MappingXYofXY.cpp

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///////////////////////////////////////////////////////////////////////////////
//
// File: MappingXYofXY.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: Mapping of the type X = X(x,y), Y = Y(x,y)
//
///////////////////////////////////////////////////////////////////////////////
 
#include <GlobalMapping/MappingXYofXY.h>
#include <MultiRegions/ExpList.h>
 
namespace Nektar
{
namespace GlobalMapping
{
 
std::string MappingXYofXY::className =
    GetMappingFactory().RegisterCreatorFunction("XYofXY", MappingXYofXY::create,
                                                "X = X(x,y), Y = Y(x,y)");
 
/**
 * @class MappingXYofXY
 * This class implements a mapping defined by the transformation
 * \f[ \bar{x} = \bar{x}(x,y) \f]
 * \f[ \bar{y} = \bar{y}(x,y) \f]
 * \f[ \bar{z} = z \f]
 * where \f$(\bar{x},\bar{y},\bar{z})\f$ are the Cartesian (physical)
 * coordinates and \f$(x,y,z)\f$ are the transformed (computational)
 *  coordinates.
 */
MappingXYofXY::MappingXYofXY(
    const LibUtilities::SessionReaderSharedPtr &pSession,
    const Array<OneD, MultiRegions::ExpListSharedPtr> &pFields)
    : Mapping(pSession, pFields)
{
}
 
/**
 *
 */
void MappingXYofXY::v_InitObject(
    const Array<OneD, MultiRegions::ExpListSharedPtr> &pFields,
    const TiXmlElement *pMapping)
{
    Mapping::v_InitObject(pFields, pMapping);
 
    m_constantJacobian = false;
 
    ASSERTL0(m_nConvectiveFields >= 2,
             "Mapping X = X(x,y), Y = Y(x,y) needs 2 velocity components.");
}
 
void MappingXYofXY::v_ContravarToCartesian(
    const Array<OneD, Array<OneD, NekDouble>> &inarray,
    Array<OneD, Array<OneD, NekDouble>> &outarray)
{
    int physTot = m_fields[0]->GetTotPoints();
 
    // U1 = fx*u1 + fy*u2
    Vmath::Vmul(physTot, m_GeometricInfo[0], 1, inarray[0], 1, outarray[0], 1);
    Vmath::Vvtvp(physTot, m_GeometricInfo[1], 1, inarray[1], 1, outarray[0], 1,
                 outarray[0], 1);
 
    // U2 = gx*u1+gy*u2
    Vmath::Vmul(physTot, m_GeometricInfo[2], 1, inarray[0], 1, outarray[1], 1);
    Vmath::Vvtvp(physTot, m_GeometricInfo[3], 1, inarray[1], 1, outarray[1], 1,
                 outarray[1], 1);
 
    // U3 = u3
    if (m_nConvectiveFields == 3)
    {
        Vmath::Vcopy(physTot, inarray[2], 1, outarray[2], 1);
    }
}
 
void MappingXYofXY::v_CovarToCartesian(
    const Array<OneD, Array<OneD, NekDouble>> &inarray,
    Array<OneD, Array<OneD, NekDouble>> &outarray)
{
    int physTot = m_fields[0]->GetTotPoints();
    Array<OneD, NekDouble> wk(physTot, 0.0);
 
    // U1 = [gy*u1-gx*u2]/(fx*gy-gx*fy)
    Vmath::Vmul(physTot, inarray[1], 1, m_GeometricInfo[2], 1, outarray[0], 1);
    Vmath::Vvtvm(physTot, inarray[0], 1, m_GeometricInfo[3], 1, outarray[0], 1,
                 outarray[0], 1);
    Vmath::Vdiv(physTot, outarray[0], 1, m_GeometricInfo[4], 1, outarray[0], 1);
 
    // U2 = [fx*u2 - fy*u1]/(fx*gy-gx*fy)
    Vmath::Vmul(physTot, inarray[0], 1, m_GeometricInfo[1], 1, outarray[1], 1);
    Vmath::Vvtvm(physTot, inarray[1], 1, m_GeometricInfo[0], 1, outarray[1], 1,
                 outarray[1], 1);
    Vmath::Vdiv(physTot, outarray[1], 1, m_GeometricInfo[4], 1, outarray[1], 1);
 
    // U3 = u3
    if (m_nConvectiveFields == 3)
    {
        Vmath::Vcopy(physTot, inarray[2], 1, outarray[2], 1);
    }
}
 
void MappingXYofXY::v_ContravarFromCartesian(
    const Array<OneD, Array<OneD, NekDouble>> &inarray,
    Array<OneD, Array<OneD, NekDouble>> &outarray)
{
    int physTot = m_fields[0]->GetTotPoints();
    Array<OneD, NekDouble> wk(physTot, 0.0);
 
