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// $Id: fe_dgq.h 20164 2009-11-25 05:22:16Z kanschat $
// Version: $Name$
//
// Copyright (C) 2001, 2002, 2003, 2004, 2005, 2006, 2009 by the deal.II authors
//
// This file is subject to QPL and may not be distributed
// without copyright and license information. Please refer
// to the file deal.II/doc/license.html for the text and
// further information on this license.
//
//---------------------------------------------------------------------------
#ifndef __deal2__fe_dgq_h
#define __deal2__fe_dgq_h
#include <base/config.h>
#include <base/tensor_product_polynomials.h>
#include <fe/fe_poly.h>
DEAL_II_NAMESPACE_OPEN
template <int dim, int spacedim> class MappingQ;
template <int dim> class Quadrature;
/*!@addtogroup fe */
/*@{*/
/**
* Implementation of scalar, discontinuous tensor product elements
* based on equidistant support points.
*
* This is a discontinuous finite element based on tensor products of
* Lagrangian polynomials. The shape functions are Lagrangian
* interpolants of an equidistant grid of points on the unit cell. The
* points are numbered in lexicographical order, with <i>x</i> running
* fastest, then <i>y</i>, then <i>z</i> (if these coordinates are present for a
* given space dimension at all). For example, these are the node
* orderings for <tt>FE_DGQ(1)</tt> in 3d:
* @verbatim
* 6-------7 6-------7
* /| | / /|
* / | | / / |
* / | | / / |
* 4 | | 4-------5 |
* | 2-------3 | | 3
* | / / | | /
* | / / | | /
* |/ / | |/
* 0-------1 0-------1
* @endverbatim
* and <tt>FE_DGQ(2)</tt>:
* @verbatim
* 24--25--26 24--25--26
* /| | / /|
* 21 | | 21 22 23 |
* / 15 16 17 / / 17
* 18 | | 18--19--20 |
* |12 6---7---8 | |14 8
* 9 / / 9 10 11 /
* | 3 4 5 | | 5
* |/ / | |/
* 0---1---2 0---1---2
* @endverbatim
* with node 13 being placed in the interior of the hex.
*
* Note, however, that these are just the Lagrange interpolation
* points of the shape functions. Even though they may physically be
* on the surface of the cell, they are logically in the interior
* since there are no continuity requirements for these shape
* functions across cell boundaries.
* This class if partially implemented for the codimension one case
* (<tt>spacedim != dim </tt>), since no passage of information
* between meshes of different refinement level is possible because
* the embedding and projection matrices are not computed in the class
* constructor.
*
* @author Ralf Hartmann, Guido Kanschat 2001, 2004
*/
template <int dim, int spacedim=dim>
class FE_DGQ : public FE_Poly<TensorProductPolynomials<dim>, dim, spacedim>
{
public:
/**
* Constructor for tensor product
* polynomials of degree
* <tt>p</tt>. The shape
* functions created using this
* constructor correspond to
* Lagrange interpolation
* polynomials for equidistantly
* spaced support points in each
* coordinate direction.
*/
FE_DGQ (const unsigned int p);
/**
* Return a string that uniquely
* identifies a finite
* element. This class returns
* <tt>FE_DGQ<dim>(degree)</tt> , with
* <tt>dim</tt> and <tt>degree</tt>
* replaced by appropriate
* values.
*/
virtual std::string get_name () const;
/**
* Return the matrix
* interpolating from the given
* finite element to the present
* one. The size of the matrix is
* then @p dofs_per_cell times
* <tt>source.dofs_per_cell</tt>.
*
* These matrices are only
* available if the source
* element is also a @p FE_DGQ
* element. Otherwise, an
* exception of type
* FiniteElement<dim>::ExcInterpolationNotImplemented
* is thrown.
*/
virtual void
get_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>::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>::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, and returns a list
* of pairs of global dof indices
* in @p 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.
*
* 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_DGQ 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 unsigned int memory_consumption () const;
protected:
/**
* Constructor for tensor product
* polynomials based on
* Polynomials::Lagrange
* interpolation of the support
* points in the quadrature rule
* <tt>points</tt>. The degree of
* these polynomials is
* <tt>points.size()-1</tt>.
*
* Note: The FE_DGQ::clone function
* does not work properly for FE with
* arbitrary nodes!
*/
FE_DGQ (const Quadrature<1>& points);
/**
* @p clone function instead of
* a copy constructor.
*
* This function is needed by the
* constructors of @p FESystem.
*/
virtual FiniteElement<dim, spacedim> *clone() 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);
/**
* Compute renumbering for rotation
* of degrees of freedom.
*
* Rotates a tensor product
* numbering of degrees of
* freedom by 90 degrees. It is
* used to compute the transfer
* matrices of the children by
* using only the matrix for the
* first child.
*
* The direction parameter
* determines the type of
* rotation. It is one character
* of @p xXyYzZ. The character
* determines the axis of
* rotation, case determines the
* direction. Lower case is
* counter-clockwise seen in
* direction of the axis.
*
* Since rotation around the
* y-axis is not used, it is not
* implemented either.
*/
void rotate_indices (std::vector<unsigned int> &indices,
const char direction) const;
/**
* Allow access from other dimensions.
*/
template <int dim1, int spacedim1> friend class FE_DGQ;
/**
* Allows @p MappingQ class to
* access to build_renumbering
* function.
*/
template <int dim1, int spacedim1> friend class MappingQ;
};
/**
* Implementation of scalar, discontinuous tensor product elements
* based on Lagrange polynomials with arbitrary nodes.
*
* See base class documentation for details.
*
* @author F. Prill 2006
*/
template <int dim>
class FE_DGQArbitraryNodes : public FE_DGQ<dim>
{
public:
/**
* Constructor for tensor product
* polynomials based on
* Polynomials::Lagrange
* interpolation of the support
* points in the quadrature rule
* <tt>points</tt>. The degree of
* these polynomials is
* <tt>points.size()-1</tt>.
*/
FE_DGQArbitraryNodes (const Quadrature<1>& points);
/**
* Return a string that uniquely
* identifies a finite
* element. This class returns
* <tt>FE_DGQArbitraryNodes<dim>(degree)</tt> ,
* with <tt>dim</tt> and <tt>degree</tt>
* replaced by appropriate
* values.
*/
virtual std::string get_name () const;
protected:
/**
* @p clone function instead of
* a copy constructor.
*
* This function is needed by the
* constructors of @p FESystem.
*/
virtual FiniteElement<dim> *clone() const;
};
/*@}*/
DEAL_II_NAMESPACE_CLOSE
#endif
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