exact_solution.c

一个用来实现偏微分方程中网格的计算库

// $Id: exact_solution.C 2501 2007-11-20 02:33:29Z benkirk $

// The Next Great Finite Element Library.
// Copyright (C) 2003  Benjamin S. Kirk
  
// This library is free software; you can redistribute it and/or
// modify it under the terms of the GNU Lesser General Public
// License as published by the Free Software Foundation; either
// version 2.1 of the License, or (at your option) any later version.
  
// This library is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
// Lesser General Public License for more details.
  
// You should have received a copy of the GNU Lesser General Public
// License along with this library; if not, write to the Free Software
// Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA



// C++ Includes
#include <math.h>

// Mesh library includes
#include "libmesh_common.h"





/**
 * 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".
 */
Real exact_solution (const Real x,
		     const Real y,
		     const Real z = 0.)
{
  static const Real pi = acos(-1.);

  return cos(.5*pi*x)*sin(.5*pi*y)*cos(.5*pi*z);
}