GlobalLinSysIterativeStaticCond.cpp

Go to the documentation of this file.

///////////////////////////////////////////////////////////////////////////////
//
// File: GlobalLinSysIterativeStaticCond.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: Implementation to linear solver using single-
//              or multi-level static condensation
//
///////////////////////////////////////////////////////////////////////////////
 
#include <LibUtilities/BasicUtils/ErrorUtil.hpp>
#include <LibUtilities/LinearAlgebra/SparseDiagBlkMatrix.hpp>
#include <LibUtilities/LinearAlgebra/SparseUtils.hpp>
#include <LibUtilities/LinearAlgebra/StorageSmvBsr.hpp>
#include <MultiRegions/GlobalLinSysIterativeStaticCond.h>
 
using namespace std;
 
namespace Nektar::MultiRegions
{
/**
 * @class GlobalLinSysIterativeStaticCond
 *
 * Solves a linear system iteratively using single- or multi-level
 * static condensation.
 */
 
/**
 * Registers the class with the Factory.
 */
string GlobalLinSysIterativeStaticCond::className =
    GetGlobalLinSysFactory().RegisterCreatorFunction(
        "IterativeStaticCond", GlobalLinSysIterativeStaticCond::create,
        "Iterative static condensation.");
 
string GlobalLinSysIterativeStaticCond::className2 =
    GetGlobalLinSysFactory().RegisterCreatorFunction(
        "IterativeMultiLevelStaticCond",
        GlobalLinSysIterativeStaticCond::create,
        "Iterative multi-level static condensation.");
 
std::string GlobalLinSysIterativeStaticCond::storagedef =
    LibUtilities::SessionReader::RegisterDefaultSolverInfo(
        "LocalMatrixStorageStrategy", "Sparse");
std::string GlobalLinSysIterativeStaticCond::storagelookupIds[3] = {
    LibUtilities::SessionReader::RegisterEnumValue(
        "LocalMatrixStorageStrategy", "Contiguous", MultiRegions::eContiguous),
    LibUtilities::SessionReader::RegisterEnumValue(
        "LocalMatrixStorageStrategy", "Non-contiguous",
        MultiRegions::eNonContiguous),
    LibUtilities::SessionReader::RegisterEnumValue(
        "LocalMatrixStorageStrategy", "Sparse", MultiRegions::eSparse),
};
 
/**
 * For a matrix system of the form @f[
 * \left[ \begin{array}{cc}
 * \boldsymbol{A} & \boldsymbol{B}\\
 * \boldsymbol{C} & \boldsymbol{D}
 * \end{array} \right]
 * \left[ \begin{array}{c} \boldsymbol{x_1}\\ \boldsymbol{x_2}
 * \end{array}\right]
 * = \left[ \begin{array}{c} \boldsymbol{y_1}\\ \boldsymbol{y_2}
 * \end{array}\right],
 * @f]
 * where @f$\boldsymbol{D}@f$ and
 * @f$(\boldsymbol{A-BD^{-1}C})@f$ are invertible, store and assemble
 * a static condensation system, according to a given local to global
 * mapping. #m_linSys is constructed by AssembleSchurComplement().
 * @param   mKey        Associated matrix key.
 * @param   pLocMatSys  LocalMatrixSystem
 * @param   locToGloMap Local to global mapping.
 */
GlobalLinSysIterativeStaticCond::GlobalLinSysIterativeStaticCond(
    const GlobalLinSysKey &pKey, const std::weak_ptr<ExpList> &pExpList,
    const std::shared_ptr<AssemblyMap> &pLocToGloMap)
    : GlobalLinSys(pKey, pExpList, pLocToGloMap),
      GlobalLinSysIterative(pKey, pExpList, pLocToGloMap),
      GlobalLinSysStaticCond(pKey, pExpList, pLocToGloMap)
{
    ASSERTL1(
        (pKey.GetGlobalSysSolnType() == eIterativeStaticCond) ||
            (pKey.GetGlobalSysSolnType() == eIterativeMultiLevelStaticCond),
        "This constructor is only valid when using static "
        "condensation");
    ASSERTL1(pKey.GetGlobalSysSolnType() ==
                 pLocToGloMap->GetGlobalSysSolnType(),
             "The local to global map is not set up for the requested "
             "solution type");
}
 
