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// $Id: mapping.h 20159 2009-11-24 03:25:41Z bangerth $
// Version: $Name$
//
// Copyright (C) 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 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__mapping_h
#define __deal2__mapping_h
#include <base/config.h>
#include <base/tensor.h>
#include <base/vector_slice.h>
#include <grid/tria.h>
#include <dofs/dof_handler.h>
#include <fe/fe_update_flags.h>
#include <cmath>
DEAL_II_NAMESPACE_OPEN
template <int dim> class Quadrature;
template <int dim, int spacedim> class FEValuesData;
template <int dim, int spacedim> class FEValuesBase;
template <int dim, int spacedim> class FEValues;
template <int dim, int spacedim> class FEFaceValues;
template <int dim, int spacedim> class FESubfaceValues;
/**
* The transformation type used
* for the Mapping::transform() functions.
*
* Special finite elements may
* need special Mapping from the
* reference cell to the actual
* mesh cell. In order to be most
* flexible, this enum provides
* an extensible interface for
* arbitrary
* transformations. Nevertheless,
* these must be implemented in
* the transform() functions of
* inheriting classes in order to
* work.
*
* Mappings are usually defined
* for vectors. If such a
* MappingType is applied to a
* rank 2 tensor, it is implied
* that the mapping is applied to
* each column.
*/
enum MappingType
{
/// No mapping
mapping_none = 0x0000,
/// Covariant mapping
mapping_covariant = 0x0001,
/// Contravariant mapping
mapping_contravariant = 0x0002,
/// Mapping of the gradient of a covariant vector field
mapping_covariant_gradient = 0x0003,
/// Mapping of the gradient of a contravariant vector field
mapping_contravariant_gradient = 0x0004,
/// The Piola transform usually used for Hdiv elements
/**
* Piola transform is the
* standard transformation of
* vector valued elements in
* H<sup>div</sup>. It amounts
* to a contravariant
* transformation scaled by the
* inverse of the volume
* element.
*
* If applied to a rank 2
* tensor, the mapping class
* will apply the correct
* transformation for the
* gradient of such a vector
* field.
*/
mapping_piola = 0x0100,
/// The mapping used for Nedelec elements
/**
* curl-conforming elements are
* mapped as covariant
* vectors. Nevertheless, we
* introduce a separate mapping
* type, such that we can use
* the same flag for the vector
* and its gradient (the
* transformation of the
* gradient differs from the
* one used by #mapping_covariant).
*/
mapping_nedelec = 0x0200,
/// The mapping used for Raviart-Thomas elements
mapping_raviart_thomas = mapping_piola,
/// The mapping used for BDM elements
mapping_bdm = mapping_piola
};
/**
* Abstract base class for mapping classes.
*
* The interface for filling the tables of FEValues is provided.
* Everything else has to happen in derived classes.
*
* The following paragraph applies to the implementation of
* FEValues. Usage of the class is as follows: first, call the
* functions @p update_once and @p update_each with the update
* flags you need. This includes the flags needed by the
* FiniteElement. Then call <tt>get_*_data</tt> and with the or'd
* results. This will initialize and return some internal data
* structures. On the first cell, call <tt>fill_fe_*_values</tt> with the
* result of @p update_once. Finally, on each cell, use
* <tt>fill_fe_*_values</tt> with the result of @p update_each to compute
* values for a special cell.
*
* A hint to implementators: no function except the two functions
* @p update_once and @p update_each may add any flags.
*
* For more information about the <tt>spacedim</tt> template parameter
* check the documentation of FiniteElement or the one of
* Triangulation.
*
* @ingroup mapping
* @author Guido Kanschat, Ralf Hartmann 2000, 2001
*/
template <int dim, int spacedim=dim>
class Mapping : public Subscriptor
{
public:
/**
* Virtual destructor.
*/
virtual ~Mapping ();
/**
* Transforms the point @p p on
* the unit cell to the point
* @p p_real on the real cell
* @p cell and returns @p p_real.
*/
virtual Point<spacedim>
transform_unit_to_real_cell (
const typename Triangulation<dim,spacedim>::cell_iterator &cell,
const Point<dim> &p) const = 0;
/**
* Transforms the point @p p on
* the real cell to the point
* @p p_unit on the unit cell
* @p cell and returns @p p_unit.
