Mapping.cpp

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///////////////////////////////////////////////////////////////////////////////
//
// File: Mapping.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: Abstract base class for mappings.
//
///////////////////////////////////////////////////////////////////////////////
 
#include <boost/core/ignore_unused.hpp>
 
#include <GlobalMapping/Mapping.h>
 
#include <boost/algorithm/string/predicate.hpp>
 
using namespace std;
 
namespace Nektar
{
namespace GlobalMapping
{
 
MappingSharedPtr Mapping::m_mappingPtr = MappingSharedPtr();
bool Mapping::m_init                   = false;
bool Mapping::m_isDefined              = false;
 
MappingFactory &GetMappingFactory()
{
    static MappingFactory instance;
    return instance;
}
 
Mapping::Mapping(const LibUtilities::SessionReaderSharedPtr &pSession,
                 const Array<OneD, MultiRegions::ExpListSharedPtr> &pFields)
    : m_session(pSession), m_fields(pFields)
{
    switch (m_fields[0]->GetExpType())
    {
        case MultiRegions::e1D:
        {
            m_nConvectiveFields = 1;
        }
        break;
 
        case MultiRegions::e2D:
        {
            m_nConvectiveFields = 2;
        }
        break;
 
        case MultiRegions::e3D:
        case MultiRegions::e3DH1D:
        case MultiRegions::e3DH2D:
        {
            m_nConvectiveFields = 3;
        }
        break;
 
        default:
            ASSERTL0(0, "Dimension not supported");
            break;
    }
 
    m_fld = LibUtilities::FieldIO::CreateDefault(pSession);
}
 
/**
 * This function initialises the Mapping object. It computes the coordinates
 * and velocity coordinates, initialises the workspace variables, and calls
 * UpdateGeomInfo, which will perform the calculations specific for each type
 * of Mapping.
 * @param pFields ExpList array used in the mapping
 * @param pMapping xml element describing the mapping
 */
void Mapping::v_InitObject(
    const Array<OneD, MultiRegions::ExpListSharedPtr> &pFields,
    const TiXmlElement *pMapping)
{
    boost::ignore_unused(pFields);
 
    int phystot    = m_fields[0]->GetTotPoints();
    m_fromFunction = true;
    // Initialise variables
    m_coords    = Array<OneD, Array<OneD, NekDouble>>(3);
    m_coordsVel = Array<OneD, Array<OneD, NekDouble>>(3);
    Array<OneD, Array<OneD, NekDouble>> coords(3);
    for (int i = 0; i < 3; i++)
    {
        m_coords[i]    = Array<OneD, NekDouble>(phystot);
        m_coordsVel[i] = Array<OneD, NekDouble>(phystot);
        coords[i]      = Array<OneD, NekDouble>(phystot);
    }
 
    // Check if mapping is defined as time-dependent
    const TiXmlElement *timeDep = pMapping->FirstChildElement("TIMEDEPENDENT");
    if (timeDep)
    {
        string sTimeDep = timeDep->GetText();
        m_timeDependent = (boost::iequals(sTimeDep, "true")) ||
                          (boost::iequals(sTimeDep, "yes"));
    }
    else
    {
        m_timeDependent = false;
    }
 
    // Load coordinates
    string fieldNames[3]             = {"x", "y", "z"};
    const TiXmlElement *funcNameElmt = pMapping->FirstChildElement("COORDS");
    if (funcNameElmt)
    {
        m_funcName = funcNameElmt->GetText();
        ASSERTL0(m_session->DefinesFunction(m_funcName),
                 "Function '" + m_funcName + "' not defined.");
 
        // Get coordinates in the domain
        m_fields[0]->GetCoords(coords[0], coords[1], coords[2]);
 
        std::string s_FieldStr;
        // Check if function from session file defines each component
        //      and evaluate them, otherwise use trivial transformation
        for (int i = 0; i < 3; i++)
        {
            s_FieldStr = fieldNames[i];
            if (m_session->DefinesFunction(m_funcName, s_FieldStr))
            {
                EvaluateFunction(m_fields, m_session, s_FieldStr, m_coords[i],
                                 m_funcName);
                if (i == 2 && m_fields[0]->GetExpType() == MultiRegions::e3DH1D)
                {
                    ASSERTL0(
                        false,
                        "3DH1D does not support mapping in the z-direction.");
                }
            }
            else
            {
                // This coordinate is not defined, so use (x^i)' = x^i
                Vmath::Vcopy(phystot, coords[i], 1, m_coords[i], 1);
            }
        }
    }
    else
    {
        m_fields[0]->GetCoords(coords[0], coords[1], coords[2]);
        for (int i = 0; i < 3; i++)
        {
            // Use (x^i)' = x^i as default. This can be useful if we
            //    have a time-dependent mapping, and then only the
            //    initial mapping will be trivial
            Vmath::Vcopy(phystot, coords[i], 1, m_coords[i], 1);
        }
    }
 
    // Load coordinate velocity if they are defined,
    //      otherwise use zero to make it general
    string velFieldNames[3]             = {"vx", "vy", "vz"};
    const TiXmlElement *velFuncNameElmt = pMapping->FirstChildElement("VEL");
    if (velFuncNameElmt)
    {
        m_velFuncName = velFuncNameElmt->GetText();
        ASSERTL0(m_session->DefinesFunction(m_velFuncName),
                 "Function '" + m_velFuncName + "' not defined.");
 
        std::string s_FieldStr;
        // Check if function from session file defines each component
        //      and evaluate them, otherwise use 0
        for (int i = 0; i < 3; i++)
        {
            s_FieldStr = velFieldNames[i];
            if (m_session->DefinesFunction(m_velFuncName, s_FieldStr))
            {
                EvaluateFunction(m_fields, m_session, s_FieldStr,
                                 m_coordsVel[i], m_velFuncName);
                if (i == 2 && m_fields[0]->GetExpType() == MultiRegions::e3DH1D)
                {
                    ASSERTL0(
                        false,
                        "3DH1D does not support mapping in the z-direction.");
                }
            }
            else
            {
                // This coordinate velocity is not defined, so use 0
                Vmath::Zero(phystot, m_coordsVel[i], 1);
            }
        }
    }
    else
    {
        for (int i = 0; i < 3; i++)
        {
            Vmath::Zero(phystot, m_coordsVel[i], 1);
        }
    }
 
