MappingGeneral.cpp

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///////////////////////////////////////////////////////////////////////////////
//
// File: MappingGeneral.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/MappingGeneral.h>
#include <MultiRegions/ExpList.h>
#include <iomanip> 

namespace Nektar
{
namespace GlobalMapping
{

std::string MappingGeneral::className =
        GetMappingFactory().RegisterCreatorFunction("General",
            MappingGeneral::create, "X = X(x,y,z), Y = Y(x,y,z), Z=Z(x,y,z)");

/**
 * @class MappingGeneral
 * This class implements the most general mapping, defined by the transformation
 * \f[ \bar{x} = \bar{x}(x,y,z) \f]
 * \f[ \bar{y} = \bar{y}(x,y,z) \f]
 * \f[ \bar{z} = \bar{z}(x,y,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.
 */
MappingGeneral::MappingGeneral(
        const LibUtilities::SessionReaderSharedPtr &pSession,
        const Array<OneD, MultiRegions::ExpListSharedPtr>&   pFields)
    : Mapping(pSession, pFields)
{
}


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

    m_constantJacobian = false;

    ASSERTL0(m_nConvectiveFields>=2,
            "General Mapping needs at least 2 velocity components.");   
}

void MappingGeneral::v_ContravarToCartesian(
    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++)
    {
        outarray[i] = Array<OneD, NekDouble> (physTot, 0.0); 
        for (int j=0; j<nvel; j++)
        {
            Vmath::Vvtvp(physTot, inarray[j], 1,
                                    m_deriv[i*nvel+j], 1,
                                    outarray[i], 1,
                                    outarray[i], 1);
        }

    }    
}

void MappingGeneral::v_CovarToCartesian(
    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++)
    {
        outarray[i] = Array<OneD, NekDouble> (physTot, 0.0); 
        for (int j=0; j<nvel; j++)
        {
            Vmath::Vvtvp(physTot, inarray[j], 1,
                                    m_invDeriv[i*nvel+j], 1,
                                    outarray[i], 1,
                                    outarray[i], 1);
        }

    }           
}

void MappingGeneral::v_ContravarFromCartesian(
    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++)
    {
        outarray[i] = Array<OneD, NekDouble> (physTot, 0.0); 
        for (int j=0; j<nvel; j++)
        {
            Vmath::Vvtvp(physTot, inarray[j], 1,
                                    m_invDeriv[j*nvel+i], 1,
                                    outarray[i], 1,
                                    outarray[i], 1);
        }

    }
}

void MappingGeneral::v_CovarFromCartesian(
    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++)
    {
        outarray[i] = Array<OneD, NekDouble> (physTot, 0.0); 
        for (int j=0; j<nvel; j++)
        {
            Vmath::Vvtvp(physTot, inarray[j], 1,
                                    m_deriv[j*nvel+i], 1,
                                    outarray[i], 1,
                                    outarray[i], 1);
        }

    } 
}

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

void MappingGeneral::v_GetMetricTensor(
    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); 
            Vmath::Vcopy(physTot, m_metricTensor[i*nvel+j], 1,
                                    outarray[i*nvel+j], 1);
        }

    }
}

void MappingGeneral::v_GetInvMetricTensor(
    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); 
            Vmath::Vcopy(physTot, m_invMetricTensor[i*nvel+j], 1,
                                    outarray[i*nvel+j], 1);
        }

    }            
}

void MappingGeneral::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;

    // Calculate {i,jk} u^j
    for (int i = 0; i <nvel; i++)
    {
        for (int k = 0; k < nvel; k++)            
        {
            outarray[i*nvel+k] = Array<OneD, NekDouble>(physTot,0.0);
            for (int j = 0; j < nvel; j++)
            {
                Vmath::Vvtvp(physTot, inarray[j], 1, 
                                    m_Christoffel[i*nvel*nvel+j*nvel+k], 1,
                                    outarray[i*nvel+k], 1,
                                    outarray[i*nvel+k], 1);
            }                
        }
    } 

}

void MappingGeneral::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;

    // Calculate {i,jk} u_i
    for (int j = 0; j < nvel; j++)
    {
        for (int k = 0; k < nvel; k++)
        {
            outarray[j*nvel+k] = Array<OneD, NekDouble>(physTot,0.0);
            for (int i = 0; i <nvel; i++)
            {
                Vmath::Vvtvp(physTot, inarray[i], 1, 
                                    m_Christoffel[i*nvel*nvel+j*nvel+k], 1,
                                    outarray[j*nvel+k], 1,
                                    outarray[j*nvel+k], 1);
            }                
        }
    } 
}

void MappingGeneral::v_UpdateGeomInfo()
{
    CalculateMetricTerms();
    CalculateChristoffel();
}

void MappingGeneral::CalculateMetricTerms()
{
    int physTot = m_fields[0]->GetTotPoints();
    int nvel = m_nConvectiveFields;

