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"
#include <cmath>
 
#pragma GCC diagnostic push
#pragma GCC diagnostic ignored "-Wunused-parameter"
 
using namespace dealii;
using namespace std;
 
template<>
double
ExactSolutionRHOAXI_PHI<true>::value(const Point<2>& p,
                                     const unsigned int component) const
{
  Point<2> r;
  r[0] = p[0];
  r[1] = 0.0;
 
  if (r.norm() <= a) {
    return rho * pow(a, 2) * (1.0 + 2.0 * log(b / a) - pow(r.norm() / a, 2)) /
           (4.0 * ep_0);
  } else {
    return rho * pow(a, 2) * log(b / r.norm()) / (2.0 * ep_0);
  }
 
  return 0.0;
}
 
template<>
Tensor<1, 2>
ExactSolutionRHOAXI_PHI<true>::gradient(const Point<2>& p,
                                        const unsigned int component) const
{
  Point<2> r;
  r[0] = p[0];
  r[1] = 0.0;
 
  if (r.norm() <= a) {
    return -rho * r / (2 * ep_0);
  } else {
    return -rho * pow(a, 2) * r / (2.0 * ep_0 * r.norm_square());
  }
 
  return Point<2>();
}
 
template<>
double
ExactSolutionRHOAXI_PHI<false>::value(const Point<2>& p,
                                      const unsigned int component) const
{
  Point<2> r;
  r[0] = p[0];
  r[1] = p[1];
 
  if (r.norm() <= a) {
    return rho *
           (pow(a, 2) + 2.0 * pow(a, 3) * (1.0 / a - 1.0 / b) -
            r.norm_square()) /
           (6.0 * ep_0);
  } else {
    return rho * pow(a, 3) * (1.0 / r.norm() - 1.0 / b) / (3.0 * ep_0);
  }
 
  return 0.0;
}
 
template<>
Tensor<1, 2>
ExactSolutionRHOAXI_PHI<false>::gradient(const Point<2>& p,
                                         const unsigned int component) const
{
  Point<2> r;
  r[0] = p[0];
  r[1] = p[1];
 
  if (r.norm() < a) {
    return -rho * r / (3.0 * ep_0);
  } else {
    return -rho * pow(a, 3) * r / (3.0 * ep_0 * pow(r.norm(), 3));
  }
 
  return Point<2>();
}
 
#pragma GCC diagnostic pop