libdeal.ii-dev 8.4.2-2+b1 / usr / include / deal.II / integrators / l2.h

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// ---------------------------------------------------------------------
//
// Copyright (C) 2010 - 2015 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__integrators_l2_h
#define dealii__integrators_l2_h


#include <deal.II/base/config.h>
#include <deal.II/base/exceptions.h>
#include <deal.II/base/quadrature.h>
#include <deal.II/lac/full_matrix.h>
#include <deal.II/fe/mapping.h>
#include <deal.II/fe/fe_values.h>
#include <deal.II/meshworker/dof_info.h>

DEAL_II_NAMESPACE_OPEN

namespace LocalIntegrators
{
  /**
   * @brief Local integrators related to <i>L<sup>2</sup></i>-inner products.
   *
   * @ingroup Integrators
   * @author Guido Kanschat
   * @date 2010
   */
  namespace L2
  {
    /**
     * The mass matrix for scalar or vector values finite elements. \f[ \int_Z
     * uv\,dx \quad \text{or} \quad \int_Z \mathbf u\cdot \mathbf v\,dx \f]
     *
     * Likewise, this term can be used on faces, where it computes  the
     * integrals \f[ \int_F uv\,ds \quad \text{or} \quad \int_F \mathbf u\cdot
     * \mathbf v\,ds \f]
     *
     * @author Guido Kanschat
     * @date 2008, 2009, 2010
     */
    template <int dim>
    void mass_matrix (
      FullMatrix<double> &M,
      const FEValuesBase<dim> &fe,
      const double factor = 1.)
    {
      const unsigned int n_dofs = fe.dofs_per_cell;
      const unsigned int n_components = fe.get_fe().n_components();

      for (unsigned int k=0; k<fe.n_quadrature_points; ++k)
        {
          const double dx = fe.JxW(k) * factor;
          for (unsigned int i=0; i<n_dofs; ++i)
            {
              double Mii = 0.0;
              for (unsigned int d=0; d<n_components; ++d)
                Mii += dx
                       * fe.shape_value_component(i,k,d)
                       * fe.shape_value_component(i,k,d);

              M(i,i) += Mii;

              for (unsigned int j=i+1; j<n_dofs; ++j)
                {
                  double Mij = 0.0;
                  for (unsigned int d=0; d<n_components; ++d)
                    Mij += dx
                           * fe.shape_value_component(j,k,d)
                           * fe.shape_value_component(i,k,d);

                  M(i,j) += Mij;
                  M(j,i) += Mij;
                }
            }
        }
    }

    /**
     * The weighted mass matrix for scalar or vector values finite elements.
     * \f[ \int_Z \omega(x) uv\,dx \quad \text{or} \quad \int_Z \omega(x)
     * \mathbf u\cdot \mathbf v\,dx \f]
     *
     * Likewise, this term can be used on faces, where it computes  the
     * integrals \f[ \int_F \omega(x) uv\,ds \quad \text{or} \quad \int_F
     * \omega(x) \mathbf u\cdot \mathbf v\,ds \f]
     *
     * The size of the vector <tt>weights</tt> must be equal to the number of
     * quadrature points in the finite element.
     *
     * @author Guido Kanschat
     * @date 2014
     */
    template <int dim>
    void weighted_mass_matrix (
      FullMatrix<double> &M,
      const FEValuesBase<dim> &fe,
      const std::vector<double> weights)
    {
      const unsigned int n_dofs = fe.dofs_per_cell;
      const unsigned int n_components = fe.get_fe().n_components();
      AssertDimension(M.m(), n_dofs);
      AssertDimension(M.n(), n_dofs);
      AssertDimension(weights.size(), fe.n_quadrature_points);

      for (unsigned int k=0; k<fe.n_quadrature_points; ++k)
        {
          const double dx = fe.JxW(k) * weights[k];
          for (unsigned int i=0; i<n_dofs; ++i)
            {
              double Mii = 0.0;
              for (unsigned int d=0; d<n_components; ++d)
                Mii += dx
                       * fe.shape_value_component(i,k,d)
                       * fe.shape_value_component(i,k,d);

              M(i,i) += Mii;

              for (unsigned int j=i+1; j<n_dofs; ++j)
                {
                  double Mij = 0.0;
                  for (unsigned int d=0; d<n_components; ++d)
                    Mij += dx
                           * fe.shape_value_component(j,k,d)
                           * fe.shape_value_component(i,k,d);

                  M(i,j) += Mij;
                  M(j,i) += Mij;
                }
            }
        }
    }

