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// $Id: mapping_q.h 20158 2009-11-24 00:03:32Z kronbichler $
// Version: $Name$
//
// Copyright (C) 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__mapping_q_h
#define __deal2__mapping_q_h
#include <base/config.h>
#include <base/table.h>
#include <fe/mapping_q1.h>
#include <fe/fe_q.h>
DEAL_II_NAMESPACE_OPEN
template <int dim> class TensorProductPolynomials;
/*!@addtogroup mapping */
/*@{*/
/**
* Mapping class that uses Qp-mappings on boundary cells. The mapping
* shape functions make use of tensor product polynomials with
* equidistant (on the unit cell) support points.
*
* For more details about Qp-mappings, see the `mapping' report at
* <tt>deal.II/doc/reports/mapping_q/index.html</tt> in the `Reports'
* section of `Documentation'.
*
* For more information about the <tt>spacedim</tt> template parameter
* check the documentation of FiniteElement or the one of
* Triangulation.
*
* @author Ralf Hartmann, 2000, 2001, 2005; Guido Kanschat 2000, 2001
*/
template <int dim, int spacedim=dim>
class MappingQ : public MappingQ1<dim,spacedim>
{
public:
/**
* Constructor. @p p gives the
* degree of mapping polynomials
* on boundary cells.
*
* The second argument determines
* whether the higher order
* mapping should also be used on
* interior cells. If its value
* is <code>false</code> (the
* default), the a lower-order
* mapping is used in the
* interior. This is sufficient
* for most cases where higher
* order mappings are only used
* to better approximate the
* boundary. In that case, cells
* bounded by straight lines are
* acceptable in the
* interior. However, there are
* cases where one would also
* like to use a higher order
* mapping in the interior. The
* MappingQEulerian class is one
* such case.
*/
MappingQ (const unsigned int p,
const bool use_mapping_q_on_all_cells = false);
/**
* Copy constructor. Performs a
* deep copy, i.e. duplicates
* what #tensor_pols points to
* instead of simply copying the
* #tensor_pols pointer as done
* by a default copy constructor.
*/
MappingQ (const MappingQ<dim,spacedim> &mapping);
/**
* Destructor.
*/
virtual ~MappingQ ();
/**
* 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;
/**
* 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;
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<Tensor<2,dim> > > input,
VectorSlice<std::vector<Tensor<2,spacedim> > > output,
const typename Mapping<dim,spacedim>::InternalDataBase &internal,
const MappingType type) const;
/**
* Return the degree of the
* mapping, i.e. the value which
* was passed to the constructor.
*/
unsigned int get_degree () 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;
/**
* Storage for internal data of
* Q_degree transformation.
*/
class InternalData : public MappingQ1<dim,spacedim>::InternalData
{
public:
/**
* Constructor.
*/
InternalData (const unsigned int n_shape_functions);
/**
* Return an estimate (in
* bytes) or the memory
* consumption of this
* object.
*/
virtual unsigned int memory_consumption () const;
/**
* Unit normal vectors. Used
* for the alternative
* computation of the normal
* vectors. See doc of the
* @p alternative_normals_computation
* flag.
*
* Filled (hardcoded) once in
* @p get_face_data.
*/
std::vector<std::vector<Point<dim> > > unit_normals;
/**
* Flag that is set by the
* <tt>fill_fe_[[sub]face]_values</tt>
* function.
*
* If this flag is @p true
* we are on an interior cell
* and the
* @p mapping_q1_data is
* used.
*/
bool use_mapping_q1_on_current_cell;
/**
* On interior cells
* @p MappingQ1 is used.
*/
typename MappingQ1<dim,spacedim>::InternalData mapping_q1_data;
};
protected:
/**
* Implementation of the interface in
* Mapping.
*/
virtual void
fill_fe_values (const typename Triangulation<dim,spacedim>::cell_iterator &cell,
const Quadrature<dim> &quadrature,
typename Mapping<dim,spacedim>::InternalDataBase &mapping_data,
typename 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 ;
/**
* Implementation of the interface in
* Mapping.
