const FiniteElement<dim,spacedim> &source,
FullMatrix<double> &matrix) const;
/**
* 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 <tt>source.dofs_per_face</tt> times
* <tt>this->dofs_per_face</tt>.
*
* Derived elements 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.
*/
virtual void
get_subface_interpolation_matrix (const FiniteElement<dim,spacedim> &source,
const unsigned int subface,
FullMatrix<double> &matrix) const;
/**
* @name Functions to support hp
* @{
*/
/**
* 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 @p 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.
*
* This being a discontinuous element, the set of such constraints
* is of course empty.
*/
virtual
std::vector<std::pair<unsigned int, unsigned int> >
hp_vertex_dof_identities (const FiniteElement<dim,spacedim> &fe_other) const;
/**
* Same as hp_vertex_dof_indices(), except that the function treats
* degrees of freedom on lines.
*
* This being a discontinuous element, the set of such constraints
* is of course empty.
*/
virtual
std::vector<std::pair<unsigned int, unsigned int> >
hp_line_dof_identities (const FiniteElement<dim,spacedim> &fe_other) const;
/**
* Same as hp_vertex_dof_indices(), except that the function treats
* degrees of freedom on quads.
*
* This being a discontinuous element, the set of such constraints
* is of course empty.
*/
virtual
std::vector<std::pair<unsigned int, unsigned int> >
hp_quad_dof_identities (const FiniteElement<dim,spacedim> &fe_other) const;
/**
* Return whether this element
* implements its hanging node
* constraints in the new way,
* which has to be used to make
* elements "hp compatible".
*
* For the FE_DGPNonparametric class the
* result is always true (independent of
* the degree of the element), as it has
* no hanging nodes (being a
* discontinuous element).
*/
virtual bool hp_constraints_are_implemented () const;
/**
* 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 @ref hp_paper "hp paper".
*/
virtual
FiniteElementDomination::Domination
compare_for_face_domination (const FiniteElement<dim,spacedim> &fe_other) const;
/**
* @}
*/
/**
* Check for non-zero values on a face.
*
* This function returns
* @p true, if the shape
* function @p shape_index has
* non-zero values on the face
* @p face_index.
*
* Implementation of the
* interface in
* FiniteElement
*/
virtual bool has_support_on_face (const unsigned int shape_index,
const unsigned int face_index) const;
/**
* 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.
*/
virtual std::size_t memory_consumption () const;
private:
/**
* Declare a nested class which
* will hold static definitions of
* various matrices such as
* constraint and embedding
* matrices. The definition of
* the various static fields are
* in the files <tt>fe_dgp_[123]d.cc</tt>
* in the source directory.
*/
struct Matrices
{
/**
* Pointers to the embedding
* matrices, one for each
* polynomial degree starting
* from constant elements
*/
static const double *const embedding[][GeometryInfo<dim>::max_children_per_cell];
/**
* Number of elements (first
* index) the above field
* has. Equals the highest
* polynomial degree plus one
* for which the embedding
* matrices have been
* computed.
*/
static const unsigned int n_embedding_matrices;
/**
* As @p embedding but for
* projection matrices.
*/
static const double *const projection_matrices[][GeometryInfo<dim>::max_children_per_cell];
/**
* As
* @p n_embedding_matrices
* but for projection
* matrices.
*/
static const unsigned int n_projection_matrices;
};
protected:
/**
* @p clone function instead of
* a copy constructor.
*
* This function is needed by the
* constructors of @p FESystem.
*/
virtual FiniteElement<dim,spacedim> *clone() const;
/**
* Prepare internal data
* structures and fill in values
* independent of the cell.
*/
virtual
typename Mapping<dim,spacedim>::InternalDataBase *
get_data (const UpdateFlags,
const Mapping<dim,spacedim> &mapping,
const Quadrature<dim> &quadrature) const ;
/**
* Implementation of the same
* function in
* FiniteElement.
*/
virtual void
fill_fe_values (const Mapping<dim,spacedim> &mapping,
const typename Triangulation<dim,spacedim>::cell_iterator &cell,
const Quadrature<dim> &quadrature,
typename Mapping<dim,spacedim>::InternalDataBase &mapping_internal,
typename Mapping<dim,spacedim>::InternalDataBase &fe_internal,
FEValuesData<dim,spacedim> &data,
CellSimilarity::Similarity &cell_similarity) const;
/**
* Implementation of the same
* function in
* FiniteElement.