/**
 *
 */
GlobalLinSysIterativeStaticCond::GlobalLinSysIterativeStaticCond(
    const GlobalLinSysKey &pKey, const std::weak_ptr<ExpList> &pExpList,
    const DNekScalBlkMatSharedPtr pSchurCompl,
    const DNekScalBlkMatSharedPtr pBinvD, const DNekScalBlkMatSharedPtr pC,
    const DNekScalBlkMatSharedPtr pInvD,
    const std::shared_ptr<AssemblyMap> &pLocToGloMap,
    const PreconditionerSharedPtr pPrecon)
    : GlobalLinSys(pKey, pExpList, pLocToGloMap),
      GlobalLinSysIterative(pKey, pExpList, pLocToGloMap),
      GlobalLinSysStaticCond(pKey, pExpList, pLocToGloMap)
{
    m_schurCompl = pSchurCompl;
    m_BinvD      = pBinvD;
    m_C          = pC;
    m_invD       = pInvD;
    m_precon     = pPrecon;
}
 
void GlobalLinSysIterativeStaticCond::v_InitObject()
{
    auto asmMap = m_locToGloMap.lock();
 
    m_precon = CreatePrecon(asmMap);
 
    // Allocate memory for top-level structure
    SetupTopLevel(asmMap);
 
    // Setup Block Matrix systems
    int n, n_exp = m_expList.lock()->GetNumElmts();
 
    // Build preconditioner
    m_precon->BuildPreconditioner();
 
    // Do transform of Schur complement matrix
    int cnt = 0;
    for (n = 0; n < n_exp; ++n)
    {
        if (m_linSysKey.GetMatrixType() != StdRegions::eHybridDGHelmBndLam)
        {
            DNekScalMatSharedPtr mat = m_schurCompl->GetBlock(n, n);
            DNekScalMatSharedPtr t =
                m_precon->TransformedSchurCompl(n, cnt, mat);
            m_schurCompl->SetBlock(n, n, t);
            cnt += mat->GetRows();
        }
    }
 
    // Construct this level
    Initialise(asmMap);
}
 
/**
 *
 */
GlobalLinSysIterativeStaticCond::~GlobalLinSysIterativeStaticCond()
{
}
 
DNekScalBlkMatSharedPtr GlobalLinSysIterativeStaticCond::v_GetStaticCondBlock(
    unsigned int n)
{
    DNekScalBlkMatSharedPtr schurComplBlock;
    DNekScalMatSharedPtr localMat = m_schurCompl->GetBlock(n, n);
    unsigned int nbdry            = localMat->GetRows();
    unsigned int nblks            = 1;
    unsigned int esize[1]         = {nbdry};
 
    schurComplBlock = MemoryManager<DNekScalBlkMat>::AllocateSharedPtr(
        nblks, nblks, esize, esize);
    schurComplBlock->SetBlock(0, 0, localMat);
 
    return schurComplBlock;
}
 
/**
 * Assemble the schur complement matrix from the block matrices stored
 * in #m_blkMatrices and the given local to global mapping information.
 * @param   locToGloMap Local to global mapping information.
 */
void GlobalLinSysIterativeStaticCond::v_AssembleSchurComplement(
    [[maybe_unused]] const AssemblyMapSharedPtr pLocToGloMap)
{
    // Set up unique map
    v_UniqueMap();
 
    // Build precon again if we in multi-level static condensation (a
    // bit of a hack)
    if (m_linSysKey.GetGlobalSysSolnType() == eIterativeMultiLevelStaticCond)
    {
        m_precon = CreatePrecon(m_locToGloMap.lock());
        m_precon->BuildPreconditioner();
    }
 