    // Set wavespace to false and store current value
    bool wavespace = m_fields[0]->GetWaveSpace();
    m_fields[0]->SetWaveSpace(false);

    // Allocate memory
    m_metricTensor =  Array<OneD, Array<OneD, NekDouble> >(nvel*nvel);
    m_invMetricTensor =  Array<OneD, Array<OneD, NekDouble> >(nvel*nvel);
    m_deriv =  Array<OneD, Array<OneD, NekDouble> >(nvel*nvel);
    m_invDeriv =  Array<OneD, Array<OneD, NekDouble> >(nvel*nvel);
    for (int i = 0; i < m_metricTensor.num_elements(); i++)
    {
        m_metricTensor[i] = Array<OneD, NekDouble>(physTot, 0.0);
        m_invMetricTensor[i] = Array<OneD, NekDouble>(physTot, 0.0);
        m_deriv[i] = Array<OneD, NekDouble>(physTot, 0.0);
        m_invDeriv[i] = Array<OneD, NekDouble>(physTot, 0.0);
    }
    m_jac = Array<OneD, NekDouble>(physTot, 0.0);

    // First, calculate derivatives of the mapping ->  dX^i/dx^j = c^i_j
    for( int i = 0; i<nvel; i++)
    {
        for( int j = 0; j<nvel; j++)
        {
            m_fields[0]->PhysDeriv(MultiRegions::DirCartesianMap[j],
                                        m_coords[i],
                                        m_deriv[i*nvel+j]);
        }
    }
    // In Homogeneous case, m_deriv(2,2) needs to be set to 1
    //  because differentiation in wavespace is not valid for non-periodic field
    if (m_fields[0]->GetExpType() == MultiRegions::e3DH1D)
    {
        Vmath::Fill(physTot, 1.0, m_deriv[2*nvel+2], 1);
    }

    // Now calculate the metric tensor -->   g_ij = sum_k  { c^k_i c^k_j }
    for( int i = 0; i<nvel; i++)
    {
        for( int j = 0; j<nvel; j++)
        {
            for( int k = 0; k<nvel; k++)
            {
                Vmath::Vvtvp(physTot, m_deriv[k*nvel+i], 1,
                                        m_deriv[k*nvel+j], 1,
                                        m_metricTensor[i*nvel+j], 1,
                                        m_metricTensor[i*nvel+j], 1);
            }
        }
    } 

    // Put the adjoint of g in m_invMetricTensor
    switch (nvel)
    {
        case 1:
            Vmath::Fill (physTot,  1.0, m_invMetricTensor[0], 1);
            break;
        case 2:
            Vmath::Vcopy(physTot,       m_metricTensor[1*nvel+1],    1,
                                        m_invMetricTensor[0*nvel+0], 1);
            Vmath::Smul (physTot, -1.0, m_metricTensor[0*nvel+1],    1, 
                                        m_invMetricTensor[1*nvel+0], 1);
            Vmath::Smul (physTot, -1.0, m_metricTensor[1*nvel+0],    1, 
                                        m_invMetricTensor[0*nvel+1], 1);
            Vmath::Vcopy(physTot,       m_metricTensor[0*nvel+0],    1,
                                        m_invMetricTensor[1*nvel+1], 1);
            break;
        case 3:
        {
            int a, b, c, d, e, i, j;

            // Compute g^{ij} by computing Cofactors(g_ij)^T
            for (i = 0; i < nvel; ++i)
            {
                for (j = 0; j < nvel; ++j)
                {
                    a = ((i+1)%nvel) * nvel + ((j+1)%nvel);
                    b = ((i+1)%nvel) * nvel + ((j+2)%nvel);
                    c = ((i+2)%nvel) * nvel + ((j+1)%nvel);
                    d = ((i+2)%nvel) * nvel + ((j+2)%nvel);
                    e = i*nvel + j;
                    // a*d - b*c
                    Vmath::Vmul(physTot,    m_metricTensor[b], 1,
                                            m_metricTensor[c], 1,
                                            m_invMetricTensor[e], 1);
                    Vmath::Vvtvm(physTot,   m_metricTensor[a], 1,
                                            m_metricTensor[d], 1,
                                            m_invMetricTensor[e], 1,
                                            m_invMetricTensor[e], 1);
                }
            }
            break;
        }
    }

