MappingXofZ.cpp

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///////////////////////////////////////////////////////////////////////////////
//
// File: MappingXofZ.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).
//
// License for the specific language governing rights and limitations under
// 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 + f(z)
//
///////////////////////////////////////////////////////////////////////////////

#include <GlobalMapping/MappingXofZ.h>
#include <MultiRegions/ExpList.h>

namespace Nektar
{
namespace GlobalMapping
{

std::string MappingXofZ::className =
        GetMappingFactory().RegisterCreatorFunction("XofZ",
                MappingXofZ::create, "X = x + f(z)");

/**
 * @class MappingXofZ
 * This class implements a constant-Jacobian mapping defined by
 *  a transformation of the type
 * \f[ \bar{x} = \bar{x}(x,z) = x + f(z) \f]
 * \f[ \bar{y} = 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.
 */
MappingXofZ::MappingXofZ(
        const LibUtilities::SessionReaderSharedPtr &pSession,
        const Array<OneD, MultiRegions::ExpListSharedPtr>&   pFields)
    : Mapping(pSession, pFields)
{
}


/**
 *
 */
void MappingXofZ::v_InitObject(
        const Array<OneD, MultiRegions::ExpListSharedPtr> &pFields,
        const TiXmlElement                                *pMapping)
{
    Mapping::v_InitObject(pFields, pMapping); 

    m_constantJacobian = true;

    ASSERTL0(m_nConvectiveFields==3,
                "Mapping X = x + f(z) needs 3 velocity components.");

}

void MappingXofZ::v_ContravarToCartesian(
    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 = u1 + fz*u3
    Vmath::Vmul(physTot, inarray[2], 1, m_GeometricInfo[0], 1, wk, 1);
    Vmath::Vadd(physTot, wk, 1, inarray[0], 1, outarray[0],1);

    // U2 = u2
    Vmath::Vcopy(physTot, inarray[1], 1, outarray[1], 1);

    // U3 = u3
    Vmath::Vcopy(physTot, inarray[2], 1, outarray[2], 1);
}

void MappingXofZ::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 = u1
    Vmath::Vcopy(physTot, inarray[0], 1, outarray[0], 1);

    // U2 = u2
    Vmath::Vcopy(physTot, inarray[1], 1, outarray[1], 1);

    // U3 = u3 - fz*u1
    Vmath::Vmul(physTot, m_GeometricInfo[0], 1, inarray[0], 1, wk, 1);
    Vmath::Vsub(physTot, inarray[2], 1, wk, 1, outarray[2], 1);
}

void MappingXofZ::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 = u1 - fz * u3
    Vmath::Vmul(physTot, m_GeometricInfo[0], 1, inarray[2], 1, wk, 1);
    Vmath::Vsub(physTot, inarray[0], 1, wk, 1, outarray[0], 1);        

    // U2 = u2
    Vmath::Vcopy(physTot, inarray[1], 1, outarray[1], 1);

    // U3 = u3
    Vmath::Vcopy(physTot, inarray[2], 1, outarray[2], 1);        
}

void MappingXofZ::v_CovarFromCartesian(
    const Array<OneD, Array<OneD, NekDouble> >        &inarray,
    Array<OneD, Array<OneD, NekDouble> >              &outarray)
{
    int physTot = m_fields[0]->GetTotPoints();

    // U1 = u1
    Vmath::Vcopy(physTot, inarray[0], 1, outarray[0], 1);

    // U2 = u2
    Vmath::Vcopy(physTot, inarray[1], 1, outarray[1], 1);

    // U3 = u3 + fz*u1
    Vmath::Vmul(physTot, m_GeometricInfo[0], 1, 
                         inarray[0], 1, outarray[2], 1);
    Vmath::Vadd(physTot, inarray[2], 1, outarray[2], 1, outarray[2], 1);
}

void MappingXofZ::v_GetJacobian(
    Array<OneD, NekDouble>               &outarray)
{
    int physTot = m_fields[0]->GetTotPoints();
    Vmath::Fill(physTot, 1.0, outarray, 1);
}

void MappingXofZ::v_DotGradJacobian(
    const Array<OneD, Array<OneD, NekDouble> >        &inarray,
    Array<OneD, NekDouble>                            &outarray)
{
    int physTot = m_fields[0]->GetTotPoints();

    Vmath::Zero(physTot, outarray, 1);   
}

void MappingXofZ::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); 
        }
        // Fill diagonal with 1.0
        for (int i=0; i<nvel; i++)
        {
            Vmath::Sadd(physTot, 1.0, outarray[i+nvel*i], 1, 
                                    outarray[i+nvel*i], 1); 
        }            

        // G_{13} and G_{31} = fz
        Vmath::Vcopy(physTot, m_GeometricInfo[0], 1, outarray[0*nvel+2], 1);
        Vmath::Vcopy(physTot, m_GeometricInfo[0], 1, outarray[2*nvel+0], 1);

