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//---------------------------------------------------------------------------
// $Id: fe_tools.h 20602 2010-02-13 17:44:17Z bangerth $
// Version: $Name$
//
// Copyright (C) 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 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_tools_H
#define __deal2__fe_tools_H
#include <base/config.h>
#include <base/exceptions.h>
#include <base/geometry_info.h>
#include <vector>
DEAL_II_NAMESPACE_OPEN
template <typename number> class FullMatrix;
template <typename number> class Vector;
template <int dim> class Quadrature;
template <int dim, int spacedim> class FiniteElement;
template <int dim, int spacedim> class DoFHandler;
namespace hp
{
template <int dim, int spacedim> class DoFHandler;
}
template <int dim> class FiniteElementData;
class ConstraintMatrix;
#include <base/config.h>
#include <base/exceptions.h>
#include <vector>
#include <string>
/*!@addtogroup feall */
/*@{*/
/**
* This class performs interpolations and extrapolations of discrete
* functions of one @p FiniteElement @p fe1 to another @p FiniteElement
* @p fe2.
*
* It also provides the local interpolation matrices that interpolate
* on each cell. Furthermore it provides the difference matrix
* $id-I_h$ that is needed for evaluating $(id-I_h)z$ for e.g. the
* dual solution $z$.
*
* For more information about the <tt>spacedim</tt> template parameter
* check the documentation of FiniteElement or the one of
* Triangulation.
*
* @author Wolfgang Bangerth, Ralf Hartmann, Guido Kanschat;
* 2000, 2003, 2004, 2005, 2006
*/
class FETools
{
public:
/**
* A base class for factory
* objects creating finite
* elements of a given
* degree. Derived classes are
* called whenever one wants to
* have a transparent way to
* create a finite element
* object.
*
* This class is used in the
* FETools::get_fe_from_name()
* and FETools::add_fe_name()
* functions.
*
* @author Guido Kanschat, 2006
*/
template <int dim, int spacedim=dim>
class FEFactoryBase
{
public:
/**
* Create a FiniteElement and
* return a pointer to it.
*/
virtual FiniteElement<dim,spacedim>*
get (const unsigned int degree) const = 0;
/**
* Virtual destructor doing
* nothing but making the
* compiler happy.
*/
virtual ~FEFactoryBase();
};
/**
* A concrete class for factory
* objects creating finite
* elements of a given degree.
*
* The class's get() function
* generates a finite element
* object of the type given as
* template argument, and with
* the degree (however the finite
* element class wishes to
* interpret this number) given
* as argument to get().
*
* @author Guido Kanschat, 2006
*/
template <class FE>
class FEFactory : public FEFactoryBase<FE::dimension,FE::dimension>
{
public:
/**
* Create a FiniteElement and
* return a pointer to it.
*/
virtual FiniteElement<FE::dimension,FE::dimension>*
get (const unsigned int degree) const;
};
/**
* @warning In most cases, you
* will probably want to use
* compute_base_renumbering().
*
* Compute the vector required to
* renumber the dofs of a cell by
* component. Furthermore,
* compute the vector storing the
* start indices of each
* component in the local block
* vector.
*
* The second vector is organized
* such that there is a vector
* for each base element
* containing the start index for
* each component served by this
* base element.
*
* While the first vector is
* checked to have the correct
* size, the second one is
* reinitialized for convenience.
*/
template<int dim, int spacedim>
static void compute_component_wise(
const FiniteElement<dim,spacedim>& fe,
std::vector<unsigned int>& renumbering,
std::vector<std::vector<unsigned int> >& start_indices);
/**
* Compute the vector required to
* renumber the dofs of a cell by
* block. Furthermore, compute
* the vector storing either the
* start indices or the size of
* each local block vector.
*
* If the @p bool parameter is
* true, @p block_data is filled
* with the start indices of each
* local block. If it is false,
* then the block sizes are
* returned.
*
* @todo Which way does this
* vector map the numbers?
*/
template<int dim, int spacedim>
static void compute_block_renumbering (
const FiniteElement<dim,spacedim>& fe,
std::vector<unsigned int>& renumbering,
std::vector<unsigned int>& block_data,
bool return_start_indices = true);
/**
* @name Generation of local matrices
* @{
*/
/**
* Gives the interpolation matrix
* that interpolates a @p fe1-
* function to a @p fe2-function on
* each cell. The interpolation_matrix
* needs to be of size
* <tt>(fe2.dofs_per_cell, fe1.dofs_per_cell)</tt>.