*/
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,
typename std::vector<Point<dim> > &quadrature_points,
std::vector<double> &JxW_values,
typename std::vector<Tensor<1,dim> > &exterior_form,
typename std::vector<Point<dim> > &normal_vectors) const ;
/**
* Implementation of the interface in
* Mapping.
*/
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,
typename std::vector<Point<dim> > &quadrature_points,
std::vector<double> &JxW_values,
typename std::vector<Tensor<1,dim> > &exterior_form,
typename std::vector<Point<dim> > &normal_vectors) const ;
/**
* For <tt>dim=2,3</tt>. Append the
* support points of all shape
* functions located on bounding
* lines to the vector
* @p a. Points located on the
* line but not on vertices are not
* included.
*
* Needed by the
* @p compute_support_points_laplace
* function . For <tt>dim=1</tt> this
* function is empty.
*
* This function is made virtual
* in order to allow derived
* classes to choose shape
* function support points
* differently than the present
* class, which chooses the
* points as interpolation points
* on the boundary.
*/
virtual void
add_line_support_points (const typename Triangulation<dim,spacedim>::cell_iterator &cell,
std::vector<Point<dim> > &a) const;
/**
* For <tt>dim=3</tt>. Append the
* support points of all shape
* functions located on bounding
* faces (quads in 3d) to the
* vector @p a. Points located
* on the quad but not on vertices
* are not included.
*
* Needed by the
* @p compute_support_points_laplace
* function. For <tt>dim=1</tt> and
* <tt>dim=2</tt> this function is
* empty.
*
* This function is made virtual
* in order to allow derived
* classes to choose shape
* function support points
* differently than the present
* class, which chooses the
* points as interpolation points
* on the boundary.
*/
virtual void
add_quad_support_points(const typename Triangulation<dim,spacedim>::cell_iterator &cell,
std::vector<Point<dim> > &a) const;
private:
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;
/**
* Compute shape values and/or
* derivatives.
*/
virtual void
compute_shapes_virtual (const std::vector<Point<dim> > &unit_points,
typename MappingQ1<dim,spacedim>::InternalData &data) const;
/**
* This function is needed by the
* constructor of <tt>MappingQ<dim,spacedim></tt>
* for <tt>dim=</tt> 2 and 3.
*
* For <tt>degree<4</tt> this function
* sets the
* @p laplace_on_quad_vector to
* the hardcoded data. For
* <tt>degree>=4</tt> and MappingQ<2>
* this vector is computed.
*
* For the definition of the
* @p laplace_on_quad_vector
* please refer to equation (8)
* of the `mapping' report.
*/
void
set_laplace_on_quad_vector(Table<2,double> &loqvs) const;
/**
* This function is needed by the
* constructor of <tt>MappingQ<3></tt>.
*
* For <tt>degree==2</tt> this function
* sets the
* @p laplace_on_hex_vector to
* the hardcoded data. For
* <tt>degree>2</tt> this vector is
* computed.
*
* For the definition of the
* @p laplace_on_hex_vector
* please refer to equation (8)
* of the `mapping' report.
*/
void set_laplace_on_hex_vector(Table<2,double> &lohvs) const;
/**
* Computes the
* <tt>laplace_on_quad(hex)_vector</tt>.
*
* Called by the
* <tt>set_laplace_on_quad(hex)_vector</tt>
* functions if the data is not
* yet hardcoded.
*
* For the definition of the
* <tt>laplace_on_quad(hex)_vector</tt>
* please refer to equation (8)
* of the `mapping' report.
*/
void compute_laplace_vector(Table<2,double> &lvs) const;
/**
* Takes a
* <tt>laplace_on_hex(quad)_vector</tt>
* and applies it to the vector
* @p a to compute the inner
* support points as a linear
* combination of the exterior
* points.
*
* The vector @p a initially
* contains the locations of the
* @p n_outer points, the
* @p n_inner computed inner
* points are appended.
*
* See equation (7) of the
* `mapping' report.
*/
void apply_laplace_vector(const Table<2,double> &lvs,
std::vector<Point<dim> > &a) const;
/**
* Computes the support points of
* the mapping.