    // U1 = [gy*u1-fy*u2]/(fx*gy-gx*fy)
    Vmath::Vmul(physTot, inarray[1], 1, m_GeometricInfo[1], 1, outarray[0], 1);
    Vmath::Vvtvm(physTot, inarray[0], 1, m_GeometricInfo[3], 1, outarray[0], 1,
                 outarray[0], 1);
    Vmath::Vdiv(physTot, outarray[0], 1, m_GeometricInfo[4], 1, outarray[0], 1);
 
    // U2 = [fx*u2-gx*u1]/(fx*gy-gx*fy)
    Vmath::Vmul(physTot, inarray[0], 1, m_GeometricInfo[2], 1, outarray[1], 1);
    Vmath::Vvtvm(physTot, inarray[1], 1, m_GeometricInfo[0], 1, outarray[1], 1,
                 outarray[1], 1);
    Vmath::Vdiv(physTot, outarray[1], 1, m_GeometricInfo[4], 1, outarray[1], 1);
 
    // U3 = u3
    if (m_nConvectiveFields == 3)
    {
        Vmath::Vcopy(physTot, inarray[2], 1, outarray[2], 1);
    }
}
 
void MappingXYofXY::v_CovarFromCartesian(
    const Array<OneD, Array<OneD, NekDouble>> &inarray,
    Array<OneD, Array<OneD, NekDouble>> &outarray)
{
    int physTot = m_fields[0]->GetTotPoints();
 
    // U1 = u1*fx +gx*u2
    Vmath::Vmul(physTot, m_GeometricInfo[0], 1, inarray[0], 1, outarray[0], 1);
    Vmath::Vvtvp(physTot, m_GeometricInfo[2], 1, inarray[1], 1, outarray[0], 1,
                 outarray[0], 1);
 
    // U2 = fy*u1 + gy*u2
    Vmath::Vmul(physTot, m_GeometricInfo[1], 1, inarray[0], 1, outarray[1], 1);
    Vmath::Vvtvp(physTot, m_GeometricInfo[3], 1, inarray[1], 1, outarray[1], 1,
                 outarray[1], 1);
 
    // U3 = u3
    if (m_nConvectiveFields == 3)
    {
        Vmath::Vcopy(physTot, inarray[2], 1, outarray[2], 1);
    }
}
 
void MappingXYofXY::v_GetJacobian(Array<OneD, NekDouble> &outarray)
{
    int physTot = m_fields[0]->GetTotPoints();
    Vmath::Vabs(physTot, m_GeometricInfo[4], 1, outarray, 1);
}
 
void MappingXYofXY::v_GetMetricTensor(
    Array<OneD, Array<OneD, NekDouble>> &outarray)
{
    int physTot = m_fields[0]->GetTotPoints();
    int nvel    = m_nConvectiveFields;
 
    for (int i = 0; i < nvel * nvel; i++)
    {
        outarray[i] = Array<OneD, NekDouble>(physTot, 0.0);
    }
 
    // g_{1,1} = m_metricTensor[0]
    Vmath::Vcopy(physTot, m_metricTensor[0], 1, outarray[0 * nvel + 0], 1);
 
    // g_{2,2} = m_metricTensor[1]
    Vmath::Vcopy(physTot, m_metricTensor[1], 1, outarray[1 * nvel + 1], 1);
 
    // g_{1,2}=g{2,1} = m_metricTensor[2]
    Vmath::Vcopy(physTot, m_metricTensor[2], 1, outarray[0 * nvel + 1], 1);
    Vmath::Vcopy(physTot, m_metricTensor[2], 1, outarray[1 * nvel + 0], 1);
 
    // g_{3,3}  = 1
    if (m_nConvectiveFields == 3)
    {
        Vmath::Sadd(physTot, 1.0, outarray[2 * nvel + 2], 1,
                    outarray[2 * nvel + 2], 1);
    }
}
 
void MappingXYofXY::v_GetInvMetricTensor(
    Array<OneD, Array<OneD, NekDouble>> &outarray)
{
    int physTot = m_fields[0]->GetTotPoints();
    int nvel    = m_nConvectiveFields;
 
    for (int i = 0; i < nvel * nvel; i++)
    {
        outarray[i] = Array<OneD, NekDouble>(physTot, 0.0);
    }
 
