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::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.size(); 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.size(); 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);
}
 
} // namespace Nektar::GlobalMapping