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

// ---------------------------------------------------------------------
// $Id: fe_dg_vector.h 30036 2013-07-18 16:55:32Z maier $
//
// Copyright (C) 2010 - 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__fe_dg_vector_h
#define __deal2__fe_dg_vector_h

#include <deal.II/base/config.h>
#include <deal.II/base/table.h>
#include <deal.II/base/polynomials_raviart_thomas.h>
#include <deal.II/base/polynomials_nedelec.h>
#include <deal.II/base/polynomials_bdm.h>
#include <deal.II/base/polynomial.h>
#include <deal.II/base/tensor_product_polynomials.h>
#include <deal.II/base/geometry_info.h>
#include <deal.II/fe/fe.h>
#include <deal.II/fe/fe_poly_tensor.h>

#include <vector>

DEAL_II_NAMESPACE_OPEN

template <int dim, int spacedim> class MappingQ;


/**
 * DG elements based on vector valued polynomials.
 *
 * These elements use vector valued polynomial spaces as they have
 * been introduced for H<sup>div</sup> and H<sup>curl</sup> conforming
 * finite elements, but do not use the usual continuity of these
 * elements. Thus, they are suitable for DG and hybrid formulations
 * involving these function spaces.
 *
 * The template argument <tt>POLY</tt> refers to a vector valued
 * polynomial space like PolynomialsRaviartThomas or
 * PolynomialsNedelec. Note that the dimension of the polynomial space
 * and the argument <tt>dim</tt> must coincide.
 *
 * @ingroup febase
 * @author Guido Kanschat
 * @date 2010
 */
template <class POLY, int dim, int spacedim=dim>
class FE_DGVector
  :
  public FE_PolyTensor<POLY, dim, spacedim>
{
public:
  /**
   * Constructor for the vector
   * element of degree @p p.
   */
  FE_DGVector (const unsigned int p, MappingType m);
public:

  FiniteElement<dim, spacedim> *clone() const;

  /**
   * Return a string that uniquely
   * identifies a finite
   * element. This class returns
   * <tt>FE_RaviartThomas<dim>(degree)</tt>, with
   * @p dim and @p degree
   * replaced by appropriate
   * values.
   */
  virtual std::string get_name () const;


  /**
   * Check whether a shape function
   * may be non-zero on a face.
   *
   * Returns always
   * @p true.
   */
  virtual bool has_support_on_face (const unsigned int shape_index,
                                    const unsigned int face_index) const;

  virtual void interpolate(std::vector<double>                &local_dofs,
                           const std::vector<double> &values) const;
  virtual void interpolate(std::vector<double>                &local_dofs,
                           const std::vector<Vector<double> > &values,
                           unsigned int offset = 0) const;
  virtual void interpolate(
    std::vector<double> &local_dofs,
    const VectorSlice<const std::vector<std::vector<double> > > &values) const;
  virtual std::size_t memory_consumption () const;

private:
  /**
   * Only for internal use. Its
   * full name is
   * @p get_dofs_per_object_vector
   * function and it creates the
   * @p dofs_per_object vector that is
   * needed within the constructor to
   * be passed to the constructor of
   * @p FiniteElementData.
   */
  static std::vector<unsigned int>
  get_dpo_vector (const unsigned int degree);

  /**
   * Initialize the @p
   * generalized_support_points
   * field of the FiniteElement
   * class and fill the tables with
   * @p interior_weights. Called
   * from the constructor.
  *
  * See the @ref GlossGeneralizedSupport "glossary entry on generalized support points"
  * for more information.
   */
  void initialize_support_points (const unsigned int degree);

  /**
   * Initialize the interpolation
   * from functions on refined mesh
   * cells onto the father
   * cell. According to the
   * philosophy of the
   * Raviart-Thomas element, this
   * restriction operator preserves
   * the divergence of a function
   * weakly.
   */
  void initialize_restriction ();

  /**
   * Fields of cell-independent data.
   *
   * For information about the
   * general purpose of this class,
   * see the documentation of the
   * base class.
   */
  class InternalData : public FiniteElement<dim>::InternalDataBase
  {
  public:
    /**
     * Array with shape function
     * values in quadrature
     * points. There is one row
     * for each shape function,
     * containing values for each
     * quadrature point. Since
     * the shape functions are
     * vector-valued (with as
     * many components as there
     * are space dimensions), the
     * value is a tensor.
     *
     * In this array, we store
     * the values of the shape
     * function in the quadrature
     * points on the unit
     * cell. The transformation
     * to the real space cell is
     * then simply done by
     * multiplication with the
     * Jacobian of the mapping.
     */
    std::vector<std::vector<Tensor<1,dim> > > shape_values;

    /**
     * Array with shape function
     * gradients in quadrature
     * points. There is one
     * row for each shape
     * function, containing
     * values for each quadrature
     * point.
     *
     * We store the gradients in
     * the quadrature points on
     * the unit cell. We then
     * only have to apply the
     * transformation (which is a
     * matrix-vector
     * multiplication) when
     * visiting an actual cell.
     */
    std::vector<std::vector<Tensor<2,dim> > > shape_gradients;
  };
  Table<3, double> interior_weights;
};



/**
 * A vector-valued DG element based on the polynomials space of FE_Nedelec.
 *
 * @ingroup fe
 * @author Guido Kanschat
 * @date 2011
 */
template <int dim, int spacedim=dim>
class FE_DGNedelec : public FE_DGVector<PolynomialsNedelec<dim>, dim, spacedim>
{
public:
  /**
   * Constructor for the discontinuous N&eacute;d&eacute;lec
   * element of degree @p p.
   */
  FE_DGNedelec (const unsigned int p);

  /**
   * Return a string that uniquely
   * identifies a finite
   * element. This class returns
   * <tt>FE_DGNedelec<dim>(degree)</tt>, with
   * @p dim and @p degree
   * replaced by appropriate
   * values.
   */
  virtual std::string get_name () const;
};



/**
 * A vector-valued DG element based on the polynomials space of FE_RaviartThomas.
 *
 * @ingroup fe
 * @author Guido Kanschat
 * @date 2011
 */
template <int dim, int spacedim=dim>
class FE_DGRaviartThomas : public FE_DGVector<PolynomialsRaviartThomas<dim>, dim, spacedim>
{
public:
  /**
   * Constructor for the Raviart-Thomas
   * element of degree @p p.
   */
  FE_DGRaviartThomas (const unsigned int p);

  /**
   * Return a string that uniquely
   * identifies a finite
   * element. This class returns
   * <tt>FE_DGRaviartThomas<dim>(degree)</tt>, with
   * @p dim and @p degree
   * replaced by appropriate
   * values.
   */
  virtual std::string get_name () const;
};



/**
 * A vector-valued DG element based on the polynomials space of FE_BDM.
 *
 * @ingroup fe
 * @author Guido Kanschat
 * @date 2011
 */
template <int dim, int spacedim=dim>
class FE_DGBDM : public FE_DGVector<PolynomialsBDM<dim>, dim, spacedim>
{
public:
  /**
   * Constructor for the discontinuous BDM
   * element of degree @p p.
   */
  FE_DGBDM (const unsigned int p);

  /**
   * Return a string that uniquely
   * identifies a finite
   * element. This class returns
   * <tt>FE_DGBDM<dim>(degree)</tt>, with
   * @p dim and @p degree
   * replaced by appropriate
   * values.
   */
  virtual std::string get_name () const;
};


DEAL_II_NAMESPACE_CLOSE

#endif