    // Get Jacobian
    Array<OneD, NekDouble> Jac(physTot, 0.0);
    GetJacobian(Jac);
 
    // Get Jacobian squared
    Array<OneD, NekDouble> wk(physTot, 0.0);
    Vmath::Vmul(physTot, Jac, 1, Jac, 1, wk, 1);
    // G^{1,1} = m_metricTensor[1]/Jac^2
    Vmath::Vcopy(physTot, m_metricTensor[1], 1, outarray[0 * nvel + 0], 1);
    Vmath::Vdiv(physTot, outarray[0 * nvel + 0], 1, wk, 1,
                outarray[0 * nvel + 0], 1);
 
    // G^{2,2} = m_metricTensor[0]/Jac^2
    Vmath::Vcopy(physTot, m_metricTensor[0], 1, outarray[1 * nvel + 1], 1);
    Vmath::Vdiv(physTot, outarray[1 * nvel + 1], 1, wk, 1,
                outarray[1 * nvel + 1], 1);
 
    // G^{1,2} = G^{2,1} = -m_metricTensor[2]/Jac^2
    Vmath::Vcopy(physTot, m_metricTensor[2], 1, outarray[0 * nvel + 1], 1);
    Vmath::Neg(physTot, outarray[0 * nvel + 1], 1);
    Vmath::Vdiv(physTot, outarray[0 * nvel + 1], 1, wk, 1,
                outarray[0 * nvel + 1], 1);
    Vmath::Vcopy(physTot, outarray[0 * nvel + 1], 1, outarray[1 * nvel + 0], 1);
 
    // G^{3,3}  = 1
    if (m_nConvectiveFields == 3)
    {
        Vmath::Sadd(physTot, 1.0, outarray[2 * nvel + 2], 1,
                    outarray[2 * nvel + 2], 1);
    }
}
 
void MappingXYofXY::v_ApplyChristoffelContravar(
    const Array<OneD, Array<OneD, NekDouble>> &inarray,
    Array<OneD, Array<OneD, NekDouble>> &outarray)
{
    int physTot = m_fields[0]->GetTotPoints();
    int nvel    = m_nConvectiveFields;
 
    for (int i = 0; i < nvel; i++)
    {
        for (int j = 0; j < nvel; j++)
        {
            outarray[i * nvel + j] = Array<OneD, NekDouble>(physTot, 0.0);
        }
    }
 
    // Calculate non-zero terms
 
    // outarray(0,0) = U1 * m_Christoffel[0] + U2 * m_Christoffel[1]
    Vmath::Vmul(physTot, m_Christoffel[0], 1, inarray[0], 1,
                outarray[0 * nvel + 0], 1);
    Vmath::Vvtvp(physTot, m_Christoffel[1], 1, inarray[1], 1,
                 outarray[0 * nvel + 0], 1, outarray[0 * nvel + 0], 1);
 
    // outarray(0,1) = U1 * m_Christoffel[1] + U2 * m_Christoffel[2]
    Vmath::Vmul(physTot, m_Christoffel[1], 1, inarray[0], 1,
                outarray[0 * nvel + 1], 1);
    Vmath::Vvtvp(physTot, m_Christoffel[2], 1, inarray[1], 1,
                 outarray[0 * nvel + 1], 1, outarray[0 * nvel + 1], 1);
 
    // outarray(1,0) = U1 * m_Christoffel[3] + U2 * m_Christoffel[4]
    Vmath::Vmul(physTot, m_Christoffel[3], 1, inarray[0], 1,
                outarray[1 * nvel + 0], 1);
    Vmath::Vvtvp(physTot, m_Christoffel[4], 1, inarray[1], 1,
                 outarray[1 * nvel + 0], 1, outarray[1 * nvel + 0], 1);
 
    // outarray(1,1) = U1 * m_Christoffel[4] + U2 * m_Christoffel[5]
    Vmath::Vmul(physTot, m_Christoffel[4], 1, inarray[0], 1,
                outarray[1 * nvel + 1], 1);
    Vmath::Vvtvp(physTot, m_Christoffel[5], 1, inarray[1], 1,
                 outarray[1 * nvel + 1], 1, outarray[1 * nvel + 1], 1);
}
 
void MappingXYofXY::v_ApplyChristoffelCovar(
    const Array<OneD, Array<OneD, NekDouble>> &inarray,
    Array<OneD, Array<OneD, NekDouble>> &outarray)
{
    int physTot = m_fields[0]->GetTotPoints();
    int nvel    = m_nConvectiveFields;
 
    for (int i = 0; i < nvel; i++)
    {
        for (int j = 0; j < nvel; j++)
        {
            outarray[i * nvel + j] = Array<OneD, NekDouble>(physTot, 0.0);
        }
    }
 
