fe_monomial_shape_3d.c

一个用来实现偏微分方程中网格的计算库

// $Id: fe_monomial_shape_3D.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<3,MONOMIAL>::shape(const ElemType,
			   const Order order,
			   const unsigned int i,
			   const Point& p)
{
#if DIM == 3
    
  const Real xi   = p(0);
  const Real eta  = p(1);
  const Real zeta = p(2);

  libmesh_assert (i < (static_cast<unsigned int>(order)+1)*
              (static_cast<unsigned int>(order)+2)*
              (static_cast<unsigned int>(order)+3)/6);

    // monomials. since they are hierarchic we only need one case block.
  switch (i)
    {
      // constant
    case 0:
      return 1.;
  
      // linears
    case 1:
      return xi;
      
    case 2:
      return eta;
      
    case 3:
      return zeta;
  
      // quadratics
    case 4:
      return xi*xi;
      
    case 5:
      return xi*eta;
      
    case 6:
      return eta*eta;
  
    case 7:
      return xi*zeta;
  
    case 8:
      return zeta*eta;
  
    case 9:
      return zeta*zeta;
  
      // cubics
    case 10:
      return xi*xi*xi;
  
    case 11:
      return xi*xi*eta;
  
    case 12:
      return xi*eta*eta;
  
    case 13:
      return eta*eta*eta;
  
    case 14:
      return xi*xi*zeta;
  
    case 15:
      return xi*eta*zeta;
  
    case 16:
      return eta*eta*zeta;
  
    case 17:
      return xi*zeta*zeta;
  
    case 18:
      return eta*zeta*zeta;
  
    case 19:
      return zeta*zeta*zeta;
  
      // quartics
    case 20:
      return xi*xi*xi*xi;
  
    case 21:
      return xi*xi*xi*eta;
  
    case 22:
      return xi*xi*eta*eta;
  
    case 23:
      return xi*eta*eta*eta;
  
    case 24:
      return eta*eta*eta*eta;
  
    case 25:
      return xi*xi*xi*zeta;
  
    case 26:
      return xi*xi*eta*zeta;
  
    case 27:
      return xi*eta*eta*zeta;
  
    case 28:
      return eta*eta*eta*zeta;
  
    case 29:
      return xi*xi*zeta*zeta;
  
    case 30:
      return xi*eta*zeta*zeta;
  
    case 31:
      return eta*eta*zeta*zeta;
  
    case 32:
      return xi*zeta*zeta*zeta;
  
    case 33:
      return eta*zeta*zeta*zeta;
  
    case 34:
      return zeta*zeta*zeta*zeta;
      	    
    default:
      unsigned int o = 0;
      for (; i >= (o+1)*(o+2)*(o+3)/6; o++) { }
      unsigned int i2 = i - (o*(o+1)*(o+2)/6);
      unsigned int block=o, nz = 0;
      for (; block < i2; block += (o-nz+1)) { nz++; }
      const unsigned int nx = block - i2;
      const unsigned int ny = o - nx - nz;
      Real val = 1.;
      for (unsigned int index=0; index != nx; index++)
        val *= xi;
      for (unsigned int index=0; index != ny; index++)
        val *= eta;
      for (unsigned int index=0; index != nz; index++)
        val *= zeta;
      return val;
    }

#endif
  
  libmesh_error();
  return 0.;
}



template <>
Real FE<3,MONOMIAL>::shape(const Elem* elem,
			   const Order order,
			   const unsigned int i,
			   const Point& p)
{
  libmesh_assert (elem != NULL);
      
  // call the orientation-independent shape functions
  return FE<3,MONOMIAL>::shape(elem->type(), static_cast<Order>(order + elem->p_level()), i, p);
}



template <>
Real FE<3,MONOMIAL>::shape_deriv(const ElemType,
				 const Order order,
				 const unsigned int i,
				 const unsigned int j,
				 const Point& p)
{
#if DIM == 3
  
  libmesh_assert (j<3);
  
  libmesh_assert (i < (static_cast<unsigned int>(order)+1)*
              (static_cast<unsigned int>(order)+2)*
              (static_cast<unsigned int>(order)+3)/6);


  const Real xi   = p(0);
  const Real eta  = p(1);
  const Real zeta = p(2);

  // monomials. since they are hierarchic we only need one case block.
  switch (j)
    {
      // d()/dxi
    case 0:
      {
        switch (i)
  	{
  	  // constant
  	case 0:
  	  return 0.;
  	  
