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
ExactSolutionSCHAXI_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 (log(b) - log(sqrt(r.square()))) / (log(b) - log(a));
  }
 
  return 1.0;
}
 
template<>
Tensor<1, 2>
ExactSolutionSCHAXI_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 -1.0 / (log(b) - log(a)) * r / r.square();
  }
 
  return Point<2>();
}
 
template<>
double
ExactSolutionSCHAXI_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 (a * b / (b - a)) * (1 / sqrt(r.square()) - 1 / b);
  }
 
  return 1.0;
}
 
template<>
Tensor<1, 2>
ExactSolutionSCHAXI_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 -a * b / (b - a) * r / pow(sqrt(r.square()), 3);
  }
 
  return Point<2>();
}
 
#pragma GCC diagnostic pop