fe_raviart_shape_3D.C

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// The libMesh Finite Element Library.
// Copyright (C) 2002-2026 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/fe.h"
#include "libmesh/elem.h"
#include "libmesh/enum_to_string.h"
 
namespace libMesh
{
 
template <>
RealGradient FE<3,RAVIART_THOMAS>::shape(const Elem * elem,
                                         const Order order,
                                         const unsigned int i,
                                         const Point & p,
                                         const bool add_p_level)
{
#if LIBMESH_DIM == 3
  libmesh_assert(elem);
 
  const Order totalorder = order + add_p_level*elem->p_level();
  libmesh_assert_less(i, n_dofs(elem->type(), totalorder));
 
  const char sign = elem->positive_face_orientation(i) ? 1 : -1;
 
  const Real xi   = p(0);
  const Real eta  = p(1);
  const Real zeta = p(2);
 
  switch (totalorder)
    {
      // linear Raviart-Thomas shape functions
    case FIRST:
      {
        switch (elem->type())
          {
          case HEX27:
            {
              // Even with a loose inverse_map tolerance we ought to
              // be nearly on the element interior in master
              // coordinates
              libmesh_assert_less_equal ( std::fabs(xi),   1.0+10*TOLERANCE );
              libmesh_assert_less_equal ( std::fabs(eta),  1.0+10*TOLERANCE );
              libmesh_assert_less_equal ( std::fabs(zeta), 1.0+10*TOLERANCE );
 
              switch(i)
                {
                case 0:
                  return sign * RealGradient( 0.0, 0.0, 0.125*(zeta-1.0) );
                case 1:
                  return sign * RealGradient( 0.0, 0.125*(eta-1.0), 0.0 );
                case 2:
                  return sign * RealGradient( 0.125*(xi+1.0), 0.0, 0.0 );
                case 3:
                  return sign * RealGradient( 0.0, 0.125*(1.0+eta), 0.0 );
                case 4:
                  return sign * RealGradient( 0.125*(xi-1.0), 0.0, 0.0 );
                case 5:
                  return sign * RealGradient( 0.0, 0.0, 0.125*(1.0+zeta) );
 
                default:
                  libmesh_error_msg("Invalid i = " << i);
                }
            }
 
          case TET14:
            {
              switch(i)
                {
                case 0:
                  return sign * RealGradient( 2.0*xi, 2.0*eta, 2.0*zeta-2.0 );
                case 1:
                  return sign * RealGradient( 2.0*xi, 2.0*eta-2.0, 2.0*zeta );
                case 2:
                  return sign * RealGradient( 2.0*xi, 2.0*eta, 2.0*zeta );
                case 3:
                  return sign * RealGradient( 2.0*xi-2.0, 2.0*eta, 2.0*zeta );
 
                default:
                  libmesh_error_msg("Invalid i = " << i);
                }
            }
 
          default:
            libmesh_error_msg("ERROR: Unsupported 3D element type!: " << Utility::enum_to_string(elem->type()));
          }
      }
 
      // unsupported order
    default:
      libmesh_error_msg("ERROR: Unsupported 3D FE order!: " << totalorder);
    }
 
#else // LIBMESH_DIM != 3
  libmesh_ignore(elem, order, i, p, add_p_level);
  libmesh_not_implemented();
#endif
}
 
 
template <>
RealGradient FE<3,L2_RAVIART_THOMAS>::shape(const Elem * elem,
                                            const Order order,
                                            const unsigned int i,
                                            const Point & p,
                                            const bool add_p_level)
{
  return FE<3,RAVIART_THOMAS>::shape(elem, order, i, p, add_p_level);
}
 
 
template <>
RealGradient FE<3,RAVIART_THOMAS>::shape(const ElemType,
                                         const Order,
                                         const unsigned int,
                                         const Point &)
{
  libmesh_error_msg("Raviart-Thomas elements require the element type \nbecause face orientation is needed.");
  return RealGradient();
}
 
 
template <>
RealGradient FE<3,L2_RAVIART_THOMAS>::shape(const ElemType,
                                            const Order,
                                            const unsigned int,
                                            const Point &)
{
  libmesh_error_msg("Raviart-Thomas elements require the element type \nbecause face orientation is needed.");
  return RealGradient();
}
 
 
template <>
RealGradient FE<3,RAVIART_THOMAS>::shape(const FEType fet,
                                         const Elem * elem,
                                         const unsigned int i,
                                         const Point & p,
                                         const bool add_p_level)
{
  return FE<3,RAVIART_THOMAS>::shape(elem, fet.order, i, p, add_p_level);
}
 
 
template <>
RealGradient FE<3,L2_RAVIART_THOMAS>::shape(const FEType fet,
                                            const Elem * elem,
                                            const unsigned int i,
                                            const Point & p,
                                            const bool add_p_level)
{
  return FE<3,L2_RAVIART_THOMAS>::shape(elem, fet.order, i, p, add_p_level);
}
 