    // Initialise workspace variables
    int nvel = m_nConvectiveFields;
    m_wk1    = Array<OneD, Array<OneD, NekDouble>>(nvel * nvel);
    m_wk2    = Array<OneD, Array<OneD, NekDouble>>(nvel * nvel);
    m_tmp    = Array<OneD, Array<OneD, NekDouble>>(nvel);
    for (int i = 0; i < nvel; i++)
    {
        m_tmp[i] = Array<OneD, NekDouble>(phystot, 0.0);
        for (int j = 0; j < nvel; j++)
        {
            m_wk1[i * nvel + j] = Array<OneD, NekDouble>(phystot, 0.0);
            m_wk2[i * nvel + j] = Array<OneD, NekDouble>(phystot, 0.0);
        }
    }
 
    // Calculate information required by the particular mapping
    UpdateGeomInfo();
}
 
/**
 * This function replaces the expansion list contained in m_fields, and then
 * proceeds reinitialising the Mapping with this new field.
 * @param pFields New field to be used by the Mapping
 */
void Mapping::ReplaceField(
    const Array<OneD, MultiRegions::ExpListSharedPtr> &pFields)
{
    m_fields = pFields;
 
    TiXmlElement *vMapping = NULL;
 
    if (m_session->DefinesElement("Nektar/Mapping"))
    {
        vMapping = m_session->GetElement("Nektar/Mapping");
    }
    InitObject(pFields, vMapping);
}
 
/**
 * This function is responsible for loading the Mapping, guaranteeing that a
 * single instance of this class exists. When it is first called, it creates a
 * Mapping and returns a pointer to it. On subsequent calls, it just returns
 * the pointer.
 * @param pSession Session reader object
 * @param pFields  Fields which will be used by the Mapping
 * @return Pointer to the Mapping
 */
MappingSharedPtr Mapping::Load(
    const LibUtilities::SessionReaderSharedPtr &pSession,
    const Array<OneD, MultiRegions::ExpListSharedPtr> &pFields)
{
    if (!m_init)
    {
        TiXmlElement *vMapping = NULL;
        string vType;
        if (pSession->DefinesElement("Nektar/Mapping"))
        {
            vMapping    = pSession->GetElement("Nektar/Mapping");
            vType       = vMapping->Attribute("TYPE");
            m_isDefined = true;
        }
        else
        {
            vType = "Translation";
        }
 
        m_mappingPtr = GetMappingFactory().CreateInstance(vType, pSession,
                                                          pFields, vMapping);
 
        m_init = true;
    }
 
    return m_mappingPtr;
}
 
/**
 * This function should be called before writing a fld or chk file. It updates
 * the metadata with information from the Mapping. Also, if the mapping is not
 * defined by a function, it writes a .map file containing the coordinates and
 * velocity of the coordinates.
 * @param fieldMetaDataMap Metadata of the output file
 * @param outname          Name of the output file
 */
void Mapping::Output(LibUtilities::FieldMetaDataMap &fieldMetaDataMap,
                     const std::string &outname)
{
    // Only do anything if mapping exists
    if (m_isDefined)
    {
        fieldMetaDataMap["MappingCartesianVel"] = std::string("False");
        if (m_fromFunction)
        {
            // Add metadata
            fieldMetaDataMap["MappingType"]       = std::string("Expression");
            fieldMetaDataMap["MappingExpression"] = m_funcName;
            if (m_timeDependent)
            {
                fieldMetaDataMap["MappingVelExpression"] = m_velFuncName;
            }
        }
        else
        {
            int expdim           = m_fields[0]->GetGraph()->GetMeshDimension();
            string fieldNames[3] = {"x", "y", "z"};
            string velFieldNames[3] = {"vx", "vy", "vz"};
 
            std::vector<LibUtilities::FieldDefinitionsSharedPtr> FieldDef =
                m_fields[0]->GetFieldDefinitions();
            std::vector<std::vector<NekDouble>> FieldData(FieldDef.size());
 
            int ncoeffs = m_fields[0]->GetNcoeffs();
            Array<OneD, NekDouble> fieldcoeffs(ncoeffs);
 
            bool wavespace = m_fields[0]->GetWaveSpace();
            m_fields[0]->SetWaveSpace(false);
            // copy coordinates Data into FieldData and set variable
            for (int j = 0; j < expdim; ++j)
            {
                m_fields[0]->FwdTransLocalElmt(m_coords[j], fieldcoeffs);
 
                for (int i = 0; i < FieldDef.size(); ++i)
                {
                    // Could do a search here to find correct variable
                    FieldDef[i]->m_fields.push_back(fieldNames[j]);
                    m_fields[0]->AppendFieldData(FieldDef[i], FieldData[i],
                                                 fieldcoeffs);
                }
            }
            if (m_timeDependent)
            {
                // copy coordinates velocity Data into FieldData and set
                // variable
                for (int j = 0; j < expdim; ++j)
                {
                    m_fields[0]->FwdTrans(m_coordsVel[j], fieldcoeffs);
 
                    for (int i = 0; i < FieldDef.size(); ++i)
                    {
                        // Could do a search here to find correct variable
                        FieldDef[i]->m_fields.push_back(velFieldNames[j]);
                        m_fields[0]->AppendFieldData(FieldDef[i], FieldData[i],
                                                     fieldcoeffs);
                    }
                }
            }
 
            std::string outfile = outname;
            outfile.erase(outfile.end() - 4, outfile.end());
            outfile += ".map";
 
            m_fld->Write(outfile, FieldDef, FieldData, fieldMetaDataMap);
 