*
* Note, that if the finite element
* space @p fe1 is a subset of
* the finite element space
* @p fe2 then the @p interpolation_matrix
* is an embedding matrix.
*/
template <int dim, typename number, int spacedim>
static
void
get_interpolation_matrix(const FiniteElement<dim,spacedim> &fe1,
const FiniteElement<dim,spacedim> &fe2,
FullMatrix<number> &interpolation_matrix);
/**
* Gives the interpolation matrix
* that interpolates a @p fe1-
* function to a @p fe2-function, and
* interpolates this to a second
* @p fe1-function on
* each cell. The interpolation_matrix
* needs to be of size
* <tt>(fe1.dofs_per_cell, fe1.dofs_per_cell)</tt>.
*
* Note, that this function only
* makes sense if the finite element
* space due to @p fe1 is not a subset of
* the finite element space due to
* @p fe2, as if it were a subset then
* the @p interpolation_matrix would be
* only the unit matrix.
*/
template <int dim, typename number, int spacedim>
static
void
get_back_interpolation_matrix(const FiniteElement<dim,spacedim> &fe1,
const FiniteElement<dim,spacedim> &fe2,
FullMatrix<number> &interpolation_matrix);
/**
* Gives the unit matrix minus the
* back interpolation matrix.
* The @p difference_matrix
* needs to be of size
* <tt>(fe1.dofs_per_cell, fe1.dofs_per_cell)</tt>.
*
* This function gives
* the matrix that transforms a
* @p fe1 function $z$ to $z-I_hz$
* where $I_h$ denotes the interpolation
* operator from the @p fe1 space to
* the @p fe2 space. This matrix hence
* is useful to evaluate
* error-representations where $z$
* denotes the dual solution.
*/
template <int dim, typename number, int spacedim>
static
void
get_interpolation_difference_matrix(const FiniteElement<dim,spacedim> &fe1,
const FiniteElement<dim,spacedim> &fe2,
FullMatrix<number> &difference_matrix);
/**
* Compute the local
* $L^2$-projection matrix from
* fe1 to fe2.
*/
template <int dim, typename number, int spacedim>
static void get_projection_matrix(const FiniteElement<dim,spacedim> &fe1,
const FiniteElement<dim,spacedim> &fe2,
FullMatrix<number> &matrix);
/**
* Compute the matrix of nodal
* values of a finite element
* applied to all its shape
* functions.
*
* This function is supposed to
* help building finite elements
* from polynomial spaces and
* should be called inside the
* constructor of an
* element. Applied to a
* completely initialized finite
* element, the result should be
* the unit matrix by definition
* of the node values.
*
* Using this matrix allows the
* construction of the basis of
* shape functions in two steps.
* <ol>
*
* <li>Define the space of shape
* functions using an arbitrary
* basis <i>w<sub>j</sub></i> and
* compute the matrix <i>M</i> of
* node functionals
* <i>N<sub>i</sub></i> applied
* to these basis functions.
*
* <li>Compute the basis
* <i>v<sub>j</sub></i> of the
* finite element shape function
* space by applying
* <i>M<sup>-1</sup></i> to the
* basis <i>w<sub>j</sub></i>.
* </ol>
*
* @note The FiniteElement must
* provide generalized support
* points and and interpolation
* functions.
*/
template <int dim, int spacedim>
static void compute_node_matrix(FullMatrix<double>& M,
const FiniteElement<dim,spacedim>& fe);
/**
* For all possible (isotropic
* and anisotropic) refinement
* cases compute the embedding
* matrices from a coarse cell to
* the child cells. Each column
* of the resulting matrices
* contains the representation of
* a coarse grid basis functon by
* the fine grid basis; the
* matrices are split such that
* there is one matrix for every
* child.
*
* This function computes the
* coarse grid function in a
* sufficiently large number of
* quadrature points and fits the
* fine grid functions using
* least squares
* approximation. Therefore, the
* use of this function is
* restricted to the case that
* the finite element spaces are
* actually nested.
*
* Note, that
* <code>matrices[refinement_case-1][child]</code>
* includes the embedding (or prolongation)
* matrix of child
* <code>child</code> for the
* RefinementCase
* <code>refinement_case</code>. Here,
* we use
* <code>refinement_case-1</code>
* instead of
* <code>refinement_case</code>
* as for
* RefinementCase::no_refinement(=0)
* there are no prolongation
* matrices available.
*
* Typically this function is
* called by the various
* implementations of
* FiniteElement classes in order
* to fill the respective
* FiniteElement::prolongation
* matrices.
*
* @param fe The finite element
* class for which we compute the
* embedding matrices.
