fe_hierarchic.c

一个用来实现偏微分方程中网格的计算库

// $Id: fe_hierarchic.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



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




// ------------------------------------------------------------
// Hierarchic-specific implementations
template <unsigned int Dim, FEFamily T>
void FE<Dim,T>::nodal_soln(const Elem* elem,
			   const Order order,
			   const std::vector<Number>& elem_soln,
			   std::vector<Number>&       nodal_soln)
{
  const unsigned int n_nodes = elem->n_nodes();
  
  const ElemType type = elem->type();

  nodal_soln.resize(n_nodes);

  const Order totalorder = static_cast<Order>(order + elem->p_level());
  
  switch (totalorder)
    {
      // Constant shape functions
    case CONSTANT:
      {
	libmesh_assert (elem_soln.size() == 1);
	
	const Number val = elem_soln[0];
	
	for (unsigned int n=0; n<n_nodes; n++)
	  nodal_soln[n] = val;
	
	return;
      }


      // For other bases do interpolation at the nodes
      // explicitly.
    default:
      {

	const unsigned int n_sf =
	  FE<Dim,T>::n_shape_functions(type, totalorder);
	
	for (unsigned int n=0; n<n_nodes; n++)
	  {
	    const Point mapped_point = FE<Dim,T>::inverse_map(elem,
							      elem->point(n));

	    libmesh_assert (elem_soln.size() == n_sf);

	    // Zero before summation
	    nodal_soln[n] = 0;

	    // u_i = Sum (alpha_i phi_i)
	    for (unsigned int i=0; i<n_sf; i++)
	      nodal_soln[n] += elem_soln[i]*FE<Dim,T>::shape(elem,
							     order,
							     i,
							     mapped_point);	    
	  }

	return;
      }
    }
}



template <unsigned int Dim, FEFamily T>
unsigned int FE<Dim,T>::n_dofs(const ElemType t, const Order o)
{
  libmesh_assert (o > 0);
  switch (t)
    {
    case EDGE2:
    case EDGE3:
      return (o+1);
    case QUAD4:
      libmesh_assert(o < 2);
    case QUAD8:
    case QUAD9:
      return ((o+1)*(o+1));
    case HEX8:
      libmesh_assert(o < 2);
    case HEX20:
      libmesh_assert(o < 2);
    case HEX27:
      return ((o+1)*(o+1)*(o+1));
    case TRI6:
      return ((o+1)*(o+2)/2);
    default:
      libmesh_error();
    }
  
  libmesh_error();  
  return 0;
}



template <unsigned int Dim, FEFamily T>
unsigned int FE<Dim,T>::n_dofs_at_node(const ElemType t,
				       const Order o,
				       const unsigned int n)
{
  libmesh_assert (o > 0);
  switch (t)
    {
    case EDGE2:
    case EDGE3:
      switch (n)
        {
	case 0:
	case 1:
	  return 1;
        // Internal DoFs are associated with the elem, not its nodes
	case 2:
	  return 0;
	default:
	  libmesh_error();		  
	}
    case TRI6:
      switch (n)
	{
	case 0:
	case 1:
	case 2:
	  return 1;

	case 3:
	case 4:
	case 5:
	  return (o-1);

        // Internal DoFs are associated with the elem, not its nodes
	default:
	  libmesh_error();
	}
    case QUAD4:
      libmesh_assert (n < 4);
      libmesh_assert (o < 2);
    case QUAD8:
    case QUAD9:
      switch (n)
	{
	case 0:
	case 1:
	case 2:
	case 3:
	  return 1;

	case 4:
	case 5:
	case 6:
	case 7:
	  return (o-1);
		  
        // Internal DoFs are associated with the elem, not its nodes
	case 8:
          return 0;
		  
	default:
	  libmesh_error();
	}
    case HEX8:
      libmesh_assert (n < 8);
      libmesh_assert (o < 2);
    case HEX20:
      libmesh_assert (n < 20);
      libmesh_assert (o < 2);
    case HEX27:
      switch (n)
	{
	case 0:
	case 1:
	case 2:
	case 3:
	case 4:
	case 5:
	case 6:
	case 7:
	  return 1;

	case 8:
	case 9:
	case 10:
	case 11:
	case 12:
	case 13:
	case 14:
	case 15:
	case 16:
	case 17:
	case 18:
	case 19:
	  return (o-1);
		  
	case 20:
	case 21:
	case 22:
	case 23:
	case 24:
	case 25:
	  return ((o-1)*(o-1));
	 
        // Internal DoFs are associated with the elem, not its nodes
	case 26:
	  return 0;
	default:
	  libmesh_error();
        }
    default:
#ifdef DEBUG
      std::cerr << "ERROR: Bad ElemType = " << t
		<< std::endl;
#endif
      libmesh_error();	    
    }
  
  libmesh_error();
  
  return 0;
}



template <unsigned int Dim, FEFamily T>
unsigned int FE<Dim,T>::n_dofs_per_elem(const ElemType t,
					const Order o)
{
  libmesh_assert (o > 0);
  switch (t)
    {
    case EDGE2:
    case EDGE3:
      return (o-1);
    case TRI3:
    case QUAD4:
      return 0;
    case TRI6:
      return ((o-1)*(o-2)/2);
    case QUAD8:
    case QUAD9:
      return ((o-1)*(o-1));
    case HEX8:
    case HEX20:
      libmesh_assert(o < 2);
      return 0;
    case HEX27:
      return ((o-1)*(o-1)*(o-1));
    default:
#ifdef DEBUG
      std::cerr << "ERROR: Bad ElemType = " << t
		<< std::endl;
#endif
      libmesh_error();	    
    }
 
  // Will never get here...
  libmesh_error();
  return 0;
}



template <unsigned int Dim, FEFamily T>
FEContinuity FE<Dim,T>::get_continuity() const
{
  return C_ZERO;
}



template <unsigned int Dim, FEFamily T>
bool FE<Dim,T>::is_hierarchic() const
{
  return true;
}



#ifdef ENABLE_AMR
template <unsigned int Dim, FEFamily T>
void FE<Dim,T>::compute_constraints (DofConstraints &constraints,
				     DofMap &dof_map,
				     const unsigned int variable_number,
				     const Elem* elem)
{
  compute_proj_constraints(constraints, dof_map, variable_number, elem);
}
#endif // #ifdef ENABLE_AMR



template <unsigned int Dim, FEFamily T>
bool FE<Dim,T>::shapes_need_reinit() const
{
  return true;
}


//--------------------------------------------------------------
// Explicit instantiation of member functions
INSTANTIATE_MBRF(1,HIERARCHIC);
INSTANTIATE_MBRF(2,HIERARCHIC);
INSTANTIATE_MBRF(3,HIERARCHIC);

#ifdef ENABLE_AMR
template void FE<2,HIERARCHIC>::compute_constraints(DofConstraints&, DofMap&, 
						    const unsigned int,
						    const Elem*);
template void FE<3,HIERARCHIC>::compute_constraints(DofConstraints&, DofMap&, 
						    const unsigned int,
						    const Elem*);
#endif // #ifdef ENABLE_AMR