            // Write metadata to orginal output
            fieldMetaDataMap["MappingType"] = std::string("File");
            fieldMetaDataMap["FileName"]    = outfile;
 
            m_fields[0]->SetWaveSpace(wavespace);
        }
    }
}
 
void Mapping::EvaluateTimeFunction(
    LibUtilities::SessionReaderSharedPtr pSession, std::string pFieldName,
    Array<OneD, NekDouble> &pArray, const std::string &pFunctionName,
    NekDouble pTime)
{
    ASSERTL0(pSession->DefinesFunction(pFunctionName),
             "Function '" + pFunctionName + "' does not exist.");
 
    LibUtilities::EquationSharedPtr ffunc =
        pSession->GetFunction(pFunctionName, pFieldName);
 
    Array<OneD, NekDouble> x0(1, 0.0);
    Array<OneD, NekDouble> x1(1, 0.0);
    Array<OneD, NekDouble> x2(1, 0.0);
 
    ffunc->Evaluate(x0, x1, x2, pTime, pArray);
}
 
void Mapping::EvaluateFunction(
    Array<OneD, MultiRegions::ExpListSharedPtr> pFields,
    LibUtilities::SessionReaderSharedPtr pSession, std::string pFieldName,
    Array<OneD, NekDouble> &pArray, const std::string &pFunctionName,
    NekDouble pTime)
{
    ASSERTL0(pSession->DefinesFunction(pFunctionName),
             "Function '" + pFunctionName + "' does not exist.");
 
    unsigned int nq = pFields[0]->GetNpoints();
    if (pArray.size() != nq)
    {
        pArray = Array<OneD, NekDouble>(nq);
    }
 
    LibUtilities::FunctionType vType;
    vType = pSession->GetFunctionType(pFunctionName, pFieldName);
    if (vType == LibUtilities::eFunctionTypeExpression)
    {
        Array<OneD, NekDouble> x0(nq);
        Array<OneD, NekDouble> x1(nq);
        Array<OneD, NekDouble> x2(nq);
 
        pFields[0]->GetCoords(x0, x1, x2);
        LibUtilities::EquationSharedPtr ffunc =
            pSession->GetFunction(pFunctionName, pFieldName);
 
        ffunc->Evaluate(x0, x1, x2, pTime, pArray);
    }
    else if (vType == LibUtilities::eFunctionTypeFile)
    {
        std::string filename =
            pSession->GetFunctionFilename(pFunctionName, pFieldName);
 
        std::vector<LibUtilities::FieldDefinitionsSharedPtr> FieldDef;
        std::vector<std::vector<NekDouble>> FieldData;
        Array<OneD, NekDouble> vCoeffs(pFields[0]->GetNcoeffs());
        Vmath::Zero(vCoeffs.size(), vCoeffs, 1);
 
        LibUtilities::FieldIOSharedPtr fld =
            LibUtilities::FieldIO::CreateForFile(pSession, filename);
        fld->Import(filename, FieldDef, FieldData);
 
        int idx = -1;
        for (int i = 0; i < FieldDef.size(); ++i)
        {
            for (int j = 0; j < FieldDef[i]->m_fields.size(); ++j)
            {
                if (FieldDef[i]->m_fields[j] == pFieldName)
                {
                    idx = j;
                }
            }
 
            if (idx >= 0)
            {
                pFields[0]->ExtractDataToCoeffs(FieldDef[i], FieldData[i],
                                                FieldDef[i]->m_fields[idx],
                                                vCoeffs);
            }
            else
            {
                cout << "Field " + pFieldName + " not found." << endl;
            }
        }
        pFields[0]->BwdTrans(vCoeffs, pArray);
    }
}
 
/**
 * This function converts a contravariant vector in transformed space
 * \f$v^{j}\f$ to the corresponding \f$\bar{v}^{i}\f$ in Cartesian (physical)
 * space using the relation
 * \f[\bar{v}^{i} = \frac{\partial \bar{x}^i}{\partial x^j}v^{j}\f]
 *
 * @param inarray  Components of the vector in transformed space (\f$v^{j}\f$)
 * @param outarray Components of the vector in Cartesian space
 * (\f$\bar{v}^{i}\f$)
 */
void Mapping::ContravarToCartesian(
    const Array<OneD, Array<OneD, NekDouble>> &inarray,
    Array<OneD, Array<OneD, NekDouble>> &outarray)
{
    if (inarray == outarray)
    {
        int physTot = m_fields[0]->GetTotPoints();
        int nvel    = m_nConvectiveFields;
 
        for (int i = 0; i < nvel; i++)
        {
            Vmath::Vcopy(physTot, inarray[i], 1, m_tmp[i], 1);
        }
        v_ContravarToCartesian(m_tmp, outarray);
    }
    else
    {
        v_ContravarToCartesian(inarray, outarray);
    }
}
 