*
* @param matrices A reference to
* RefinementCase<dim>::isotropic_refinement
* vectors of FullMatrix
* objects. Each vector
* corresponds to one
* RefinementCase @p
* refinement_case and is of the
* vector size
* GeometryInfo<dim>::n_children(refinement_case). This
* is the format used in
* FiniteElement, where we want
* to use this function mostly.
*
* @param isotropic_only Set
* to <code>true</code> if you only
* want to compute matrices for
* isotropic refinement.
*/
template <int dim, typename number, int spacedim>
static void compute_embedding_matrices(const FiniteElement<dim,spacedim> &fe,
std::vector<std::vector<FullMatrix<number> > >& matrices,
const bool isotropic_only = false);
/**
* Compute the embedding matrices
* on faces needed for constraint
* matrices.
*
* @param fe The finite element
* for which to compute these
* matrices. @param matrices An
* array of
* <i>GeometryInfo<dim>::subfaces_per_face
* = 2<sup>dim-1</sup></i>
* FullMatrix objects,holding the
* embedding matrix for each
* subface. @param face_coarse
* The number of the face on the
* coarse side of the face for
* which this is computed.
* @param face_fine The number of
* the face on the refined side
* of the face for which this is
* computed.
*
* @warning This function will be
* used in computing constraint
* matrices. It is not
* sufficiently tested yet.
*/
template <int dim, typename number, int spacedim>
static void
compute_face_embedding_matrices(const FiniteElement<dim,spacedim>& fe,
FullMatrix<number> (&matrices)[GeometryInfo<dim>::max_children_per_face],
const unsigned int face_coarse,
const unsigned int face_fine);
/**
* For all possible (isotropic
* and anisotropic) refinement
* cases compute the
* <i>L<sup>2</sup></i>-projection
* matrices from the children to
* a coarse cell.
*
* Note, that
* <code>matrices[refinement_case-1][child]</code>
* includes the projection (or restriction)
* matrix of child
* <code>child</code> for the
* RefinementCase
* <code>refinement_case</code>. Here,
* we use
* <code>refinement_case-1</code>
* instead of
* <code>refinement_case</code>
* as for
* RefinementCase::no_refinement(=0)
* there are no projection
* matrices available.
*
* Typically this function is
* called by the various
* implementations of
* FiniteElement classes in order
* to fill the respective
* FiniteElement::restriction
* matrices.
*
* @arg fe The finite element
* class for which we compute the
* projection matrices. @arg
* matrices A reference to
* <tt>RefinementCase<dim>::isotropic_refinement</tt>
* vectors of FullMatrix
* objects. Each vector
* corresponds to one
* RefinementCase @p
* refinement_case and is of the
* vector size
* <tt>GeometryInfo<dim>::n_children(refinement_case)</tt>. This
* is the format used in
* FiniteElement, where we want
* to use this function mostly.
*/
template <int dim, typename number, int spacedim>
static void compute_projection_matrices(const FiniteElement<dim,spacedim> &fe,
std::vector<std::vector<FullMatrix<number> > >& matrices);
/**
* Projects scalar data defined in
* quadrature points to a finite element
* space on a single cell.
*
* What this function does is the
* following: assume that there is scalar
* data <tt>u<sub>q</sub>, 0 <= q <
* Q:=quadrature.size()</tt>
* defined at the quadrature points of a
* cell, with the points defined by the
* given <tt>rhs_quadrature</tt>
* object. We may then want to ask for
* that finite element function (on a
* single cell) <tt>v<sub>h</sub></tt> in
* the finite-dimensional space defined
* by the given FE object that is the
* projection of <tt>u</tt> in the
* following sense:
*
* Usually, the projection
* <tt>v<sub>h</sub></tt> is that
* function that satisfies
* <tt>(v<sub>h</sub>,w)=(u,w)</tt> for
* all discrete test functions
* <tt>w</tt>. In the present case, we
* can't evaluate the right hand side,
* since <tt>u</tt> is only defined in
* the quadrature points given by
* <tt>rhs_quadrature</tt>, so we replace
* it by a quadrature
* approximation. Likewise, the left hand
* side is approximated using the
* <tt>lhs_quadrature</tt> object; if
* this quadrature object is chosen
* appropriately, then the integration of
* the left hand side can be done
* exactly, without any
* approximation. The use of different
* quadrature objects is necessary if the
* quadrature object for the right hand
* side has too few quadrature points --
* for example, if data <tt>q</tt> is
* only defined at the cell center, then
* the corresponding one-point quadrature
* formula is obviously insufficient to
* approximate the scalar product on the
* left hand side by a definite form.
