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<>
ExactSolutionSLDII_THETA<2>::ExactSolutionSLDII_THETA()
  : Function<2>()
  , SettingsSLDII()
{
  double mur = mur_2;
  double a2 = std::pow(a, 2.0);
  double b2 = std::pow(b, 2.0);
 
  OMEGA = ((mur - 1.0) / (mur + 1.0)) * (a2 / b2);
  gamma_1 = (-2.0 * b2 * H_0 * OMEGA) / ((mur + 1.0) - (mur - 1.0) * OMEGA);
  beta_1 = (mur + 1.0) * gamma_1 / ((mur - 1.0) * a2);
  alpha_1 = -b2 * H_0 + mur * gamma_1 - mur * b2 * beta_1;
  delta_1 = (mur * a2 * beta_1 - mur * gamma_1) / a2;
}
 
template<>
double
ExactSolutionSLDII_THETA<2>::value(const Point<2>& r,
                                   unsigned int component) const
{
  double rn = r.norm();
  double r2 = std::pow(rn, 2.0);
 
  if (rn < a)
    return delta_1 * r[0] + H_0 * r[0];
 
  if (rn > b)
    return (-H_0 + alpha_1 / r2) * r[0] + H_0 * r[0];
 
  return (beta_1 + gamma_1 / r2) * r[0] + H_0 * r[0];
}
 
template<>
Tensor<1, 2>
ExactSolutionSLDII_THETA<2>::gradient(const Point<2>& r,
                                      unsigned int component) const
{
  double rn = r.norm();
  double r2 = std::pow(rn, 2.0);
  double xx = -2.0 * r[0] * r[0] / std::pow(rn, 4.0);
  double xy = -2.0 * r[0] * r[1] / std::pow(rn, 4.0);
 
  Point<2> grad_phi;
 
  if (rn < a) {
    grad_phi[0] = delta_1 + H_0;
    grad_phi[1] = 0.0;
    return grad_phi;
  }
 
  if (rn > b) {
    grad_phi[0] = -H_0 + alpha_1 / r2 + alpha_1 * xx + H_0;
    grad_phi[1] = alpha_1 * xy;
    return grad_phi;
  }
 
  grad_phi[0] = beta_1 + gamma_1 / r2 + gamma_1 * xx + H_0;
  grad_phi[1] = gamma_1 * xy;
  return grad_phi;
}
 
template<>
ExactSolutionSLDII_THETA<3>::ExactSolutionSLDII_THETA()
  : Function<3>()
  , SettingsSLDII()
{
  double mur = mur_2;
  double a3 = std::pow(a, 3.0);
  double b3 = std::pow(b, 3.0);
 
  OMEGA = ((mur - 1.0) / (mur + 2.0)) * (a3 / b3);
  gamma_1 =
    (-3.0 * b3 * H_0 * OMEGA) / ((2.0 * mur + 1.0) - 2.0 * (mur - 1.0) * OMEGA);
  beta_1 = ((2.0 * mur + 1.0) * gamma_1) / ((mur - 1.0) * a3);
  alpha_1 = (-b3 * H_0 + 2.0 * mur * gamma_1 - mur * b3 * beta_1) / 2.0;
  delta_1 = (mur * a3 * beta_1 - 2.0 * mur * gamma_1) / a3;
}
 
template<>
double
ExactSolutionSLDII_THETA<3>::value(const Point<3>& r,
                                   unsigned int componet) const
{
  double rn = r.norm();
  double r3 = std::pow(rn, 3.0);
 
  if (rn < a)
    return delta_1 * r[2] + H_0 * r[2];
 
  if (rn > b)
    return (-H_0 + alpha_1 / r3) * r[2] + H_0 * r[2];
 
  return (beta_1 + gamma_1 / r3) * r[2] + H_0 * r[2];
}
 
template<>
Tensor<1, 3>
ExactSolutionSLDII_THETA<3>::gradient(const Point<3>& r,
                                      unsigned int component) const
{
  double rn = r.norm();
  double r3 = std::pow(rn, 3.0);
  double zz = -3.0 * r[2] * r[2] / std::pow(rn, 5.0);
  double xz = -3.0 * r[0] * r[2] / std::pow(rn, 5.0);
  double yz = -3.0 * r[1] * r[2] / std::pow(rn, 5.0);
 
  Point<3> grad_phi;
 
  if (rn < a) {
    grad_phi[0] = 0.0;
    grad_phi[1] = 0.0;
    grad_phi[2] = delta_1 + H_0;
    return grad_phi;
  }
 
  if (rn > b) {
    grad_phi[0] = alpha_1 * xz;
    grad_phi[1] = alpha_1 * yz;
    grad_phi[2] = -H_0 + alpha_1 / r3 + alpha_1 * zz + H_0;
    return grad_phi;
  }
 
  grad_phi[0] = gamma_1 * xz;
  grad_phi[1] = gamma_1 * yz;
  grad_phi[2] = beta_1 + gamma_1 / r3 + gamma_1 * zz + H_0;
  return grad_phi;
}
 
#pragma GCC diagnostic pop