GlobalLinSysDirectStaticCond.cpp

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///////////////////////////////////////////////////////////////////////////////
//
// File: GlobalLinSysDirectStaticCond.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).
//
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// Description: GlobalLinSysDirectStaticCond definition
//
///////////////////////////////////////////////////////////////////////////////
 
#include <MultiRegions/GlobalLinSysDirectStaticCond.h>
 
namespace Nektar::MultiRegions
{
/**
 * @class GlobalLinSysDirect
 *
 * Solves a linear system using single- or multi-level static
 * condensation.
 */
 
/**
 * Registers the class with the Factory.
 */
std::string GlobalLinSysDirectStaticCond::className =
    GetGlobalLinSysFactory().RegisterCreatorFunction(
        "DirectStaticCond", GlobalLinSysDirectStaticCond::create,
        "Direct static condensation.");
 
std::string GlobalLinSysDirectStaticCond::className2 =
    GetGlobalLinSysFactory().RegisterCreatorFunction(
        "DirectMultiLevelStaticCond", GlobalLinSysDirectStaticCond::create,
        "Direct multi-level static condensation.");
 
/**
 * 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.
 */
GlobalLinSysDirectStaticCond::GlobalLinSysDirectStaticCond(
    const GlobalLinSysKey &pKey, const std::weak_ptr<ExpList> &pExpList,
    const std::shared_ptr<AssemblyMap> &pLocToGloMap)
    : GlobalLinSys(pKey, pExpList, pLocToGloMap),
      GlobalLinSysDirect(pKey, pExpList, pLocToGloMap),
      GlobalLinSysStaticCond(pKey, pExpList, pLocToGloMap)
{
    ASSERTL1((pKey.GetGlobalSysSolnType() == eDirectStaticCond) ||
                 (pKey.GetGlobalSysSolnType() == eDirectMultiLevelStaticCond),
             "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");
}
 
/**
 *
 */
GlobalLinSysDirectStaticCond::GlobalLinSysDirectStaticCond(
    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)
    : GlobalLinSys(pKey, pExpList, pLocToGloMap),
      GlobalLinSysDirect(pKey, pExpList, pLocToGloMap),
      GlobalLinSysStaticCond(pKey, pExpList, pLocToGloMap)
{
    m_schurCompl = pSchurCompl;
    m_BinvD      = pBinvD;
    m_C          = pC;
    m_invD       = pInvD;
}
 
/**
 *
 */
GlobalLinSysDirectStaticCond::~GlobalLinSysDirectStaticCond()
{
}
 
MatrixStorage GlobalLinSysDirectStaticCond::DetermineMatrixStorage(
    const AssemblyMapSharedPtr &pLocToGloMap)
{
    int nBndDofs      = pLocToGloMap->GetNumGlobalBndCoeffs();
    int NumDirBCs     = pLocToGloMap->GetNumGlobalDirBndCoeffs();
    unsigned int rows = nBndDofs - NumDirBCs;
    int bwidth        = pLocToGloMap->GetBndSystemBandWidth();
 
    MatrixStorage matStorage;
 
    switch (m_linSysKey.GetMatrixType())
    {
            // case for all symmetric matices
        case StdRegions::eMass:
        case StdRegions::eLaplacian:
        case StdRegions::eHelmholtz:
        case StdRegions::eHybridDGHelmBndLam:
        {
            if ((2 * (bwidth + 1)) < rows)
            {
                matStorage = ePOSITIVE_DEFINITE_SYMMETRIC_BANDED;
            }
            else
            {
                matStorage = ePOSITIVE_DEFINITE_SYMMETRIC;
            }
        }
        break;
        case StdRegions::eLinearAdvection:
        case StdRegions::eLinearAdvectionReaction:
        case StdRegions::eLinearAdvectionDiffusionReaction:
        default:
        {
            // Current inversion techniques do not seem to
            // allow banded matrices to be used as a linear
            // system
            matStorage = eFULL;
        }
        break;
    }
 
    return matStorage;
}
 
/**
 * 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 GlobalLinSysDirectStaticCond::v_AssembleSchurComplement(
    const AssemblyMapSharedPtr pLocToGloMap)
{
    int i, j, n, cnt, gid1, gid2;
    NekDouble sign1, sign2, value;
 
    int nBndDofs  = pLocToGloMap->GetNumGlobalBndCoeffs();
    int NumDirBCs = pLocToGloMap->GetNumGlobalDirBndCoeffs();
 