 
template <>
RealGradient FE<3,RAVIART_THOMAS>::shape_deriv(const Elem * elem,
                                               const Order order,
                                               const unsigned int i,
                                               const unsigned int j,
                                               const Point &,
                                               const bool add_p_level)
{
#if LIBMESH_DIM == 3
  libmesh_assert(elem);
  libmesh_assert_less (j, 3);
 
  const Order totalorder = order + add_p_level*elem->p_level();
  libmesh_assert_less(i, n_dofs(elem->type(), totalorder));
 
  const char sign = elem->positive_face_orientation(i) ? 1 : -1;
 
  switch (totalorder)
    {
      // linear Raviart-Thomas shape function first derivatives
    case FIRST:
      {
        switch (elem->type())
          {
          case HEX27:
            {
              switch (j)
                {
                  // d()/dxi
                case 0:
                  {
                    switch(i)
                      {
                      case 0:
                      case 1:
                      case 3:
                      case 5:
                        return RealGradient();
                      case 2:
                      case 4:
                        return sign * RealGradient( 0.125, 0.0, 0.0 );
 
                      default:
                        libmesh_error_msg("Invalid i = " << i);
                      } // switch(i)
 
                  } // j = 0
 
                  // d()/deta
                case 1:
                  {
                    switch(i)
                      {
                      case 0:
                      case 2:
                      case 4:
                      case 5:
                        return RealGradient();
                      case 1:
                      case 3:
                        return sign * RealGradient( 0.0, 0.125, 0.0 );
 
                      default:
                        libmesh_error_msg("Invalid i = " << i);
                      } // switch(i)
 
                  } // j = 1
 
                  // d()/dzeta
                case 2:
                  {
                    switch(i)
                      {
                      case 1:
                      case 2:
                      case 3:
                      case 4:
                        return RealGradient();
                      case 0:
                      case 5:
                        return sign * RealGradient( 0.0, 0.0, 0.125 );
 
                      default:
                        libmesh_error_msg("Invalid i = " << i);
                      } // switch(i)
 
                  } // j = 2
 
                default:
                  libmesh_error_msg("Invalid j = " << j);
                }
            }
 
          case TET14:
            {
              switch (j)
                {
                  // d()/dxi
                case 0:
                  {
                    switch(i)
                    {
                    case 0:
                    case 1:
                    case 2:
                    case 3:
                      return sign * RealGradient( 2.0, 0.0, 0.0 );
 
                    default:
                      libmesh_error_msg("Invalid i = " << i);
                    } // switch(i)
 
                  } // j = 0
 
                  // d()/deta
                case 1:
                  {
                    switch(i)
                    {
                    case 0:
                    case 1:
                    case 2:
                    case 3:
                      return sign * RealGradient( 0.0, 2.0, 0.0 );
 
                    default:
                      libmesh_error_msg("Invalid i = " << i);
                    } // switch(i)
 
                  } // j = 1
 
                  // d()/dzeta
                case 2:
                  {
                    switch(i)
                    {
                    case 0:
                    case 1:
                    case 2:
                    case 3:
                      return sign * RealGradient( 0.0, 0.0, 2.0 );
 
                    default:
                      libmesh_error_msg("Invalid i = " << i);
                    } // switch(i)
 
                  } // j = 2
 
                default:
                  libmesh_error_msg("Invalid j = " << j);
                }
            }
 
          default:
            libmesh_error_msg("ERROR: Unsupported 3D element type!: " << Utility::enum_to_string(elem->type()));
          }
      }
      // unsupported order
    default:
      libmesh_error_msg("ERROR: Unsupported 3D FE order!: " << totalorder);
    }
 
#else // LIBMESH_DIM != 3
  libmesh_ignore(elem, order, i, j, p, add_p_level);
  libmesh_not_implemented();
#endif
}
 
 
template <>
RealGradient FE<3,L2_RAVIART_THOMAS>::shape_deriv(const Elem * elem,
                                                  const Order order,
                                                  const unsigned int i,
                                                  const unsigned int j,
                                                  const Point & p,
                                                  const bool add_p_level)
{
  return FE<3,RAVIART_THOMAS>::shape_deriv(elem, order, i, j, p, add_p_level);
}
 
 
template <>
RealGradient FE<3,RAVIART_THOMAS>::shape_deriv(const ElemType,
                                               const Order,
                                               const unsigned int,
                                               const unsigned int,
                                               const Point &)
{
  libmesh_error_msg("Raviart-Thomas elements require the element type \nbecause face orientation is needed.");
  return RealGradient();
}
 
 
template <>
RealGradient FE<3,L2_RAVIART_THOMAS>::shape_deriv(const ElemType,
                                                  const Order,
                                                  const unsigned int,
                                                  const unsigned int,
                                                  const Point &)
{
  libmesh_error_msg("Raviart-Thomas elements require the element type \nbecause face orientation is needed.");
  return RealGradient();
}
 
