EigenValuesAdvection.cpp

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///////////////////////////////////////////////////////////////////////////////
//
// File EigenValuesAdvection.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
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// DEALINGS IN THE SOFTWARE.
//
// Description:
//
///////////////////////////////////////////////////////////////////////////////
 
#include <iostream>
 
#include <ADRSolver/EquationSystems/EigenValuesAdvection.h>
 
using namespace std;
 
namespace Nektar
{
    string EigenValuesAdvection::className = GetEquationSystemFactory().RegisterCreatorFunction("EigenValuesAdvection", EigenValuesAdvection::create, "Eigenvalues of the weak advection operator.");
 
    EigenValuesAdvection::EigenValuesAdvection(
        const LibUtilities::SessionReaderSharedPtr& pSession,
        const SpatialDomains::MeshGraphSharedPtr& pGraph)
        : EquationSystem(pSession, pGraph)
    {
    }
 
    void EigenValuesAdvection::v_InitObject()
    {
        EquationSystem::v_InitObject();
 
        // Define Velocity fields
        m_velocity = Array<OneD, Array<OneD, NekDouble> >(m_spacedim);
        std::vector<std::string> vel;
        vel.push_back("Vx");
        vel.push_back("Vy");
        vel.push_back("Vz");
        vel.resize(m_spacedim);
 
        GetFunction( "AdvectionVelocity")->Evaluate(vel,  m_velocity);
 
        // Type of advection class to be used
        switch(m_projectionType)
        {
            // Discontinuous field
            case MultiRegions::eDiscontinuous:
            {
                // Define the normal velocity fields
                if (m_fields[0]->GetTrace())
                {
                    m_traceVn = Array<OneD, NekDouble>(GetTraceNpoints());
                }
 
                string advName;
                string riemName;
                m_session->LoadSolverInfo(
                    "AdvectionType", advName, "WeakDG");
                m_advObject = SolverUtils::
                    GetAdvectionFactory().CreateInstance(advName, advName);
                m_advObject->SetFluxVector(
                    &EigenValuesAdvection::GetFluxVector, this);
                m_session->LoadSolverInfo(
                    "UpwindType", riemName, "Upwind");
                m_riemannSolver = SolverUtils::
                    GetRiemannSolverFactory().CreateInstance(
                        riemName, m_session);
                m_riemannSolver->SetScalar(
                    "Vn", &EigenValuesAdvection::GetNormalVelocity, this);
 
                m_advObject->SetRiemannSolver(m_riemannSolver);
                m_advObject->InitObject(m_session, m_fields);
                break;
            }
            // Continuous field
            case MultiRegions::eGalerkin:
            case MultiRegions::eMixed_CG_Discontinuous:
            {
                string advName;
                m_session->LoadSolverInfo(
                    "AdvectionType", advName, "NonConservative");
                m_advObject = SolverUtils::
                    GetAdvectionFactory().CreateInstance(advName, advName);
                m_advObject->SetFluxVector(
                    &EigenValuesAdvection::GetFluxVector, this);
                break;
            }
            default:
            {
                ASSERTL0(false, "Unsupported projection type.");
                break;
            }
        }
    }
 
    /**
     * @brief Get the normal velocity
     */
    Array<OneD, NekDouble> &EigenValuesAdvection::GetNormalVelocity()
    {
        // Number of trace (interface) points
        int nTracePts = GetTraceNpoints();
 
        // Auxiliary variable to compute the normal velocity
        Array<OneD, NekDouble> tmp(nTracePts);
 
        // Reset the normal velocity
        Vmath::Zero(nTracePts, m_traceVn, 1);
 
        for (int i = 0; i < m_velocity.size(); ++i)
        {
            m_fields[0]->ExtractTracePhys(m_velocity[i], tmp);
 
            Vmath::Vvtvp(nTracePts,
                         m_traceNormals[i], 1,
                         tmp,               1,
                         m_traceVn,         1,
                         m_traceVn,         1);
        }
 
        return m_traceVn;
    }
 
    void EigenValuesAdvection::v_DoInitialise()
    {
 
    }
 
    EigenValuesAdvection::~EigenValuesAdvection()
    {
 
    }
 
    void EigenValuesAdvection::v_DoSolve()
    {
        int nvariables = 1;
        int dofs = GetNcoeffs();
        //bool UseContCoeffs = false;
 
        Array<OneD, Array<OneD, NekDouble> > inarray(nvariables);
        Array<OneD, Array<OneD, NekDouble> > tmp(nvariables);
        Array<OneD, Array<OneD, NekDouble> > outarray(nvariables);
        Array<OneD, Array<OneD, NekDouble> > WeakAdv(nvariables);
 
        int npoints = GetNpoints();
        int ncoeffs = GetNcoeffs();
 
        switch (m_projectionType)
        {
                case MultiRegions::eDiscontinuous:
                    {
                        dofs = ncoeffs;
                        break;
                    }
                case MultiRegions::eGalerkin:
                case MultiRegions::eMixed_CG_Discontinuous:
                    {
                        //dofs = GetContNcoeffs();
                        //UseContCoeffs = true;
                        break;
                    }
        }
 
        cout << endl;
        cout << "Num Phys Points = " << npoints << endl; // phisical points
        cout << "Num Coeffs      = " << ncoeffs << endl; //
        cout << "Num Cont Coeffs = " << dofs << endl;
 
        inarray[0]  = Array<OneD, NekDouble>(npoints,0.0);
        outarray[0] = Array<OneD, NekDouble>(npoints,0.0);
        tmp[0] = Array<OneD, NekDouble>(npoints,0.0);
 
        WeakAdv[0]  = Array<OneD, NekDouble>(ncoeffs,0.0);
        Array<OneD, NekDouble> MATRIX(npoints*npoints,0.0);
 
        for (int j = 0; j < npoints; j++)
        {
 
        inarray[0][j] = 1.0;
 
        /// Feeding the weak Advection oprator with  a vector (inarray)
        /// Looping on inarray and changing the position of the only non-zero entry
        /// we simulate the multiplication by the identity matrix.
        /// The results stored in outarray is one of the columns of the weak advection oprators
        /// which are then stored in MATRIX for the futher eigenvalues calculation.
        m_advObject->Advect(nvariables, m_fields, m_velocity, inarray,
                            outarray, 0.0);
        Vmath::Neg(npoints,outarray[0],1);
        switch (m_projectionType)
        {
        case MultiRegions::eDiscontinuous:
            {
                break;
            }
        case MultiRegions::eGalerkin:
        case MultiRegions::eMixed_CG_Discontinuous:
            {
                for(int i = 0; i < nvariables; ++i)
                {
                    //m_fields[i]->MultiplyByInvMassMatrix(WeakAdv[i],WeakAdv[i]);
                    //Projection
                    m_fields[i]->FwdTrans(outarray[i],WeakAdv[i]);
 
                    m_fields[i]->BwdTrans_IterPerExp(WeakAdv[i],outarray[i]);
                }
                break;
            }
        }
 
        /// The result is stored in outarray (is the j-th columns of the weak advection operator).
        /// We now store it in MATRIX(j)
        Vmath::Vcopy(npoints,&(outarray[0][0]),1,&(MATRIX[j]),npoints);
 
        /// Set the j-th entry of inarray back to zero
        inarray[0][j] = 0.0;
        }
 
        ////////////////////////////////////////////////////////////////////////////////
        /// Calulating the eigenvalues of the weak advection operator stored in (MATRIX)
        /// using Lapack routines
 
        char jobvl = 'N';
        char jobvr = 'N';
        int info = 0, lwork = 3*npoints;
        NekDouble dum;
 
        Array<OneD, NekDouble> EIG_R(npoints);
        Array<OneD, NekDouble> EIG_I(npoints);
 
        Array<OneD, NekDouble> work(lwork);
 
        Lapack::Dgeev(jobvl,jobvr,npoints,MATRIX.get(),npoints,EIG_R.get(),EIG_I.get(),&dum,1,&dum,1,&work[0],lwork,info);
 
        ////////////////////////////////////////////////////////
        //Print Matrix
        FILE *mFile;
 
        mFile = fopen ("WeakAdvMatrix.txt","w");
        for(int j = 0; j<npoints; j++)
        {
            for(int k = 0; k<npoints; k++)
            {
                fprintf(mFile,"%e ",MATRIX[j*npoints+k]);
            }
            fprintf(mFile,"\n");
        }
        fclose (mFile);
 
        ////////////////////////////////////////////////////////
        //Output of the EigenValues
        FILE *pFile;
 
        pFile = fopen ("Eigenvalues.txt","w");
        for(int j = 0; j<npoints; j++)
        {
            fprintf(pFile,"%e %e\n",EIG_R[j],EIG_I[j]);
        }
        fclose (pFile);
 
        cout << "\nEigenvalues : " << endl;
        for(int j = 0; j<npoints; j++)
        {
            cout << EIG_R[j] << "\t" << EIG_I[j] << endl;
        }
        cout << endl;
    }
 
    void EigenValuesAdvection::GetFluxVector(
        const Array<OneD, Array<OneD, NekDouble> >               &physfield,
              Array<OneD, Array<OneD, Array<OneD, NekDouble> > > &flux)
    {
        ASSERTL1(flux[0].size() == m_velocity.size(),
                 "Dimension of flux array and velocity array do not match");
 
        int nq = physfield[0].size();
 
        for (int i = 0; i < flux.size(); ++i)
        {
            for (int j = 0; j < flux[0].size(); ++j)
            {
                Vmath::Vmul(nq, physfield[i], 1, m_velocity[j], 1,
                            flux[i][j], 1);
            }
        }
    }
}