// abc.java  User problem definitions for a specific PDE to be solved   
//           this includes the user choice of degree and discretization 
//                                                                   
//        The problem must be well posed and the solution must be    
//        continuous and continuously differentiable                 
//                                                                   
// The general PDE to be solved is:                                  
//  a1(x,y)*uxx(x,y) + b1(x,y)*uxy(x,y) + c1(x,y)*uyy(x,y) +         
//  d1(x,y)*ux(x,y) + e1(x,y)*uy(x,y) + f1(x,y)*u(x,y) = c(x,y)      
//                                                                   

class abc
{
  // number of points for descretization, must be odd and > 1          
  int nd = 5;

  // Define the region for the solution:                               
  // xmin <= x <= xmax, ymin <= y <= ymax  using  nx by ny points      

  double xmin = -1.0;
  double xmax =  1.0;
  double ymin = -1.0;
  double ymax =  1.0;
  int nx =      7;
  int ny =      7;
  int ifcheck = 5;

  // the user must provide all functions, even if only  return 0.0; 
  // the functions are implemented here               
  // A specific set of test functions is covered in abc.txt         

  abc() // nothing to do, just providing functions
  {
  }
 
  double a1(double x, double y)
  {
    return Math.exp(x/2.0)*Math.exp(y)/2.0;
  }

  double b1(double x, double y)
  {
    return 0.7/(x*x*y*y+0.5);
  }

  double c1(double x, double y)
  {
    return (4.0 - Math.exp(x) - Math.exp(y/2.0))*2.0;
  }

  double d1(double x, double y)
  {
    return x*x+y;
  }

  double e1(double x, double y)
  {
    return x*y*y;
  }

  double f1(double x, double y)
  {
    return 3.0*x + 2.0*y;
  }

  // must compute boundary.
  // If solution for checking, then compute all values 
  // and set  ifcheck = 1 to 5, else ifcheck = 0       
  double u(double x, double y)
  {
    return x*x*x + 2.0*y*y*y + 3.0*x*x*y + 4.0*x*y*y + 5.0*x*y +
           6.0*x + 7.0*y + 8.0;
  }

  // RHS, this becomes defined by u and a1 ... f1  
  double c(double x, double y)
  {
    return 0.5*Math.exp(x/2.0)*Math.exp(y)*(6.0*x+6.0*y)             +
      0.7*(6.0*x + 8.0*y + 5.0)/(x*x*y*y+0.5)              +
      (8.0 - 2.0*Math.exp(x) - 2.0*Math.exp(y/2.0))*(12.0*y + 8.0*x) +
      (x*x+y)*(3.0*x*x + 6.0*x*y + 4.0*y*y + 5.0*y + 6.0)  +
      x*y*y*(6.0*y*y + 3.0*x*x + 8.0*x*y + 5.0*x +7.0)     +
      (3.0*x + 2.0*y)*(x*x*x + 2.0*y*y*y + 3.0*x*x*y + 4.0*x*y*y + 5.0*x*y +
      6.0*x + 7.0*y + 8.0);
  }

} // end class abc