*
* After these quadrature approximations,
* we end up with a nodal representation
* <tt>V<sub>h</sub></tt> of
* <tt>v<sub>h</sub></tt> that satisfies
* the following system of linear
* equations: <tt>M V<sub>h</sub> = Q
* U</tt>, where
* <tt>M<sub>ij</sub>=(phi_i,phi_j)</tt>
* is the mass matrix approximated by
* <tt>lhs_quadrature</tt>, and
* <tt>Q</tt> is the matrix
* <tt>Q<sub>iq</sub>=phi<sub>i</sub>(x<sub>q</sub>)
* w<sub>q</sub></tt> where
* <tt>w<sub>q</sub></tt> are quadrature
* weights; <tt>U</tt> is the vector of
* quadrature point data
* <tt>u<sub>q</sub></tt>.
*
* In order to then get the nodal
* representation <tt>V<sub>h</sub></tt>
* of the projection of <tt>U</tt>, one
* computes <tt>V<sub>h</sub> = X U,
* X=M<sup>-1</sup> Q</tt>. The purpose
* of this function is to compute the
* matrix <tt>X</tt> and return it
* through the last argument of this
* function.
*
* Note that this function presently only
* supports scalar data. An extension of
* the mass matrix is of course trivial,
* but one has to define the order of
* data in the vector <tt>U</tt> if it
* contains vector valued data in all
* quadrature points.
*
* A use for this function is described
* in the introduction to the step-18
* example program.
*
* The opposite of this function,
* interpolation of a finite element
* function onto quadrature points is
* essentially what the
* <tt>FEValues::get_function_values</tt>
* functions do; to make things a little
* simpler, the
* <tt>FETools::compute_interpolation_to_quadrature_points_matrix</tt>
* provides the matrix form of this.
*
* Note that this function works
* on a single cell, rather than
* an entire triangulation. In
* effect, it therefore doesn't
* matter if you use a continuous
* or discontinuous version of
* the finite element.
*
* It is worth noting that there
* are a few confusing cases of
* this function. The first one
* is that it really only makes
* sense to project onto a finite
* element that has at most as
* many degrees of freedom per
* cell as there are quadrature
* points; the projection of N
* quadrature point data into a
* space with M>N unknowns is
* well-defined, but often yields
* funny and non-intuitive
* results. Secondly, one would
* think that if the quadrature
* point data is defined in the
* support points of the finite
* element, i.e. the quadrature
* points of
* <tt>ths_quadrature</tt> equal
* <tt>fe.get_unit_support_points()</tt>,
* then the projection should be
* the identity, i.e. each degree
* of freedom of the finite
* element equals the value of
* the given data in the support
* point of the corresponding
* shape function. However, this
* is not generally the case:
* while the matrix <tt>Q</tt> in
* that case is the identity
* matrix, the mass matrix
* <tt>M</tt> is not equal to the
* identity matrix, except for
* the special case that the
* quadrature formula
* <tt>lhs_quadrature</tt> also
* has its quadrature points in
* the support points of the
* finite element.
*/
template <int dim, int spacedim>
static
void
compute_projection_from_quadrature_points_matrix (const FiniteElement<dim,spacedim> &fe,
const Quadrature<dim> &lhs_quadrature,
const Quadrature<dim> &rhs_quadrature,
FullMatrix<double> &X);
/**
* Given a (scalar) local finite element
* function, compute the matrix that maps
* the vector of nodal values onto the
* vector of values of this function at
* quadrature points as given by the
* second argument. In a sense, this
* function does the opposite of the @p
* compute_projection_from_quadrature_points_matrix
* function.
*/
template <int dim, int spacedim>
static
void
compute_interpolation_to_quadrature_points_matrix (const FiniteElement<dim,spacedim> &fe,
const Quadrature<dim> &quadrature,
FullMatrix<double> &I_q);
/**
* This method implements the
* FETools::compute_projection_from_quadrature_points_matrix
* method for faces of a mesh.
* The matrix that it returns, X, is face specific
* and its size is fe.dofs_per_cell by
* rhs_quadrature.size().
* The dimension, dim must be larger than 1 for this class,
* since Quadrature<dim-1> objects are required. See the
* documentation on the Quadrature class for more information.
*/
template <int dim, int spacedim>
static
void
compute_projection_from_face_quadrature_points_matrix (const FiniteElement<dim, spacedim> &fe,
const Quadrature<dim-1> &lhs_quadrature,
const Quadrature<dim-1> &rhs_quadrature,
const typename DoFHandler<dim, spacedim>::active_cell_iterator & cell,
unsigned int face,
FullMatrix<double> &X);
//@}
/**
* @name Functions which should be in DoFTools
*/
//@{
/**
* Gives the interpolation of a the
* @p dof1-function @p u1 to a
* @p dof2-function @p u2. @p dof1 and
* @p dof2 need to be DoFHandlers
* based on the same triangulation.
