fe_szabab_shape_1D.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
 
 
 
// C++ includes
 
// Local includes
#include "libmesh/libmesh_config.h"
 
#ifdef LIBMESH_ENABLE_HIGHER_ORDER_SHAPES
 
#include "libmesh/fe.h"
#include "libmesh/elem.h"
 
 
namespace libMesh
{
 
 
LIBMESH_DEFAULT_VECTORIZED_FE(1,SZABAB)
 
 
template <>
Real FE<1,SZABAB>::shape(const ElemType,
                         const Order libmesh_dbg_var(order),
                         const unsigned int i,
                         const Point & p)
{
  const Real xi  = p(0);
  const Real xi2 = xi*xi;
 
 
  // Use this libmesh_assert rather than a switch with a single entry...
  // It will go away in optimized mode, essentially has the same effect.
  libmesh_assert_less_equal (order, SEVENTH);
 
  //   switch (order)
  //     {
  //     case FIRST:
  //     case SECOND:
  //     case THIRD:
  //     case FOURTH:
  //     case FIFTH:
  //     case SIXTH:
  //     case SEVENTH:
 
  switch(i)
    {
      //nodal shape functions
    case 0: return 1./2.-1./2.*xi;
    case 1: return 1./2.+1./2.*xi;
    case 2: return 1./4.  *2.4494897427831780982*(xi2-1.);
    case 3: return 1./4.  *3.1622776601683793320*(xi2-1.)*xi;
    case 4: return 1./16. *3.7416573867739413856*((5.*xi2-6.)*xi2+1.);
    case 5: return 3./16. *1.4142135623730950488*(3.+(-10.+7.*xi2)*xi2)*xi;
    case 6: return 1./32. *4.6904157598234295546*(-1.+(15.+(-35.+21.*xi2)*xi2)*xi2);
    case 7: return 1./32. *5.0990195135927848300*(-5.+(35.+(-63.+33.*xi2)*xi2)*xi2)*xi;
    case 8: return 1./256.*5.4772255750516611346*(5.+(-140.+(630.+(-924.+429.*xi2)*xi2)*xi2)*xi2);
 
    default:
      libmesh_error_msg("Invalid shape function index!");
    }
}
 
 
 
template <>
Real FE<1,SZABAB>::shape(const Elem * elem,
                         const Order order,
                         const unsigned int i,
                         const Point & p,
                         const bool add_p_level)
{
  libmesh_assert(elem);
 
  return FE<1,SZABAB>::shape(elem->type(), order + add_p_level*elem->p_level(), i, p);
}
 
 
template <>
Real FE<1,SZABAB>::shape(const FEType fet,
                         const Elem * elem,
                         const unsigned int i,
                         const Point & p,
                         const bool add_p_level)
{
  libmesh_assert(elem);
 
  return FE<1,SZABAB>::shape(elem->type(), fet.order + add_p_level*elem->p_level(), i, p);
}
 
 
 
template <>
Real FE<1,SZABAB>::shape_deriv(const ElemType,
                               const Order libmesh_dbg_var(order),
                               const unsigned int i,
                               const unsigned int libmesh_dbg_var(j),
                               const Point & p)
{
  // only d()/dxi in 1D!
  libmesh_assert_equal_to (j, 0);
 
  const Real xi  = p(0);
  const Real xi2 = xi*xi;
 
  // Use this libmesh_assert rather than a switch with a single entry...
  // It will go away in optimized mode, essentially has the same effect.
  libmesh_assert_less_equal (order, SEVENTH);
 
  //   switch (order)
  //     {
  //     case FIRST:
  //     case SECOND:
  //     case THIRD:
  //     case FOURTH:
  //     case FIFTH:
  //     case SIXTH:
  //     case SEVENTH:
 
  switch(i)
    {
    case 0:return -1./2.;
    case 1:return 1./2.;
    case 2:return 1./2.*2.4494897427831780982*xi;
    case 3:return -1./4.*3.1622776601683793320+3./4.*3.1622776601683793320*xi2;
    case 4:return 1./16.*3.7416573867739413856*(-12.+20*xi2)*xi;
    case 5:return 9./16.*1.4142135623730950488+(-45./8.*1.4142135623730950488+105./16.*1.4142135623730950488*xi2)*xi2;
    case 6:return 1./32.*4.6904157598234295546*(30.+(-140.+126.*xi2)*xi2)*xi;
    case 7:return -5./32.*5.0990195135927848300+(105./32.*5.0990195135927848300+(-315./32.*5.0990195135927848300+231./32.*5.0990195135927848300*xi2)*xi2)*xi2;
    case 8:return 1./256.*5.4772255750516611346*(-280.+(2520.+(-5544.+3432.*xi2)*xi2)*xi2)*xi;
 
    default:
      libmesh_error_msg("Invalid shape function index!");
    }
}
 
 
 
template <>
Real FE<1,SZABAB>::shape_deriv(const Elem * elem,
                               const Order order,
                               const unsigned int i,
                               const unsigned int j,
                               const Point & p,
                               const bool add_p_level)
{
  libmesh_assert(elem);
 
  return FE<1,SZABAB>::shape_deriv(elem->type(),
                                   order + add_p_level*elem->p_level(), i, j, p);
}
 
 
 
template <>
Real FE<1,SZABAB>::shape_deriv(const FEType fet,
                               const Elem * elem,
                               const unsigned int i,
                               const unsigned int j,
                               const Point & p,
                               const bool add_p_level)
{
  libmesh_assert(elem);
 
  return FE<1,SZABAB>::shape_deriv(elem->type(),
                                   fet.order + add_p_level*elem->p_level(),
                                   i,
                                   j,
                                   p);
}
 
#ifdef LIBMESH_ENABLE_SECOND_DERIVATIVES
 
template <>
Real FE<1,SZABAB>::shape_second_deriv(const ElemType,
                                      const Order,
                                      const unsigned int,
                                      const unsigned int,
                                      const Point &)
{
  static bool warning_given = false;
 
  if (!warning_given)
    libMesh::err << "Second derivatives for Szabab elements "
                 << " are not yet implemented!"
                 << std::endl;
 
  warning_given = true;
  return 0.;
}
 
 
 
template <>
Real FE<1,SZABAB>::shape_second_deriv(const Elem *,
                                      const Order,
                                      const unsigned int,
                                      const unsigned int,
                                      const Point &,
                                      const bool)
{
  static bool warning_given = false;
 
  if (!warning_given)
    libMesh::err << "Second derivatives for Szabab elements "
                 << " are not yet implemented!"
                 << std::endl;
 
  warning_given = true;
  return 0.;
}
 
 
template <>
Real FE<1,SZABAB>::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)
{
  libmesh_assert(elem);
 
  return FE<1,SZABAB>::shape_second_deriv(elem->type(),
                                          fet.order + add_p_level*elem->p_level(),
                                          i,
                                          j,
                                          p);
}
 
 
#endif
 
} // namespace libMesh
 
 
#endif //LIBMESH_ENABLE_HIGHER_ORDER_SHAPES