exact_solution.hpp

/******************************************************************************
 * Copyright (C) Siarhei Uzunbajakau, 2023.
 *
 * This program is free software. You can use, modify, and redistribute it under
 * the terms of the GNU Lesser General Public License as published by the Free
 * Software Foundation, either version 3 or (at your option) any later version.
 * This program is distributed without any warranty.
 *
 * Refer to COPYING.LESSER for more details.
 ******************************************************************************/
 
#ifndef ExactSolutionsMMSVTI_H__
#define ExactSolutionsMMSVTI_H__
 
#include "constants.hpp"
#include "settings.hpp"
#include <deal.II/base/function.h>
#include <deal.II/lac/vector.h>
 
#include <cmath>
 
using namespace dealii;
 
inline double
permeability(double x, double y, double mu_0)
{
  return mu_0 * (pow(x, 2) + pow(y, 2) + 1.0);
}
 
inline double
robin_gamma(double x, double y, double mu_0)
{
  return (sqrt(pow(x, 2) + pow(y, 2)) + 2.0) / permeability(x, y, mu_0);
}
 
inline Tensor<1, 3>
volume_free_current_density(double x, double y, double mu_0, double k)
{
  Tensor<1, 3> J;
  const double mu = permeability(x, y, mu_0);
 
  J[0] = (1 / mu) *
         ((mu_0 / mu) * (-2 * y * (cos(k * x) + cos(k * y))) - k * sin(k * y));
  J[1] = -(1 / mu) *
         ((mu_0 / mu) * (-2 * x * (cos(k * x) + cos(k * y))) - k * sin(k * x));
  J[2] = 0.0;
 
  return J;
}
 
inline Tensor<1, 3>
current_vector_potential(double x, double y, double mu_0, double k)
{
  Tensor<1, 3> T;
  const double mu = permeability(x, y, mu_0);
 
  T[0] = 0.0;
  T[1] = 0.0;
  T[2] = (cos(k * x) + cos(k * y)) / mu;
 
  return T;
}
 
inline Tensor<1, 3>
magnetic_vector_potential(double x, double y, double k)
{
  Tensor<1, 3> A;
 
  A[0] = -sin(k * y) / k;
  A[1] = sin(k * x) / k;
  A[2] = 0.0;
 
  return A;
}
 
inline Tensor<1, 3>
magnetic_field(double x, double y, double k)
{
  Tensor<1, 3> B;
 
  B[0] = 0.0;
  B[1] = 0.0;
  B[2] = (cos(k * x) + cos(k * y));
 
  return B;
}
 
class ExactSolutionMMSVTI_Jf
  : public Function<3>
  , public SettingsMMSVTI
{
public:
  ExactSolutionMMSVTI_Jf();
 
  virtual void vector_value_list(
    const std::vector<Point<3>>& r,
    std::vector<Vector<double>>& values) const override final;
};
 
class ExactSolutionMMSVTI_B
  : public Function<3>
  , public SettingsMMSVTI
{
public:
  ExactSolutionMMSVTI_B();
 
  virtual void vector_value_list(
    const std::vector<Point<3>>& r,
    std::vector<Vector<double>>& values) const override final;
};
 
class DirichletBC_MMSVTI_T
  : public Function<3>
  , public SettingsMMSVTI
{
public:
  DirichletBC_MMSVTI_T();
 
  virtual void vector_value_list(
    const std::vector<Point<3>>& r,
    std::vector<Vector<double>>& values) const override final;
};
 
class DirichletBC_MMSVTI_A
  : public Function<3>
  , public SettingsMMSVTI
{
public:
  DirichletBC_MMSVTI_A();
 
  virtual void vector_value_list(
    const std::vector<Point<3>>& r,
    std::vector<Vector<double>>& values) const override final;
};
 
#endif