    /**
     * <i>L<sup>2</sup></i>-inner product for scalar functions.
     *
     * \f[ \int_Z fv\,dx \quad \text{or} \quad \int_F fv\,ds \f]
     *
     * @author Guido Kanschat
     * @date 2008, 2009, 2010
     */
    template <int dim, typename number>
    void L2 (
      Vector<number> &result,
      const FEValuesBase<dim> &fe,
      const std::vector<double> &input,
      const double factor = 1.)
    {
      const unsigned int n_dofs = fe.dofs_per_cell;
      AssertDimension(result.size(), n_dofs);
      AssertDimension(fe.get_fe().n_components(), 1);
      AssertDimension(input.size(), fe.n_quadrature_points);

      for (unsigned int k=0; k<fe.n_quadrature_points; ++k)
        for (unsigned int i=0; i<n_dofs; ++i)
          result(i) += fe.JxW(k) * factor * input[k] * fe.shape_value(i,k);
    }

    /**
     * <i>L<sup>2</sup></i>-inner product for a slice of a vector valued right
     * hand side. \f[ \int_Z \mathbf f\cdot \mathbf v\,dx \quad \text{or}
     * \quad \int_F \mathbf f\cdot \mathbf v\,ds \f]
     *
     * @author Guido Kanschat
     * @date 2008, 2009, 2010
     */
    template <int dim, typename number>
    void L2 (
      Vector<number> &result,
      const FEValuesBase<dim> &fe,
      const VectorSlice<const std::vector<std::vector<double> > > &input,
      const double factor = 1.)
    {
      const unsigned int n_dofs = fe.dofs_per_cell;
      const unsigned int fe_components = fe.get_fe().n_components();
      const unsigned int n_components = input.size();

      AssertDimension(result.size(), n_dofs);
      AssertDimension(input.size(), fe_components);

      for (unsigned int k=0; k<fe.n_quadrature_points; ++k)
        for (unsigned int i=0; i<n_dofs; ++i)
          for (unsigned int d=0; d<n_components; ++d)
            result(i) += fe.JxW(k) * factor * fe.shape_value_component(i,k,d) * input[d][k];
    }

    /**
     * The jump matrix between two cells for scalar or vector values finite
     * elements. Note that the factor $\gamma$ can be used to implement
     * weighted jumps. \f[ \int_F [\gamma u][\gamma v]\,ds \quad \text{or}
     * \int_F [\gamma \mathbf u]\cdot [\gamma \mathbf v]\,ds \f]
     *
     * Using appropriate weights, this term can be used to penalize violation
     * of conformity in <i>H<sup>1</sup></i>.
     *
     * @author Guido Kanschat
     * @date 2008, 2009, 2010
     */
    template <int dim>
    void jump_matrix (
      FullMatrix<double> &M11,
      FullMatrix<double> &M12,
      FullMatrix<double> &M21,
      FullMatrix<double> &M22,
      const FEValuesBase<dim> &fe1,
      const FEValuesBase<dim> &fe2,
      const double factor1 = 1.,
      const double factor2 = 1.)
    {
      const unsigned int n1_dofs = fe1.dofs_per_cell;
      const unsigned int n2_dofs = fe2.dofs_per_cell;
      const unsigned int n_components = fe1.get_fe().n_components();

      Assert(n1_dofs == n2_dofs, ExcNotImplemented());
      AssertDimension(n_components, fe2.get_fe().n_components());
      AssertDimension(M11.m(), n1_dofs);
      AssertDimension(M12.m(), n1_dofs);
      AssertDimension(M21.m(), n2_dofs);
      AssertDimension(M22.m(), n2_dofs);
      AssertDimension(M11.n(), n1_dofs);
      AssertDimension(M12.n(), n2_dofs);
      AssertDimension(M21.n(), n1_dofs);
      AssertDimension(M22.n(), n2_dofs);

      for (unsigned int k=0; k<fe1.n_quadrature_points; ++k)
        {
          const double dx = fe1.JxW(k);

          for (unsigned int i=0; i<n1_dofs; ++i)
            for (unsigned int j=0; j<n1_dofs; ++j)
              for (unsigned int d=0; d<n_components; ++d)
                {
                  const double u1 = factor1*fe1.shape_value_component(j,k,d);
                  const double u2 =-factor2*fe2.shape_value_component(j,k,d);
                  const double v1 = factor1*fe1.shape_value_component(i,k,d);
                  const double v2 =-factor2*fe2.shape_value_component(i,k,d);

                  M11(i,j) += dx * u1*v1;
                  M12(i,j) += dx * u2*v1;
                  M21(i,j) += dx * u1*v2;
                  M22(i,j) += dx * u2*v2;
                }
        }
    }
  }
}

DEAL_II_NAMESPACE_CLOSE

#endif

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