fe_monomial_shape_1d.c

一个用来实现偏微分方程中网格的计算库

// $Id: fe_monomial_shape_1D.C 2789 2008-04-13 02:24:40Z roystgnr $

// The libMesh Finite Element Library.
// Copyright (C) 2002-2007  Benjamin S. Kirk, John W. Peterson
  
// 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++ inlcludes

// Local includes
#include "fe.h"
#include "elem.h"




template <>
Real FE<1,MONOMIAL>::shape(const ElemType,
			   const Order order,
			   const unsigned int i,
			   const Point& p)
{
  const Real xi = p(0);

  libmesh_assert (i <= static_cast<unsigned int>(order));
	
  // monomials. since they are hierarchic we only need one case block.
  switch (i)
    {
    case 0:
      return 1.;

    case 1:
      return xi;
    
    case 2:
      return xi*xi;
    
    case 3:
      return xi*xi*xi;
    
    case 4:
      return xi*xi*xi*xi;
    
    default:
      Real val = 1.;
      for (unsigned int index = 0; index != i; ++index)
        val *= xi;
      return val;
    }
      
  libmesh_error();
  return 0.;
}



template <>
Real FE<1,MONOMIAL>::shape(const Elem* elem,
			   const Order order,
			   const unsigned int i,
			   const Point& p)
{
  libmesh_assert (elem != NULL);
  
  return FE<1,MONOMIAL>::shape(elem->type(), static_cast<Order>(order + elem->p_level()), i, p);
}



template <>
Real FE<1,MONOMIAL>::shape_deriv(const ElemType,
				 const Order order,
				 const unsigned int i,
				 const unsigned int j,
				 const Point& p)
{
  // only d()/dxi in 1D!
  
  libmesh_assert (j == 0);
	
  const Real xi = p(0);

  libmesh_assert (i <= static_cast<unsigned int>(order));
	
  // monomials. since they are hierarchic we only need one case block.
  switch (i)
    {
    case 0:
      return 0.;

    case 1:
      return 1.;
    
    case 2:
      return 2.*xi;
    
    case 3:
      return 3.*xi*xi;
    
    case 4:
      return 4.*xi*xi*xi;
    
    default:
      Real val = i;
      for (unsigned int index = 1; index != i; ++index)
        val *= xi;
      return val;
    }

  libmesh_error();
  return 0.;
}



template <>
Real FE<1,MONOMIAL>::shape_deriv(const Elem* elem,
				 const Order order,
				 const unsigned int i,
				 const unsigned int j,
				 const Point& p)
{
  libmesh_assert (elem != NULL);
  
  return FE<1,MONOMIAL>::shape_deriv(elem->type(),
				     static_cast<Order>(order + elem->p_level()), i, j, p);
}



template <>
Real FE<1,MONOMIAL>::shape_second_deriv(const ElemType,
				        const Order order,
				        const unsigned int i,
				        const unsigned int j,
				        const Point& p)
{
  // only d()/dxi in 1D!
  
  libmesh_assert (j == 0);
	
  const Real xi = p(0);

  libmesh_assert (i <= static_cast<unsigned int>(order));

  switch (i)
    {
    case 0:
    case 1:
      return 0.;
	    
    case 2:
      return 2.;
    
    case 3:
      return 6.*xi;
    
    case 4:
      return 12.*xi*xi;
    
    default:
      Real val = 2.;
      for (unsigned int index = 2; index != i; ++index)
        val *= (index+1) * xi;
      return val;
    }

  libmesh_error();
  return 0.;
}



template <>
Real FE<1,MONOMIAL>::shape_second_deriv(const Elem* elem,
				        const Order order,
				        const unsigned int i,
				        const unsigned int j,
				        const Point& p)
{
  libmesh_assert (elem != NULL);
  
  return FE<1,MONOMIAL>::shape_second_deriv(elem->type(),
				            static_cast<Order>(order + elem->p_level()), i, j, p);
}