*/
virtual Point<dim>
transform_real_to_unit_cell (
const typename Triangulation<dim,spacedim>::cell_iterator &cell,
const Point<spacedim> &p) const = 0;
/**
* Base class for internal data
* of finite element and mapping
* objects. The internal
* mechanism is that upon
* construction of a @p FEValues
* objects, it asks the mapping
* and finite element classes
* that are to be used to
* allocate memory for their own
* purpose in which they may
* store data that only needs to
* be computed once. For example,
* most finite elements will
* store the values of the shape
* functions at the quadrature
* points in this object, since
* they do not change from cell
* to cell and only need to be
* computed once. Since different
* @p FEValues objects using
* different quadrature rules
* might access the same finite
* element object at the same
* time, it is necessary to
* create one such object per
* @p FEValues object. Ownership
* of this object is then
* transferred to the
* @p FEValues object, but a
* pointer to this object is
* passed to the finite element
* object every time it shall
* compute some data so that it
* has access to the precomputed
* values stored there.
*/
class InternalDataBase: public Subscriptor
{
private:
/**
* Copy constructor forbidden.
*/
InternalDataBase (const InternalDataBase&);
public:
/**
* Constructor. Sets
* @p UpdateFlags to
* @p update_default and
* @p first_cell to @p true.
*/
InternalDataBase ();
/**
* Virtual destructor for
* derived classes
*/
virtual ~InternalDataBase ();
/**
* Values updated by the constructor or
* by reinit.
*/
UpdateFlags update_flags;
/**
* Values computed by
* constructor.
*/
UpdateFlags update_once;
/**
* Values updated on each
* cell by reinit.
*/
UpdateFlags update_each;
/**
* If <tt>first_cell==true</tt>
* this function returns
* @p update_flags,
* i.e. <tt>update_once|update_each</tt>.
* If <tt>first_cell==false</tt>
* it returns
* @p update_each.
*/
UpdateFlags current_update_flags() const;
/**
* Return whether we are
* presently initializing
* data for the first
* cell. The value of the
* field this function is
* returning is set to
* @p true in the
* constructor, and cleared
* by the @p FEValues class
* after the first cell has
* been initialized.
*
* This function is used to
* determine whether we need
* to use the @p update_once
* flags for computing data,
* or whether we can use the
* @p update_each flags.
*/
bool is_first_cell () const;
/**
* Set the @p first_cell
* flag to @p false. Used by
* the @p FEValues class to
* indicate that we have
* already done the work on
* the first cell.
*/
virtual void clear_first_cell ();
/**
* Return an estimate (in
* bytes) or the memory
* consumption of this
* object.
*/
virtual unsigned int memory_consumption () const;
/**
* The determinant of the
* Jacobian in each
* quadrature point. Filled
* if #update_volume_elements.
*/
std::vector<double> volume_elements;
/**
* The positions of the
* mapped (generalized)
* support points.
*/
std::vector<Point<spacedim> > support_point_values;
/*
* The Jacobian of the
* transformation in the
* (generalized) support
* points.
*/
std::vector<Tensor<2,spacedim> > support_point_gradients;
/*
* The inverse of the
* Jacobian of the
* transformation in the
* (generalized) support
* points.
*/
std::vector<Tensor<2,spacedim> > support_point_inverse_gradients;
private:
/**
* The value returned by
* @p is_first_cell.
*/
bool first_cell;
};
/**
* Transform a field of
* vectors accorsing to
* the selected MappingType.
*/
virtual
void
transform (const VectorSlice<const std::vector<Tensor<1,dim> > > input,
VectorSlice<std::vector<Tensor<1,spacedim> > > output,
const InternalDataBase &internal,
const MappingType type) const = 0;
/**
* Transform a field of
* rank two tensors accorsing to
* the selected MappingType.
*/
virtual
void
transform (const VectorSlice<const std::vector<Tensor<2,dim> > > input,
VectorSlice<std::vector<Tensor<2,spacedim> > > output,
const InternalDataBase &internal,
const MappingType type) const = 0;
/**
* @deprecated Use transform() instead.
*/
void
transform_covariant (const VectorSlice<const std::vector<Tensor<1,dim> > > input,
const unsigned int offset,
VectorSlice<std::vector<Tensor<1,spacedim> > > output,
const InternalDataBase &internal) const;
/**
* @deprecated Use transform() instead.
*/
void
transform_covariant (const VectorSlice<const std::vector<Tensor<2,dim> > > input,
const unsigned int offset,
VectorSlice<std::vector<Tensor<2,spacedim> > > output,
const InternalDataBase &internal) const;
/**
* @deprecated Use transform() instead.
