fe_hierarchic_shape_1d.c

一个用来实现偏微分方程中网格的计算库

// $Id: fe_hierarchic_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"
#include "utility.h"




template <>
Real FE<1,HIERARCHIC>::shape(const ElemType,
			     const Order order,
			     const unsigned int i,
			     const Point& p)
{
  libmesh_assert(i < order+1u);

  // Declare that we are using our own special power function
  // from the Utility namespace.  This saves typing later.
  using Utility::pow;

  const Real xi = p(0);

  Real returnval = 1.;

  switch (i)
    {
    case 0:
      returnval = .5*(1. - xi);
      break;
    case 1:
      returnval = .5*(1.  + xi);
      break;
      // All even-terms have the same form.
      // (xi^p - 1.)/p!
    case 2:
      returnval = (xi*xi - 1.)/2.;
      break;
    case 4:
      returnval = (pow<4>(xi) - 1.)/24.;
      break;
    case 6:
      returnval = (pow<6>(xi) - 1.)/720.;
      break;

      // All odd-terms have the same form.
      // (xi^p - xi)/p!
    case 3:
      returnval = (xi*xi*xi - xi)/6.;
      break;
    case 5:
      returnval = (pow<5>(xi) - xi)/120.;
      break;
    case 7:
      returnval = (pow<7>(xi) - xi)/5040.;	    
      break;
    default:
      Real denominator = 1.;
      for (unsigned int n=1; n <= i; ++n)
        {
          returnval *= xi;
          denominator *= n;
        }
      // Odd:
      if (i % 2)
        returnval = (returnval - xi)/denominator;
      // Even:
      else
        returnval = (returnval - 1.)/denominator;
      break;
    }

  return returnval;
}



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



template <>
Real FE<1,HIERARCHIC>::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);
  libmesh_assert(i < order+1u);

  // Declare that we are using our own special power function
  // from the Utility namespace.  This saves typing later.
  using Utility::pow;

  const Real xi = p(0);

  Real returnval = 1.;

  switch (i)
    {
    case 0:
      returnval = -.5;
      break;
    case 1:
      returnval =  .5;
      break;
      // All even-terms have the same form.
      // xi^(p-1)/(p-1)!
    case 2:
      returnval = xi;
      break;
    case 4:
      returnval = pow<3>(xi)/6.;
      break;
    case 6:
      returnval = pow<5>(xi)/120.;
      break;
      // All odd-terms have the same form.
      // (p*xi^(p-1) - 1.)/p!
    case 3:
      returnval = (3*xi*xi - 1.)/6.;
      break;
    case 5:
      returnval = (5.*pow<4>(xi) - 1.)/120.;
      break;
    case 7:
      returnval = (7.*pow<6>(xi) - 1.)/5040.;	    
      break;
    default:
      Real denominator = 1.;
      for (unsigned int n=1; n != i; ++n)
        {
          returnval *= xi;
          denominator *= n;
        }
      // Odd:
      if (i % 2)
        returnval = (i * returnval - 1.)/denominator/i;
      // Even:
      else
        returnval = returnval/denominator;
      break;
    }

  return returnval;
}



template <>
Real FE<1,HIERARCHIC>::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,HIERARCHIC>::shape_deriv(elem->type(),
				       static_cast<Order>(order + elem->p_level()), i, j, p);
}



template <>
Real FE<1,HIERARCHIC>::shape_second_deriv(const ElemType,
				          const Order order,
				          const unsigned int i,
				          const unsigned int j,
				          const Point& p)
{
  // only d2()/d2xi in 1D!
  
  libmesh_assert (j == 0);
  libmesh_assert (i < order+1u);

  // Declare that we are using our own special power function
  // from the Utility namespace.  This saves typing later.
  using Utility::pow;

  const Real xi = p(0);
	
  Real returnval = 1.;

  switch (i)
    {
    case 0:
    case 1:
      returnval = 0;
      break;
      // All terms have the same form.
      // xi^(p-2)/(p-2)!
    case 2:
      returnval = 1;
      break;
    case 3:
      returnval = xi;
      break;
    case 4:
      returnval = pow<2>(xi)/2.;
      break;
    case 5:
      returnval = pow<3>(xi)/6.;
      break;
    case 6:
      returnval = pow<4>(xi)/24.;
      break;
    case 7:
      returnval = pow<5>(xi)/120.;	    
      break;
    
    default:
      Real denominator = 1.;
      for (unsigned int n=1; n != i; ++n)
        {
          returnval *= xi;
          denominator *= n;
        }
      // Odd:
      if (i % 2)
        returnval = (i * returnval - 1.)/denominator/i;
      // Even:
      else
        returnval = returnval/denominator;
      break;
    }

  return returnval;
}



template <>
Real FE<1,HIERARCHIC>::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,HIERARCHIC>::shape_second_deriv(elem->type(),
				              static_cast<Order>(order + elem->p_level()), i, j, p);
}