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// $Id: mapping_cartesian.h 30036 2013-07-18 16:55:32Z maier $
//
// Copyright (C) 2001 - 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__mapping_cartesian_h
#define __deal2__mapping_cartesian_h
#include <deal.II/base/config.h>
#include <deal.II/base/table.h>
#include <cmath>
#include <deal.II/fe/mapping.h>
DEAL_II_NAMESPACE_OPEN
/*!@addtogroup mapping */
/*@{*/
/**
* Mapping of an axis-parallel cell.
*
* This class maps the unit cell to a grid cell with surfaces parallel
* to the coordinate lines/planes. The mapping is therefore a scaling
* along the coordinate directions. It is specifically developed for
* cartesian meshes. Apply this mapping to a general mesh to get
* strange results.
*
* For more information about the <tt>spacedim</tt> template parameter
* check the documentation of FiniteElement or the one of
* Triangulation.
*
* @author Guido Kanschat, 2001; Ralf Hartmann, 2005
*/
template <int dim, int spacedim=dim>
class MappingCartesian : public Mapping<dim,spacedim>
{
public:
virtual
typename Mapping<dim, spacedim>::InternalDataBase *
get_data (const UpdateFlags,
const Quadrature<dim> &quadrature) const;
virtual
typename Mapping<dim, spacedim>::InternalDataBase *
get_face_data (const UpdateFlags flags,
const Quadrature<dim-1>& quadrature) const;
virtual
typename Mapping<dim, spacedim>::InternalDataBase *
get_subface_data (const UpdateFlags flags,
const Quadrature<dim-1>& quadrature) const;
virtual void
fill_fe_values (const typename Triangulation<dim,spacedim>::cell_iterator &cell,
const Quadrature<dim> &quadrature,
typename Mapping<dim, spacedim>::InternalDataBase &mapping_data,
std::vector<Point<spacedim> > &quadrature_points,
std::vector<double> &JxW_values,
std::vector<DerivativeForm<1,dim,spacedim> > &jacobians,
std::vector<DerivativeForm<2,dim,spacedim> > &jacobian_grads,
std::vector<DerivativeForm<1,spacedim,dim> > &inverse_jacobians,
std::vector<Point<spacedim> > &,
CellSimilarity::Similarity &cell_similarity) const ;
virtual void
fill_fe_face_values (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,
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 ;
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,
typename Mapping<dim, spacedim>::InternalDataBase &mapping_data,
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 ;
virtual void
transform (const VectorSlice<const std::vector<Tensor<1,dim> > > input,
VectorSlice<std::vector<Tensor<1,spacedim> > > output,
const typename Mapping<dim,spacedim>::InternalDataBase &internal,
const MappingType type) const;
virtual void
transform (const VectorSlice<const std::vector<DerivativeForm<1, dim,spacedim> > > input,
VectorSlice<std::vector<Tensor<2,spacedim> > > output,
const typename Mapping<dim,spacedim>::InternalDataBase &internal,
const MappingType type) const;
virtual
void
transform (const VectorSlice<const std::vector<Tensor<2, dim> > > input,
VectorSlice<std::vector<Tensor<2,spacedim> > > output,
const typename Mapping<dim,spacedim>::InternalDataBase &internal,
const MappingType type) const;
virtual Point<spacedim>
transform_unit_to_real_cell (
const typename Triangulation<dim,spacedim>::cell_iterator &cell,
const Point<dim> &p) const;
/**
* 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.
*
* Uses Newton iteration and the
* @p transform_unit_to_real_cell
* function.
*/
virtual Point<dim>
transform_real_to_unit_cell (
const typename Triangulation<dim,spacedim>::cell_iterator &cell,
const Point<spacedim> &p) const;
/**
* Return a pointer to a copy of the
* present object. The caller of this
* copy then assumes ownership of it.
*/
virtual
Mapping<dim, spacedim> *clone () const;
/**
* Always returns @p true because
* MappingCartesian preserves vertex
* locations.
*/
bool preserves_vertex_locations () const;
protected:
/**
* Storage for internal data of
* the scaling.
*/
class InternalData : public Mapping<dim, spacedim>::InternalDataBase
{
public:
/**
* Constructor.
*/
InternalData (const Quadrature<dim> &quadrature);
/**
* Return an estimate (in
* bytes) or the memory
* consumption of this
* object.
*/
virtual std::size_t memory_consumption () const;
/**
* Length of the cell in
* different coordinate
* directions, <i>h<sub>x</sub></i>,
* <i>h<sub>y</sub></i>, <i>h<sub>z</sub></i>.
*/
Tensor<1,dim> length;
/**
* The volume element
*/
double volume_element;
/**
* Vector of all quadrature
* points. Especially, all
* points on all faces.
*/
std::vector<Point<dim> > quadrature_points;
};
/**
* Do the computation for the
* <tt>fill_*</tt> functions.
*/
void compute_fill (const typename Triangulation<dim,spacedim>::cell_iterator &cell,
const unsigned int face_no,
const unsigned int sub_no,
const CellSimilarity::Similarity cell_similarity,
InternalData &data,
std::vector<Point<dim> > &quadrature_points,
std::vector<Point<dim> > &normal_vectors) const;
private:
virtual UpdateFlags update_once (const UpdateFlags) const;
virtual UpdateFlags update_each (const UpdateFlags) const;
/**
* Value to indicate that a given
* face or subface number is
* invalid.
*/
static const unsigned int invalid_face_number = numbers::invalid_unsigned_int;
};
/*@}*/
/* -------------- declaration of explicit specializations ------------- */
#ifndef DOXYGEN
template <int dim, int spacedim>
inline
bool
MappingCartesian<dim,spacedim>::preserves_vertex_locations () const
{
return true;
}
#endif // DOXYGEN
DEAL_II_NAMESPACE_CLOSE
#endif
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