    PrepareLocalSchurComplement();
}
 
/**
 * Populates sparse block-diagonal schur complement matrix from
 * the block matrices stored in #m_blkMatrices.
 */
void GlobalLinSysIterativeStaticCond::PrepareLocalSchurComplement()
{
    LocalMatrixStorageStrategy storageStrategy =
        m_expList.lock()
            ->GetSession()
            ->GetSolverInfoAsEnum<LocalMatrixStorageStrategy>(
                "LocalMatrixStorageStrategy");
 
    switch (storageStrategy)
    {
        case MultiRegions::eContiguous:
        case MultiRegions::eNonContiguous:
        {
            size_t storageSize = 0;
            int nBlk           = m_schurCompl->GetNumberOfBlockRows();
 
            m_scale = Array<OneD, NekDouble>(nBlk, 1.0);
            m_rows  = Array<OneD, unsigned int>(nBlk, 0U);
 
            // Determine storage requirements for dense blocks.
            for (int i = 0; i < nBlk; ++i)
            {
                m_rows[i]  = m_schurCompl->GetBlock(i, i)->GetRows();
                m_scale[i] = m_schurCompl->GetBlock(i, i)->Scale();
                storageSize += m_rows[i] * m_rows[i];
            }
 
            // Assemble dense storage blocks.
            DNekScalMatSharedPtr loc_mat;
            m_denseBlocks.resize(nBlk);
            double *ptr = nullptr;
 
            if (MultiRegions::eContiguous == storageStrategy)
            {
                m_storage.resize(storageSize);
                ptr = &m_storage[0];
            }
 
            for (unsigned int n = 0; n < nBlk; ++n)
            {
                loc_mat = m_schurCompl->GetBlock(n, n);
 
                if (MultiRegions::eContiguous == storageStrategy)
                {
                    int loc_lda      = loc_mat->GetRows();
                    int blockSize    = loc_lda * loc_lda;
                    m_denseBlocks[n] = ptr;
                    for (int i = 0; i < loc_lda; ++i)
                    {
                        for (int j = 0; j < loc_lda; ++j)
                        {
                            ptr[j * loc_lda + i] = (*loc_mat)(i, j);
                        }
                    }
                    ptr += blockSize;
                    GlobalLinSys::v_DropStaticCondBlock(n);
                }
                else
                {
                    m_denseBlocks[n] = loc_mat->GetRawPtr();
                }
            }
            break;
        }
        case MultiRegions::eSparse:
        {
            DNekScalMatSharedPtr loc_mat;
            int loc_lda;
            int blockSize = 0;
 
            // First run through to split the set of local matrices into
            // partitions of fixed block size, and count number of local
            // matrices that belong to each partition.
            std::vector<std::pair<int, int>> partitions;
            for (int n = 0; n < m_schurCompl->GetNumberOfBlockRows(); ++n)
            {
                loc_mat = m_schurCompl->GetBlock(n, n);
                loc_lda = loc_mat->GetRows();
 
                ASSERTL1(loc_lda >= 0,
                         std::to_string(n) +
                             "-th "
                             "matrix block in Schur complement has "
                             "rank 0!");
 
                if (blockSize == loc_lda)
                {
                    partitions[partitions.size() - 1].first++;
                }
                else
                {
                    blockSize = loc_lda;
                    partitions.push_back(make_pair(1, loc_lda));
                }
            }
 
            MatrixStorage matStorage = eFULL;
 
            // Create a vector of sparse storage holders
            DNekSmvBsrDiagBlkMat::SparseStorageSharedPtrVector sparseStorage(
                partitions.size());
 
            for (int part = 0, n = 0; part < partitions.size(); ++part)
            {
                BCOMatType partMat;
 
                for (int k = 0; k < partitions[part].first; ++k, ++n)
                {
                    loc_mat = m_schurCompl->GetBlock(n, n);
                    loc_lda = loc_mat->GetRows();
 
                    ASSERTL1(loc_lda == partitions[part].second,
                             std::to_string(n) +
                                 "-th"
                                 " matrix block in Schur complement has "
                                 "unexpected rank");
 
                    NekDouble scale = loc_mat->Scale();
                    if (fabs(scale - 1.0) > NekConstants::kNekZeroTol)
                    {
                        Array<OneD, NekDouble> matarray(loc_lda * loc_lda);
                        Vmath::Smul(loc_lda * loc_lda, scale,
                                    loc_mat->GetRawPtr(), 1, &matarray[0], 1);
                        partMat[make_pair(k, k)] = BCOEntryType(matarray);
                    }
                    else // scale factor is 1.0
                    {
                        partMat[make_pair(k, k)] = BCOEntryType(
                            loc_lda * loc_lda, loc_mat->GetRawPtr());
                    }
 