/**
 * This function converts a covariant vector in transformed space
 * \f$v_{j}\f$ to the corresponding \f$\bar{v}_{i}\f$ in Cartesian (physical)
 * space using the relation
 * \f[\bar{v}_{i} = \frac{\partial x^j}{\partial \bar{x}^i}v_{j}\f]
 *
 * @param inarray  Components of the vector in transformed space (\f$v_{j}\f$)
 * @param outarray Components of the vector in Cartesian space
 * (\f$\bar{v}_{i}\f$)
 */
void Mapping::CovarToCartesian(
    const Array<OneD, Array<OneD, NekDouble>> &inarray,
    Array<OneD, Array<OneD, NekDouble>> &outarray)
{
    if (inarray == outarray)
    {
        int physTot = m_fields[0]->GetTotPoints();
        int nvel    = m_nConvectiveFields;
 
        for (int i = 0; i < nvel; i++)
        {
            Vmath::Vcopy(physTot, inarray[i], 1, m_tmp[i], 1);
        }
        v_CovarToCartesian(m_tmp, outarray);
    }
    else
    {
        v_CovarToCartesian(inarray, outarray);
    }
}
 
/**
 * This function converts a contravariant vector in Cartesian space
 * \f$\bar{v}^{i}\f$ to the corresponding \f$v^{j}\f$ in transformed
 * space using the relation
 * \f[v^{j} = \frac{\partial x^j}{\partial \bar{x}^i}\bar{v}^{i}\f]
 *
 * @param inarray  Components of the vector in Cartesian space
 * (\f$\bar{v}^{i}\f$)
 * @param outarray Components of the vector in transformed space (\f$v^{j}\f$)
 */
void Mapping::ContravarFromCartesian(
    const Array<OneD, Array<OneD, NekDouble>> &inarray,
    Array<OneD, Array<OneD, NekDouble>> &outarray)
{
    if (inarray == outarray)
    {
        int physTot = m_fields[0]->GetTotPoints();
        int nvel    = m_nConvectiveFields;
 
        for (int i = 0; i < nvel; i++)
        {
            Vmath::Vcopy(physTot, inarray[i], 1, m_tmp[i], 1);
        }
        v_ContravarFromCartesian(m_tmp, outarray);
    }
    else
    {
        v_ContravarFromCartesian(inarray, outarray);
    }
}
 
/**
 * This function converts a covariant vector in Cartesian space
 * \f$\bar{v}_{i}\f$ to the corresponding \f$v_{j}\f$ in transformed
 * space using the relation
 * \f[\bar{v}_{j} = \frac{\partial \bar{x}^i}{\partial x^j}v_{i}\f]
 *
 * @param inarray  Components of the vector in Cartesian space
 * (\f$\bar{v}_{i}\f$)
 * @param outarray Components of the vector in transformed space (\f$v_{j}\f$)
 */
void Mapping::CovarFromCartesian(
    const Array<OneD, Array<OneD, NekDouble>> &inarray,
    Array<OneD, Array<OneD, NekDouble>> &outarray)
{
    if (inarray == outarray)
    {
        int physTot = m_fields[0]->GetTotPoints();
        int nvel    = m_nConvectiveFields;
 
        for (int i = 0; i < nvel; i++)
        {
            Vmath::Vcopy(physTot, inarray[i], 1, m_tmp[i], 1);
        }
        v_CovarFromCartesian(m_tmp, outarray);
    }
    else
    {
        v_CovarFromCartesian(inarray, outarray);
    }
}
 
/**
 * This function lowers the index of the contravariant vector \f$v^{i}\f$,
 * transforming it into its associated covariant vector \f$v_{j}\f$
 *  according to the relation
 * \f[v_{j} = g_{ij}v^{i}\f]
 * where \f$g_{ij}\f$ is the metric tensor.
 *
 * @param inarray  Components of the contravariant vector \f$v^{i}\f$
 * @param outarray Components of the covariant vector \f$v_{j}\f$
 */
void Mapping::LowerIndex(const Array<OneD, Array<OneD, NekDouble>> &inarray,
                         Array<OneD, Array<OneD, NekDouble>> &outarray)
{
    if (inarray == outarray)
    {
        int physTot = m_fields[0]->GetTotPoints();
        int nvel    = m_nConvectiveFields;
 
        for (int i = 0; i < nvel; i++)
        {
            Vmath::Vcopy(physTot, inarray[i], 1, m_tmp[i], 1);
        }
        v_LowerIndex(m_tmp, outarray);
    }
    else
    {
        v_LowerIndex(inarray, outarray);
    }
}
 
/**
 * This function raises the index of the covariant vector \f$v_{j}\f$,
 * transforming it into its associated contravariant vector \f$v^{i}\f$
 *  according to the relation
 * \f[v^{i} = g^{ij}v_{j}\f]
 * where \f$g^{ij}\f$ is the inverse of the metric tensor.
 *
 * @param inarray  Components of the contravariant vector \f$v^{i}\f$
 * @param outarray Components of the covariant vector \f$v_{j}\f$
 */
void Mapping::RaiseIndex(const Array<OneD, Array<OneD, NekDouble>> &inarray,
                         Array<OneD, Array<OneD, NekDouble>> &outarray)
{
    if (inarray == outarray)
    {
        int physTot = m_fields[0]->GetTotPoints();
        int nvel    = m_nConvectiveFields;
 
        for (int i = 0; i < nvel; i++)
        {
            Vmath::Vcopy(physTot, inarray[i], 1, m_tmp[i], 1);
        }
        v_RaiseIndex(m_tmp, outarray);
    }
    else
    {
        v_RaiseIndex(inarray, outarray);
    }
}
 
void Mapping::v_GetCartesianCoordinates(Array<OneD, NekDouble> &out0,
                                        Array<OneD, NekDouble> &out1,
                                        Array<OneD, NekDouble> &out2)
{
    int physTot = m_fields[0]->GetTotPoints();
 
    out0 = Array<OneD, NekDouble>(physTot, 0.0);
    out1 = Array<OneD, NekDouble>(physTot, 0.0);
    out2 = Array<OneD, NekDouble>(physTot, 0.0);
 