    // Calculate non-zero terms
 
    // outarray(0,0) = U1 * m_Christoffel[0] + U2 * m_Christoffel[3]
    Vmath::Vmul(physTot, m_Christoffel[0], 1, inarray[0], 1,
                outarray[0 * nvel + 0], 1);
    Vmath::Vvtvp(physTot, m_Christoffel[3], 1, inarray[1], 1,
                 outarray[0 * nvel + 0], 1, outarray[0 * nvel + 0], 1);
 
    // outarray(0,1) = U1 * m_Christoffel[1] + U2 * m_Christoffel[4]
    Vmath::Vmul(physTot, m_Christoffel[1], 1, inarray[0], 1,
                outarray[0 * nvel + 1], 1);
    Vmath::Vvtvp(physTot, m_Christoffel[4], 1, inarray[1], 1,
                 outarray[0 * nvel + 1], 1, outarray[0 * nvel + 1], 1);
 
    // outarray(1,0) = U1 * m_Christoffel[1] + U2 * m_Christoffel[4]
    Vmath::Vmul(physTot, m_Christoffel[1], 1, inarray[0], 1,
                outarray[1 * nvel + 0], 1);
    Vmath::Vvtvp(physTot, m_Christoffel[4], 1, inarray[1], 1,
                 outarray[1 * nvel + 0], 1, outarray[1 * nvel + 0], 1);
 
    // outarray(1,1) = U1 * m_Christoffel[2] + U2 * m_Christoffel[5]
    Vmath::Vmul(physTot, m_Christoffel[2], 1, inarray[0], 1,
                outarray[1 * nvel + 1], 1);
    Vmath::Vvtvp(physTot, m_Christoffel[5], 1, inarray[1], 1,
                 outarray[1 * nvel + 1], 1, outarray[1 * nvel + 1], 1);
}
 
void MappingXYofXY::v_UpdateGeomInfo()
{
    int phystot = m_fields[0]->GetTotPoints();
    // Allocation of geometry memory
    m_GeometricInfo = Array<OneD, Array<OneD, NekDouble>>(5);
    for (int i = 0; i < m_GeometricInfo.size(); i++)
    {
        m_GeometricInfo[i] = Array<OneD, NekDouble>(phystot, 0.0);
    }
 
    bool waveSpace = m_fields[0]->GetWaveSpace();
    m_fields[0]->SetWaveSpace(false);
 
    // Calculate derivatives of x transformation --> m_GeometricInfo 0-1
    m_fields[0]->PhysDeriv(MultiRegions::DirCartesianMap[0], m_coords[0],
                           m_GeometricInfo[0]);
    m_fields[0]->PhysDeriv(MultiRegions::DirCartesianMap[1], m_coords[0],
                           m_GeometricInfo[1]);
 
    // Calculate derivatives of y transformation m_GeometricInfo 2-3
    m_fields[0]->PhysDeriv(MultiRegions::DirCartesianMap[0], m_coords[1],
                           m_GeometricInfo[2]);
    m_fields[0]->PhysDeriv(MultiRegions::DirCartesianMap[1], m_coords[1],
                           m_GeometricInfo[3]);
 
    // Calculate fx*gy-gx*fy --> m_GeometricInfo4
    Vmath::Vmul(phystot, m_GeometricInfo[1], 1, m_GeometricInfo[2], 1,
                m_GeometricInfo[4], 1);
    Vmath::Vvtvm(phystot, m_GeometricInfo[0], 1, m_GeometricInfo[3], 1,
                 m_GeometricInfo[4], 1, m_GeometricInfo[4], 1);
    //
    CalculateMetricTensor();
    CalculateChristoffel();
 
