libdeal.ii-dev 8.1.0-4 / usr / include / deal.II / fe / mapping_q1_eulerian.h

// ---------------------------------------------------------------------
// $Id: mapping_q1_eulerian.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_q1_eulerian_h
#define __deal2__mapping_q1_eulerian_h

#include <deal.II/base/config.h>
#include <deal.II/base/smartpointer.h>
#include <deal.II/fe/mapping_q1.h>

DEAL_II_NAMESPACE_OPEN

/*!@addtogroup mapping */
/*@{*/

/**
 * Eulerian mapping of general unit cells by d-linear shape
 * functions. Each cell is thus shifted in space by values given to
 * the mapping through a finite element field.
 *
 * <h3>Usage</h3>
 *
 * The constructor of this class takes two arguments: a reference to
 * the vector that defines the mapping from the reference
 * configuration to the current configuration and a reference to the
 * DoFHandler. The vector should then represent a (flattened out
 * version of a) vector valued field defined at nodes defined by the
 * the DoFHandler, where the number of components of the vector
 * field equals the number of space dimensions. Thus, the
 * DoFHandler shall operate on a finite element that has as many
 * components as space dimensions. As an additional requirement, we
 * impose that it have as many degree of freedom per vertex as there
 * are space dimensions; since this object only evaluates the finite
 * element field at the vertices, the values
 * of all other degrees of freedom (not associated to vertices) are
 * ignored. These requirements are met if the finite element which the
 * given DoFHandler operates on is constructed as a system
 * element (FESystem) from @p dim continuous FE_Q()
 * objects.
 *
 * In many cases, the shift vector will also be the solution vector of
 * the problem under investigation. If this is not the case (i.e. the
 * number of components of the solution variable is not equal to the
 * space dimension, e.g. for scalar problems in <tt>dim>1</tt> where the
 * Eulerian coordinates only give a background field) or for coupled
 * problems where more variables are computed than just the flow
 * field), then a different DoFHandler has to be set up on the
 * given triangulation, and the shift vector has then to be associated
 * to it.
 *
 * An example is shown below:
 * @code
 *    FESystem<dim> fe(FE_Q<dim>(1), dim);
 *    DoFHandler<dim> flowfield_dof_handler(triangulation);
 *    flowfield_dof_handler.distribute_dofs(fe);
 *    Vector<double> map_points(flowfield_dof_handler.n_dofs());
 *    MappingQ1Eulerian<dim> mymapping(map_points, flowfield_dof_handler);
 * @endcode
 *
 * Note that since the vector of shift values and the dof handler are
 * only associated to this object at construction time, you have to
 * make sure that whenever you use this object, the given objects
 * still represent valid data.
 *
 * To enable the use of the MappingQ1Eulerian class also in the context
 * of parallel codes using the PETSc wrapper classes, the type of
 * the vector can be specified as template parameter <tt>EulerVectorType</tt>
 * Not specifying this template argument in applications using the PETSc
 * vector classes leads to the construction of a copy of the vector
 * which is not acccessible afterwards!
 *
 * For more information about the <tt>spacedim</tt> template parameter
 * check the documentation of FiniteElement or the one of
 * Triangulation.
 *
 * @author Michael Stadler, 2001
 */
template <int dim, class VECTOR = Vector<double>, int spacedim=dim >
class MappingQ1Eulerian : public MappingQ1<dim,spacedim>
{
public:

  /**
   * Constructor. It takes a
   * <tt>Vector<double> &</tt> as its
   * first argument to specify the
   * transformation of the whole
   * problem from the reference to
   * the current configuration.
   * The organization of the
   * elements in the @p Vector
   * must follow the concept how
   * deal.II stores solutions that
   * are associated to a
   * triangulation.  This is
   * automatically the case if the
   * @p Vector represents the
   * solution of the previous step
   * of a nonlinear problem.
   * Alternatively, the @p Vector
   * can be initialized by
   * <tt>DoFAccessor::set_dof_values()</tt>.
   */
  MappingQ1Eulerian (const VECTOR  &euler_transform_vectors,
                     const DoFHandler<dim,spacedim> &shiftmap_dof_handler);

  /**
   * 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 false because
   * MappingQ1Eulerian does not in general
   * preserve vertex locations (unless the
   * translation vector happens to provide
   * for zero displacements at vertex
   * locations).
   */
  bool preserves_vertex_locations () const;

  /**
   * Exception.
   */
  DeclException0 (ExcInactiveCell);



protected:
  /**
   * Implementation of the interface in
   * MappingQ1. Overrides the function in
   * the base class, since we cannot use
   * any cell similarity for this class.
   */
  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<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> >                             &cell_normal_vectors,
                  CellSimilarity::Similarity                           &cell_similarity) const;

  /**
   * Reference to the vector of
   * shifts.
   */
  SmartPointer<const VECTOR, MappingQ1Eulerian<dim,VECTOR,spacedim> > euler_transform_vectors;

  /**
   * Pointer to the DoFHandler to
   * which the mapping vector is
   * associated.
   */
  SmartPointer<const DoFHandler<dim,spacedim>,MappingQ1Eulerian<dim,VECTOR,spacedim> > shiftmap_dof_handler;


private:
  /**
   * Computes the support points of
   * the mapping. For
   * @p MappingQ1Eulerian these
   * are the vertices.
   */
  virtual void compute_mapping_support_points(
    const typename Triangulation<dim,spacedim>::cell_iterator &cell,
    std::vector<Point<spacedim> > &a) const;

};

/*@}*/

/*----------------------------------------------------------------------*/

#ifndef DOXYGEN

template <int dim, class VECTOR, int spacedim>
inline
bool
MappingQ1Eulerian<dim,VECTOR,spacedim>::preserves_vertex_locations () const
{
  return false;
}

#endif // DOXYGEN

DEAL_II_NAMESPACE_CLOSE

#endif