                    GlobalLinSys::v_DropStaticCondBlock(n);
                }
 
                sparseStorage[part] =
                    MemoryManager<DNekSmvBsrDiagBlkMat::StorageType>::
                        AllocateSharedPtr(
                            partitions[part].first, partitions[part].first,
                            partitions[part].second, partMat, matStorage);
            }
 
            // Create block diagonal matrix
            m_sparseSchurCompl =
                MemoryManager<DNekSmvBsrDiagBlkMat>::AllocateSharedPtr(
                    sparseStorage);
 
            break;
        }
        default:
            ErrorUtil::NekError("Solver info property \
                        LocalMatrixStorageStrategy takes values \
                        Contiguous, Non-contiguous and Sparse");
    }
}
 
/**
 *
 */
void GlobalLinSysIterativeStaticCond::v_DoMatrixMultiply(
    const Array<OneD, NekDouble> &pInput, Array<OneD, NekDouble> &pOutput)
{
    if (m_linsol->IsLocal())
    {
        if (m_sparseSchurCompl)
        {
            m_sparseSchurCompl->Multiply(pInput, pOutput);
        }
        else
        {
            // Do matrix multiply locally, using direct BLAS calls
            int i, cnt;
            for (i = cnt = 0; i < m_denseBlocks.size(); cnt += m_rows[i], ++i)
            {
                const int rows = m_rows[i];
                Blas::Dgemv('N', rows, rows, m_scale[i], m_denseBlocks[i], rows,
                            pInput.get() + cnt, 1, 0.0, pOutput.get() + cnt, 1);
            }
        }
    }
    else
    {
        int nLocal = m_locToGloMap.lock()->GetNumLocalBndCoeffs();
        AssemblyMapSharedPtr asmMap = m_locToGloMap.lock();
 
        if (m_sparseSchurCompl)
        {
            // Do matrix multiply locally using block-diagonal sparse matrix
            Array<OneD, NekDouble> tmp = m_wsp + nLocal;
 
            asmMap->GlobalToLocalBnd(pInput, m_wsp);
            m_sparseSchurCompl->Multiply(m_wsp, tmp);
            asmMap->AssembleBnd(tmp, pOutput);
        }
        else
        {
            // Do matrix multiply locally, using direct BLAS calls
            asmMap->GlobalToLocalBnd(pInput, m_wsp);
            int i, cnt;
            Array<OneD, NekDouble> tmpout = m_wsp + nLocal;
            for (i = cnt = 0; i < m_denseBlocks.size(); cnt += m_rows[i], ++i)
            {
                const int rows = m_rows[i];
                Blas::Dgemv('N', rows, rows, m_scale[i], m_denseBlocks[i], rows,
                            m_wsp.get() + cnt, 1, 0.0, tmpout.get() + cnt, 1);
            }
            asmMap->AssembleBnd(tmpout, pOutput);
        }
    }
}
 
void GlobalLinSysIterativeStaticCond::v_UniqueMap()
{
    m_map = m_locToGloMap.lock()->GetGlobalToUniversalBndMapUnique();
}
 
void GlobalLinSysIterativeStaticCond::v_PreSolve(int scLevel,
                                                 Array<OneD, NekDouble> &F_bnd)
{
    if (scLevel == 0)
    {
        // When matrices are supplied to the constructor at the top
        // level, the preconditioner is never set up.
        if (!m_precon)
        {
            m_precon = CreatePrecon(m_locToGloMap.lock());
            m_precon->BuildPreconditioner();
        }
 
        if (m_isAbsoluteTolerance)
        {
            m_rhs_magnitude = 1.0;
            return;
        }
 
        int nGloBndDofs = m_locToGloMap.lock()->GetNumGlobalBndCoeffs();
        Array<OneD, NekDouble> F_gloBnd(nGloBndDofs);
        NekVector<NekDouble> F_GloBnd(nGloBndDofs, F_gloBnd, eWrapper);
        m_locToGloMap.lock()->AssembleBnd(F_bnd, F_gloBnd);
 
