Interp.h

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///////////////////////////////////////////////////////////////////////////////
//
// File: Interp.h
//
// For more information, please see: http://www.nektar.info
//
// The MIT License
//
// Copyright (c) 2006 Division of Applied Mathematics, Brown University (USA),
// Department of Aeronautics, Imperial College London (UK), and Scientific
// Computing and Imaging Institute, University of Utah (USA).
//
// Permission is hereby granted, free of charge, to any person obtaining a
// copy of this software and associated documentation files (the "Software"),
// to deal in the Software without restriction, including without limitation
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// and/or sell copies of the Software, and to permit persons to whom the
// Software is furnished to do so, subject to the following conditions:
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// The above copyright notice and this permission notice shall be included
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//
// Description: Definition of interpolation routines
//
///////////////////////////////////////////////////////////////////////////////
 
#ifndef NEKTAR_LIB_UTILTIES_FOUNDATIONS_INTERP_H
#define NEKTAR_LIB_UTILTIES_FOUNDATIONS_INTERP_H
 
#include <LibUtilities/BasicConst/NektarUnivTypeDefs.hpp>
#include <LibUtilities/Foundations/FoundationsFwd.hpp>
#include <LibUtilities/LibUtilitiesDeclspec.h>
 
namespace Nektar
{
template <typename Dim, typename DataType> class Array;
}
 
namespace Nektar
{
namespace LibUtilities
{
 
// Physical Space Interpolation methods
 
/** \brief this function interpolates a 1D function \f$f\f$ evaluated
 *  at the quadrature points of the basis \a fbasis0 to the
 *  function values at the quadrature points of the basis \a tbasis0
 *
 *  Given a function \f$ f\f$ evaluated at the \a Q quadrature points
 *  of the basis \a fbasis0, this routine calculates, using
 *  \a (Q-1)th order polynomial interpolation, the function values
 *  at the \a Q2 quadrature points of the basis \a tbasis0.
 *
 *  \param fbasis0 the basis at which's quadrature points the
 *  function is given
 *  \param from the array containg the function \f$ f\f$  evaluated
 *   at the quadrature points of \a fbasis0
 *  \param tbasis0 the basis to which's quadrature points the
 *  function should be interpolated
 *  \param to the array containg the function \f$ f\f$  evaluated
 *   at the quadrature points of \a tbasis0 (output of the function)
 */
// 1D Interpolation
LIB_UTILITIES_EXPORT void Interp1D(const BasisKey &fbasis0,
                                   const Array<OneD, const NekDouble> &from,
                                   const BasisKey &tbasis0,
                                   Array<OneD, NekDouble> &to);
 
LIB_UTILITIES_EXPORT void Interp1D(const PointsKey &fpoints0,
                                   const Array<OneD, const NekDouble> &from,
                                   const PointsKey &tpoints0,
                                   Array<OneD, NekDouble> &to);
 
LIB_UTILITIES_EXPORT void Interp1D(const BasisKey &fbasis0,
                                   const NekDouble *from,
                                   const BasisKey &tbasis0, NekDouble *to);
 
LIB_UTILITIES_EXPORT void Interp1D(const PointsKey &fpoints0,
                                   const NekDouble *from,
                                   const PointsKey &tpoints0, NekDouble *to);
 
/** \brief this function interpolates a 2D function \f$f\f$ evaluated
 *  at the quadrature points of the 2D basis, constructed by
 *  \a fbasis0 and \a fbasis1, to the function values at the
 *  quadrature points of the 2D basis, constructed by \a tbasis0 and
 *  \a tbasis1
 *
 *  Given a function \f$ f\f$ evaluated at the \a Q quadrature points
 *  of the first expansion basis, this routine calculates, using
 *  \a (Q-1)th order polynomial interpolation, the function values
 *  at the \a Q2 quadrature points of the second basis.
 *
 *  \param fbasis0 the basis at which's quadrature points the
 *  function is given
 *  \param from the array containg the function \f$ f\f$  evaluated
 *   at the quadrature points of \a fbasis0
 *  \param tbasis0 the basis to which's quadrature points the
 *  function should be interpolated
 *  \param to the array containg the function \f$ f\f$  evaluated
 *   at the quadrature points of \a tbasis0 (output of the function)
 */
// 2D Interpolation
LIB_UTILITIES_EXPORT void Interp2D(const BasisKey &fbasis0,
                                   const BasisKey &fbasis1,
                                   const Array<OneD, const NekDouble> &from,
                                   const BasisKey &tbasis0,
                                   const BasisKey &tbasis1,
                                   Array<OneD, NekDouble> &to);
 
LIB_UTILITIES_EXPORT void Interp2D(const PointsKey &fpoints0,
                                   const PointsKey &fpoints1,
                                   const Array<OneD, const NekDouble> &from,
                                   const PointsKey &tpoints0,
                                   const PointsKey &tpoints1,
                                   Array<OneD, NekDouble> &to);
 
LIB_UTILITIES_EXPORT void Interp2D(const PointsKey &fpoints0,
                                   const PointsKey &fpoints1,
                                   const NekDouble *from,
                                   const PointsKey &tpoints0,
                                   const PointsKey &tpoints1, NekDouble *to);
 
/** \brief this function interpolates a 3D function \f$f\f$ evaluated
 *  at the quadrature points of the 3D basis, constructed by
 *  \a fbasis0, \a fbasis1, and \a fbasis2 to the function values at the
 *  quadrature points of the 3D basis, constructed by \a tbasis0,
 *  \a tbasis1, and \a tbasis2.
 *
 *  Given a function \f$ f\f$ evaluated at the \a Q quadrature points
 *  of the first expansion basis, this routine calculates, using
 *  \a (Q-1)th order polynomial interpolation, the function values
 *  at the \a Q2 quadrature points of the second basis, and the function
 *  values at the \a Q3 quadrature points of the third basis.
 *
 *  \param fbasis0 the basis at which's quadrature points the
 *  function is given
 *  \param from the array containg the function \f$ f\f$  evaluated
 *   at the quadrature points of \a fbasis0
 *  \param tbasis0 the basis to which's quadrature points the
 *  function should be interpolated
 *  \param to the array containg the function \f$ f\f$  evaluated
 *   at the quadrature points of \a tbasis0 (output of the function)
 */
// 3D interpolation
LIB_UTILITIES_EXPORT void Interp3D(
    const BasisKey &fbasis0, const BasisKey &fbasis1, const BasisKey &fbasis2,
    const Array<OneD, const NekDouble> &from, const BasisKey &tbasis0,
    const BasisKey &tbasis1, const BasisKey &tbasis2,
    Array<OneD, NekDouble> &to);
 
LIB_UTILITIES_EXPORT void Interp3D(
    const PointsKey &fpoints0, const PointsKey &fpoints1,
    const PointsKey &fpoints2, const Array<OneD, const NekDouble> &from,
    const PointsKey &tpoints0, const PointsKey &tpoints1,
    const PointsKey &tpoints2, Array<OneD, NekDouble> &to);
 
LIB_UTILITIES_EXPORT void Interp3D(
    const PointsKey &fpoints0, const PointsKey &fpoints1,
    const PointsKey &fpoints2, const NekDouble *from, const PointsKey &tpoints0,
    const PointsKey &tpoints1, const PointsKey &tpoints2, NekDouble *to);
 
} // namespace LibUtilities
} // namespace Nektar
 
#endif // FOUNDATIONS_H