  	  // linear
  	case 1:
  	  return 1.;
  	  
  	case 2:
  	  return 0.;
  	  
  	case 3:
  	  return 0.;
  
  	  // quadratic
  	case 4:
  	  return 2.*xi;
  	  
  	case 5:
  	  return eta;
  	  
  	case 6:
  	  return 0.;
  	  
  	case 7:
  	  return zeta;
  	  
  	case 8:
  	  return 0.;
  	  
  	case 9:
  	  return 0.;
  
  	  // cubic
  	case 10:
  	  return 3.*xi*xi;
  
  	case 11:
  	  return 2.*xi*eta;
  
  	case 12:
  	  return eta*eta;
  
  	case 13:
  	  return 0.;
  
  	case 14:
  	  return 2.*xi*zeta;
  
  	case 15:
  	  return eta*zeta;
  
  	case 16:
  	  return 0.;
  
  	case 17:
  	  return zeta*zeta;
  
  	case 18:
  	  return 0.;
  
  	case 19:
  	  return 0.;
  
  	  // quartics
  	case 20:
  	  return 4.*xi*xi*xi;
  
  	case 21:
  	  return 3.*xi*xi*eta;
  
  	case 22:
  	  return 2.*xi*eta*eta;
  
  	case 23:
  	  return eta*eta*eta;
  
  	case 24:
  	  return 0.;
  
  	case 25:
  	  return 3.*xi*xi*zeta;
  
  	case 26:
  	  return 2.*xi*eta*zeta;
  
  	case 27:
  	  return eta*eta*zeta;
  
  	case 28:
  	  return 0.;
  
  	case 29:
  	  return 2.*xi*zeta*zeta;
  
  	case 30:
  	  return eta*zeta*zeta;
  
  	case 31:
  	  return 0.;
  
  	case 32:
  	  return zeta*zeta*zeta;
  
  	case 33:
  	  return 0.;
  
  	case 34:
  	  return 0.;
  	  
  	default:
          unsigned int o = 0;
          for (; i >= (o+1)*(o+2)*(o+3)/6; o++) { }
          unsigned int i2 = i - (o*(o+1)*(o+2)/6);
          unsigned int block=o, nz = 0;
          for (; block < i2; block += (o-nz+1)) { nz++; }
          const unsigned int nx = block - i2;
          const unsigned int ny = o - nx - nz;
          Real val = nx;
          for (unsigned int index=1; index < nx; index++)
            val *= xi;
          for (unsigned int index=0; index != ny; index++)
            val *= eta;
          for (unsigned int index=0; index != nz; index++)
            val *= zeta;
          return val;
  	}
      }
  
      
      // d()/deta
    case 1:
      {
        switch (i)
  	{
  	  // constant
  	case 0:
  	  return 0.;
  	  
  	  // linear
  	case 1:
  	  return 0.;
  	  
  	case 2:
  	  return 1.;
  	  
  	case 3:
  	  return 0.;
  
  	  // quadratic
  	case 4:
  	  return 0.;
  	  
  	case 5:
  	  return xi;
  	  
  	case 6:
  	  return 2.*eta;
  	  
  	case 7:
  	  return 0.;
  	  
  	case 8:
  	  return zeta;
  	  
  	case 9:
  	  return 0.;
  
  	  // cubic
  	case 10:
  	  return 0.;
  
  	case 11:
  	  return xi*xi;
  
  	case 12:
  	  return 2.*xi*eta;
  
  	case 13:
  	  return 3.*eta*eta;
  
  	case 14:
  	  return 0.;
  
  	case 15:
  	  return xi*zeta;
  
  	case 16:
  	  return 2.*eta*zeta;
  
  	case 17:
  	  return 0.;
  
  	case 18:
  	  return zeta*zeta;
  
  	case 19:
  	  return 0.;
  