*
* If the elements @p fe1 and @p fe2
* are either both continuous or
* both discontinuous then this
* interpolation is the usual point
* interpolation. The same is true
* if @p fe1 is a continuous and
* @p fe2 is a discontinuous finite
* element. For the case that @p fe1
* is a discontinuous and @p fe2 is
* a continuous finite element
* there is no point interpolation
* defined at the discontinuities.
* Therefore the meanvalue is taken
* at the DoF values on the
* discontinuities.
*
* Note that for continuous
* elements on grids with hanging
* nodes (i.e. locally refined
* grids) this function does not
* give the expected output.
* Indeed, the resulting output
* vector does not necessarily
* respect continuity
* requirements at hanging nodes:
* if, for example, you are
* interpolating a Q2 field to a
* Q1 field, then at hanging
* nodes the output field will
* have the function value of the
* input field, which however is
* not usually the mean value of
* the two adjacent nodes. It is
* thus not part of the Q1
* function space on the whole
* triangulation, although it is
* of course Q1 on each cell.
*
* For this case (continuous
* elements on grids with hanging
* nodes), please use the
* @p interpolate function with
* an additional
* @p ConstraintMatrix argument,
* see below, or make the field
* conforming yourself by calling
* the @p distribute function of
* your hanging node constraints
* object.
*/
template <int dim, int spacedim,
template <int,int> class DH1,
template <int,int> class DH2,
class InVector, class OutVector>
static
void
interpolate (const DH1<dim,spacedim> &dof1,
const InVector &u1,
const DH2<dim,spacedim> &dof2,
OutVector &u2);
/**
* Gives the interpolation of a
* the @p dof1-function @p u1 to
* a @p dof2-function @p u2. @p
* dof1 and @p dof2 need to be
* DoFHandlers (or
* hp::DoFHandlers) based on the
* same triangulation. @p
* constraints is a hanging node
* constraints object
* corresponding to @p dof2. This
* object is particular important
* when interpolating onto
* continuous elements on grids
* with hanging nodes (locally
* refined grids).
*
* If the elements @p fe1 and @p fe2
* are either both continuous or
* both discontinuous then this
* interpolation is the usual point
* interpolation. The same is true
* if @p fe1 is a continuous and
* @p fe2 is a discontinuous finite
* element. For the case that @p fe1
* is a discontinuous and @p fe2 is
* a continuous finite element
* there is no point interpolation
* defined at the discontinuities.
* Therefore the meanvalue is taken
* at the DoF values on the
* discontinuities.
*/
template <int dim, int spacedim,
template <int, int> class DH1,
template <int, int> class DH2,
class InVector, class OutVector>
static void interpolate (const DH1<dim,spacedim> &dof1,
const InVector &u1,
const DH2<dim,spacedim> &dof2,
const ConstraintMatrix &constraints,
OutVector& u2);
/**
* Gives the interpolation of the
* @p fe1-function @p u1 to a
* @p fe2-function, and
* interpolates this to a second
* @p fe1-function named
* @p u1_interpolated.
*
* Note, that this function does
* not work on continuous
* elements at hanging nodes. For
* that case use the
* @p back_interpolate function,
* below, that takes an
* additional
* @p ConstraintMatrix object.
*
* Furthermore note, that for the
* specific case when the finite
* element space corresponding to
* @p fe1 is a subset of the
* finite element space
* corresponding to @p fe2, this
* function is simply an identity
* mapping.
*/
template <int dim, class InVector, class OutVector, int spacedim>
static void back_interpolate (const DoFHandler<dim,spacedim> &dof1,
const InVector &u1,
const FiniteElement<dim,spacedim> &fe2,
OutVector &u1_interpolated);
/**
* Same as last function, except
* that the dof handler objects
* might be of type
* @p hp::DoFHandler.
*/
template <int dim,
template <int> class DH,
class InVector, class OutVector, int spacedim>
static void back_interpolate (const DH<dim> &dof1,
const InVector &u1,
const FiniteElement<dim,spacedim> &fe2,
OutVector &u1_interpolated);
/**
* Gives the interpolation of the
* @p dof1-function @p u1 to a
* @p dof2-function, and
* interpolates this to a second
* @p dof1-function named
* @p u1_interpolated.