*/
void
transform_contravariant (const VectorSlice<const std::vector<Tensor<1,dim> > > input,
const unsigned int offset,
VectorSlice<std::vector<Tensor<1,spacedim> > > output,
const typename Mapping<dim,spacedim>::InternalDataBase &internal) const;
/**
* @deprecated Use transform() instead.
*/
void
transform_contravariant (const VectorSlice<const std::vector<Tensor<2,dim> > > intput,
const unsigned int offset,
const VectorSlice<std::vector<Tensor<2,spacedim> > > output,
const typename Mapping<dim,spacedim>::InternalDataBase &internal) const;
/**
* The transformed (generalized)
* support point.
*/
const Point<spacedim>& support_point_value(
const unsigned int index,
const typename Mapping<dim,spacedim>::InternalDataBase &internal) const;
/**
* The Jacobian
* matrix of the transformation
* in the (generalized) support
* point.
*/
const Tensor<2,spacedim>& support_point_gradient(
const unsigned int index,
const typename Mapping<dim,spacedim>::InternalDataBase &internal) const;
/**
* The inverse Jacobian
* matrix of the transformation
* in the (generalized) support
* point.
*/
const Tensor<2,spacedim>& support_point_inverse_gradient(
const unsigned int index,
const typename Mapping<dim,spacedim>::InternalDataBase &internal) const;
/**
* Return a pointer to a copy of the
* present object. The caller of this
* copy then assumes ownership of it.
*
* Since one can't create
* objects of class Mapping, this
* function of course has to be
* implemented by derived classes.
*
* This function is mainly used by the
* hp::MappingCollection class.
*/
virtual
Mapping<dim,spacedim> * clone () const = 0;
/**
* Returns whether the mapping preserves
* vertex locations, i.e. whether the
* mapped location of the reference cell
* vertices (given by
* GeometryInfo::unit_cell_vertex())
* equals the result of
* <code>cell-@>vertex()</code>.
*
* For example, implementations in
* derived classes return @p true for
* MappingQ, MappingQ1, MappingCartesian,
* but @p false for MappingQEulerian,
* MappingQ1Eulerian.
*/
virtual
bool preserves_vertex_locations () const = 0;
/**
* Exception
*/
DeclException0 (ExcInvalidData);
private:
/**
* Indicate fields to be updated
* in the constructor of
* FEValues. Especially,
* fields not asked for by
* FEValues, but computed
* for efficiency reasons will be
* notified here.
*
* See @ref UpdateFlagsEssay.
*/
virtual UpdateFlags update_once (const UpdateFlags) const = 0;
/**
* The same as update_once(),
* but for the flags to be updated for
* each grid cell.
*
* See @ref UpdateFlagsEssay.
*/
virtual UpdateFlags update_each (const UpdateFlags) const = 0;
/**
* Prepare internal data
* structures and fill in values
* independent of the cell.
*/
virtual InternalDataBase*
get_data (const UpdateFlags,
const Quadrature<dim>& quadrature) const = 0;
/**
* Prepare internal data
* structure for transformation
* of faces and fill in values
* independent of the cell.
*/
virtual InternalDataBase*
get_face_data (const UpdateFlags flags,
const Quadrature<dim-1>& quadrature) const = 0;
/**
* Prepare internal data
* structure for transformation
* of children of faces and fill
* in values independent of the
* cell.
*/
virtual InternalDataBase*
get_subface_data (const UpdateFlags flags,
const Quadrature<dim-1>& quadrature) const = 0;
/**
* Fill the transformation fields
* of @p FEValues. Given a grid
* cell and the quadrature points
* on the unit cell, it computes
* all values specified by
* @p flags. The arrays to be
* filled have to have the
* correct size.
*
* Values are split into two
* groups: first,
* @p quadrature_points and
* @p JxW_values are
* filled with the quadrature
* rule transformed to the
* cell in physical space.
*
* The second group contains the
* matrices needed to transform
* vector-valued functions,
* namely
* @p jacobians,
* the derivatives
* @p jacobian_grads,
* and the inverse operations in
* @p inverse_jacobians.