        NekDouble vExchange(0.0);
        if (m_map.size() > 0)
        {
            vExchange = Vmath::Dot2(F_GloBnd.GetDimension(), &F_GloBnd[0],
                                    &F_GloBnd[0], &m_map[0]);
        }
 
        m_expList.lock()->GetComm()->GetRowComm()->AllReduce(
            vExchange, Nektar::LibUtilities::ReduceSum);
 
        // To ensure that very different rhs values are not being
        // used in subsequent solvers such as the velocity solve in
        // INC NS. If this works we then need to work out a better
        // way to control this.
        NekDouble new_rhs_mag = (vExchange > 1e-6) ? vExchange : 1.0;
 
        if (m_rhs_magnitude == NekConstants::kNekUnsetDouble)
        {
            m_rhs_magnitude = new_rhs_mag;
        }
        else
        {
            m_rhs_magnitude = (m_rhs_mag_sm * (m_rhs_magnitude) +
                               (1.0 - m_rhs_mag_sm) * new_rhs_mag);
        }
    }
    else
    {
        // for multilevel iterative solver always use rhs
        // vector value with no weighting
        m_rhs_magnitude = NekConstants::kNekUnsetDouble;
    }
}
 
void GlobalLinSysIterativeStaticCond::v_BasisFwdTransform(
    Array<OneD, NekDouble> &pInOut)
{
    m_precon->DoTransformBasisToLowEnergy(pInOut);
}
 
void GlobalLinSysIterativeStaticCond::v_CoeffsBwdTransform(
    Array<OneD, NekDouble> &pInOut)
{
    m_precon->DoTransformCoeffsFromLowEnergy(pInOut);
}
 
void GlobalLinSysIterativeStaticCond::v_CoeffsFwdTransform(
    const Array<OneD, NekDouble> &pInput, Array<OneD, NekDouble> &pOutput)
{
    m_precon->DoTransformCoeffsToLowEnergy(pInput, pOutput);
}
 
GlobalLinSysStaticCondSharedPtr GlobalLinSysIterativeStaticCond::v_Recurse(
    const GlobalLinSysKey &mkey, const std::weak_ptr<ExpList> &pExpList,
    const DNekScalBlkMatSharedPtr pSchurCompl,
    const DNekScalBlkMatSharedPtr pBinvD, const DNekScalBlkMatSharedPtr pC,
    const DNekScalBlkMatSharedPtr pInvD,
    const std::shared_ptr<AssemblyMap> &l2gMap)
{
    GlobalLinSysIterativeStaticCondSharedPtr sys =
        MemoryManager<GlobalLinSysIterativeStaticCond>::AllocateSharedPtr(
            mkey, pExpList, pSchurCompl, pBinvD, pC, pInvD, l2gMap, m_precon);
    sys->Initialise(l2gMap);
    return sys;
}
 
/**
 *
 */
void GlobalLinSysIterativeStaticCond::v_SolveLinearSystem(
    const int nGlobal, const Array<OneD, const NekDouble> &pInput,
    Array<OneD, NekDouble> &pOutput, const AssemblyMapSharedPtr &plocToGloMap,
    const int nDir)
{
 
    if (!m_linsol)
    {
        LibUtilities::CommSharedPtr vRowComm =
            m_expList.lock()->GetComm()->GetRowComm();
        LibUtilities::SessionReaderSharedPtr pSession =
            m_expList.lock()->GetSession();
 
        // Check such a module exists for this equation.
        ASSERTL0(LibUtilities::GetNekLinSysIterFactory().ModuleExists(
                     m_linSysIterSolver),
                 "NekLinSysIter '" + m_linSysIterSolver +
                     "' is not defined.\n");
 
        // Create the key to hold solver settings
        auto sysKey     = LibUtilities::NekSysKey();
        string variable = plocToGloMap->GetVariable();
 