* @p constraints1 and
* @p constraints2 are the
* hanging node constraints
* corresponding to @p dof1 and
* @p dof2, respectively. These
* objects are particular
* important when continuous
* elements on grids with hanging
* nodes (locally refined grids)
* are involved.
*
* Furthermore note, that for the
* specific case when the finite
* element space corresponding to
* @p dof1 is a subset of the
* finite element space
* corresponding to @p dof2, this
* function is simply an identity
* mapping.
*/
template <int dim, class InVector, class OutVector, int spacedim>
static void back_interpolate (const DoFHandler<dim,spacedim>& dof1,
const ConstraintMatrix& constraints1,
const InVector& u1,
const DoFHandler<dim,spacedim>& dof2,
const ConstraintMatrix& constraints2,
OutVector& u1_interpolated);
/**
* Gives $(Id-I_h)z_1$ for a given
* @p dof1-function $z_1$, where $I_h$
* is the interpolation from @p fe1
* to @p fe2. The result $(Id-I_h)z_1$ is
* written into @p z1_difference.
*
* Note, that this function does
* not work for continuous
* elements at hanging nodes. For
* that case use the
* @p interpolation_difference
* function, below, that takes an
* additional
* @p ConstraintMatrix object.
*/
template <int dim, class InVector, class OutVector, int spacedim>
static void interpolation_difference(const DoFHandler<dim,spacedim> &dof1,
const InVector &z1,
const FiniteElement<dim,spacedim> &fe2,
OutVector &z1_difference);
/**
* Gives $(Id-I_h)z_1$ for a given
* @p dof1-function $z_1$, where $I_h$
* is the interpolation from @p fe1
* to @p fe2. The result $(Id-I_h)z_1$ is
* written into @p z1_difference.
* @p constraints1 and
* @p constraints2 are the
* hanging node constraints
* corresponding to @p dof1 and
* @p dof2, respectively. These
* objects are particular
* important when continuous
* elements on grids with hanging
* nodes (locally refined grids)
* are involved.
*/
template <int dim, class InVector, class OutVector, int spacedim>
static void interpolation_difference(const DoFHandler<dim,spacedim>& dof1,
const ConstraintMatrix& constraints1,
const InVector& z1,
const DoFHandler<dim,spacedim>& dof2,
const ConstraintMatrix& constraints2,
OutVector& z1_difference);
/**
* $L^2$ projection for
* discontinuous
* elements. Operates the same
* direction as interpolate.
*
* The global projection can be
* computed by local matrices if
* the finite element spaces are
* discontinuous. With continuous
* elements, this is impossible,
* since a global mass matrix
* must be inverted.
*/
template <int dim, class InVector, class OutVector, int spacedim>
static void project_dg (const DoFHandler<dim,spacedim>& dof1,
const InVector& u1,
const DoFHandler<dim,spacedim>& dof2,
OutVector& u2);
/**
* Gives the patchwise
* extrapolation of a @p dof1
* function @p z1 to a @p dof2
* function @p z2. @p dof1 and
* @p dof2 need to be DoFHandler
* based on the same triangulation.
*
* This function is interesting
* for e.g. extrapolating
* patchwise a piecewise linear
* solution to a piecewise
* quadratic solution.
*
* Note that the resulting field
* does not satisfy continuity
* requirements of the given
* finite elements.
*
* When you use continuous
* elements on grids with hanging
* nodes, please use the
* @p extrapolate function with
* an additional
* ConstraintMatrix argument,
* see below.
*
* Since this function operates
* on patches of cells, it is
* required that the underlying
* grid is refined at least once
* for every coarse grid cell. If
* this is not the case, an
* exception will be raised.
*/
template <int dim, class InVector, class OutVector, int spacedim>
static void extrapolate (const DoFHandler<dim,spacedim>& dof1,
const InVector& z1,
const DoFHandler<dim,spacedim>& dof2,
OutVector& z2);
/**
* Gives the patchwise
* extrapolation of a @p dof1
* function @p z1 to a @p dof2
* function @p z2. @p dof1 and
* @p dof2 need to be DoFHandler
* based on the same triangulation.
* @p constraints is a hanging
* node constraints object
* corresponding to
* @p dof2. This object is
* particular important when
* interpolating onto continuous
* elements on grids with hanging
* nodes (locally refined grids).
*
* Otherwise, the same holds as
* for the other @p extrapolate
* function.
