exact_solution.C File Reference

Go to the source code of this file.

Functions
Real	exact_solution (const int component, const Real x, const Real y, const Real z=0.)
	This is the exact solution that we are trying to obtain.
Real	forcing_function (const int component, const Real x, const Real y, const Real z=0.)

Function Documentation

exact_solution()

Real exact_solution	(	const int	component,
		const Real	x,
		const Real	y,
		const Real	z = 0.
	)

This is the exact solution that we are trying to obtain.

We will solve

• (u_xx + u_yy) = f

and take a finite difference approximation using this function to get f. This is the well-known "method of manufactured solutions".

Definition at line 38 of file exact_solution.C.

{
  static const Real pi = acos(-1.);
 
  switch (component)
  {
    case 0:
      return cos(.5 * pi * x) * sin(.5 * pi * y) * cos(.5 * pi * z);
    case 1:
      return sin(.5 * pi * x) * cos(.5 * pi * y) * cos(.5 * pi * z);
    case 2:
      return 0;
    default:
      libmesh_error_msg("Invalid component = " << component);
  }
 
  // dummy
  return 0.0;
}

References libMesh::pi, and libMesh::Real.

forcing_function()

Real forcing_function	(	const int	component,
		const Real	x,
		const Real	y,
		const Real	z = 0.
	)

Definition at line 59 of file exact_solution.C.

{
  static const Real pi = acos(-1.);
 
  switch (component)
  {
    case 0:
      return -3. * pi * pi * sin(pi * y / 2.) * cos(pi * x / 2.) * cos(pi * z / 2.) / 4.;
    case 1:
      return -3. * pi * pi * sin(pi * x / 2.) * cos(pi * y / 2.) * cos(pi * z / 2.) / 4.;
    case 2:
      return 0;
    default:
      libmesh_error_msg("Invalid component = " << component);
  }
 
  // dummy
  return 0.0;
}

References libMesh::pi, and libMesh::Real.