l2.h

// ---------------------------------------------------------------------
//
// Copyright (C) 2010 - 2017 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
{
  namespace L2
  {
    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;
                }
            }
        }
    }

    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;
                }
            }
        }
    }

    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);
    }

    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 n_components = input.size();

      AssertDimension(result.size(), n_dofs);
      AssertDimension(input.size(), fe.get_fe().n_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];
    }

    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());
      (void) n2_dofs;
      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