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;
 
double
ExactSolutionMWR_A::value(const Point<2>& r, const unsigned int component) const
{
  if (r.norm() < a) {
    return -0.25 * mu * J_f * (r[0] * r[0] + r[1] * r[1]) + A_0;
  } else {
    return -0.25 * mu_0 * J_f * a * a *
             log(exp(mu_r) * (r[0] * r[0] + r[1] * r[1]) / (a * a)) +
           A_0;
  }
}
 
Tensor<1, 2>
ExactSolutionMWR_A::gradient(const Point<2>& r,
                             const unsigned int component) const
{
  Point<2> grad_A;
 
  if (r.norm() <= a) {
    grad_A(0) = -0.5 * mu * J_f * r[0];
    grad_A(1) = -0.5 * mu * J_f * r[1];
  } else {
    grad_A(0) = -0.5 * mu_0 * J_f * a * a * r[0] / (r[0] * r[0] + r[1] * r[1]);
    grad_A(1) = -0.5 * mu_0 * J_f * a * a * r[1] / (r[0] * r[0] + r[1] * r[1]);
  }
 
  return grad_A;
}
 
void
ExactSolutionMWR_H::vector_value_list(const std::vector<Point<2>>& r,
                                      std::vector<Vector<double>>& values) const
{
  Assert(values.size() == r.size(),
         ExcDimensionMismatch(values.size(), r.size()));
 
  Tensor<1, 2> grad_A;
  double coef;
 
  for (unsigned int i = 0; i < r.size(); i++) {
    if (r[i].norm() < a) {
      coef = mu;
    } else {
      coef = mu_0;
    }
 
    grad_A = A.gradient(r[i]);
    values[i][0] = grad_A[1] / coef;
    values[i][1] = -grad_A[0] / coef;
  }
}
 
void
ExactSolutionMWR_B::vector_value_list(const std::vector<Point<2>>& r,
                                      std::vector<Vector<double>>& values) const
{
  Assert(values.size() == r.size(),
         ExcDimensionMismatch(values.size(), r.size()));
 
  Tensor<1, 2> grad_A;
 
  for (unsigned int i = 0; i < r.size(); i++) {
    grad_A = A.gradient(r[i]);
    values[i][0] = grad_A[1];
    values[i][1] = -grad_A[0];
  }
}
 
#pragma GCC diagnostic pop