        // Either get the solnInfo from <GlobalSysSolInfo> or from
        // <Parameters>
        if (pSession->DefinesGlobalSysSolnInfo(variable,
                                               "IterativeSolverTolerance"))
        {
            sysKey.m_NekLinSysTolerance = boost::lexical_cast<double>(
                pSession
                    ->GetGlobalSysSolnInfo(variable, "IterativeSolverTolerance")
                    .c_str());
        }
        else
        {
            pSession->LoadParameter("IterativeSolverTolerance",
                                    sysKey.m_NekLinSysTolerance,
                                    NekConstants::kNekIterativeTol);
        }
 
        if (pSession->DefinesGlobalSysSolnInfo(variable,
                                               "NekLinSysMaxIterations"))
        {
            sysKey.m_NekLinSysMaxIterations = boost::lexical_cast<int>(
                pSession
                    ->GetGlobalSysSolnInfo(variable, "NekLinSysMaxIterations")
                    .c_str());
        }
        else
        {
            pSession->LoadParameter("NekLinSysMaxIterations",
                                    sysKey.m_NekLinSysMaxIterations, 5000);
        }
 
        if (pSession->DefinesGlobalSysSolnInfo(variable, "LinSysMaxStorage"))
        {
            sysKey.m_LinSysMaxStorage = boost::lexical_cast<int>(
                pSession->GetGlobalSysSolnInfo(variable, "LinSysMaxStorage")
                    .c_str());
        }
        else
        {
            pSession->LoadParameter("LinSysMaxStorage",
                                    sysKey.m_LinSysMaxStorage, 100);
        }
 
        if (pSession->DefinesGlobalSysSolnInfo(variable, "GMRESMaxHessMatBand"))
        {
            sysKey.m_KrylovMaxHessMatBand = boost::lexical_cast<int>(
                pSession->GetGlobalSysSolnInfo(variable, "GMRESMaxHessMatBand")
                    .c_str());
        }
        else
        {
            pSession->LoadParameter("GMRESMaxHessMatBand",
                                    sysKey.m_KrylovMaxHessMatBand,
                                    sysKey.m_LinSysMaxStorage + 1);
        }
 
        // The following settings have no correponding tests and are rarely
        // used.
        pSession->MatchSolverInfo("GMRESLeftPrecon", "True",
                                  sysKey.m_NekLinSysLeftPrecon, false);
        pSession->MatchSolverInfo("GMRESRightPrecon", "True",
                                  sysKey.m_NekLinSysRightPrecon, true);
 
        m_linsol = LibUtilities::GetNekLinSysIterFactory().CreateInstance(
            m_linSysIterSolver, pSession, vRowComm, nGlobal - nDir, sysKey);
 
        m_linsol->SetSysOperators(m_NekSysOp);
        v_UniqueMap();
        m_linsol->SetUniversalUniqueMap(m_map);
    }
 
    if (!m_precon)
    {
        m_precon = CreatePrecon(plocToGloMap);
        m_precon->BuildPreconditioner();
    }
 
    m_linsol->SetRhsMagnitude(m_rhs_magnitude);
 
    if (m_useProjection)
    {
        Array<OneD, NekDouble> gloIn(nGlobal);
        Array<OneD, NekDouble> gloOut(nGlobal, 0.0);
        plocToGloMap->AssembleBnd(pInput, gloIn);
        DoProjection(nGlobal, gloIn, gloOut, nDir, m_isAconjugate);
        plocToGloMap->GlobalToLocalBnd(gloOut, pOutput);
    }
    else
    {
        if (m_linsol->IsLocal())
        {
            int nLocDofs = plocToGloMap->GetNumLocalBndCoeffs();
            Vmath::Zero(nLocDofs, pOutput, 1);
            m_linsol->SolveSystem(nLocDofs, pInput, pOutput, nDir);
        }
        else
        {
            Array<OneD, NekDouble> gloIn(nGlobal);
            Array<OneD, NekDouble> gloOut(nGlobal, 0.0);
            plocToGloMap->AssembleBnd(pInput, gloIn);
            m_linsol->SolveSystem(nGlobal, gloIn, gloOut, nDir);
            plocToGloMap->GlobalToLocalBnd(gloOut, pOutput);
        }
    }
}
 
} // namespace Nektar::MultiRegions