    DNekScalBlkMatSharedPtr SchurCompl = m_schurCompl;
    DNekScalBlkMatSharedPtr BinvD      = m_BinvD;
    DNekScalBlkMatSharedPtr C          = m_C;
    DNekScalBlkMatSharedPtr invD       = m_invD;
 
    unsigned int rows = nBndDofs - NumDirBCs;
    unsigned int cols = nBndDofs - NumDirBCs;
 
    DNekMatSharedPtr Gmat;
    int bwidth = pLocToGloMap->GetBndSystemBandWidth();
 
    MatrixStorage matStorage = DetermineMatrixStorage(pLocToGloMap);
 
    switch (matStorage)
    {
        case ePOSITIVE_DEFINITE_SYMMETRIC_BANDED:
        {
            try
            {
                Gmat = MemoryManager<DNekMat>::AllocateSharedPtr(
                    rows, cols, 0.0, matStorage, bwidth, bwidth);
            }
            catch (...)
            {
                NEKERROR(ErrorUtil::efatal,
                         "Insufficient memory for GlobalLinSys.");
            }
            break;
        }
 
        case ePOSITIVE_DEFINITE_SYMMETRIC:
        case eFULL:
        {
            Gmat = MemoryManager<DNekMat>::AllocateSharedPtr(rows, cols, 0.0,
                                                             matStorage);
            break;
        }
 
        default:
        {
            NEKERROR(ErrorUtil::efatal,
                     "Unknown matrix storage type of type not set up");
        }
    }
 
    // fill global matrix
    DNekScalMatSharedPtr loc_mat;
    int loc_lda;
    for (n = cnt = 0; n < SchurCompl->GetNumberOfBlockRows(); ++n)
    {
        loc_mat = SchurCompl->GetBlock(n, n);
        loc_lda = loc_mat->GetRows();
 
        // Set up  Matrix;
        for (i = 0; i < loc_lda; ++i)
        {
            gid1  = pLocToGloMap->GetLocalToGlobalBndMap(cnt + i) - NumDirBCs;
            sign1 = pLocToGloMap->GetLocalToGlobalBndSign(cnt + i);
 
            if (gid1 >= 0)
            {
                for (j = 0; j < loc_lda; ++j)
                {
                    gid2 = pLocToGloMap->GetLocalToGlobalBndMap(cnt + j) -
                           NumDirBCs;
                    sign2 = pLocToGloMap->GetLocalToGlobalBndSign(cnt + j);
 
                    if (gid2 >= 0)
                    {
                        // As the global matrix should be symmetric,
                        // only add the value for the upper triangular
                        // part in order to avoid entries to be entered
                        // twice
                        if ((matStorage == eFULL) || (gid2 >= gid1))
                        {
                            value = Gmat->GetValue(gid1, gid2) +
                                    sign1 * sign2 * (*loc_mat)(i, j);
                            Gmat->SetValue(gid1, gid2, value);
                        }
                    }
                }
            }
        }
        cnt += loc_lda;
    }
 
    if (rows)
    {
        PointerWrapper w = eWrapper;
        m_linSys = MemoryManager<DNekLinSys>::AllocateSharedPtr(Gmat, w);
    }
}
 
GlobalLinSysStaticCondSharedPtr GlobalLinSysDirectStaticCond::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)
{
    GlobalLinSysDirectStaticCondSharedPtr sys =
        MemoryManager<GlobalLinSysDirectStaticCond>::AllocateSharedPtr(
            mkey, pExpList, pSchurCompl, pBinvD, pC, pInvD, l2gMap);
    sys->Initialise(l2gMap);
    return sys;
}
 
/// Solve the linear system for given input and output vectors.
void GlobalLinSysDirectStaticCond::v_SolveLinearSystem(
    const int pNumRows, const Array<OneD, const NekDouble> &pInput,
    Array<OneD, NekDouble> &pOutput, const AssemblyMapSharedPtr &pLocToGloMap,
    const int pNumDir)
{
    Array<OneD, NekDouble> tmp(pNumRows);
    Array<OneD, NekDouble> global(pNumRows, 0.0);
 
    pLocToGloMap->AssembleBnd(pInput, tmp);
 
    const int nHomDofs = pNumRows - pNumDir;
    DNekVec Vin(nHomDofs, tmp + pNumDir);
 
    Array<OneD, NekDouble> tmp1 = global + pNumDir;
    DNekVec Vout(nHomDofs, tmp1, eWrapper);
 
    m_linSys->Solve(Vin, Vout);
 
    pLocToGloMap->GlobalToLocalBnd(global, pOutput);
}
 
} // namespace Nektar::MultiRegions