Home
Publications
Presentations
Support
Download
Examples
Developers
Class Docs
Namespaces
Classes
Files
Mailing Lists
Gallery
Wiki

fe_bernstein.C

Go to the documentation of this file.

// The libMesh Finite Element Library.
// Copyright (C) 2002-2012 Benjamin S. Kirk, John W. Peterson, Roy H. Stogner

// 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 "libmesh/libmesh_config.h"
#ifdef LIBMESH_ENABLE_HIGHER_ORDER_SHAPES

#include "libmesh/fe.h"
#include "libmesh/elem.h"
#include "libmesh/fe_interface.h"

namespace libMesh
{

  // ------------------------------------------------------------
  // Bernstein-specific implementations, Steffen Petersen 2005

  // Anonymous namespace for local helper functions
  namespace {

    void bernstein_nodal_soln(const Elem* elem,
                              const Order order,
                              const std::vector<Number>& elem_soln,
                              std::vector<Number>&       nodal_soln,
                              unsigned Dim)
    {
      const unsigned int n_nodes = elem->n_nodes();

      const ElemType elem_type = elem->type();

      nodal_soln.resize(n_nodes);

      const Order totalorder = static_cast<Order>(order + elem->p_level());

      // FEType object to be passed to various FEInterface functions below.
      FEType fe_type(totalorder, BERNSTEIN);

      switch (totalorder)
        {
          // Constant shape functions
        case CONSTANT:
          {
            libmesh_assert_equal_to (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.
        case FIRST:
        case SECOND:
        case THIRD:
        case FOURTH:
        case FIFTH:
        case SIXTH:
          {

            const unsigned int n_sf =
              // FE<Dim,T>::n_shape_functions(elem_type, totalorder);
              FEInterface::n_shape_functions(Dim, fe_type, elem_type);

            std::vector<Point> refspace_nodes;
            FEBase::get_refspace_nodes(elem_type,refspace_nodes);
            libmesh_assert_equal_to (refspace_nodes.size(), n_nodes);

            for (unsigned int n=0; n<n_nodes; n++)
              {
                libmesh_assert_equal_to (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);
                    FEInterface::shape(Dim, fe_type, elem, i, refspace_nodes[n]);
              }

            return;
          }

        default:
          {
            libmesh_error();
            return;
          }
        }


      // How did we get here?
      libmesh_error();
      return;
    } //  bernstein_nodal_soln()



    unsigned int bernstein_n_dofs(const ElemType t, const Order o)
    {
      switch (t)
        {
        case NODEELEM:
          return 1;
        case EDGE2:
        case EDGE3:
          return (o+1);
        case QUAD4:
          libmesh_assert_less (o, 2);
        case QUAD8:
          {
            if (o == 1)
              return 4;
            else if (o == 2)
              return 8;
            else
              libmesh_error();
          }
        case QUAD9:
          return ((o+1)*(o+1));
        case HEX8:
          libmesh_assert_less (o, 2);
        case HEX20:
          {
            if (o == 1)
              return 8;
            else if (o == 2)
              return 20;
            else
              libmesh_error();
          }
        case HEX27:
          return ((o+1)*(o+1)*(o+1));
        case TRI3:
          libmesh_assert_less (o, 2);
        case TRI6:
          return ((o+1)*(o+2)/2);
        case TET4:
          libmesh_assert_less (o, 2);
        case TET10:
          {
            libmesh_assert_less (o, 3);
            return ((o+1)*(o+2)*(o+3)/6);
          }
        default:
          libmesh_error();
        }

      libmesh_error();
      return 0;
    } // bernstein_n_dofs()




    unsigned int bernstein_n_dofs_at_node(const ElemType t,
                                          const Order o,
                                          const unsigned int n)
    {
      switch (t)
        {
        case NODEELEM:
          return 1;

        case EDGE2:
        case EDGE3:
          switch (n)
            {
            case 0:
            case 1:
              return 1;
            case 2:
              libmesh_assert (o>1);
              return (o-1);
            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 QUAD8:
          libmesh_assert_less (n, 8);
          libmesh_assert_less (o, 3);
        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_less (n, 8);
          libmesh_assert_less (o, 2);
        case HEX20:
          libmesh_assert_less (n, 20);
          libmesh_assert_less (o, 3);
        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();
            }
        case TET4:
          libmesh_assert_less (n, 4);
          libmesh_assert_less (o, 2);
        case TET10:
          libmesh_assert_less (o, 3);
          libmesh_assert_less (n, 10);
          switch (n)
            {
            case 0:
            case 1:
            case 2:
            case 3:
              return 1;

            case 4:
            case 5:
            case 6:
            case 7:
            case 8:
            case 9:
              return (o-1);

            default:
              libmesh_error();
            }

        default:
          libmesh_error();