*/
virtual void compute_mapping_support_points(
const typename Triangulation<dim,spacedim>::cell_iterator &cell,
std::vector<Point<dim> > &a) const;
/**
* Computes all support points of
* the mapping shape
* functions. The inner support
* points (ie. support points in
* quads for 2d, in hexes for 3d)
* are computed using the
* solution of a Laplace equation
* with the position of the outer
* support points as boundary
* values, in order to make the
* transformation as smooth as
* possible.
*/
void compute_support_points_laplace(
const typename Triangulation<dim,spacedim>::cell_iterator &cell,
std::vector<Point<dim> > &a) const;
/**
* Needed by the
* @p laplace_on_quad function
* (for <tt>dim==2</tt>). Filled by the
* constructor.
*
* Sizes:
* laplace_on_quad_vector.size()=
* number of inner
* unit_support_points
* laplace_on_quad_vector[i].size()=
* number of outer
* unit_support_points, i.e.
* unit_support_points on the
* boundary of the quad
*
* For the definition of this
* vector see equation (8) of the
* `mapping' report.
*/
Table<2,double> laplace_on_quad_vector;
/**
* Needed by the
* @p laplace_on_hex function
* (for <tt>dim==3</tt>). Filled by the
* constructor.
*
* For the definition of this
* vector see equation (8) of the
* `mapping' report.
*/
Table<2,double> laplace_on_hex_vector;
/**
* Exception.
*/
DeclException1 (ExcLaplaceVectorNotSet,
int,
<< "laplace_vector not set for degree=" << arg1 << ".");
/**
* Degree @p p of the
* polynomials used as shape
* functions for the Qp mapping
* of cells at the boundary.
*/
const unsigned int degree;
/**
* Number of inner mapping shape
* functions.
*/
const unsigned int n_inner;
/**
* Number of mapping shape
* functions on the boundary.
*/
const unsigned int n_outer;
/**
* Pointer to the
* @p dim-dimensional tensor
* product polynomials used as
* shape functions for the Qp
* mapping of cells at the
* boundary.
*/
const TensorProductPolynomials<dim> *tensor_pols;
/**
* Number of the Qp tensor
* product shape functions.
*/
const unsigned int n_shape_functions;
/**
* Mapping from lexicographic to
* to the Qp shape function
* numbering. Its size is
* @p dofs_per_cell.
*/
const std::vector<unsigned int> renumber;
/**
* If this flag is set @p true
* then @p MappingQ is used on
* all cells, not only on
* boundary cells.
*/
const bool use_mapping_q_on_all_cells;
/**
* An FE_Q object which is only needed in
* 3D, since it knows how to reorder shape
* functions/DoFs on non-standard
* faces. This is used to reorder support
* points in the same way. We could make
* this a pointer to prevent construction
* in 1D and 2D, but since memory and time
* requirements are not particularly high
* this seems unnecessary at the moment.
*/
const FE_Q<dim> feq;
};
/*@}*/
/* -------------- declaration of explicit specializations ------------- */
#ifndef DOXYGEN
template<> MappingQ<1>::MappingQ (const unsigned int,
const bool);
template<> MappingQ<1>::~MappingQ ();
template<> void MappingQ<1>::compute_shapes_virtual (
const std::vector<Point<1> > &unit_points,
MappingQ1<1>::InternalData &data) const;
template <> void MappingQ<1>::set_laplace_on_quad_vector(
Table<2,double> &) const;
template <> void MappingQ<3>::set_laplace_on_hex_vector(
Table<2,double> &lohvs) const;
template <> void MappingQ<1>::compute_laplace_vector(
Table<2,double> &) const;
template <> void MappingQ<1>::add_line_support_points (
const Triangulation<1>::cell_iterator &,
std::vector<Point<1> > &) const;
template<> void MappingQ<3>::add_quad_support_points(
const Triangulation<3>::cell_iterator &cell,
std::vector<Point<3> > &a) const;
#endif // DOXYGEN
DEAL_II_NAMESPACE_CLOSE
#endif
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