DTK_BuhmannBasis_impl.hpp

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/*
  Copyright (c) 2012, Stuart R. Slattery
  All rights reserved.

  Redistribution and use in source and binary forms, with or without
  modification, are permitted provided that the following conditions are
  met:

  *: Redistributions of source code must retain the above copyright
  notice, this list of conditions and the following disclaimer.

  *: Redistributions in binary form must reproduce the above copyright
  notice, this list of conditions and the following disclaimer in the
  documentation and/or other materials provided with the distribution.

  *: Neither the name of the University of Wisconsin - Madison nor the
  names of its contributors may be used to endorse or promote products
  derived from this software without specific prior written permission.

  THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
  "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
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*/
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#ifndef DTKBUHMANNBASIS_IMPL_HPP
#define DTKBUHMANNBASIS_IMPL_HPP

#include <cmath>
#include <limits>

#include "DTK_EuclideanDistance.hpp"

namespace DataTransferKit
{
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template <>
inline double BuhmannBasis<3>::evaluateValue( const double radius,
                                              const double x ) const
{
    double xval = x / radius;
    double xp2 = xval * xval;
    double xp4 = xp2 * xp2;
    double xp6 = xp4 * xp2;
    double xp72 = std::sqrt( xp6 * xval );
    double q1 = 84.0 / 5.0;
    double q2 = 1024.0 / 5.0;
    return ( x > radius ) ? 0.0
                          : xp4 * xp4 - q1 * xp6 + q2 * xval * xp72 -
                                378.0 * xp4 + q2 * xp72 - q1 * xp2 + 1.0;
}

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template <>
inline double BuhmannBasis<3>::evaluateGradient( const double radius,
                                                 const double x ) const
{
    double xval = x / radius;
    double xp2 = xval * xval;
    double xp3 = xp2 * xval;
    double xp5 = xp3 * xp2;
    double xp52 = std::sqrt( xp5 );
    return ( x > radius )
               ? 0.0
               : ( 8.0 / 5.0 ) *
                     ( 576.0 * xval * xp52 + 448.0 * xp52 + 5.0 * xp5 * xp2 -
                       63.0 * xp5 - 945.0 * xp3 - 21.0 * xval );
}

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} // end namespace DataTransferKit

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#endif // end DTKBUHMANNBASIS_IMPL_HPP

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// end DTK_BuhmannBasis_impl.hpp
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