radial_basis_functions.h

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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
 
 
 
#ifndef LIBMESH_RADIAL_BASIS_FUNCTIONS_H
#define LIBMESH_RADIAL_BASIS_FUNCTIONS_H
 
// C++ includes
#include <limits>
 
// Local includes
#include "libmesh/libmesh_common.h"
#include "libmesh/utility.h"
 
 
 
namespace libMesh
{
 
// /**
//  * Simple radial basis function.
//  */
// class SimpleRBF
// {
// private:
//   const Real _rcut;
 
// public:
 
//   /**
//    * Constructor.
//    */
//   SimpleRBF (const Real r_cut = 1.) :
//     _rcut (r_cut)
//   {}
 
//   /**
//    * Evaluate the radial basis function at the requested location.
//    */
//   Real operator()(Real rad) const
//   {
//     if (rad > _rcut) return 0.;
 
//     rad /= _rcut;
 
//     return std::sqrt( 1+ rad*rad );
//   }
// };
 
 
 
template <unsigned int SpaceDim, unsigned int Continuity>
class WendlandRBF
{
private:
  const Real _rcut;
 
public:
 
  WendlandRBF (const Real r_cut = 1.) :
    _rcut (r_cut)
  { libmesh_experimental(); }
 
  Real operator()(Real /* rad */) const { libmesh_not_implemented(); return 0.; }
};
 
 
 
//-------------------------------------------------------
// Explicit specializations
template<>
inline
Real WendlandRBF<3,0>::operator()(Real rad) const
{
  if (rad > _rcut) return 0.;
 
  rad /= _rcut;
 
  return Utility::pow<2>(1.-rad);
}
 
template<>
inline
Real WendlandRBF<3,2>::operator()(Real rad) const
{
  if (rad > _rcut) return 0.;
 
  rad /= _rcut;
 
  return Utility::pow<4>(1.-rad)*(4.*rad + 1.);
}
 
template<>
inline
Real WendlandRBF<3,4>::operator()(Real rad) const
{
  if (rad > _rcut) return 0.;
 
  rad /= _rcut;
 
  return Utility::pow<6>(1.-rad)*((35.*rad + 18.)*rad + 3.);
}
 
template<>
inline
Real WendlandRBF<3,8>::operator()(Real rad) const
{
  if (rad > _rcut) return 0.;
 
  rad /= _rcut;
 
  return Utility::pow<8>(1.-rad)*(((32.*rad + 25.)*rad + 8.)*rad + 1.);
}
 
 
} // namespace libMesh
 
 
#endif // #define LIBMESH_RADIAL_BASIS_FUNCTIONS_H