*/
template <int dim, class InVector, class OutVector, int spacedim>
static void extrapolate (const DoFHandler<dim,spacedim>& dof1,
const InVector& z1,
const DoFHandler<dim,spacedim>& dof2,
const ConstraintMatrix& constraints,
OutVector& z2);
//@}
/**
* The numbering of the degrees
* of freedom in continous finite
* elements is hierarchic,
* i.e. in such a way that we
* first number the vertex dofs,
* in the order of the vertices
* as defined by the
* triangulation, then the line
* dofs in the order and
* respecting the direction of
* the lines, then the dofs on
* quads, etc. However, we could
* have, as well, numbered them
* in a lexicographic way,
* i.e. with indices first
* running in x-direction, then
* in y-direction and finally in
* z-direction. Discontinuous
* elements of class FE_DGQ()
* are numbered in this way, for
* example.
*
* This function constructs a
* table which lexicographic
* index each degree of freedom
* in the hierarchic numbering
* would have. It operates on the
* continuous finite element
* given as first argument, and
* outputs the lexicographic
* indices in the second.
*
* Note that since this function
* uses specifics of the
* continuous finite elements, it
* can only operate on
* FiniteElementData<dim> objects
* inherent in FE_Q(). However,
* this function does not take a
* FE_Q object as it is also
* invoked by the FE_Q()
* constructor.
*
* It is assumed that the size of
* the output argument already
* matches the correct size,
* which is equal to the number
* of degrees of freedom in the
* finite element.
*/
template <int dim>
static void
hierarchic_to_lexicographic_numbering (const FiniteElementData<dim> &fe_data,
std::vector<unsigned int> &h2l);
/**
* Like the previous function but
* instead of returning its
* result through the last
* argument return it as a value.
*/
template <int dim>
static
std::vector<unsigned int>
hierarchic_to_lexicographic_numbering (const FiniteElementData<dim> &fe_data);
/**
* This is the reverse function
* to the above one, generating
* the map from the lexicographic
* to the hierarchical
* numbering. All the remarks
* made about the above function
* are also valid here.
*/
template <int dim>
static void
lexicographic_to_hierarchic_numbering (const FiniteElementData<dim> &fe_data,
std::vector<unsigned int> &l2h);
/**
* Like the previous function but
* instead of returning its
* result through the last
* argument return it as a value.
*/
template <int dim>
static
std::vector<unsigned int>
lexicographic_to_hierarchic_numbering (const FiniteElementData<dim> &fe_data);
/**
* Parse the name of a finite
* element and generate a finite
* element object accordingly.
*
* The name must be in the form which
* is returned by the
* FiniteElement::get_name
* function, where a few
* modifications are allowed:
*
* <ul><li> Dimension template
* parameters <2> etc. can
* be omitted. Alternatively, the
* explicit number can be
* replaced by <tt>dim</tt> or
* <tt>d</tt>. If a number is
* given, it <b>must</b> match
* the template parameter of this
* function.
*
* <li> The powers used for
* FESystem may either be numbers
* or can be
* replaced by <tt>dim</tt> or
* <tt>d</tt>.
* </ul>
*
* If no finite element can be
* reconstructed from this
* string, an exception of type
* @p FETools::ExcInvalidFEName
* is thrown.
*
* The function returns a pointer
* to a newly create finite
* element. It is in the caller's
* responsibility to destroy the
* object pointed to at an
* appropriate later time.
*
* Since the value of the template
* argument can't be deduced from the
* (string) argument given to this
* function, you have to explicitly
* specify it when you call this
* function.
*
* This function knows about all
* the standard elements defined
* in the library. However, it
* doesn't by default know about
* elements that you may have
* defined in your program. To
* make your own elements known
* to this function, use the
* add_fe_name() function.
* This function does not work
* if one wants to get a codimension
* 1 finite element.
*/
template <int dim>
static
FiniteElement<dim, dim> *
get_fe_from_name (const std::string &name);
/**
* Extend the list of finite
* elements that can be generated
* by get_fe_from_name() by the
* one given as @p name. If
* get_fe_from_name() is later
* called with this name, it will
* use the object given as second
* argument to create a finite
* element object.
*
* The format of the @p name
* parameter should include the
* name of a finite
* element. However, it is safe
* to use either the class name
* alone or to use the result of
* FiniteElement::get_name (which
* includes the space dimension
* as well as the polynomial
* degree), since everything
* after the first non-name
* character will be ignored.
*
* The FEFactory object should be
* an object newly created with
* <tt>new</tt>. FETools will
* take ownership of this object
* and delete it once it is not
* used anymore.
*
* In most cases, if you want
* objects of type
* <code>MyFE</code> be created
* whenever the name
* <code>my_fe</code> is given to
* get_fe_from_name, you will
* want the second argument to
* this function be of type
* FEFactory@<MyFE@>, but you can
* of course create your custom
* finite element factory class.