*/
/* virtual void */
/* fill_fe_values (const typename Triangulation<dim,spacedim>::cell_iterator &cell, */
/* const Quadrature<dim> &quadrature, */
/* InternalDataBase &internal, */
/* std::vector<Point<spacedim> > &quadrature_points, */
/* std::vector<double> &JxW_values) const = 0; */
/** The function above adjusted
* with the variable
* cell_normal_vectors for the
* case of codimension 1
*/
virtual void
fill_fe_values (const typename Triangulation<dim,spacedim>::cell_iterator &cell,
const Quadrature<dim> &quadrature,
InternalDataBase &internal,
std::vector<Point<spacedim> > &quadrature_points,
std::vector<double> &JxW_values,
std::vector<Tensor<2,spacedim> > &jacobians,
std::vector<Tensor<3,spacedim> > &jacobian_grads,
std::vector<Tensor<2,spacedim> > &inverse_jacobians,
std::vector<Point<spacedim> > &cell_normal_vectors,
CellSimilarity::Similarity &cell_similarity
) const=0;
/**
* Performs the same as @p fill_fe_values
* on a face.
* Additionally, @p boundary_form and
* @p normal_vectors can be
* computed on surfaces. The
* boundary form is the vector
* product of the image of
* coordinate vectors on the
* surface of the unit
* cell. It is a
* vector normal to the surface,
* pointing outwards and having
* the length of the surface
* element.
* Therefore, it is more economic
* to use the boundary form
* instead of the product of the
* unit normal and the
* transformed quadrature weight.
*/
virtual void
fill_fe_face_values (const typename Triangulation<dim,spacedim>::cell_iterator &cell,
const unsigned int face_no,
const Quadrature<dim-1> &quadrature,
InternalDataBase &internal,
std::vector<Point<dim> > &quadrature_points,
std::vector<double> &JxW_values,
std::vector<Tensor<1,dim> > &boundary_form,
std::vector<Point<spacedim> > &normal_vectors) const = 0;
/**
* See above.
*/
virtual void
fill_fe_subface_values (const typename Triangulation<dim,spacedim>::cell_iterator &cell,
const unsigned int face_no,
const unsigned int sub_no,
const Quadrature<dim-1> &quadrature,
InternalDataBase &internal,
std::vector<Point<dim> > &quadrature_points,
std::vector<double> &JxW_values,
std::vector<Tensor<1,dim> > &boundary_form,
std::vector<Point<spacedim> > &normal_vectors) const = 0;
/**
* Give class @p FEValues access
* to the private <tt>get_...data</tt>
* and <tt>fill_fe_...values</tt>
* functions.
*/
friend class FEValuesBase<dim,spacedim>;
friend class FEValues<dim,spacedim>;
friend class FEFaceValues<dim,spacedim>;
friend class FESubfaceValues<dim,spacedim>;
};
/* ------------------------- inline functions ------------------------- */
#ifndef DOXYGEN
template <int dim, int spacedim>
inline
UpdateFlags
Mapping<dim,spacedim>::InternalDataBase::current_update_flags () const
{
if (first_cell)
{
Assert (update_flags==(update_once|update_each),
ExcInternalError());
return update_flags;
}
else
return update_each;
}
template <int dim, int spacedim>
inline
bool
Mapping<dim,spacedim>::InternalDataBase::is_first_cell () const
{
return first_cell;
}
template <int dim, int spacedim>
inline
void
Mapping<dim,spacedim>::InternalDataBase::clear_first_cell ()
{
first_cell = false;
}
template <int dim, int spacedim>
inline
const Point<spacedim>&
Mapping<dim,spacedim>::support_point_value(
const unsigned int index,
const typename Mapping<dim,spacedim>::InternalDataBase& internal) const
{
AssertIndexRange(index, internal.support_point_values.size());
return internal.support_point_values[index];
}
template <int dim, int spacedim>
inline
const Tensor<2,spacedim>&
Mapping<dim,spacedim>::support_point_gradient(
const unsigned int index,
const typename Mapping<dim,spacedim>::InternalDataBase& internal) const
{
AssertIndexRange(index, internal.support_point_gradients.size());
return internal.support_point_gradients[index];
}
template <int dim, int spacedim>
inline
const Tensor<2,spacedim>&
Mapping<dim,spacedim>::support_point_inverse_gradient(
const unsigned int index,
const typename Mapping<dim,spacedim>::InternalDataBase& internal) const
{
AssertIndexRange(index, internal.support_point_inverse_gradients.size());
return internal.support_point_inverse_gradients[index];
}
#endif // DOXYGEN
DEAL_II_NAMESPACE_CLOSE
#endif
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