allen_cahn/polynomial.h

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/**********************************************************************
 *  Copyright (C) 2011 - 2014 by the authors
 *  Distributed under the MIT License
 *
 * See the files AUTHORS and LICENSE in the project root directory
 *
 **********************************************************************/

#ifndef __allen_cahn_polynomial_h
#define __allen_cahn_polynomial_h

#include <amandus/integrator.h>
#include <deal.II/base/polynomial.h>
#include <deal.II/base/tensor.h>
#include <deal.II/integrators/divergence.h>
#include <deal.II/integrators/l2.h>
#include <deal.II/integrators/laplace.h>

namespace AllenCahn
{
using namespace dealii;
using namespace LocalIntegrators;
using namespace MeshWorker;

template <int dim>
class PolynomialResidual : public AmandusIntegrator<dim>
{
public:
  PolynomialResidual(double diffusion, const Polynomials::Polynomial<double> solution_1d);

  virtual void cell(DoFInfo<dim>& dinfo, IntegrationInfo<dim>& info) const;
  virtual void boundary(DoFInfo<dim>& dinfo, IntegrationInfo<dim>& info) const;
  virtual void face(DoFInfo<dim>& dinfo1, DoFInfo<dim>& dinfo2, IntegrationInfo<dim>& info1,
                    IntegrationInfo<dim>& info2) const;

private:
  double D;
  Polynomials::Polynomial<double> solution_1d;
};

template <int dim>
class PolynomialError : public AmandusIntegrator<dim>
{
public:
  PolynomialError(const Polynomials::Polynomial<double> solution_1d);

  virtual void cell(DoFInfo<dim>& dinfo, IntegrationInfo<dim>& info) const;
  virtual void boundary(DoFInfo<dim>& dinfo, IntegrationInfo<dim>& info) const;
  virtual void face(DoFInfo<dim>& dinfo1, DoFInfo<dim>& dinfo2, IntegrationInfo<dim>& info1,
                    IntegrationInfo<dim>& info2) const;

private:
  Polynomials::Polynomial<double> solution_1d;
};

//----------------------------------------------------------------------//

template <int dim>
PolynomialResidual<dim>::PolynomialResidual(double diffusion,
                                            const Polynomials::Polynomial<double> solution_1d)
  : D(diffusion)
  , solution_1d(solution_1d)
{
  this->use_boundary = false;
  this->use_face = true;
  this->input_vector_names.push_back("Newton iterate");
}

template <int dim>
void
PolynomialResidual<dim>::cell(DoFInfo<dim>& dinfo, IntegrationInfo<dim>& info) const
{
  Assert(info.values.size() >= 1, ExcDimensionMismatch(info.values.size(), 1));
  Assert(info.gradients.size() >= 1, ExcDimensionMismatch(info.values.size(), 1));

  std::vector<double> rhs(info.fe_values(0).n_quadrature_points, 0.);

  std::vector<double> px(3);
  std::vector<double> py(3);
  for (unsigned int k = 0; k < info.fe_values(0).n_quadrature_points; ++k)
  {
    const double x = info.fe_values(0).quadrature_point(k)(0);
    const double y = info.fe_values(0).quadrature_point(k)(1);
    solution_1d.value(x, px);
    solution_1d.value(y, py);

    // negative Laplacian
    rhs[k] = D * px[2] * py[0] + D * px[0] * py[2];
    // nonlinearity of true solution
    rhs[k] -= px[0] * py[0] * (px[0] * py[0] * px[0] * py[0] - 1.);

    const double u = info.values[0][0][k];
    rhs[k] += u * (u * u - 1.);
  }

  L2::L2(dinfo.vector(0).block(0), info.fe_values(0), rhs);
  Laplace::cell_residual(dinfo.vector(0).block(0), info.fe_values(0), info.gradients[0][0], D);
}

template <int dim>
void
PolynomialResidual<dim>::boundary(DoFInfo<dim>& dinfo, IntegrationInfo<dim>& info) const
{
  std::vector<double> null(info.fe_values(0).n_quadrature_points, 0.);

  const unsigned int deg = info.fe_values(0).get_fe().tensor_degree();
  Laplace::nitsche_residual(dinfo.vector(0).block(0),
                            info.fe_values(0),
                            info.values[0][0],
                            info.gradients[0][0],
                            null,
                            Laplace::compute_penalty(dinfo, dinfo, deg, deg),
                            D);
}

template <int dim>
void
PolynomialResidual<dim>::face(DoFInfo<dim>& dinfo1, DoFInfo<dim>& dinfo2,
                              IntegrationInfo<dim>& info1, IntegrationInfo<dim>& info2) const
{
  const unsigned int deg = info1.fe_values(0).get_fe().tensor_degree();
  Laplace::ip_residual(dinfo1.vector(0).block(0),
                       dinfo2.vector(0).block(0),
                       info1.fe_values(0),
                       info2.fe_values(0),
                       info1.values[0][0],
                       info1.gradients[0][0],
                       info2.values[0][0],
                       info2.gradients[0][0],
                       Laplace::compute_penalty(dinfo1, dinfo2, deg, deg),
                       D);
}

//----------------------------------------------------------------------//

template <int dim>
PolynomialError<dim>::PolynomialError(const Polynomials::Polynomial<double> solution_1d)
  : solution_1d(solution_1d)
{
  this->use_boundary = false;
  this->use_face = false;
}

template <int dim>
void
PolynomialError<dim>::cell(DoFInfo<dim>& dinfo, IntegrationInfo<dim>& info) const
{
  //  Assert(dinfo.n_values() >= 4, ExcDimensionMismatch(dinfo.n_values(), 4));

  std::vector<double> px(2);
  std::vector<double> py(2);
  for (unsigned int k = 0; k < info.fe_values(0).n_quadrature_points; ++k)
  {
    const double x = info.fe_values(0).quadrature_point(k)(0);
    const double y = info.fe_values(0).quadrature_point(k)(1);
    solution_1d.value(x, px);
    solution_1d.value(y, py);
    const double dx = info.fe_values(0).JxW(k);

    Tensor<1, dim> Du = info.gradients[0][0][k];
    Du[0] -= px[1] * py[0];
    Du[1] -= px[0] * py[1];
    double u = info.values[0][0][k];
    u -= px[0] * py[0];
    unsigned int i = 0;
    // 0. L^2(u)
    dinfo.value(i++) += u * u * dx;
    // 1. H^1(u)
    dinfo.value(i++) += (Du * Du) * dx;
  }
}

template <int dim>
void
PolynomialError<dim>::boundary(DoFInfo<dim>&, IntegrationInfo<dim>&) const
{
}

template <int dim>
void
PolynomialError<dim>::face(DoFInfo<dim>&, DoFInfo<dim>&, IntegrationInfo<dim>&,
                           IntegrationInfo<dim>&) const
{
}
}

#endif