*
* This function takes over
* ownership of the object given
* as second argument, i.e. you
* should never attempt to
* destroy it later on. The
* object will be deleted at the
* end of the program's lifetime.
*
* If the name of the element
* is already in use, an exception
* is thrown. Thus, functionality
* of get_fe_from_name() can only
* be added, not changed.
*
* @note This function
* manipulates a global table
* (one table for each space
* dimension). It is thread safe
* in the sense that every access
* to this table is secured by a
* lock. Nevertheless, since each
* name can be added only once,
* user code has to make sure
* that only one thread adds a
* new element.
*
* Note also that this table
* exists once for each space
* dimension. If you have a
* program that works with finite
* elements in different space
* dimensions (for example, @ref
* step_4 "step-4" does something
* like this), then you should
* call this function for each
* space dimension for which you
* want your finite element added
* to the map.
*/
template <int dim, int spacedim>
static void add_fe_name (const std::string& name,
const FEFactoryBase<dim,spacedim>* factory);
/**
* The string used for
* get_fe_from_name() cannot be
* translated to a finite
* element.
*
* Either the string is badly
* formatted or you are using a
* custom element that must be
* added using add_fe_name()
* first.
*
* @ingroup Exceptions
*/
DeclException1 (ExcInvalidFEName,
std::string,
<< "Can't re-generate a finite element from the string '"
<< arg1 << "'.");
/**
* The string used for
* get_fe_from_name() cannot be
* translated to a finite
* element.
*
* Dimension arguments in finite
* element names should be
* avoided. If they are there,
* the dimension should be
* <tt>dim</tt> or
* <tt>d</tt>. Here, you gave a
* numeric dimension argument,
* which does not match the
* template dimension of the
* finite element class.
*
* @ingroup Exceptions
*/
DeclException2 (ExcInvalidFEDimension,
char, int,
<< "The dimension " << arg1
<< " in the finite element string must match "
<< "the space dimension "
<< arg2 << ".");
/**
* Exception
*
* @ingroup Exceptions
*/
DeclException0 (ExcInvalidFE);
/**
* The finite element must be
* @ref GlossPrimitive "primitive".
*
* @ingroup Exceptions
*/
DeclException0 (ExcFENotPrimitive);
/**
* Exception
*
* @ingroup Exceptions
*/
DeclException0 (ExcTriangulationMismatch);
/**
* A continuous element is used
* on a mesh with hanging nodes,
* but the constraint matrices
* are missing.
*
* @ingroup Exceptions
*/
DeclException1 (ExcHangingNodesNotAllowed,
int,
<< "You are using continuous elements on a grid with "
<< "hanging nodes but without providing hanging node "
<< "constraints. Use the respective function with "
<< "additional ConstraintMatrix argument(s), instead.");
/**
* You need at least two grid levels.
*
* @ingroup Exceptions
*/
DeclException0 (ExcGridNotRefinedAtLeastOnce);
/**
* The dimensions of the matrix
* used did not match the
* expected dimensions.
*
* @ingroup Exceptions
*/
DeclException4 (ExcMatrixDimensionMismatch,
int, int, int, int,
<< "This is a " << arg1 << "x" << arg2 << " matrix, "
<< "but should be a " << arg3 << "x" << arg4 << " matrix.");
/**
* Exception thrown if an
* embedding matrix was computed
* inaccurately.
*
* @ingroup Exceptions
*/
DeclException1(ExcLeastSquaresError, double,
<< "Least squares fit leaves a gap of " << arg1);
/**
* Exception thrown if one variable
* may not be greater than another.
*
* @ingroup Exceptions
*/
DeclException2 (ExcNotGreaterThan,
int, int,
<< arg1 << " must be greater than " << arg2);
private:
/**
* Return a finite element that
* is created using the beginning
* of <tt>name</tt> and eat away
* the part of <tt>name</tt>
* defining this element.
*/
template <int dim, int spacedim>
static
FiniteElement<dim,spacedim> *
get_fe_from_name_aux (std::string &name);
};
template<class FE>
FiniteElement<FE::dimension, FE::dimension>*
FETools::FEFactory<FE>::get (const unsigned int degree) const
{
return new FE(degree);
}
/*@}*/
DEAL_II_NAMESPACE_CLOSE
/*---------------------------- fe_tools.h ---------------------------*/
/* end of #ifndef __deal2__fe_tools_H */
#endif
/*---------------------------- fe_tools.h ---------------------------*/
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