TestCaseStefanPME.hpp

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// Class to provide various test cases (diffusion, exact solution, and their derivatives)
//
//
// Author: Jerome Droniou (jerome.droniou@monash.edu)
//
 
/*
*
*   This library was developed around HHO methods, although some parts of it have a more
* general purpose. If you use this code or part of it in a scientific publication, 
* please mention the following book as a reference for the underlying principles
* of HHO schemes:
*
* The Hybrid High-Order Method for Polytopal Meshes: Design, Analysis, and Applications.
* D. A. Di Pietro and J. Droniou. 2019, 516p. 
* url: https://hal.archives-ouvertes.fr/hal-02151813.
*
*/
 
 
#ifndef _TEST_CASE_STEFANPME_HPP
#define _TEST_CASE_STEFANPME_HPP
 
#include <functional>
#include <memory>
#include <string>
#include <vector>
 
#include <Eigen/Dense>
#include "TestCase.hpp"
 
//namespace HArDCore2D {        // Forward declaration
//  class Cell;
//}
 
using namespace HArDCore2D;
 
 
// ----------------------------------------------------------------------------
//                            Class definition
// ----------------------------------------------------------------------------
 
// @addtogroup TestCases
 
class TestCaseStefanPME {
 
public:
  TestCaseStefanPME(
    const std::vector<int> iTCS  
  );
 
    double sol(
        const double x,
        const double y
    );
 
    Eigen::Vector2d grad_sol(
        const double x,
        const double y,
        const Cell* cell            
    );
 
    Eigen::Matrix2d hess_sol(
        const double x,
        const double y,
        const Cell* cell            
    );
 
 
    Eigen::Matrix2d diff(
        const double x,
        const double y,
        const Cell* cell            
    );
 
    Eigen::Vector2d div_diff(
        const double x,
        const double y,
        const Cell* cell            
    );
 
    double source(
        const double x,
        const double y,
        const Cell* cell            
    );
 
    inline double get_lambda();
 
    void validate();
 
    inline size_t get_deg_diff();
 
  // Re-center and radial coordinates
  Eigen::Vector2d translate(double x, double y) const { return Eigen::Vector2d(x,y) - center;};
  double radial(const double x, const double y) const { return translate(x,y).norm();};
 
private:
  // Parameters: id of test case, pi
  const std::vector<int> m_iTCS;
    const double pi = acos(-1);
    const double sqrt2 = std::pow(2,0.5);
    const double gamma = 1.0/3.0;
    const double eps = 1e-5;        // constant for rotating diffusion case
 
    size_t _deg_diff;
  // Generic parameter (e.g. for changing anisotropy etc.)
  double _lambda;
 
  // For classical test cases (positive id solutions)
  TestCase m_tcase;
 
  // Parameter for compactly-supported solution
  const double rho = std::pow(0.3, 2);
  const Eigen::Vector2d center = Eigen::Vector2d(0.5, 0.5);
 
 
};
 
inline size_t TestCaseStefanPME::get_deg_diff() { return _deg_diff; };
inline double TestCaseStefanPME::get_lambda() { return _lambda; };
 
 
#endif //_TEST_CASE_STEFANPME_HPP