    m_fields[0]->SetWaveSpace(waveSpace);
}
 
void MappingXYofXY::CalculateMetricTensor()
{
    int physTot = m_fields[0]->GetTotPoints();
    // Allocate memory
    m_metricTensor = Array<OneD, Array<OneD, NekDouble>>(3);
    for (int i = 0; i < m_metricTensor.size(); i++)
    {
        m_metricTensor[i] = Array<OneD, NekDouble>(physTot, 0.0);
    }
    // g_{1,1} = fx^2+gx^2
    Vmath::Vmul(physTot, m_GeometricInfo[0], 1, m_GeometricInfo[0], 1,
                m_metricTensor[0], 1);
    Vmath::Vvtvp(physTot, m_GeometricInfo[2], 1, m_GeometricInfo[2], 1,
                 m_metricTensor[0], 1, m_metricTensor[0], 1);
    // g_{2,2} = fy^2+gy^2
    Vmath::Vmul(physTot, m_GeometricInfo[1], 1, m_GeometricInfo[1], 1,
                m_metricTensor[1], 1);
    Vmath::Vvtvp(physTot, m_GeometricInfo[3], 1, m_GeometricInfo[3], 1,
                 m_metricTensor[1], 1, m_metricTensor[1], 1);
    // g_{1,2} = g_{2,1} = fy*fx+gx*gy
    Vmath::Vmul(physTot, m_GeometricInfo[0], 1, m_GeometricInfo[1], 1,
                m_metricTensor[2], 1);
    Vmath::Vvtvp(physTot, m_GeometricInfo[2], 1, m_GeometricInfo[3], 1,
                 m_metricTensor[2], 1, m_metricTensor[2], 1);
}
 
void MappingXYofXY::CalculateChristoffel()
{
    int physTot = m_fields[0]->GetTotPoints();
    int nvel    = m_nConvectiveFields;
 
    Array<OneD, Array<OneD, NekDouble>> G(nvel * nvel);
    Array<OneD, Array<OneD, NekDouble>> G_inv(nvel * nvel);
    Array<OneD, Array<OneD, NekDouble>> gradG(2 * 2 * 2);
    Array<OneD, Array<OneD, NekDouble>> tmp(2 * 2 * 2);
    m_Christoffel = Array<OneD, Array<OneD, NekDouble>>(6);
    // Allocate memory
    for (int i = 0; i < gradG.size(); i++)
    {
        gradG[i] = Array<OneD, NekDouble>(physTot, 0.0);
        tmp[i]   = Array<OneD, NekDouble>(physTot, 0.0);
    }
    for (int i = 0; i < G.size(); i++)
    {
        G[i]     = Array<OneD, NekDouble>(physTot, 0.0);
        G_inv[i] = Array<OneD, NekDouble>(physTot, 0.0);
    }
 
    // Get the metric tensor and its inverse
    GetMetricTensor(G);
    GetInvMetricTensor(G_inv);
 
    bool waveSpace = m_fields[0]->GetWaveSpace();
    m_fields[0]->SetWaveSpace(false);
    // Calculate gradients of g
    //   consider only 2 dimensions, since the 3rd is trivial
    for (int i = 0; i < 2; i++)
    {
        for (int j = 0; j < 2; j++)
        {
            for (int k = 0; k < 2; k++)
            {
                m_fields[0]->PhysDeriv(MultiRegions::DirCartesianMap[k],
                                       G[i * nvel + j],
                                       gradG[i * 2 * 2 + j * 2 + k]);
            }
        }
    }
 
    // Calculate tmp[p,j,k] = 1/2( gradG[pj,k]+ gradG[pk,j]-gradG[jk,p])
    for (int p = 0; p < 2; p++)
    {
        for (int j = 0; j < 2; j++)
        {
            for (int k = 0; k < 2; k++)
            {
                Vmath::Vadd(physTot, gradG[p * 2 * 2 + j * 2 + k], 1,
                            gradG[p * 2 * 2 + k * 2 + j], 1,
                            tmp[p * 2 * 2 + j * 2 + k], 1);
                Vmath::Vsub(physTot, tmp[p * 2 * 2 + j * 2 + k], 1,
                            gradG[j * 2 * 2 + k * 2 + p], 1,
                            tmp[p * 2 * 2 + j * 2 + k], 1);
                Vmath::Smul(physTot, 0.5, tmp[p * 2 * 2 + j * 2 + k], 1,
                            tmp[p * 2 * 2 + j * 2 + k], 1);
            }
        }
    }
 
    // Calculate Christoffel symbols = g^ip tmp[p,j,k]
    int n = 0;
    for (int i = 0; i < 2; i++)
    {
        for (int j = 0; j < 2; j++)
        {
            for (int k = 0; k <= j; k++)
            {
                m_Christoffel[n] = Array<OneD, NekDouble>(physTot, 0.0);
                for (int p = 0; p < 2; p++)
                {
                    Vmath::Vvtvp(physTot, G_inv[i * nvel + p], 1,
                                 tmp[p * 2 * 2 + j * 2 + k], 1,
                                 m_Christoffel[n], 1, m_Christoffel[n], 1);
                }
                n = n + 1;
            }
        }
    }
 
    m_fields[0]->SetWaveSpace(waveSpace);
}
 
} // namespace GlobalMapping
} // namespace Nektar