        // G^{33} = (1+fz^2)
        Vmath::Vadd(physTot, m_GeometricInfo[2], 1, outarray[2*nvel+2], 1, 
                                    outarray[2*nvel+2], 1);
}

void MappingXofZ::v_GetInvMetricTensor(
    Array<OneD, Array<OneD, NekDouble> >              &outarray)
{
        int physTot = m_fields[0]->GetTotPoints();
        int nvel = m_nConvectiveFields;
        Array<OneD, NekDouble> wk(physTot, 0.0);

        for (int i=0; i<nvel*nvel; i++)
        {
            outarray[i] = Array<OneD, NekDouble> (physTot, 0.0); 
        }
        // Fill diagonal with 1.0
        for (int i=0; i<nvel; i++)
        {
            Vmath::Sadd(physTot, 1.0, outarray[i+nvel*i], 1, 
                                        outarray[i+nvel*i], 1); 
        }            

        // G^{13} and G^{31} = -fz
        Vmath::Vcopy(physTot, m_GeometricInfo[0],1,wk,1); // fz
        Vmath::Neg(physTot, wk, 1);
        Vmath::Vcopy(physTot, wk, 1, outarray[0*nvel+2], 1);
        Vmath::Vcopy(physTot, wk, 1, outarray[2*nvel+0], 1);

        // G^{11} = (1+fz^2)
        Vmath::Vadd(physTot, m_GeometricInfo[2], 1, outarray[0*nvel+0], 1, 
                                    outarray[0*nvel+0], 1);
}

void MappingXofZ::v_LowerIndex(
    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);

    // out[0] = in[0] + in[2] * fz
    Vmath::Vmul(physTot, m_GeometricInfo[0], 1, inarray[2], 1, 
                                                outarray[0], 1); //in[2]*fz
    Vmath::Vmul(physTot, m_GeometricInfo[0], 1, inarray[0], 1, 
                                                outarray[2], 1); //in[0]*fz

    Vmath::Vadd(physTot, outarray[0], 1, inarray[0], 1, 
                                                outarray[0], 1); 

    // out[1] = in[1]
    Vmath::Vcopy(physTot, inarray[1], 1, outarray[1], 1); 

    // out[2] = fz*in[0] + (1+fz^2)*in[2]
    Vmath::Sadd(physTot, 1.0, m_GeometricInfo[2], 1, wk, 1); // 1+fz^2
    Vmath::Vmul(physTot, wk, 1, inarray[2],1, wk, 1); // (1+fz^2)*in[2]
    Vmath::Vadd(physTot, wk, 1, outarray[2],1, outarray[2], 1); 
}

void MappingXofZ::v_RaiseIndex(
    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);

    // out[2] = in[2] - in[0] * fz
    Vmath::Vmul(physTot, m_GeometricInfo[0], 1, inarray[2], 1, 
                                                outarray[0], 1); // in[2]*fz
    Vmath::Vmul(physTot, m_GeometricInfo[0], 1, inarray[0], 1, 
                                                outarray[2], 1); //in[0]*fz       
    Vmath::Vsub(physTot, inarray[2], 1, outarray[2], 1, 
                                                outarray[2], 1); 

    // out[1] = in[1]]
    Vmath::Vcopy(physTot, inarray[1], 1, outarray[1], 1); 

    // out[0] = in[0]*(1+fz^2)- in[2] * fz
    Vmath::Sadd(physTot, 1.0, m_GeometricInfo[2], 1, wk, 1); // 1+fz^2
    Vmath::Vmul(physTot, wk, 1, inarray[0],1, wk, 1); // in[0]*(1+fz^2)
    Vmath::Vsub(physTot, wk, 1, outarray[0], 1, outarray[0], 1); 
}

void MappingXofZ::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(0,2) = U3 * fzz
    Vmath::Vmul(physTot,m_GeometricInfo[1],1,inarray[2],1,
                                        outarray[0*nvel+2],1); // U1 * fzz

}

void MappingXofZ::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(2,2) = U1 * fzz
    Vmath::Vmul(physTot,m_GeometricInfo[1],1,inarray[0],1,
                                    outarray[2*nvel+2],1); // U1 * fzz 
}   

void MappingXofZ::v_UpdateGeomInfo()
{
    int phystot         = m_fields[0]->GetTotPoints();
    // Allocation of geometry memory
    m_GeometricInfo =  Array<OneD, Array<OneD, NekDouble> >(4);
    for (int i = 0; i < m_GeometricInfo.num_elements(); i++)
    {
        m_GeometricInfo[i] = Array<OneD, NekDouble>(phystot, 0.0);
    }

    bool waveSpace = m_fields[0]->GetWaveSpace();
    m_fields[0]->SetWaveSpace(false);
    // Calculate derivatives of transformation
    m_fields[0]->PhysDeriv(MultiRegions::DirCartesianMap[2],
                                m_coords[0],m_GeometricInfo[0]);
    m_fields[0]->PhysDeriv(MultiRegions::DirCartesianMap[2],
                                m_GeometricInfo[0],m_GeometricInfo[1]);
    // m_GeometricInfo[2] = fz^2
    Vmath::Vmul(phystot,m_GeometricInfo[0],1,
                                m_GeometricInfo[0],1,m_GeometricInfo[2],1);

    m_fields[0]->SetWaveSpace(waveSpace);
}

}
}