 
template <>
RealGradient FE<3,RAVIART_THOMAS>::shape_deriv(const FEType fet,
                                               const Elem * elem,
                                               const unsigned int i,
                                               const unsigned int j,
                                               const Point & p,
                                               const bool add_p_level)
{
  return FE<3,RAVIART_THOMAS>::shape_deriv(elem, fet.order, i, j, p, add_p_level);
}
 
 
template <>
RealGradient FE<3,L2_RAVIART_THOMAS>::shape_deriv(const FEType fet,
                                                  const Elem * elem,
                                                  const unsigned int i,
                                                  const unsigned int j,
                                                  const Point & p,
                                                  const bool add_p_level)
{
  return FE<3,L2_RAVIART_THOMAS>::shape_deriv(elem, fet.order, i, j, p, add_p_level);
}
 
 
#ifdef LIBMESH_ENABLE_SECOND_DERIVATIVES
 
template <>
RealGradient FE<3,RAVIART_THOMAS>::shape_second_deriv(const Elem * elem,
                                                      const Order order,
                                                      const unsigned int libmesh_dbg_var(i),
                                                      const unsigned int libmesh_dbg_var(j),
                                                      const Point &,
                                                      const bool add_p_level)
{
#if LIBMESH_DIM == 3
 
  libmesh_assert(elem);
 
  // j = 0 ==> d^2 phi / dxi^2
  // j = 1 ==> d^2 phi / dxi deta
  // j = 2 ==> d^2 phi / deta^2
  // j = 3 ==> d^2 phi / dxi dzeta
  // j = 4 ==> d^2 phi / deta dzeta
  // j = 5 ==> d^2 phi / dzeta^2
  libmesh_assert_less (j, 6);
 
  const Order totalorder = order + add_p_level*elem->p_level();
  libmesh_assert_less(i, n_dofs(elem->type(), totalorder));
 
  switch (totalorder)
    {
      // linear Raviart-Thomas shape function second derivatives
    case FIRST:
      {
        switch (elem->type())
          {
            // All second derivatives for linear hexes and tets are zero.
          case HEX27:
          case TET14:
            return RealGradient();
 
          default:
            libmesh_error_msg("ERROR: Unsupported 3D element type!: " << Utility::enum_to_string(elem->type()));
 
          } //switch(type)
      }
 
      // unsupported order
    default:
      libmesh_error_msg("ERROR: Unsupported 3D FE order!: " << totalorder);
    }
 
#else // LIBMESH_DIM != 3
  libmesh_assert(true || p(0));
  libmesh_ignore(elem, order, i, j, add_p_level);
  libmesh_not_implemented();
#endif
}
 
 
template <>
RealGradient FE<3,L2_RAVIART_THOMAS>::shape_second_deriv(const Elem * elem,
                                                         const Order order,
                                                         const unsigned int i,
                                                         const unsigned int j,
                                                         const Point & p,
                                                         const bool add_p_level)
{
  return FE<3,RAVIART_THOMAS>::shape_second_deriv(elem, order, i, j, p, add_p_level);
}
 
 
template <>
RealGradient FE<3,RAVIART_THOMAS>::shape_second_deriv(const ElemType,
                                                      const Order,
                                                      const unsigned int,
                                                      const unsigned int,
                                                      const Point &)
{
  libmesh_error_msg("Raviart-Thomas elements require the element type \nbecause face orientation is needed.");
  return RealGradient();
}
 
 
template <>
RealGradient FE<3,L2_RAVIART_THOMAS>::shape_second_deriv(const ElemType,
                                                         const Order,
                                                         const unsigned int,
                                                         const unsigned int,
                                                         const Point &)
{
  libmesh_error_msg("Raviart-Thomas elements require the element type \nbecause face orientation is needed.");
  return RealGradient();
}
 
 
template <>
RealGradient FE<3,RAVIART_THOMAS>::shape_second_deriv(const FEType fet,
                                                      const Elem * elem,
                                                      const unsigned int i,
                                                      const unsigned int j,
                                                      const Point & p,
                                                      const bool add_p_level)
{
  return FE<3,RAVIART_THOMAS>::shape_second_deriv(elem, fet.order, i, j, p, add_p_level);
}
 
 
template <>
RealGradient FE<3,L2_RAVIART_THOMAS>::shape_second_deriv(const FEType fet,
                                                         const Elem * elem,
                                                         const unsigned int i,
                                                         const unsigned int j,
                                                         const Point & p,
                                                         const bool add_p_level)
{
  return FE<3,L2_RAVIART_THOMAS>::shape_second_deriv(elem, fet.order, i, j, p, add_p_level);
}
 
#endif
 
} // namespace libMesh