    Vmath::Vcopy(physTot, m_coords[0], 1, out0, 1);
    Vmath::Vcopy(physTot, m_coords[1], 1, out1, 1);
    Vmath::Vcopy(physTot, m_coords[2], 1, out2, 1);
}
 
void Mapping::v_GetCoordVelocity(Array<OneD, Array<OneD, NekDouble>> &outarray)
{
    int physTot = m_fields[0]->GetTotPoints();
 
    for (int i = 0; i < m_nConvectiveFields; ++i)
    {
        outarray[i] = Array<OneD, NekDouble>(physTot, 0.0);
        Vmath::Vcopy(physTot, m_coordsVel[i], 1, outarray[i], 1);
    }
}
 
void Mapping::v_DotGradJacobian(
    const Array<OneD, Array<OneD, NekDouble>> &inarray,
    Array<OneD, NekDouble> &outarray)
{
    int physTot = m_fields[0]->GetTotPoints();
 
    outarray = Array<OneD, NekDouble>(physTot, 0.0);
    if (!HasConstantJacobian())
    {
        // Set wavespace to false and store current value
        bool wavespace = m_fields[0]->GetWaveSpace();
        m_fields[0]->SetWaveSpace(false);
 
        // Get Mapping Jacobian
        Array<OneD, NekDouble> Jac(physTot, 0.0);
        GetJacobian(Jac);
 
        // Calculate inarray . grad(Jac)
        Array<OneD, NekDouble> wk(physTot, 0.0);
        for (int i = 0; i < m_nConvectiveFields; ++i)
        {
            m_fields[0]->PhysDeriv(MultiRegions::DirCartesianMap[i], Jac, wk);
            Vmath::Vvtvp(physTot, inarray[i], 1, wk, 1, outarray, 1, outarray,
                         1);
        }
        m_fields[0]->SetWaveSpace(wavespace);
    }
}
 
void Mapping::v_LowerIndex(const Array<OneD, Array<OneD, NekDouble>> &inarray,
                           Array<OneD, Array<OneD, NekDouble>> &outarray)
{
    int physTot = m_fields[0]->GetTotPoints();
    int nvel    = m_nConvectiveFields;
 
    Array<OneD, Array<OneD, NekDouble>> g(nvel * nvel);
 
    GetMetricTensor(g);
 
    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, g[i * nvel + j], 1, inarray[j], 1,
                         outarray[i], 1, outarray[i], 1);
        }
    }
}
 
void Mapping::v_RaiseIndex(const Array<OneD, Array<OneD, NekDouble>> &inarray,
                           Array<OneD, Array<OneD, NekDouble>> &outarray)
{
    int physTot = m_fields[0]->GetTotPoints();
    int nvel    = m_nConvectiveFields;
 
    Array<OneD, Array<OneD, NekDouble>> g(nvel * nvel);
 
    GetInvMetricTensor(g);
 
    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, g[i * nvel + j], 1, inarray[j], 1,
                         outarray[i], 1, outarray[i], 1);
        }
    }
}
 
void Mapping::v_Divergence(const Array<OneD, Array<OneD, NekDouble>> &inarray,
                           Array<OneD, NekDouble> &outarray)
{
    int physTot = m_fields[0]->GetTotPoints();
    Array<OneD, NekDouble> wk(physTot, 0.0);
 
    Vmath::Zero(physTot, outarray, 1);
 
    // Set wavespace to false and store current value
    bool wavespace = m_fields[0]->GetWaveSpace();
    m_fields[0]->SetWaveSpace(false);
 
    // Get Mapping Jacobian
    Array<OneD, NekDouble> Jac(physTot, 0.0);
    GetJacobian(Jac);
 
    for (int i = 0; i < m_nConvectiveFields; ++i)
    {
        Vmath::Vmul(physTot, Jac, 1, inarray[i], 1, wk, 1); // J*Ui
        m_fields[0]->PhysDeriv(MultiRegions::DirCartesianMap[i], wk,
                               wk); // (J*Ui)_i
        Vmath::Vadd(physTot, wk, 1, outarray, 1, outarray, 1);
    }
    Vmath::Vdiv(physTot, outarray, 1, Jac, 1, outarray, 1); // 1/J*(J*Ui)_i
 
    m_fields[0]->SetWaveSpace(wavespace);
}
 
void Mapping::v_VelocityLaplacian(
    const Array<OneD, Array<OneD, NekDouble>> &inarray,
    Array<OneD, Array<OneD, NekDouble>> &outarray, const NekDouble alpha)
{
    int physTot = m_fields[0]->GetTotPoints();
    int nvel    = m_nConvectiveFields;
 
    Array<OneD, Array<OneD, NekDouble>> tmp(nvel);
 
    // Set wavespace to false and store current value
    bool wavespace = m_fields[0]->GetWaveSpace();
    m_fields[0]->SetWaveSpace(false);
 