        }

      libmesh_error();
      return 0;
    } // bernstein_n_dofs_at_node()




    unsigned int bernstein_n_dofs_per_elem(const ElemType t, const Order o)
    {
      switch (t)
        {
        case NODEELEM:
        case EDGE2:
        case EDGE3:
          return 0;
        case TRI3:
        case QUAD4:
          return 0;
        case TRI6:
          return ((o-1)*(o-2)/2);
        case QUAD8:
          if (o <= 2)
            return 0;
        case QUAD9:
          return ((o-1)*(o-1));
        case HEX8:
          libmesh_assert_less (o, 2);
        case HEX20:
          libmesh_assert_less (o, 3);
          return 0;
        case HEX27:
          return ((o-1)*(o-1)*(o-1));
        case TET4:
          libmesh_assert_less (o, 2);
        case TET10:
          libmesh_assert_less (o, 3);
          return 0;
        default:
          libmesh_error();
        }

      libmesh_error();
      return 0;
    } // bernstein_n_dofs_per_elem

  } // anonymous namespace




  // Do full-specialization of nodal_soln() function for every
  // dimension, instead of explicit instantiation at the end of this
  // file.
  // This could be macro-ified so that it fits on one line...
  template <>
  void FE<0,BERNSTEIN>::nodal_soln(const Elem* elem,
                                  const Order order,
                                  const std::vector<Number>& elem_soln,
                                  std::vector<Number>& nodal_soln)
  { bernstein_nodal_soln(elem, order, elem_soln, nodal_soln, /*Dim=*/0); }

  template <>
  void FE<1,BERNSTEIN>::nodal_soln(const Elem* elem,
                                  const Order order,
                                  const std::vector<Number>& elem_soln,
                                  std::vector<Number>& nodal_soln)
  { bernstein_nodal_soln(elem, order, elem_soln, nodal_soln, /*Dim=*/1); }

  template <>
  void FE<2,BERNSTEIN>::nodal_soln(const Elem* elem,
                                  const Order order,
                                  const std::vector<Number>& elem_soln,
                                  std::vector<Number>& nodal_soln)
  { bernstein_nodal_soln(elem, order, elem_soln, nodal_soln, /*Dim=*/2); }

  template <>
  void FE<3,BERNSTEIN>::nodal_soln(const Elem* elem,
                                  const Order order,
                                  const std::vector<Number>& elem_soln,
                                  std::vector<Number>& nodal_soln)
  { bernstein_nodal_soln(elem, order, elem_soln, nodal_soln, /*Dim=*/3); }


  // Full specialization of n_dofs() function for every dimension
  template <> unsigned int FE<0,BERNSTEIN>::n_dofs(const ElemType t, const Order o) { return bernstein_n_dofs(t, o); }
  template <> unsigned int FE<1,BERNSTEIN>::n_dofs(const ElemType t, const Order o) { return bernstein_n_dofs(t, o); }
  template <> unsigned int FE<2,BERNSTEIN>::n_dofs(const ElemType t, const Order o) { return bernstein_n_dofs(t, o); }
  template <> unsigned int FE<3,BERNSTEIN>::n_dofs(const ElemType t, const Order o) { return bernstein_n_dofs(t, o); }

  // Full specialization of n_dofs_at_node() function for every dimension.
  template <> unsigned int FE<0,BERNSTEIN>::n_dofs_at_node(const ElemType t, const Order o, const unsigned int n) { return bernstein_n_dofs_at_node(t, o, n); }
  template <> unsigned int FE<1,BERNSTEIN>::n_dofs_at_node(const ElemType t, const Order o, const unsigned int n) { return bernstein_n_dofs_at_node(t, o, n); }
  template <> unsigned int FE<2,BERNSTEIN>::n_dofs_at_node(const ElemType t, const Order o, const unsigned int n) { return bernstein_n_dofs_at_node(t, o, n); }
  template <> unsigned int FE<3,BERNSTEIN>::n_dofs_at_node(const ElemType t, const Order o, const unsigned int n) { return bernstein_n_dofs_at_node(t, o, n); }

  // Full specialization of n_dofs_per_elem() function for every dimension.
  template <> unsigned int FE<0,BERNSTEIN>::n_dofs_per_elem(const ElemType t, const Order o) { return bernstein_n_dofs_per_elem(t, o); }
  template <> unsigned int FE<1,BERNSTEIN>::n_dofs_per_elem(const ElemType t, const Order o) { return bernstein_n_dofs_per_elem(t, o); }
  template <> unsigned int FE<2,BERNSTEIN>::n_dofs_per_elem(const ElemType t, const Order o) { return bernstein_n_dofs_per_elem(t, o); }
  template <> unsigned int FE<3,BERNSTEIN>::n_dofs_per_elem(const ElemType t, const Order o) { return bernstein_n_dofs_per_elem(t, o); }

  // Bernstein FEMs are C^0 continuous
  template <> FEContinuity FE<0,BERNSTEIN>::get_continuity() const { return C_ZERO; }
  template <> FEContinuity FE<1,BERNSTEIN>::get_continuity() const { return C_ZERO; }
  template <> FEContinuity FE<2,BERNSTEIN>::get_continuity() const { return C_ZERO; }
  template <> FEContinuity FE<3,BERNSTEIN>::get_continuity() const { return C_ZERO; }

  // Bernstein FEMs are not hierarchic
  template <> bool FE<0,BERNSTEIN>::is_hierarchic() const { return false; }
  template <> bool FE<1,BERNSTEIN>::is_hierarchic() const { return false; }
  template <> bool FE<2,BERNSTEIN>::is_hierarchic() const { return false; }
  template <> bool FE<3,BERNSTEIN>::is_hierarchic() const { return false; }

  // Bernstein shapes need reinit only for approximation orders >= 3,
  // but we might reach that with p refinement
  template <> bool FE<0,BERNSTEIN>::shapes_need_reinit() const { return true; }
  template <> bool FE<1,BERNSTEIN>::shapes_need_reinit() const { return true; }
  template <> bool FE<2,BERNSTEIN>::shapes_need_reinit() const { return true; }
  template <> bool FE<3,BERNSTEIN>::shapes_need_reinit() const { return true; }

} // namespace libMesh

#endif //LIBMESH_ENABLE_HIGHER_ORDER_SHAPES

---

Site Created By: libMesh Developers
Last modified: February 05 2013 19:54:46 UTC

Hosted By: