AdjointAdvection.cpp

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///////////////////////////////////////////////////////////////////////////////
//
// File AdjointAdvection.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
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// OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
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// DEALINGS IN THE SOFTWARE.
//
// Description: Evaluation of the adjoint advective term
//
///////////////////////////////////////////////////////////////////////////////

#include <IncNavierStokesSolver/AdvectionTerms/AdjointAdvection.h>
#include <StdRegions/StdSegExp.h>

#include <MultiRegions/ContField1D.h>
#include <MultiRegions/ContField2D.h>
#include <MultiRegions/ContField3D.h>
#include <MultiRegions/DisContField1D.h>
#include <MultiRegions/DisContField2D.h>
#include <MultiRegions/ContField3DHomogeneous1D.h>
#include <MultiRegions/DisContField3DHomogeneous1D.h>
#include <MultiRegions/ContField3DHomogeneous2D.h>
#include <MultiRegions/DisContField3DHomogeneous2D.h>


namespace Nektar
{

string AdjointAdvection::className = SolverUtils
        ::GetAdvectionFactory().RegisterCreatorFunction("Adjoint",
                                                    AdjointAdvection::create);

/**
 *
 */
AdjointAdvection::AdjointAdvection()
    : Advection()
{
}


void AdjointAdvection::v_InitObject(
       LibUtilities::SessionReaderSharedPtr        pSession,
       Array<OneD, MultiRegions::ExpListSharedPtr> pFields)
{

    Advection::v_InitObject(pSession, pFields);

    m_session            = pSession;
    m_boundaryConditions = MemoryManager<SpatialDomains::BoundaryConditions>
                    ::AllocateSharedPtr(m_session, pFields[0]->GetGraph());
    m_spacedim           = pFields[0]->GetGraph()->GetSpaceDimension();
    m_expdim             = pFields[0]->GetGraph()->GetMeshDimension();
    m_CoeffState         = MultiRegions::eLocal;

    //Setting parameters for homogeneous problems
    m_HomoDirec          = 0;
    m_useFFT             = false;
    m_HomogeneousType    = eNotHomogeneous;
    m_SingleMode         = false;
    m_HalfMode           = false;
    m_MultipleModes      = false;
    m_homogen_dealiasing = false;

    if(m_session->DefinesSolverInfo("HOMOGENEOUS"))
    {
        std::string HomoStr = m_session->GetSolverInfo("HOMOGENEOUS");
        m_spacedim          = 3;

        if((HomoStr == "HOMOGENEOUS1D")||(HomoStr == "Homogeneous1D")||
           (HomoStr == "1D")||(HomoStr == "Homo1D"))
        {
            m_HomogeneousType = eHomogeneous1D;
            m_LhomZ           = m_session->GetParameter("LZ");
            m_HomoDirec       = 1;

            m_homogen_dealiasing = pSession->DefinesSolverInfo("DEALIASING");

            if(m_session->DefinesSolverInfo("ModeType"))
            {
                m_session->MatchSolverInfo("ModeType","SingleMode",m_SingleMode,false);
                m_session->MatchSolverInfo("ModeType","HalfMode",m_HalfMode,false);
                m_session->MatchSolverInfo("ModeType","MultipleModes",m_MultipleModes,false);
            }
            if(m_session->DefinesSolverInfo("ModeType"))
            {
                if(m_SingleMode)
                {
                    m_npointsZ=2;
                }
                else if(m_HalfMode)
                {
                    m_npointsZ=1;
                }
                else if(m_MultipleModes)
                {
                    m_npointsZ        = m_session->GetParameter("HomModesZ");
                }
                else
                {
                    ASSERTL0(false, "SolverInfo ModeType not valid");
                }
            }
            else
            {
                m_session->LoadParameter("HomModesZ",m_npointsZ);

            }

        }

        if((HomoStr == "HOMOGENEOUS2D")||(HomoStr == "Homogeneous2D")||
           (HomoStr == "2D")||(HomoStr == "Homo2D"))
        {
            m_HomogeneousType = eHomogeneous2D;
            m_session->LoadParameter("HomModesY", m_npointsY);
            m_session->LoadParameter("LY",        m_LhomY);
            m_session->LoadParameter("HomModesZ", m_npointsZ);
            m_session->LoadParameter("LZ",        m_LhomZ);
            m_HomoDirec       = 2;
        }

        if((HomoStr == "HOMOGENEOUS3D")||(HomoStr == "Homogeneous3D")||
           (HomoStr == "3D")||(HomoStr == "Homo3D"))
        {
            m_HomogeneousType = eHomogeneous3D;
            m_session->LoadParameter("HomModesX",m_npointsX);
            m_session->LoadParameter("LX",       m_LhomX   );
            m_session->LoadParameter("HomModesY",m_npointsY);
            m_session->LoadParameter("LY",       m_LhomY   );
            m_session->LoadParameter("HomModesZ",m_npointsZ);
            m_session->LoadParameter("LZ",       m_LhomZ   );
            m_HomoDirec       = 3;
        }

        if(m_session->DefinesSolverInfo("USEFFT"))
        {
            m_useFFT = true;
        }
    }
    else
    {
        m_npointsZ = 1; // set to default value so can use to identify 2d or 3D (homogeneous) expansions
    }

    if(m_session->DefinesSolverInfo("PROJECTION"))
    {
        std::string ProjectStr
        = m_session->GetSolverInfo("PROJECTION");

        if((ProjectStr == "Continuous")||(ProjectStr == "Galerkin")||
           (ProjectStr == "CONTINUOUS")||(ProjectStr == "GALERKIN"))
        {
            m_projectionType = MultiRegions::eGalerkin;
        }
        else if(ProjectStr == "DisContinuous")
        {
            m_projectionType = MultiRegions::eDiscontinuous;
        }
        else
        {
            ASSERTL0(false,"PROJECTION value not recognised");
        }
    }
    else
    {
        cerr << "Projection type not specified in SOLVERINFO,"
        "defaulting to continuous Galerkin" << endl;
        m_projectionType = MultiRegions::eGalerkin;
    }

    int nvar = m_session->GetVariables().size();
    m_baseflow = Array<OneD, Array<OneD, NekDouble> >(nvar);
    for (int i = 0; i < nvar; ++i)
    {
        m_baseflow[i] = Array<OneD, NekDouble>(pFields[i]->GetTotPoints(), 0.0);
    }
    //SetUpBaseFields(pFields[0]->GetGraph());
    ASSERTL0(m_session->DefinesFunction("BaseFlow"),
             "Base flow must be defined for linearised forms.");
    string file = m_session->GetFunctionFilename("BaseFlow", 0);


    //Periodic base flows
    if(m_session->DefinesParameter("N_slices"))
    {
        m_session->LoadParameter("N_slices",m_slices);
        if(m_slices>1)
        {
            DFT(file,pFields,m_slices);
        }
        else
        {
            ASSERTL0(false,"Number of slices must be a positive number greater than 1");
        }
    }
    //Steady base-flow
    else
    {
        m_slices=1;

        //BaseFlow from file
        if (m_session->GetFunctionType("BaseFlow", m_session->GetVariable(0))
            == LibUtilities::eFunctionTypeFile)
        {
            ImportFldBase(file,pFields,1);

        }
        //analytic base flow
        else
        {
            int nq = pFields[0]->GetNpoints();
            Array<OneD,NekDouble> x0(nq);
            Array<OneD,NekDouble> x1(nq);
            Array<OneD,NekDouble> x2(nq);

            // get the coordinates (assuming all fields have the same
            // discretisation)
            pFields[0]->GetCoords(x0,x1,x2);
            for(unsigned int i = 0 ; i < m_baseflow.num_elements(); i++)
            {
                LibUtilities::EquationSharedPtr ifunc
                = m_session->GetFunction("BaseFlow", i);

                ifunc->Evaluate(x0,x1,x2,m_baseflow[i]);
            }

        }

    }
}


AdjointAdvection::~AdjointAdvection()
{
}


void AdjointAdvection::v_Advect(
    const int nConvectiveFields,
    const Array<OneD, MultiRegions::ExpListSharedPtr> &fields,
    const Array<OneD, Array<OneD, NekDouble> >        &advVel,
    const Array<OneD, Array<OneD, NekDouble> >        &inarray,
    Array<OneD, Array<OneD, NekDouble> >              &outarray,
    const NekDouble                                   &time)
{
    int nqtot            = fields[0]->GetTotPoints();
    ASSERTL1(nConvectiveFields == inarray.num_elements(),"Number of convective fields and Inarray are not compatible");

    Array<OneD, NekDouble > Deriv = Array<OneD, NekDouble> (nqtot*nConvectiveFields);

    for(int n = 0; n < nConvectiveFields; ++n)
    {
        //v_ComputeAdvectionTerm(fields,advVel,inarray[i],outarray[i],i,time,Deriv);
        int ndim       = advVel.num_elements();
        int nPointsTot = fields[0]->GetNpoints();
        Array<OneD, NekDouble> grad0,grad1,grad2;

        //Evaluation of the gradiend of each component of the base flow
        //\nabla U
        Array<OneD, NekDouble> grad_base_u0,grad_base_u1,grad_base_u2;
        // \nabla V
        Array<OneD, NekDouble> grad_base_v0,grad_base_v1,grad_base_v2;
        // \nabla W
        Array<OneD, NekDouble> grad_base_w0,grad_base_w1,grad_base_w2;


        grad0 = Array<OneD, NekDouble> (nPointsTot);
        grad_base_u0 = Array<OneD, NekDouble> (nPointsTot);
        grad_base_v0 = Array<OneD, NekDouble> (nPointsTot);
        grad_base_w0 = Array<OneD, NekDouble> (nPointsTot);


        //Evaluation of the base flow for periodic cases
        //(it requires fld files)
        if(m_slices>1)
        {
            if (m_session->GetFunctionType("BaseFlow", 0)
                == LibUtilities::eFunctionTypeFile)
            {
                for(int i=0; i<ndim;++i)
                {
                    UpdateBase(m_slices,m_interp[i],m_baseflow[i],time,m_period);
                }
            }
            else
            {
                ASSERTL0(false, "Periodic Base flow requires .fld files");
            }
        }

        //Evaluate the Adjoint advection term
        switch(ndim)
        {
                    // 1D
                case 1:
                    fields[0]->PhysDeriv(inarray[n],grad0);
                    fields[0]->PhysDeriv(m_baseflow[0],grad_base_u0);
                    //Evaluate  U du'/dx
                    Vmath::Vmul(nPointsTot,grad0,1,m_baseflow[0],1,outarray[n],1);
                    //Evaluate U du'/dx+ u' dU/dx
                    Vmath::Vvtvp(nPointsTot,grad_base_u0,1,advVel[0],1,outarray[n],1,outarray[n],1);
                    break;

                    //2D
                case 2:

                    grad1 = Array<OneD, NekDouble> (nPointsTot);
                    grad_base_u1 = Array<OneD, NekDouble> (nPointsTot);
                    grad_base_v1 = Array<OneD, NekDouble> (nPointsTot);

                    fields[0]->PhysDeriv(inarray[n],grad0,grad1);

                    //Derivates of the base flow
                    fields[0]-> PhysDeriv(m_baseflow[0], grad_base_u0, grad_base_u1);
                    fields[0]-> PhysDeriv(m_baseflow[1], grad_base_v0, grad_base_v1);

                    //Since the components of the velocity are passed one by one, it is necessary to distinguish which
                    //term is consider
                    switch (n)
                    {
                        //x-equation
                    case 0:
                        // Evaluate U du'/dx
                        Vmath::Vmul (nPointsTot,grad0,1,m_baseflow[0],1,outarray[n],1);
                        //Evaluate U du'/dx+ V du'/dy
                        Vmath::Vvtvp(nPointsTot,grad1,1,m_baseflow[1],1,outarray[n],1,outarray[n],1);
                        //Evaluate - (U du'/dx+ V du'/dy)
                        Vmath::Neg(nPointsTot,outarray[n],1);
                        //Evaluate -(U du'/dx+ V du'/dy)+u' dU/dx
                        Vmath::Vvtvp(nPointsTot,grad_base_u0,1,advVel[0],1,outarray[n],1,outarray[n],1);
                        //Evaluate -(U du'/dx+ V du'/dy) +u' dU/dx +v' dV/dx
                        Vmath::Vvtvp(nPointsTot,grad_base_v0,1,advVel[1],1,outarray[n],1,outarray[n],1);
                        break;

                        //y-equation
                    case 1:
                        // Evaluate U dv'/dx
                        Vmath::Vmul (nPointsTot,grad0,1,m_baseflow[0],1,outarray[n],1);
                        //Evaluate U dv'/dx+ V dv'/dy
                        Vmath::Vvtvp(nPointsTot,grad1,1,m_baseflow[1],1,outarray[n],1,outarray[n],1);
                        //Evaluate -(U dv'/dx+ V dv'/dy)
                        Vmath::Neg(nPointsTot,outarray[n],1);
                        //Evaluate (U dv'/dx+ V dv'/dy)+u' dU/dy
                        Vmath::Vvtvp(nPointsTot,grad_base_u1,1,advVel[0],1,outarray[n],1,outarray[n],1);
                        //Evaluate (U dv'/dx+ V dv'/dy +u' dv/dx)+v' dV/dy
                        Vmath::Vvtvp(nPointsTot,grad_base_v1,1,advVel[1],1,outarray[n],1,outarray[n],1);
                        break;
                }
                    break;


                    //3D
                case 3:

                    grad1 = Array<OneD, NekDouble> (nPointsTot);
                    grad2 = Array<OneD, NekDouble> (nPointsTot);
                    grad_base_u1 = Array<OneD, NekDouble> (nPointsTot);
                    grad_base_v1 = Array<OneD, NekDouble> (nPointsTot);
                    grad_base_w1 = Array<OneD, NekDouble> (nPointsTot);

                    grad_base_u2 = Array<OneD, NekDouble> (nPointsTot);
                    grad_base_v2 = Array<OneD, NekDouble> (nPointsTot);
                    grad_base_w2 = Array<OneD, NekDouble> (nPointsTot);

                    fields[0]->PhysDeriv(m_baseflow[0], grad_base_u0, grad_base_u1,grad_base_u2);
                    fields[0]->PhysDeriv(m_baseflow[1], grad_base_v0, grad_base_v1,grad_base_v2);
                    fields[0]->PhysDeriv(m_baseflow[2], grad_base_w0, grad_base_w1, grad_base_w2);

                    //HalfMode has W(x,y,t)=0
                    if(m_HalfMode || m_SingleMode)
                    {
                        for(int i=0; i<grad_base_u2.num_elements();++i)
                        {
                            grad_base_u2[i]=0;
                            grad_base_v2[i]=0;
                            grad_base_w2[i]=0;

                        }
                    }

                fields[0]->PhysDeriv(inarray[n], grad0, grad1, grad2);

                switch (n)
                {
                        //x-equation
                    case 0:
                        //Evaluate U du'/dx
                        Vmath::Vmul (nPointsTot,grad0,1,m_baseflow[0],1,outarray[n],1);
                        //Evaluate U du'/dx+ V du'/dy
                        Vmath::Vvtvp(nPointsTot,grad1,1,m_baseflow[1],1,outarray[n],1,outarray[n],1);
                        //Evaluate U du'/dx+ V du'/dy+W du'/dz
                        Vmath::Vvtvp(nPointsTot,grad2,1,m_baseflow[2],1,outarray[n],1,outarray[n],1);
                        //Evaluate -(U du'/dx+ V du'/dy+W du'/dz)
                        Vmath::Neg(nPointsTot,outarray[n],1);
                        //Evaluate -(U du'/dx+ V du'/dy+W du'/dz)+u' dU/dx
                        Vmath::Vvtvp(nPointsTot,grad_base_u0,1,advVel[0],1,outarray[n],1,outarray[n],1);
                        //Evaluate -(U du'/dx+ V du'/dy+W du'/dz)+u'dU/dx+ v' dV/dx
                        Vmath::Vvtvp(nPointsTot,grad_base_v0,1,advVel[1],1,outarray[n],1,outarray[n],1);
                        //Evaluate -(U du'/dx+ V du'/dy+W du'/dz)+u'dU/dx+ v' dV/dx+ w' dW/dz
                        Vmath::Vvtvp(nPointsTot,grad_base_w0,1,advVel[2],1,outarray[n],1,outarray[n],1);
                        break;
                        //y-equation
                    case 1:
                        //Evaluate U dv'/dx
                        Vmath::Vmul (nPointsTot,grad0,1,m_baseflow[0],1,outarray[n],1);
                        //Evaluate U dv'/dx+ V dv'/dy
                        Vmath::Vvtvp(nPointsTot,grad1,1,m_baseflow[1],1,outarray[n],1,outarray[n],1);
                        //Evaluate U dv'/dx+ V dv'/dy+W dv'/dz
                        Vmath::Vvtvp(nPointsTot,grad2,1,m_baseflow[2],1,outarray[n],1,outarray[n],1);
                        //Evaluate -(U dv'/dx+ V dv'/dy+W dv'/dz)
                        Vmath::Neg(nPointsTot,outarray[n],1);
                        //Evaluate  -(U dv'/dx+ V dv'/dy+W dv'/dz)+u' dU/dy
                        Vmath::Vvtvp(nPointsTot,grad_base_u1,1,advVel[0],1,outarray[n],1,outarray[n],1);
                        //Evaluate  -(U dv'/dx+ V dv'/dy+W dv'/dz)+u' dU/dy +v' dV/dy
                        Vmath::Vvtvp(nPointsTot,grad_base_v1,1,advVel[1],1,outarray[n],1,outarray[n],1);
                        //Evaluate  -(U dv'/dx+ V dv'/dy+W dv'/dz)+u' dU/dy +v' dV/dy+ w' dW/dy
                        Vmath::Vvtvp(nPointsTot,grad_base_w1,1,advVel[2],1,outarray[n],1,outarray[n],1);
                        break;

                        //z-equation
                    case 2:
                        //Evaluate U dw'/dx
                        Vmath::Vmul (nPointsTot,grad0,1,m_baseflow[0],1,outarray[n],1);
                        //Evaluate U dw'/dx+ V dw'/dx
                        Vmath::Vvtvp(nPointsTot,grad1,1,m_baseflow[1],1,outarray[n],1,outarray[n],1);
                        //Evaluate U dw'/dx+ V dw'/dx+ W dw'/dz
                        Vmath::Vvtvp(nPointsTot,grad2,1,m_baseflow[2],1,outarray[n],1,outarray[n],1);
                        //Evaluate -(U dw'/dx+ V dw'/dx+ W dw'/dz)
                        Vmath::Neg(nPointsTot,outarray[n],1);
                        //Evaluate -(U dw'/dx+ V dw'/dx+ W dw'/dz)+u' dU/dz
                        Vmath::Vvtvp(nPointsTot,grad_base_u2,1,advVel[0],1,outarray[n],1,outarray[n],1);
                        //Evaluate -(U dw'/dx+ V dw'/dx+ W dw'/dz)+u' dU/dz+v'dV/dz
                        Vmath::Vvtvp(nPointsTot,grad_base_v2,1,advVel[1],1,outarray[n],1,outarray[n],1);
                        //Evaluate -(U dw'/dx+ V dw'/dx+ W dw'/dz)+u' dU/dz+v'dV/dz + w' dW/dz
                        Vmath::Vvtvp(nPointsTot,grad_base_w2,1,advVel[2],1,outarray[n],1,outarray[n],1);
                        break;
                }
                    break;
        default:
            ASSERTL0(false,"dimension unknown");
        }

        Vmath::Neg(nqtot,outarray[n],1);
    }

}


void AdjointAdvection::v_SetBaseFlow(
        const Array<OneD, Array<OneD, NekDouble> >    &inarray)
{
    ASSERTL1(inarray.num_elements() == m_baseflow.num_elements(),
             "Number of base flow variables does not match what is"
             "expected.");

    int npts = inarray[0].num_elements();
    for (int i = 0; i < inarray.num_elements(); ++i)
    {
        ASSERTL1(npts == m_baseflow.num_elements(),
                "Size of base flow array does not match expected.");
        Vmath::Vcopy(npts, inarray[i], 1, m_baseflow[i], 1);
    }
}


/**
 * Import field from infile and load into \a m_fields. This routine will
 * also perform a \a BwdTrans to ensure data is in both the physical and
 * coefficient storage.
 * @param   infile          Filename to read.
 */
void AdjointAdvection::ImportFldBase(std::string pInfile,
        Array<OneD, MultiRegions::ExpListSharedPtr>& pFields, int slice)
{
    std::vector<LibUtilities::FieldDefinitionsSharedPtr> FieldDef;
    std::vector<std::vector<NekDouble> > FieldData;

    int nqtot = pFields[0]->GetTotPoints();
    Array<OneD, NekDouble> tmp_coeff(pFields[0]->GetNcoeffs(), 0.0);

    //Get Homogeneous
    LibUtilities::FieldIOSharedPtr fld =
            MemoryManager<LibUtilities::FieldIO>::AllocateSharedPtr(
                                                    m_session->GetComm());
    fld->Import(pInfile, FieldDef, FieldData);

    int nvar = m_session->GetVariables().size();
    int s;

    if(m_session->DefinesSolverInfo("HOMOGENEOUS"))
    {
        std::string HomoStr = m_session->GetSolverInfo("HOMOGENEOUS");
    }

    // copy FieldData into m_fields
    for(int j = 0; j < nvar; ++j)
    {
        for(int i = 0; i < FieldDef.size(); ++i)
        {
            if ((m_session->DefinesSolverInfo("HOMOGENEOUS") &&
                (m_session->GetSolverInfo("HOMOGENEOUS")=="HOMOGENEOUS1D" ||
                 m_session->GetSolverInfo("HOMOGENEOUS")=="1D" ||
                 m_session->GetSolverInfo("HOMOGENEOUS")=="Homo1D")) &&
                nvar==4)
            {
                // w-component must be ignored and set to zero.
                if (j != nvar - 2)
                {
                    // p component (it is 4th variable of the 3D and corresponds 3nd variable of 2D)
                    s = (j == nvar - 1) ? 2 : j;

                    //extraction of the 2D
                    pFields[j]->ExtractDataToCoeffs(
                                        FieldDef[i],
                                        FieldData[i],
                                        FieldDef[i]->m_fields[s],
                                        tmp_coeff);
                }

                // Put zero on higher modes
                int ncplane = (pFields[0]->GetNcoeffs()) / m_npointsZ;

                if (m_npointsZ > 2)
                {
                    Vmath::Zero(ncplane*(m_npointsZ-2),
                                &tmp_coeff[2*ncplane],1);
                }
            }
            //2D cases and Homogeneous1D Base Flows
            else
            {
                bool flag = FieldDef[i]->m_fields[j] ==
                                                m_session->GetVariable(j);

                ASSERTL0(flag, (std::string("Order of ") + pInfile
                                + std::string(" data and that defined in "
                                              "m_boundaryconditions differs")).c_str());

                pFields[j]->ExtractDataToCoeffs(FieldDef[i], FieldData[i],
                                               FieldDef[i]->m_fields[j],
                                               tmp_coeff);
            }
        }

        if(m_SingleMode || m_HalfMode)
        {
            pFields[j]->GetPlane(0)->BwdTrans(tmp_coeff, m_baseflow[j]);

            if(m_SingleMode)
            {
                //copy the bwd into the second plane for single Mode Analysis
                int ncplane=(pFields[0]->GetNpoints())/m_npointsZ;
                Vmath::Vcopy(ncplane,&m_baseflow[j][0],1,&m_baseflow[j][ncplane],1);
            }
        }
        else
        {
            pFields[j]->BwdTrans(tmp_coeff, m_baseflow[j]);
        }
    }

    if(m_session->DefinesParameter("N_slices"))
    {
        int n = pFields.num_elements()-1;

        for(int i=0; i<n;++i)
        {
            Vmath::Vcopy(nqtot, &m_baseflow[i][0], 1, &m_interp[i][slice*nqtot], 1);
        }

    }
}


void AdjointAdvection::UpdateBase(
        const NekDouble                     m_slices,
        const Array<OneD, const NekDouble> &inarray,
              Array<OneD, NekDouble>       &outarray,
        const NekDouble                     m_time,
        const NekDouble                     m_period)
{

    int npoints=m_baseflow[0].num_elements();

    NekDouble BetaT=2*M_PI*fmod (m_time, m_period) / m_period;
    NekDouble phase;
    Array<OneD, NekDouble> auxiliary(npoints);

    Vmath::Vcopy(npoints,&inarray[0],1,&outarray[0],1);
    Vmath::Svtvp(npoints, cos(0.5*m_slices*BetaT),&inarray[npoints],1,&outarray[0],1,&outarray[0],1);

    for (int i = 2; i < m_slices; i += 2)
    {
        phase = (i>>1) * BetaT;

        Vmath::Svtvp(npoints, cos(phase),&inarray[i*npoints],1,&outarray[0],1,&outarray[0],1);
        Vmath::Svtvp(npoints, sin(phase), &inarray[(i+1)*npoints], 1, &outarray[0], 1,&outarray[0],1);
    }

}

DNekBlkMatSharedPtr AdjointAdvection::GetFloquetBlockMatrix(FloquetMatType mattype, bool UseContCoeffs) const
{
    DNekMatSharedPtr    loc_mat;
    DNekBlkMatSharedPtr BlkMatrix;
    int n_exp = 0;

    n_exp = m_baseflow[0].num_elements(); // will operatore on m_phys

    Array<OneD,unsigned int> nrows(n_exp);
    Array<OneD,unsigned int> ncols(n_exp);

    nrows = Array<OneD, unsigned int>(n_exp,m_slices);
    ncols = Array<OneD, unsigned int>(n_exp,m_slices);

    MatrixStorage blkmatStorage = eDIAGONAL;
    BlkMatrix = MemoryManager<DNekBlkMat>
    ::AllocateSharedPtr(nrows,ncols,blkmatStorage);


    const LibUtilities::PointsKey Pkey(m_slices,LibUtilities::eFourierEvenlySpaced);
    const LibUtilities::BasisKey  BK(LibUtilities::eFourier,m_slices,Pkey);
    StdRegions::StdSegExp StdSeg(BK);

    StdRegions::StdMatrixKey matkey(StdRegions::eFwdTrans,
                                                StdSeg.DetShapeType(),
                                                StdSeg);

    loc_mat = StdSeg.GetStdMatrix(matkey);

    // set up array of block matrices.
    for(int i = 0; i < n_exp; ++i)
    {
        BlkMatrix->SetBlock(i,i,loc_mat);
    }

    return BlkMatrix;
}

//Discrete Fourier Transform for Floquet analysis
void AdjointAdvection::DFT(const string file,
        Array<OneD, MultiRegions::ExpListSharedPtr>& pFields,
        const NekDouble m_slices)
{
    int npoints=m_baseflow[0].num_elements();

    //Convected fields
    int ConvectedFields=m_baseflow.num_elements()-1;

    m_interp= Array<OneD, Array<OneD, NekDouble> > (ConvectedFields);
    for(int i=0; i<ConvectedFields;++i)
    {
        m_interp[i]=Array<OneD,NekDouble>(npoints*m_slices);
    }

    // Import the slides into auxiliary vector
    // The base flow should be stored in the form "filename_%d.ext"
    // A subdirectory can also be included, such as "dir/filename_%d.ext"
    size_t found = file.find("%d");
    ASSERTL0(found != string::npos && file.find("%d", found+1) == string::npos,
             "Since N_slices is specified, the filename provided for function "
             "'BaseFlow' must include exactly one instance of the format "
             "specifier '%d', to index the time-slices.");
    char* buffer = new char[file.length() + 8];
    for (int i = 0; i < m_slices; ++i)
    {
        sprintf(buffer, file.c_str(), i);
        ImportFldBase(buffer,pFields,i);
    }
    delete[] buffer;


    // Discrete Fourier Transform of the fields
    for(int k=0; k< ConvectedFields;++k)
    {
#ifdef NEKTAR_USING_FFTW

        //Discrete Fourier Transform using FFTW


        Array<OneD, NekDouble> fft_in(npoints*m_slices);
        Array<OneD, NekDouble> fft_out(npoints*m_slices);

        Array<OneD, NekDouble> m_tmpIN(m_slices);
        Array<OneD, NekDouble> m_tmpOUT(m_slices);

        //Shuffle the data
        for(int j= 0; j < m_slices; ++j)
        {
            Vmath::Vcopy(npoints,&m_interp[k][j*npoints],1,&(fft_in[j]),m_slices);
        }

        m_FFT = LibUtilities::GetNektarFFTFactory().CreateInstance("NekFFTW", m_slices);

        //FFT Transform
        for(int i=0; i<npoints; i++)
        {
            m_FFT->FFTFwdTrans(m_tmpIN =fft_in + i*m_slices, m_tmpOUT =fft_out + i*m_slices);

        }

        //Reshuffle data
        for(int s = 0; s < m_slices; ++s)
        {
            Vmath::Vcopy(npoints,&fft_out[s],m_slices,&m_interp[k][s*npoints],1);

        }

        Vmath::Zero(fft_in.num_elements(),&fft_in[0],1);
        Vmath::Zero(fft_out.num_elements(),&fft_out[0],1);
#else
        //Discrete Fourier Transform using MVM


        DNekBlkMatSharedPtr blkmat;
        blkmat = GetFloquetBlockMatrix(eForwardsPhys);

        int nrows = blkmat->GetRows();
        int ncols = blkmat->GetColumns();

        Array<OneD, NekDouble> sortedinarray(ncols);
        Array<OneD, NekDouble> sortedoutarray(nrows);

        //Shuffle the data
        for(int j= 0; j < m_slices; ++j)
        {
            Vmath::Vcopy(npoints,&m_interp[k][j*npoints],1,&(sortedinarray[j]),m_slices);
        }

        // Create NekVectors from the given data arrays
        NekVector<NekDouble> in (ncols,sortedinarray,eWrapper);
        NekVector<NekDouble> out(nrows,sortedoutarray,eWrapper);

        // Perform matrix-vector multiply.
        out = (*blkmat)*in;

        //Reshuffle data
        for(int s = 0; s < m_slices; ++s)
        {
            Vmath::Vcopy(npoints,&sortedoutarray[s],m_slices,&m_interp[k][s*npoints],1);
        }

        Vmath::Zero(sortedinarray.num_elements(),&sortedinarray[0],1);
        Vmath::Zero(sortedoutarray.num_elements(),&sortedoutarray[0],1);

#endif

        //scaling of the Fourier coefficients
        NekDouble j=-1;
        for (int i = 2; i < m_slices; i += 2)
        {
            Vmath::Smul(2*npoints,j,&m_interp[k][i*npoints],1,&m_interp[k][i*npoints],1);
            j=-j;

        }

    }

    if(m_session->DefinesParameter("period"))
    {
        m_period=m_session->GetParameter("period");
    }
    else
    {
        m_period=(m_session->GetParameter("TimeStep")*m_slices)/(m_slices-1.);
    }
}


} //end of namespace