    // Calculate vector gradient wk2 = u^i_(,k) = du^i/dx^k + {i,jk}*u^j
    ApplyChristoffelContravar(inarray, m_wk1);
    for (int i = 0; i < nvel; i++)
    {
        if (nvel == 2)
        {
            m_fields[0]->PhysDeriv(inarray[i], m_wk2[i * nvel + 0],
                                   m_wk2[i * nvel + 1]);
        }
        else
        {
            m_fields[0]->PhysDeriv(inarray[i], m_wk2[i * nvel + 0],
                                   m_wk2[i * nvel + 1], m_wk2[i * nvel + 2]);
        }
        for (int k = 0; k < nvel; k++)
        {
            Vmath::Vadd(physTot, m_wk1[i * nvel + k], 1, m_wk2[i * nvel + k], 1,
                        m_wk1[i * nvel + k], 1);
        }
    }
    // Calculate wk1 = A^(ij) = g^(jk)*u^i_(,k)
    for (int i = 0; i < nvel; i++)
    {
        for (int k = 0; k < nvel; k++)
        {
            tmp[k] = m_wk1[i * nvel + k];
        }
        RaiseIndex(tmp, m_tmp);
        for (int j = 0; j < nvel; j++)
        {
            Vmath::Vcopy(physTot, m_tmp[j], 1, m_wk1[i * nvel + j], 1);
        }
    }
    //
    // Calculate L(U)^i = (A^(ij))_(,j) - alpha*d^2(u^i)/dx^jdx^j
    //
 
    // Step 1 :
    //      d(A^(ij) - alpha*du^i/dx^j)/d(x^j)
    for (int i = 0; i < nvel; i++)
    {
        outarray[i] = Array<OneD, NekDouble>(physTot, 0.0);
        for (int j = 0; j < nvel; j++)
        {
            Vmath::Smul(physTot, alpha, m_wk2[i * nvel + j], 1, m_tmp[0], 1);
            Vmath::Vsub(physTot, m_wk1[i * nvel + j], 1, m_tmp[0], 1, m_tmp[0],
                        1);
 
            m_fields[0]->PhysDeriv(MultiRegions::DirCartesianMap[j], m_tmp[0],
                                   m_tmp[1]);
            Vmath::Vadd(physTot, outarray[i], 1, m_tmp[1], 1, outarray[i], 1);
        }
    }
 
    // Step 2: d(A^(ij))/d(x^j) + {j,pj}*A^(ip)
    for (int i = 0; i < nvel; i++)
    {
        for (int p = 0; p < nvel; p++)
        {
            tmp[p] = m_wk1[i * nvel + p];
        }
        ApplyChristoffelContravar(tmp, m_wk2);
        for (int j = 0; j < nvel; j++)
        {
            Vmath::Vadd(physTot, outarray[i], 1, m_wk2[j * nvel + j], 1,
                        outarray[i], 1);
        }
    }
 
    // Step 3: d(A^(ij))/d(x^j) + {j,pj}*A^(ip) + {i,pj} A^(pj)
    for (int j = 0; j < nvel; j++)
    {
        for (int p = 0; p < nvel; p++)
        {
            tmp[p] = m_wk1[p * nvel + j];
        }
        ApplyChristoffelContravar(tmp, m_wk2);
        for (int i = 0; i < nvel; i++)
        {
            Vmath::Vadd(physTot, outarray[i], 1, m_wk2[i * nvel + j], 1,
                        outarray[i], 1);
        }
    }
 
    // Restore value of wavespace
    m_fields[0]->SetWaveSpace(wavespace);
}
 
void Mapping::v_gradgradU(const Array<OneD, Array<OneD, NekDouble>> &inarray,
                          Array<OneD, Array<OneD, NekDouble>> &outarray)
{
    int physTot = m_fields[0]->GetTotPoints();
    int nvel    = m_nConvectiveFields;
 
    // Declare variables
    outarray = Array<OneD, Array<OneD, NekDouble>>(nvel * nvel * nvel);
    Array<OneD, Array<OneD, NekDouble>> tmp(nvel);
    for (int i = 0; i < nvel * nvel * nvel; i++)
    {
        outarray[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 vector gradient u^i_(,j) = du^i/dx^j + {i,pj}*u^p
    ApplyChristoffelContravar(inarray, m_wk1);
    for (int i = 0; i < nvel; i++)
    {
        if (nvel == 2)
        {
            m_fields[0]->PhysDeriv(inarray[i], m_wk2[i * nvel + 0],
                                   m_wk2[i * nvel + 1]);
        }
        else
        {
            m_fields[0]->PhysDeriv(inarray[i], m_wk2[i * nvel + 0],
                                   m_wk2[i * nvel + 1], m_wk2[i * nvel + 2]);
        }
        for (int j = 0; j < nvel; j++)
        {
            Vmath::Vadd(physTot, m_wk1[i * nvel + j], 1, m_wk2[i * nvel + j], 1,
                        m_wk1[i * nvel + j], 1);
        }
    }
 
    //
    // Calculate (u^i_,j),k
    //
 
    // Step 1 : d(u^i_,j))/d(x^k)
    for (int i = 0; i < nvel; i++)
    {
        for (int j = 0; j < nvel; j++)
        {
            if (nvel == 2)
            {
                m_fields[0]->PhysDeriv(
                    m_wk1[i * nvel + j],
                    outarray[i * nvel * nvel + j * nvel + 0],
                    outarray[i * nvel * nvel + j * nvel + 1]);
            }
            else
            {
                m_fields[0]->PhysDeriv(
                    m_wk1[i * nvel + j],
                    outarray[i * nvel * nvel + j * nvel + 0],
                    outarray[i * nvel * nvel + j * nvel + 1],
                    outarray[i * nvel * nvel + j * nvel + 2]);
            }
        }
    }
 
    // Step 2: d(u^i_,j)/d(x^k) - {p,jk}*u^i_,p
    for (int i = 0; i < nvel; i++)
    {
        for (int p = 0; p < nvel; p++)
        {
            tmp[p] = m_wk1[i * nvel + p];
        }
        ApplyChristoffelCovar(tmp, m_wk2);
        for (int j = 0; j < nvel; j++)
        {
            for (int k = 0; k < nvel; k++)
            {
                Vmath::Vsub(physTot, outarray[i * nvel * nvel + j * nvel + k],
                            1, m_wk2[j * nvel + k], 1,
                            outarray[i * nvel * nvel + j * nvel + k], 1);
            }
        }
    }
 
