fe_xyz_shape_1D.C

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// The libMesh Finite Element Library.
// Copyright (C) 2002-2018 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/fe.h"
#include "libmesh/elem.h"



namespace libMesh
{


template <>
Real FE<1,XYZ>::shape(const ElemType,
                      const Order,
                      const unsigned int,
                      const Point &)
{
  libmesh_error_msg("XYZ polynomials require the element \n because the centroid is needed.");
  return 0.;
}



template <>
Real FE<1,XYZ>::shape(const Elem * elem,
                      const Order libmesh_dbg_var(order),
                      const unsigned int i,
                      const Point & point_in)
{
  libmesh_assert(elem);
  libmesh_assert_less_equal (i, order + elem->p_level());

  Point centroid = elem->centroid();
  Real max_distance = 0.;
  for (unsigned int p = 0; p < elem->n_nodes(); p++)
    {
      const Real distance = std::abs(centroid(0) - elem->point(p)(0));
      max_distance = std::max(distance, max_distance);
    }

  const Real x  = point_in(0);
  const Real xc = centroid(0);
  const Real dx = (x - xc)/max_distance;

  // monomials. since they are hierarchic we only need one case block.
  switch (i)
    {
    case 0:
      return 1.;

    case 1:
      return dx;

    case 2:
      return dx*dx;

    case 3:
      return dx*dx*dx;

    case 4:
      return dx*dx*dx*dx;

    default:
      Real val = 1.;
      for (unsigned int index = 0; index != i; ++index)
        val *= dx;
      return val;
    }
}



template <>
Real FE<1,XYZ>::shape_deriv(const ElemType,
                            const Order,
                            const unsigned int,
                            const unsigned int,
                            const Point &)
{
  libmesh_error_msg("XYZ polynomials require the element \nbecause the centroid is needed.");
  return 0.;
}



template <>
Real FE<1,XYZ>::shape_deriv(const Elem * elem,
                            const Order libmesh_dbg_var(order),
                            const unsigned int i,
                            const unsigned int libmesh_dbg_var(j),
                            const Point & point_in)
{
  libmesh_assert(elem);
  libmesh_assert_less_equal (i, order + elem->p_level());

  // only d()/dxi in 1D!

  libmesh_assert_equal_to (j, 0);

  Point centroid = elem->centroid();
  Real max_distance = 0.;
  for (unsigned int p = 0; p < elem->n_nodes(); p++)
    {
      const Real distance = std::abs(centroid(0) - elem->point(p)(0));
      max_distance = std::max(distance, max_distance);
    }

  const Real x  = point_in(0);
  const Real xc = centroid(0);
  const Real dx = (x - xc)/max_distance;

  // monomials. since they are hierarchic we only need one case block.
  switch (i)
    {
    case 0:
      return 0.;

    case 1:
      return 1.;

    case 2:
      return 2.*dx/max_distance;

    case 3:
      return 3.*dx*dx/max_distance;

    case 4:
      return 4.*dx*dx*dx/max_distance;

    default:
      Real val = i;
      for (unsigned int index = 1; index != i; ++index)
        val *= dx;
      return val/max_distance;
    }
}



template <>
Real FE<1,XYZ>::shape_second_deriv(const ElemType,
                                   const Order,
                                   const unsigned int,
                                   const unsigned int,
                                   const Point &)
{
  libmesh_error_msg("XYZ polynomials require the element \nbecause the centroid is needed.");
  return 0.;
}



template <>
Real FE<1,XYZ>::shape_second_deriv(const Elem * elem,
                                   const Order libmesh_dbg_var(order),
                                   const unsigned int i,
                                   const unsigned int libmesh_dbg_var(j),
                                   const Point & point_in)
{
  libmesh_assert(elem);
  libmesh_assert_less_equal (i, order + elem->p_level());

  // only d2()/dxi2 in 1D!

  libmesh_assert_equal_to (j, 0);

  Point centroid = elem->centroid();
  Real max_distance = 0.;
  for (unsigned int p = 0; p < elem->n_nodes(); p++)
    {
      const Real distance = std::abs(centroid(0) - elem->point(p)(0));
      max_distance = std::max(distance, max_distance);
    }

  const Real x  = point_in(0);
  const Real xc = centroid(0);
  const Real dx = (x - xc)/max_distance;
  const Real dist2 = pow(max_distance,2.);

  // monomials. since they are hierarchic we only need one case block.
  switch (i)
    {
    case 0:
    case 1:
      return 0.;

    case 2:
      return 2./dist2;

    case 3:
      return 6.*dx/dist2;

    case 4:
      return 12.*dx*dx/dist2;

    default:
      Real val = 2.;
      for (unsigned int index = 2; index != i; ++index)
        val *= (index+1) * dx;
      return val/dist2;
    }
}

} // namespace libMesh