  	  // quartics
  	case 20:
  	  return 0.;
  
  	case 21:
  	  return xi*xi*xi;
  
  	case 22:
  	  return 2.*xi*xi*eta;
  
  	case 23:
  	  return 3.*xi*eta*eta;
  
  	case 24:
  	  return 4.*eta*eta*eta;
  
  	case 25:
  	  return 0.;
  
  	case 26:
  	  return xi*xi*zeta;
  
  	case 27:
  	  return 2.*xi*eta*zeta;
  
  	case 28:
  	  return 3.*eta*eta*zeta;
  
  	case 29:
  	  return 0.;
  
  	case 30:
  	  return xi*zeta*zeta;
  
  	case 31:
  	  return 2.*eta*zeta*zeta;
  
  	case 32:
  	  return 0.;
  
  	case 33:
  	  return zeta*zeta*zeta;
  
  	case 34:
  	  return 0.;
  	  
  	default:
          unsigned int o = 0;
          for (; i >= (o+1)*(o+2)*(o+3)/6; o++) { }
          unsigned int i2 = i - (o*(o+1)*(o+2)/6);
          unsigned int block=o, nz = 0;
          for (; block < i2; block += (o-nz+1)) { nz++; }
          const unsigned int nx = block - i2;
          const unsigned int ny = o - nx - nz;
          Real val = ny;
          for (unsigned int index=0; index != nx; index++)
            val *= xi;
          for (unsigned int index=1; index < ny; index++)
            val *= eta;
          for (unsigned int index=0; index != nz; index++)
            val *= zeta;
          return val;
  	}
      }
  
      
      // d()/dzeta
    case 2:
      {
        switch (i)
  	{
  	  // constant
  	case 0:
  	  return 0.;
  	  
  	  // linear
  	case 1:
  	  return 0.;
  	  
  	case 2:
  	  return 0.;
  	  
  	case 3:
  	  return 1.;
  
  	  // quadratic
  	case 4:
  	  return 0.;
  	  
  	case 5:
  	  return 0.;
  	  
  	case 6:
  	  return 0.;
  	  
  	case 7:
  	  return xi;
  	  
  	case 8:
  	  return eta;
  	  
  	case 9:
  	  return 2.*zeta;
  
  	  // cubic
  	case 10:
  	  return 0.;
  
  	case 11:
  	  return 0.;
  
  	case 12:
  	  return 0.;
  
  	case 13:
  	  return 0.;
  
  	case 14:
  	  return xi*xi;
  
  	case 15:
  	  return xi*eta;
  
  	case 16:
  	  return eta*eta;
  
  	case 17:
  	  return 2.*xi*zeta;
  
  	case 18:
  	  return 2.*eta*zeta;
  
  	case 19:
  	  return 3.*zeta*zeta;
  
  	  // quartics
  	case 20:
  	  return 0.;
  
  	case 21:
  	  return 0.;
  
  	case 22:
  	  return 0.;
  
  	case 23:
  	  return 0.;
  
  	case 24:
  	  return 0.;
  
  	case 25:
  	  return xi*xi*xi;
  
  	case 26:
  	  return xi*xi*eta;
  
  	case 27:
  	  return xi*eta*eta;
  
  	case 28:
  	  return eta*eta*eta;
  
  	case 29:
  	  return 2.*xi*xi*zeta;
  
  	case 30:
  	  return 2.*xi*eta*zeta;
  
  	case 31:
  	  return 2.*eta*eta*zeta;
  
  	case 32:
  	  return 3.*xi*zeta*zeta;
  
  	case 33:
  	  return 3.*eta*zeta*zeta;
  
  	case 34:
  	  return 4.*zeta*zeta*zeta;
  	  
  	default:
          unsigned int o = 0;
          for (; i >= (o+1)*(o+2)*(o+3)/6; o++) { }
          unsigned int i2 = i - (o*(o+1)*(o+2)/6);
          unsigned int block=o, nz = 0;
          for (; block < i2; block += (o-nz+1)) { nz++; }
          const unsigned int nx = block - i2;
          const unsigned int ny = o - nx - nz;
          Real val = nz;
          for (unsigned int index=0; index != nx; index++)
            val *= xi;
          for (unsigned int index=0; index != ny; index++)
            val *= eta;
          for (unsigned int index=1; index < nz; index++)
            val *= zeta;
          return val;
  	}
      }
    }

#endif
  
  libmesh_error();
  return 0.;  
}



template <>
Real FE<3,MONOMIAL>::shape_deriv(const Elem* elem,
				 const Order order,
				 const unsigned int i,
				 const unsigned int j,
				 const Point& p)
{
  libmesh_assert (elem != NULL);
      
  // call the orientation-independent shape function derivatives
  return FE<3,MONOMIAL>::shape_deriv(elem->type(), static_cast<Order>(order + elem->p_level()), i, j, p);
}



template <>
Real FE<3,MONOMIAL>::shape_second_deriv(const ElemType,
				        const Order order,
				        const unsigned int i,
				        const unsigned int j,
				        const Point& p)
{