exact_solution.cpp

/******************************************************************************
 * 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.
 ******************************************************************************/
 
#include "exact_solution.hpp"
 
#pragma GCC diagnostic push
#pragma GCC diagnostic ignored "-Wunused-parameter"
 
using namespace dealii;
using namespace std;
 
template<>
double
ExactSolutionRHO_PHI<2>::value(const Point<2>& r,
                               const unsigned int component) const
{
 
  if (r.norm() <= a) {
    return rho_0 * pow(a, 2) * (1.0 + 2.0 * log(b / a) - pow(r.norm() / a, 2)) /
           (4.0 * ep_0);
  } else {
    return rho_0 * pow(a, 2) * log(b / r.norm()) / (2.0 * ep_0);
  }
 
  return 0.0;
}
 
template<>
Tensor<1, 2>
ExactSolutionRHO_PHI<2>::gradient(const Point<2>& r,
                                  const unsigned int component) const
{
 
  if (r.norm() <= a) {
    return -rho_0 * r / (2 * ep_0);
  } else {
    return -rho_0 * pow(a, 2) * r / (2.0 * ep_0 * r.norm_square());
  }
 
  return Point<2>();
}
 
template<>
double
ExactSolutionRHO_PHI<3>::value(const Point<3>& r,
                               const unsigned int component) const
{
  if (r.norm() <= a) {
    return rho_0 *
           (pow(a, 2) + 2.0 * pow(a, 3) * (1.0 / a - 1.0 / b) -
            r.norm_square()) /
           (6.0 * ep_0);
  } else {
    return rho_0 * pow(a, 3) * (1.0 / r.norm() - 1.0 / b) / (3.0 * ep_0);
  }
  return 0.0;
}
 
template<>
Tensor<1, 3>
ExactSolutionRHO_PHI<3>::gradient(const Point<3>& r,
                                  const unsigned int component) const
{
  if (r.norm() < a) {
    return -rho_0 * r / (3.0 * ep_0);
  } else {
    return -rho_0 * pow(a, 3) * r / (3.0 * ep_0 * pow(r.norm(), 3));
  }
 
  return Point<3>();
}
 
#pragma GCC diagnostic pop