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//
// Copyright (C) 2001 - 2016 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 dealii__mapping_cartesian_h
#define dealii__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 */
/*@{*/
/**
* A class providing a mapping from the reference cell to cells that are
* axiparallel.
*
* This class maps the unit cell to a grid cell with surfaces parallel to the
* coordinate lines/planes. It is specifically developed for Cartesian meshes.
* In other words, the mapping is meant for cells for which the mapping from
* the reference to the real cell is a scaling along the coordinate
* directions: The transformation from reference coordinates $\hat {\mathbf
* x}$ to real coordinates $\mathbf x$ on each cell is of the form
* @f{align*}{
* {\mathbf x}(\hat {\mathbf x}) = \begin{pmatrix} h_x & 0 \\ 0 & h_y
* \end{pmatrix} \hat{\mathbf x} + {\mathbf v}_0
* @f}
* in 2d, and
* @f{align*}{
* {\mathbf x}(\hat {\mathbf x}) = \begin{pmatrix} h_x & 0 & 0 \\ 0 & h_y & 0
* \\ 0 & 0 & h_z \end{pmatrix} \hat{\mathbf x} + {\mathbf v}_0
* @f}
* in 3d, where ${\mathbf v}_0$ is the bottom left vertex and $h_x,h_y,h_z$
* are the extents of the cell along the axes.
*
* The class is intended for efficiency, and it does not do a whole lot of
* error checking. If you apply this mapping to a cell that does not conform
* to the requirements above, you will get strange results.
*
* @author Guido Kanschat, 2001; Ralf Hartmann, 2005
*/
template <int dim, int spacedim=dim>
class MappingCartesian : public Mapping<dim,spacedim>
{
public:
// for documentation, see the Mapping base class
virtual
Mapping<dim, spacedim> *clone () const;
/**
* Always returns @p true because MappingCartesian preserves vertex
* locations.
*/
bool preserves_vertex_locations () const;
/**
* @name Mapping points between reference and real cells
* @{
*/
// for documentation, see the Mapping base class
virtual
Point<spacedim>
transform_unit_to_real_cell (const typename Triangulation<dim,spacedim>::cell_iterator &cell,
const Point<dim> &p) const;
// for documentation, see the Mapping base class
virtual
Point<dim>
transform_real_to_unit_cell (const typename Triangulation<dim,spacedim>::cell_iterator &cell,
const Point<spacedim> &p) const;
/**
* @}
*/
/**
* @name Functions to transform tensors from reference to real coordinates
* @{
*/
// for documentation, see the Mapping base class
virtual
void
transform (const ArrayView<const Tensor<1,dim> > &input,
const MappingType type,
const typename Mapping<dim,spacedim>::InternalDataBase &internal,
const ArrayView<Tensor<1,spacedim> > &output) const;
// for documentation, see the Mapping base class
virtual
void
transform (const ArrayView<const DerivativeForm<1, dim, spacedim> > &input,
const MappingType type,
const typename Mapping<dim,spacedim>::InternalDataBase &internal,
const ArrayView<Tensor<2,spacedim> > &output) const;
// for documentation, see the Mapping base class
virtual
void
transform (const ArrayView<const Tensor<2, dim> > &input,
const MappingType type,
const typename Mapping<dim,spacedim>::InternalDataBase &internal,
const ArrayView<Tensor<2,spacedim> > &output) const;
// for documentation, see the Mapping base class
virtual
void
transform (const ArrayView<const DerivativeForm<2, dim, spacedim> > &input,
const MappingType type,
const typename Mapping<dim,spacedim>::InternalDataBase &internal,
const ArrayView<Tensor<3,spacedim> > &output) const;
// for documentation, see the Mapping base class
virtual
void
transform (const ArrayView<const Tensor<3, dim> > &input,
const MappingType type,
const typename Mapping<dim,spacedim>::InternalDataBase &internal,
const ArrayView<Tensor<3,spacedim> > &output) const;
/**
* @}
*/
private:
/**
* @name Interface with FEValues
* @{
*/
/**
* Storage for internal data of the mapping. See Mapping::InternalDataBase
* for an extensive description.
*
* This includes data that is computed once when the object is created (in
* get_data()) as well as data the class wants to store from between the
* call to fill_fe_values(), fill_fe_face_values(), or
* fill_fe_subface_values() until possible later calls from the finite
* element to functions such as transform(). The latter class of member
* variables are marked as 'mutable'.
*/
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;
/**
* Extents of the last cell we have seen in the coordinate directions,
* i.e., <i>h<sub>x</sub></i>, <i>h<sub>y</sub></i>, <i>h<sub>z</sub></i>.
*/
mutable Tensor<1,dim> cell_extents;
/**
* The volume element
*/
mutable double volume_element;
/**
* Vector of all quadrature points. Especially, all points on all faces.
*/
std::vector<Point<dim> > quadrature_points;
};
// documentation can be found in Mapping::requires_update_flags()
virtual
UpdateFlags
requires_update_flags (const UpdateFlags update_flags) const;
// documentation can be found in Mapping::get_data()
virtual
typename Mapping<dim, spacedim>::InternalDataBase *
get_data (const UpdateFlags,
const Quadrature<dim> &quadrature) const;
// documentation can be found in Mapping::get_face_data()
virtual
typename Mapping<dim, spacedim>::InternalDataBase *
get_face_data (const UpdateFlags flags,
const Quadrature<dim-1>& quadrature) const;
// documentation can be found in Mapping::get_subface_data()
virtual
typename Mapping<dim, spacedim>::InternalDataBase *
get_subface_data (const UpdateFlags flags,
const Quadrature<dim-1>& quadrature) const;
// documentation can be found in Mapping::fill_fe_values()
virtual
CellSimilarity::Similarity
fill_fe_values (const typename Triangulation<dim,spacedim>::cell_iterator &cell,
const CellSimilarity::Similarity cell_similarity,
const Quadrature<dim> &quadrature,
const typename Mapping<dim,spacedim>::InternalDataBase &internal_data,
internal::FEValues::MappingRelatedData<dim,spacedim> &output_data) const;
// documentation can be found in Mapping::fill_fe_face_values()
virtual void
fill_fe_face_values (const typename Triangulation<dim,spacedim>::cell_iterator &cell,
const unsigned int face_no,
const Quadrature<dim-1> &quadrature,
const typename Mapping<dim,spacedim>::InternalDataBase &internal_data,
internal::FEValues::MappingRelatedData<dim,spacedim> &output_data) const;
// documentation can be found in Mapping::fill_fe_subface_values()
virtual void
fill_fe_subface_values (const typename Triangulation<dim,spacedim>::cell_iterator &cell,
const unsigned int face_no,
const unsigned int subface_no,
const Quadrature<dim-1> &quadrature,
const typename Mapping<dim,spacedim>::InternalDataBase &internal_data,
internal::FEValues::MappingRelatedData<dim,spacedim> &output_data) const;
/**
* @}
*/
/**
* 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,
const InternalData &data,
std::vector<Point<dim> > &quadrature_points,
std::vector<Tensor<1,dim> > &normal_vectors) const;
/**
* Value to indicate that a given face or subface number is invalid.
*/
static const unsigned int invalid_face_number = numbers::invalid_unsigned_int;
};
/*@}*/
DEAL_II_NAMESPACE_CLOSE
#endif
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