    // Step 3: d(u^i_,j)/d(x^k) - {p,jk}*u^i_,p + {i,pk} u^p_,j
    for (int j = 0; j < nvel; j++)
    {
        for (int p = 0; p < nvel; p++)
        {
            tmp[p] = m_wk1[p * nvel + j];
        }
        ApplyChristoffelContravar(tmp, m_wk2);
        for (int i = 0; i < nvel; i++)
        {
            for (int k = 0; k < nvel; k++)
            {
                Vmath::Vadd(physTot, outarray[i * nvel * nvel + j * nvel + k],
                            1, m_wk2[i * nvel + k], 1,
                            outarray[i * nvel * nvel + j * nvel + k], 1);
            }
        }
    }
 
    // Restore value of wavespace
    m_fields[0]->SetWaveSpace(wavespace);
}
 
void Mapping::v_CurlCurlField(Array<OneD, Array<OneD, NekDouble>> &inarray,
                              Array<OneD, Array<OneD, NekDouble>> &outarray,
                              const bool generalized)
{
    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);
 
    // For implicit treatment of viscous terms, we want the generalized
    //   curlcurl and for explicit treatment, we want the cartesian one.
    if (generalized)
    {
        // Get the second derivatives u^i_{,jk}
        Array<OneD, Array<OneD, NekDouble>> tmp(nvel);
        Array<OneD, Array<OneD, NekDouble>> ddU(nvel * nvel * nvel);
        gradgradU(inarray, ddU);
 
        // Raise index to obtain A^{ip}_{k} = g^pj u^i_{,jk}
        for (int i = 0; i < nvel; ++i)
        {
            for (int k = 0; k < nvel; ++k)
            {
                // Copy to wk
                for (int j = 0; j < nvel; ++j)
                {
                    tmp[j] = ddU[i * nvel * nvel + j * nvel + k];
                }
                RaiseIndex(tmp, m_tmp);
                for (int p = 0; p < nvel; ++p)
                {
                    Vmath::Vcopy(physTot, m_tmp[p], 1,
                                 ddU[i * nvel * nvel + p * nvel + k], 1);
                }
            }
        }
        // The curlcurl is g^ji u^k_{kj} - g^jk u^i_kj = A^{ki}_k - A^{ik}_k
        for (int i = 0; i < nvel; ++i)
        {
            outarray[i] = Array<OneD, NekDouble>(physTot, 0.0);
            for (int k = 0; k < nvel; ++k)
            {
                Vmath::Vadd(physTot, outarray[i], 1,
                            ddU[k * nvel * nvel + i * nvel + k], 1, outarray[i],
                            1);
                Vmath::Vsub(physTot, outarray[i], 1,
                            ddU[i * nvel * nvel + k * nvel + k], 1, outarray[i],
                            1);
            }
        }
    }
    else
    {
        m_fields[0]->CurlCurl(inarray, outarray);
    }
 
    // Restore value of wavespace
    m_fields[0]->SetWaveSpace(wavespace);
}
 
void Mapping::v_UpdateBCs(const NekDouble time)
{
    int physTot = m_fields[0]->GetTotPoints();
    int nvel    = m_nConvectiveFields;
    int nfields = m_fields.size();
    int nbnds   = m_fields[0]->GetBndConditions().size();
 
    // Declare variables
    Array<OneD, const SpatialDomains::BoundaryConditionShPtr> BndConds;
    Array<OneD, MultiRegions::ExpListSharedPtr> BndExp;
 
    Array<OneD, bool> isDirichlet(nfields);
 
    Array<OneD, Array<OneD, NekDouble>> values(nfields);
    for (int i = 0; i < nfields; i++)
    {
        values[i] = Array<OneD, NekDouble>(physTot, 0.0);
    }
 
    Array<OneD, Array<OneD, NekDouble>> tmp(nvel);
    Array<OneD, Array<OneD, NekDouble>> tmp2(nvel);
    Array<OneD, Array<OneD, NekDouble>> coordVel(nvel);
    for (int i = 0; i < nvel; i++)
    {
        tmp[i]      = Array<OneD, NekDouble>(physTot, 0.0);
        tmp2[i]     = Array<OneD, NekDouble>(physTot, 0.0);
        coordVel[i] = Array<OneD, NekDouble>(physTot, 0.0);
    }
 
    // Get coordinates velocity in transformed system (for MovingBody regions)
    GetCoordVelocity(tmp);
    ContravarFromCartesian(tmp, coordVel);
 
    // Get  Cartesian coordinates for evaluating boundary conditions
    Array<OneD, Array<OneD, NekDouble>> coords(3);
    for (int dir = 0; dir < 3; dir++)
    {
        coords[dir] = Array<OneD, NekDouble>(physTot, 0.0);
    }
    GetCartesianCoordinates(coords[0], coords[1], coords[2]);
 
