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<>
ExactSolutionFLCAXI_PHI<true>::ExactSolutionFLCAXI_PHI()
{
  alpha = 1.0 / (ep_1 * log(b / d_2) + ep_2 * log(d_1 / a));
  beta = (ep_1 / ep_2) * log(b / d_2);
  phi_d = alpha * ep_1 * log(b / d_2);
}
 
template<>
double
ExactSolutionFLCAXI_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() < d_1)
    return (-alpha * ep_2 * (log(r.norm() / d_1) - beta));
 
  if (r.norm() > d_2)
    return (-alpha * ep_1 * (log(r.norm() / b)));
 
  return phi_d;
}
 
template<>
Tensor<1, 2>
ExactSolutionFLCAXI_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() < d_1)
    return -alpha * ep_2 * (1 / r.square()) * r;
 
  if (r.norm() > d_2)
    return -alpha * ep_1 * (1 / r.square()) * r;
 
  return Point<2>();
}
 
template<>
ExactSolutionFLCAXI_PHI<false>::ExactSolutionFLCAXI_PHI()
{
  alpha = 1.0 / (ep_1 * (1.0 / b - 1.0 / d_2) + ep_2 * (1.0 / d_1 - 1.0 / a));
  beta = 1.0 / d_1 + (ep_1 / ep_2) * (1.0 / b - 1.0 / d_2);
  phi_d = alpha * ep_1 * (1.0 / b - 1.0 / d_2);
}
 
template<>
double
ExactSolutionFLCAXI_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() < d_1)
    return (-alpha * ep_2 * (1.0 / r.norm() - beta));
 
  if (r.norm() > d_2)
    return (-alpha * ep_1 * (1.0 / r.norm() - 1.0 / b));
 
  return phi_d;
}
 
template<>
Tensor<1, 2>
ExactSolutionFLCAXI_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() < d_1)
    return alpha * ep_2 * r / pow(r.norm(), 3);
 
  if (r.norm() > d_2)
    return alpha * ep_1 * r / pow(r.norm(), 3);
 
  return Point<2>();
}
 
#pragma GCC diagnostic pop