    // Compute g = det(g_{ij}) (= Jacobian squared) and store
    // temporarily in m_jac.
    for (int i = 0; i < nvel; ++i)
    {
        Vmath::Vvtvp(physTot, m_metricTensor[i], 1, 
                             m_invMetricTensor[i*nvel], 1,
                             m_jac, 1, m_jac, 1);
    }

    // Calculate g^ij (the inverse of g_ij) by dividing by jac
    for (int i = 0; i < nvel*nvel; ++i)
    {
        Vmath::Vdiv(physTot, m_invMetricTensor[i], 1, m_jac, 1,
                                m_invMetricTensor[i], 1);
    }

    // Compute the Jacobian = sqrt(g)
    Vmath::Vsqrt(physTot, m_jac, 1, m_jac, 1);        

    // Calculate the derivatives of the inverse transformation
    //          c'^j_i = dx^j/dX^i = sum_k {g^jk c^i_k}
    for (int i = 0; i < nvel; ++i)
    {
        for (int j = 0; j < nvel; ++j)
        {
            for (int k = 0; k < nvel; ++k)
            {
                Vmath::Vvtvp(physTot, m_deriv[i*nvel+k],           1,
                                      m_invMetricTensor[j*nvel+k], 1,
                                      m_invDeriv[i*nvel+j],        1,
                                      m_invDeriv[i*nvel+j],        1);
            }
        }
    }

    // Restore value of wavespace
    m_fields[0]->SetWaveSpace(wavespace);
}

void MappingGeneral::CalculateChristoffel()
{
    int physTot = m_fields[0]->GetTotPoints();
    int nvel = m_nConvectiveFields;

    Array<OneD, Array<OneD, NekDouble> >   gradG(nvel*nvel*nvel);
    Array<OneD, Array<OneD, NekDouble> >   tmp(nvel*nvel*nvel);
    m_Christoffel = Array<OneD, Array<OneD, NekDouble> > (nvel*nvel*nvel);
    // Allocate memory
    for (int i = 0; i < gradG.num_elements(); i++)
    {
        gradG[i] = Array<OneD, NekDouble>(physTot, 0.0);
        tmp[i] = Array<OneD, NekDouble>(physTot, 0.0);
        m_Christoffel[i] = Array<OneD, NekDouble>(physTot, 0.0);
    }

    // Set wavespace to false and store current value
    bool waveSpace = m_fields[0]->GetWaveSpace();
    m_fields[0]->SetWaveSpace(false);

    //Calculate gradients of g_ij
    for (int i = 0; i <nvel; i++)
    {
        for(int j=0; j<nvel; j++)
        {
            for(int k=0; k<nvel; k++)
            {
                m_fields[0]->PhysDeriv(MultiRegions::DirCartesianMap[k],
                                        m_metricTensor[i*nvel+j],
                                        gradG[i*nvel*nvel + j*nvel + k]);
            }
        }
    }

    // Calculate tmp[p,j,k] = 1/2( gradG[pj,k]+ gradG[pk,j]-gradG[jk,p])
    for (int p = 0; p <nvel; p++)
    {
        for (int j = 0; j < nvel; j++)
        {
            for (int k = 0; k < nvel; k++)
            {
                Vmath::Vadd(physTot, gradG[p*nvel*nvel + j*nvel + k], 1,
                                     gradG[p*nvel*nvel + k*nvel + j], 1,
                                     tmp[p*nvel*nvel + j*nvel + k], 1);
                Vmath::Vsub(physTot, tmp[p*nvel*nvel + j*nvel + k], 1,
                                     gradG[j*nvel*nvel + k*nvel + p], 1,
                                     tmp[p*nvel*nvel + j*nvel + k], 1);
                Vmath::Smul(physTot, 0.5, tmp[p*nvel*nvel + j*nvel + k], 1,
                                           tmp[p*nvel*nvel + j*nvel + k], 1);
            }
        }
    }

    // Calculate Christoffel symbols = g^ip tmp[p,j,k]
    for (int i = 0; i <nvel; i++)
    {
        for (int j = 0; j < nvel; j++)
        {
            for (int k = 0; k < nvel; k++)
            {
                for (int p = 0; p < nvel; p++)
                {
                    Vmath::Vvtvp(physTot, m_invMetricTensor[i*nvel+p], 1,
                                    tmp[p*nvel*nvel + j*nvel + k], 1,
                                    m_Christoffel[i*nvel*nvel+j*nvel+k], 1,
                                    m_Christoffel[i*nvel*nvel+j*nvel+k], 1);
                }
            }                
        }
    }        
    // Restore wavespace
    m_fields[0]->SetWaveSpace(waveSpace);

}    

}
}