    // Loop boundary conditions looking for Dirichlet bc's
    for (int n = 0; n < nbnds; ++n)
    {
        // Evaluate original Dirichlet boundary conditions in whole domain
        for (int i = 0; i < nfields; ++i)
        {
            BndConds = m_fields[i]->GetBndConditions();
            BndExp   = m_fields[i]->GetBndCondExpansions();
            if (BndConds[n]->GetBoundaryConditionType() ==
                SpatialDomains::eDirichlet)
            {
                isDirichlet[i] = true;
                // If we have the a velocity component
                //      check if all vel bc's are also Dirichlet
                if (i < nvel)
                {
                    for (int j = 0; j < nvel; ++j)
                    {
                        ASSERTL0(m_fields[j]
                                         ->GetBndConditions()[n]
                                         ->GetBoundaryConditionType() ==
                                     SpatialDomains::eDirichlet,
                                 "Mapping only supported when all velocity "
                                 "components have the same type of boundary "
                                 "conditions");
                    }
                }
                // Check if bc is time-dependent
                ASSERTL0(!BndConds[n]->IsTimeDependent(),
                         "Time-dependent Dirichlet boundary conditions not "
                         "supported with mapping yet.");
 
                // Get boundary condition
                LibUtilities::Equation condition =
                    std::static_pointer_cast<
                        SpatialDomains::DirichletBoundaryCondition>(BndConds[n])
                        ->m_dirichletCondition;
                // Evaluate
                condition.Evaluate(coords[0], coords[1], coords[2], time,
                                   values[i]);
            }
            else
            {
                isDirichlet[i] = false;
            }
        }
        // Convert velocity vector to transformed system
        if (isDirichlet[0])
        {
            for (int i = 0; i < nvel; ++i)
            {
                Vmath::Vcopy(physTot, values[i], 1, tmp[i], 1);
            }
            ContravarFromCartesian(tmp, tmp2);
            for (int i = 0; i < nvel; ++i)
            {
                Vmath::Vcopy(physTot, tmp2[i], 1, values[i], 1);
            }
        }
 
        // Now, project result to boundary
        for (int i = 0; i < nfields; ++i)
        {
            BndConds = m_fields[i]->GetBndConditions();
            BndExp   = m_fields[i]->GetBndCondExpansions();
            if (BndConds[n]->GetUserDefined() == "" ||
                BndConds[n]->GetUserDefined() == "MovingBody")
            {
                m_fields[i]->ExtractPhysToBnd(n, values[i],
                                              BndExp[n]->UpdatePhys());
 
                // Apply MovingBody correction
                if ((i < nvel) && BndConds[n]->GetUserDefined() == "MovingBody")
                {
                    // Get coordinate velocity on boundary
                    Array<OneD, NekDouble> coordVelBnd(
                        BndExp[n]->GetTotPoints());
                    m_fields[i]->ExtractPhysToBnd(n, coordVel[i], coordVelBnd);
 
                    // Apply correction
                    Vmath::Vadd(BndExp[n]->GetTotPoints(), coordVelBnd, 1,
                                BndExp[n]->UpdatePhys(), 1,
                                BndExp[n]->UpdatePhys(), 1);
                }
            }
        }
    }
 
    // Finally, perform FwdTrans in all fields
    for (int i = 0; i < m_fields.size(); ++i)
    {
        // Get boundary condition information
        BndConds = m_fields[i]->GetBndConditions();
        BndExp   = m_fields[i]->GetBndCondExpansions();
        for (int n = 0; n < BndConds.size(); ++n)
        {
            if (BndConds[n]->GetBoundaryConditionType() ==
                SpatialDomains::eDirichlet)
            {
                if (BndConds[n]->GetUserDefined() == "" ||
                    BndConds[n]->GetUserDefined() == "MovingBody")
                {
                    if (m_fields[i]->GetExpType() == MultiRegions::e3DH1D)
                    {
                        BndExp[n]->SetWaveSpace(false);
                    }
 
                    BndExp[n]->FwdTransBndConstrained(
                        BndExp[n]->GetPhys(), BndExp[n]->UpdateCoeffs());
                }
            }
        }
    }
}
 
void Mapping::v_UpdateMapping(
    const NekDouble time, const Array<OneD, Array<OneD, NekDouble>> &coords,
    const Array<OneD, Array<OneD, NekDouble>> &coordsVel)
{
    if (m_fromFunction)
    {
        std::string s_FieldStr;
        string fieldNames[3]    = {"x", "y", "z"};
        string velFieldNames[3] = {"vx", "vy", "vz"};
        // Check if function from session file defines each component
        //      and evaluate them, otherwise there is no need to update
        //          coords
        for (int i = 0; i < 3; i++)
        {
            s_FieldStr = fieldNames[i];
            if (m_session->DefinesFunction(m_funcName, s_FieldStr))
            {
                EvaluateFunction(m_fields, m_session, s_FieldStr, m_coords[i],
                                 m_funcName, time);
                if (i == 2 && m_fields[0]->GetExpType() == MultiRegions::e3DH1D)
                {
                    ASSERTL0(
                        false,
                        "3DH1D does not support mapping in the z-direction.");
                }
            }
            s_FieldStr = velFieldNames[i];
            if (m_session->DefinesFunction(m_velFuncName, s_FieldStr))
            {
                EvaluateFunction(m_fields, m_session, s_FieldStr,
                                 m_coordsVel[i], m_velFuncName, time);
                if (i == 2 && m_fields[0]->GetExpType() == MultiRegions::e3DH1D)
                {
                    ASSERTL0(
                        false,
                        "3DH1D does not support mapping in the z-direction.");
                }
            }
        }
    }
    else
    {
        int physTot = m_fields[0]->GetTotPoints();
        int nvel    = m_nConvectiveFields;
        // Copy coordinates
        for (int i = 0; i < 3; i++)
        {
            Vmath::Vcopy(physTot, coords[i], 1, m_coords[i], 1);
        }
 
        for (int i = 0; i < nvel; i++)
        {
            Vmath::Vcopy(physTot, coordsVel[i], 1, m_coordsVel[i], 1);
        }
    }
 
    // Update the information required by the specific mapping
    UpdateGeomInfo();
}
 
} // namespace GlobalMapping
} // namespace Nektar