*/
virtual void
fill_fe_face_values (const Mapping<dim,spacedim> &mapping,
const typename Triangulation<dim,spacedim>::cell_iterator &cell,
const unsigned int face_no,
const Quadrature<dim-1> &quadrature,
typename Mapping<dim,spacedim>::InternalDataBase &mapping_internal,
typename Mapping<dim,spacedim>::InternalDataBase &fe_internal,
FEValuesData<dim,spacedim> &data) const ;
/**
* Implementation of the same
* function in
* FiniteElement.
*/
virtual void
fill_fe_subface_values (const Mapping<dim,spacedim> &mapping,
const typename Triangulation<dim,spacedim>::cell_iterator &cell,
const unsigned int face_no,
const unsigned int sub_no,
const Quadrature<dim-1> &quadrature,
typename Mapping<dim,spacedim>::InternalDataBase &mapping_internal,
typename Mapping<dim,spacedim>::InternalDataBase &fe_internal,
FEValuesData<dim,spacedim> &data) const ;
private:
/**
* Only for internal use. Its
* full name is
* @p get_dofs_per_object_vector
* function and it creates the
* @p dofs_per_object vector that is
* needed within the constructor to
* be passed to the constructor of
* @p FiniteElementData.
*/
static std::vector<unsigned int> get_dpo_vector (const unsigned int degree);
/**
* Given a set of flags indicating
* what quantities are requested
* from a @p FEValues object,
* return which of these can be
* precomputed once and for
* all. Often, the values of
* shape function at quadrature
* points can be precomputed, for
* example, in which case the
* return value of this function
* would be the logical and of
* the input @p flags and
* @p update_values.
*
* For the present kind of finite
* element, this is exactly the
* case.
*/
virtual UpdateFlags update_once (const UpdateFlags flags) const;
/**
* This is the opposite to the
* above function: given a set of
* flags indicating what we want
* to know, return which of these
* need to be computed each time
* we visit a new cell.
*
* If for the computation of one
* quantity something else is
* also required (for example, we
* often need the covariant
* transformation when gradients
* need to be computed), include
* this in the result as well.
*/
virtual UpdateFlags update_each (const UpdateFlags flags) const;
/**
* Degree of the polynomials.
*/
const unsigned int degree;
/**
* Pointer to an object
* representing the polynomial
* space used here.
*/
const PolynomialSpace<dim> polynomial_space;
/**
* Fields of cell-independent data.
*
* For information about the
* general purpose of this class,
* see the documentation of the
* base class.
*/
class InternalData : public FiniteElement<dim,spacedim>::InternalDataBase
{
public:
// have some scratch arrays
std::vector<double> values;
std::vector<Tensor<1,dim> > grads;
std::vector<Tensor<2,dim> > grad_grads;
};
/**
* Allow access from other dimensions.
*/
template <int, int> friend class FE_DGPNonparametric;
/**
* Allows @p MappingQ class to
* access to build_renumbering
* function.
*/
template <int, int> friend class MappingQ;
// friend class MappingQ<dim>;
};
/*@}*/
#ifndef DOXYGEN
// declaration of explicit specializations of member variables, if the
// compiler allows us to do that (the standard says we must)
#ifndef DEAL_II_MEMBER_VAR_SPECIALIZATION_BUG
template <>
const double *const FE_DGPNonparametric<1,1>::Matrices::embedding[][GeometryInfo<1>::max_children_per_cell];
template <>
const unsigned int FE_DGPNonparametric<1,1>::Matrices::n_embedding_matrices;
template <>
const double *const FE_DGPNonparametric<1,1>::Matrices::projection_matrices[][GeometryInfo<1>::max_children_per_cell];
template <>
const unsigned int FE_DGPNonparametric<1,1>::Matrices::n_projection_matrices;
template <>
const double *const FE_DGPNonparametric<2,2>::Matrices::embedding[][GeometryInfo<2>::max_children_per_cell];
template <>
const unsigned int FE_DGPNonparametric<2,2>::Matrices::n_embedding_matrices;
template <>
const double *const FE_DGPNonparametric<2,2>::Matrices::projection_matrices[][GeometryInfo<2>::max_children_per_cell];
template <>
const unsigned int FE_DGPNonparametric<2,2>::Matrices::n_projection_matrices;
template <>
const double *const FE_DGPNonparametric<3,3>::Matrices::embedding[][GeometryInfo<3>::max_children_per_cell];
template <>
const unsigned int FE_DGPNonparametric<3,3>::Matrices::n_embedding_matrices;
template <>
const double *const FE_DGPNonparametric<3,3>::Matrices::projection_matrices[][GeometryInfo<3>::max_children_per_cell];
template <>
const unsigned int FE_DGPNonparametric<3,3>::Matrices::n_projection_matrices;
#endif
#endif // DOXYGEN
DEAL_II_NAMESPACE_CLOSE
#endif
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