# include <cstdlib>
# include <iostream>
# include <iomanip>
# include <fstream>
# include <ctime>
# include <cmath>

using namespace std;

//****************************************************************************80

void dirichlet_condition ( int node_num, double node_xy[], double node_bc[] )

//****************************************************************************80
//
//  Purpose:
//
//    DIRICHLET_CONDITION sets the value of a Dirichlet boundary condition.
//
//  Discussion:
//
//    The equation is 
//
//      -DEL H(X,Y) DEL U(X,Y) + K(X,Y) * U(X,Y) = F(X,Y)
//
//    This routine is set up for the L-shaped region, with exact solution
//    U = X**2 + Y**2.
//
//  Modified:
//
//    06 December 2010
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int NODE_NUM, the number of nodes.
//
//    Input, double NODE_XY[2*NODE_NUM], the coordinates of the points.
//
//    Output, double NODE_BC[NODE_NUM], the value of the 
//    Dirichlet boundary conditions at the points.
//
{
  int node;

  for ( node = 0; node < node_num; node++ )
  {
    node_bc[node] = pow ( node_xy[0+node*2], 2 )
                  + pow ( node_xy[1+node*2], 2 );
  }

  return;
}
//****************************************************************************80

void h_coef ( int node_num, double node_xy[], double node_h[] )

//****************************************************************************80
//
//  Purpose:
//
//    H_COEF evaluates the coefficient H(X,Y) of DEL U in the Poisson equation.
//
//  Discussion:
//
//    The equation is 
//
//      -DEL H(X,Y) DEL U(X,Y) + K(X,Y) * U(X,Y) = F(X,Y)
//
//  Modified:
//
//    06 December 2010
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int NODE_NUM, the number of nodes.
//
//    Input, double NODE_XY[2*NODE_NUM], the coordinates of the points.
//
//    Output, double NODE_H[NODE_NUM], the value of the 
//    K function at the points.
//
{
  int node;

  for ( node = 0; node < node_num; node++ )
  {
    node_h[node] = 1.0;
  }

  return;
}
//****************************************************************************80

void k_coef ( int node_num, double node_xy[], double node_k[] )

//****************************************************************************80
//
//  Purpose:
//
//    K_COEF evaluates the coefficient K(X,Y) of U in the Poisson equation.
//
//  Discussion:
//
//    The equation is 
//
//      -DEL H(X,Y) DEL U(X,Y) + K(X,Y) * U(X,Y) = F(X,Y)
//
//  Modified:
//
//    06 December 2010
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int NODE_NUM, the number of nodes.
//
//    Input, double NODE_XY[2*NODE_NUM], the coordinates of the points.
//
//    Output, double NODE_K[NODE_NUM], the value of the 
//    K function at the points.
//
{
  int node;

  for ( node = 0; node < node_num; node++ )
  {
    node_k[node] = 1.0;
  }

  return;
}
//****************************************************************************80

void rhs ( int node_num, double node_xy[], double node_rhs[] )

//****************************************************************************80
//
//  Purpose:
//
//    RHS gives the right-hand side of the differential equation.
//
//  Discussion:
//
//    The equation is 
//
//      -DEL H(X,Y) DEL U(X,Y) + K(X,Y) * U(X,Y) = F(X,Y)
//
//    This routine is set up for the L-shaped region, with exact solution
//    U = X**2 + Y**2.  Hence, the right hand side of the equation is
//    exactly -4 + X**2 + Y**2.
//
//  Modified:
//
//    15 July 2007
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int NODE_NUM, the number of nodes.
//
//    Input, double NODE_XY[2*NODE_NUM], the coordinates of the points.
//
//    Output, double NODE_RHS[NODE_NUM], the value of the 
//    right hand side function at the points.
//
{
  int node;

  for ( node = 0; node < node_num; node++ )
  {
    node_rhs[node] = -4.0 +
                   + pow ( node_xy[0+node*2], 2 )
                   + pow ( node_xy[1+node*2], 2 );
  }

  return;
}