FourierPoints.cpp

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///////////////////////////////////////////////////////////////////////////////
//
// File: FourierPoints.cpp
//
// 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
// the rights to use, copy, modify, merge, publish, distribute, sublicense,
// 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:
//
// The above copyright notice and this permission notice shall be included
// in all copies or substantial portions of the Software.
//
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
// OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
// THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
// DEALINGS IN THE SOFTWARE.
//
// Description: 1D Evenly-Spaced Points
//
///////////////////////////////////////////////////////////////////////////////
 
#include <LibUtilities/Foundations/FourierPoints.h>
#include <LibUtilities/Foundations/ManagerAccess.h>
 
namespace Nektar::LibUtilities
{
bool FourierPoints::initPointsManager[] = {PointsManager().RegisterCreator(
    PointsKey(0, eFourierEvenlySpaced), FourierPoints::Create)};
 
void FourierPoints::v_CalculatePoints()
{
    // Allocate the storage for points
    PointsBaseType::v_CalculatePoints();
 
    size_t npts = m_pointsKey.GetNumPoints();
    ASSERTL0(!(npts % 2), "Fourier points need to be of even order");
 
    NekDouble dx = 2.0 / (NekDouble)(npts);
    for (size_t i = 0; i < npts; ++i)
    {
        m_points[0][i] = -1.0 + i * dx;
    }
}
 
void FourierPoints::v_CalculateWeights()
{
    // Allocate the storage for points
    PointsBaseType::v_CalculateWeights();
 
    size_t npts = m_pointsKey.GetNumPoints();
    for (size_t i = 0; i < npts; ++i)
    {
        m_weights[i] = 1.0 / (NekDouble)npts;
    }
}
 
void FourierPoints::v_CalculateDerivMatrix()
{
    //// Allocate the derivative matrix.
    Points<NekDouble>::v_CalculateDerivMatrix();
 
    size_t npts = m_pointsKey.GetNumPoints();
 
    for (size_t i = 1; i < npts; ++i)
    {
        m_derivmatrix[0]->SetValue(i, i, 0.0);
    }
 
    for (size_t i = 1; i < npts; ++i)
    {
        m_derivmatrix[0]->SetValue(0, i,
                                   -0.5 * M_PI * pow(-1.0, NekDouble(i)) *
                                       cos(M_PI * i / npts) /
                                       sin(M_PI * i / npts));
    }
 
    for (size_t i = 1; i < npts; ++i)
    {
        for (size_t j = 0; j < npts; ++j)
        {
            m_derivmatrix[0]->SetValue(
                i, j, (*m_derivmatrix[0])(0, (j - i + npts) % npts));
        }
    }
}
 
std::shared_ptr<Points<NekDouble>> FourierPoints::Create(const PointsKey &key)
{
    std::shared_ptr<Points<NekDouble>> returnval(
        MemoryManager<FourierPoints>::AllocateSharedPtr(key));
 
    returnval->Initialize();
 
    return returnval;
}
 
std::shared_ptr<NekMatrix<NekDouble>> FourierPoints::CreateMatrix(
    const PointsKey &pkey)
{
    size_t numpoints = pkey.GetNumPoints();
    Array<OneD, const NekDouble> xpoints;
 
    PointsManager()[pkey]->GetPoints(xpoints);
 
    /// Delegate to function below.
    return GetI(numpoints, xpoints);
}
 
const std::shared_ptr<NekMatrix<NekDouble>> FourierPoints::v_GetI(
    const PointsKey &pkey)
{
    ASSERTL0(pkey.GetPointsDim() == 1,
             "Fourier Points can only interp to other 1d point distributions");
 
    return m_InterpManager[pkey];
}
 
const std::shared_ptr<NekMatrix<NekDouble>> FourierPoints::v_GetI(
    const Array<OneD, const NekDouble> &x)
{
    size_t numpoints = 1;
 
    /// Delegate to function below.
    return GetI(numpoints, x);
}
 
const std::shared_ptr<NekMatrix<NekDouble>> FourierPoints::v_GetI(
    size_t numpoints, const Array<OneD, const NekDouble> &x)
{
    Array<OneD, NekDouble> interp(GetNumPoints() * numpoints);
 
    CalculateInterpMatrix(numpoints, x, interp);
 
    NekDouble *t = interp.data();
    size_t np    = GetNumPoints();
    std::shared_ptr<NekMatrix<NekDouble>> returnval(
        MemoryManager<NekMatrix<NekDouble>>::AllocateSharedPtr(numpoints, np,
                                                               t));
 
    return returnval;
}
 
void FourierPoints::CalculateInterpMatrix(
    size_t npts, const Array<OneD, const NekDouble> &xpoints,
    Array<OneD, NekDouble> &interp)
{
    const NekDouble h = 2.0 / m_pointsKey.GetNumPoints();
    for (size_t i = 0; i < npts; ++i)
    {
        for (size_t j = 0; j < m_pointsKey.GetNumPoints(); ++j)
        {
            interp[i * m_pointsKey.GetNumPoints() + j] =
                PeriodicSincFunction(M_PI * (xpoints[i] - m_points[0][j]), h);
        }
    }
}
 
NekDouble FourierPoints::PeriodicSincFunction(const NekDouble x,
                                              const NekDouble h)
{
    // This formula is based upon a mapped version of
    // the periodic sinc presented in Trefethen's "Spectral Methods
    // in Matlab"
 
    NekDouble y = 1.0;
 
    if (fabs(x) > 1.0e-12)
    {
        y = sin(M_PI * x / (M_PI * h)) / ((2.0 / h) * tan(0.5 * x));
    }
 
    return y;
}
 
} // namespace Nektar::LibUtilities