GlobalLinSysXxtStaticCond.cpp

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///////////////////////////////////////////////////////////////////////////////
//
// File: GlobalLinSysXxtStaticCond.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: GlobalLinSysXxtStaticCond definition
//
///////////////////////////////////////////////////////////////////////////////
 
#include <LibUtilities/BasicUtils/VDmathArray.hpp>
#include <LibUtilities/Communication/Xxt.hpp>
#include <MultiRegions/GlobalLinSysXxtStaticCond.h>
 
using namespace std;
 
namespace Nektar
{
namespace MultiRegions
{
/**
 * @class GlobalLinSysIterativeStaticCond
 *
 * Solves a linear system iteratively using single- or multi-level
 * static condensation.
 */
 
/**
 * Registers the class with the Factory.
 */
string GlobalLinSysXxtStaticCond::className =
    GetGlobalLinSysFactory().RegisterCreatorFunction(
        "XxtStaticCond", GlobalLinSysXxtStaticCond::create,
        "Iterative static condensation.");
 
string GlobalLinSysXxtStaticCond::className2 =
    GetGlobalLinSysFactory().RegisterCreatorFunction(
        "XxtMultiLevelStaticCond", GlobalLinSysXxtStaticCond::create,
        "Xxt 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.
 */
GlobalLinSysXxtStaticCond::GlobalLinSysXxtStaticCond(
    const GlobalLinSysKey &pKey, const std::weak_ptr<ExpList> &pExpList,
    const std::shared_ptr<AssemblyMap> &pLocToGloMap)
    : GlobalLinSys(pKey, pExpList, pLocToGloMap),
      GlobalLinSysXxt(pKey, pExpList, pLocToGloMap),
      GlobalLinSysStaticCond(pKey, pExpList, pLocToGloMap)
{
    ASSERTL1((pKey.GetGlobalSysSolnType() == eXxtStaticCond) ||
                 (pKey.GetGlobalSysSolnType() == eXxtMultiLevelStaticCond),
             "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");
}
 
/**
 *
 */
GlobalLinSysXxtStaticCond::GlobalLinSysXxtStaticCond(
    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),
      GlobalLinSysXxt(pKey, pExpList, pLocToGloMap),
      GlobalLinSysStaticCond(pKey, pExpList, pLocToGloMap)
{
    m_schurCompl  = pSchurCompl;
    m_BinvD       = pBinvD;
    m_C           = pC;
    m_invD        = pInvD;
    m_locToGloMap = pLocToGloMap;
}
 
/**
 *
 */
GlobalLinSysXxtStaticCond::~GlobalLinSysXxtStaticCond()
{
}
 
/**
 * Create the inverse multiplicity map.
 * @param   locToGloMap Local to global mapping information.
 */
void GlobalLinSysXxtStaticCond::CreateMap(
    const std::shared_ptr<AssemblyMap> &pLocToGloMap)
{
    const Array<OneD, const int> &vMap = pLocToGloMap->GetLocalToGlobalBndMap();
    unsigned int nGlo                  = pLocToGloMap->GetNumGlobalBndCoeffs();
    unsigned int nEntries              = pLocToGloMap->GetNumLocalBndCoeffs();
    unsigned int i;
 
    // Count the multiplicity of each global DOF on this process
    Array<OneD, NekDouble> vCounts(nGlo, 0.0);
    for (i = 0; i < nEntries; ++i)
    {
        vCounts[vMap[i]] += 1.0;
    }
 
    // Get universal multiplicity by globally assembling counts
    pLocToGloMap->UniversalAssembleBnd(vCounts);
 
    // Construct a map of 1/multiplicity for use in XXT solve
    m_locToGloSignMult = Array<OneD, NekDouble>(nEntries);
    for (i = 0; i < nEntries; ++i)
    {
        m_locToGloSignMult[i] = 1.0 / vCounts[vMap[i]];
    }
 
    m_map = pLocToGloMap->GetLocalToGlobalBndMap();
}
 
/**
 * Construct the local matrix row index, column index and value index
 * arrays and initialize the XXT data structure with this information.
 * @param   locToGloMap Local to global mapping information.
 */
void GlobalLinSysXxtStaticCond::v_AssembleSchurComplement(
    std::shared_ptr<AssemblyMap> pLocToGloMap)
{
    CreateMap(pLocToGloMap);
 
    ExpListSharedPtr vExp = m_expList.lock();
    unsigned int nElmt    = m_schurCompl->GetNumberOfBlockRows();
    DNekScalMatSharedPtr loc_mat;
    unsigned int iCount    = 0;
    unsigned int rCount    = 0;
    unsigned int nRows     = 0;
    unsigned int nEntries  = 0;
    unsigned int numDirBnd = pLocToGloMap->GetNumGlobalDirBndCoeffs();
    unsigned int nLocal    = pLocToGloMap->GetNumLocalBndCoeffs();
    const Array<OneD, NekDouble> &vMapSign =
        pLocToGloMap->GetLocalToGlobalBndSign();
    bool doSign    = pLocToGloMap->GetSignChange();
    unsigned int i = 0, j = 0, k = 0, n = 0;
    int gid1;
    Array<OneD, unsigned int> vSizes(nElmt);
 
    // First construct a map of the number of local DOFs in each block
    // and the number of matrix entries for each block
    for (n = 0; n < nElmt; ++n)
    {
        loc_mat   = m_schurCompl->GetBlock(n, n);
        vSizes[n] = loc_mat->GetRows();
        nEntries += vSizes[n] * vSizes[n];
    }
 
    // Set up i-index, j-index and value arrays
    m_Ai = Array<OneD, unsigned int>(nEntries);
    m_Aj = Array<OneD, unsigned int>(nEntries);
    m_Ar = Array<OneD, double>(nEntries, 0.0);
 
    // Set up the universal ID array for XXT
    Array<OneD, unsigned long> vId(nLocal);
 
    // Loop over each elemental block, extract matrix indices and value
    // and set the universal ID array
    for (n = iCount = 0; n < nElmt; ++n)
    {
        loc_mat = m_schurCompl->GetBlock(n, n);
        nRows   = loc_mat->GetRows();
 
        for (i = 0; i < nRows; ++i)
        {
            gid1 = pLocToGloMap->GetLocalToGlobalBndMap(iCount + i);
            for (j = 0; j < nRows; ++j)
            {
                k       = rCount + i * vSizes[n] + j;
                m_Ai[k] = iCount + i;
                m_Aj[k] = iCount + j;
                m_Ar[k] = (*loc_mat)(i, j);
                if (doSign)
                {
                    m_Ar[k] *= vMapSign[iCount + i] * vMapSign[iCount + j];
                }
            }
 
            // Dirichlet DOFs are not included in the solve, so we set
            // these to the special XXT id=0.
            if (gid1 < numDirBnd)
            {
                vId[iCount + i] = 0;
            }
            else
            {
                vId[iCount + i] =
                    pLocToGloMap->GetGlobalToUniversalBndMap()[gid1];
            }
        }
        iCount += vSizes[n];
        rCount += vSizes[n] * vSizes[n];
    }
 
    // Set up XXT and output some stats
    LibUtilities::CommSharedPtr vComm = pLocToGloMap->GetComm()->GetRowComm();
    m_crsData = Xxt::Init(nLocal, vId, m_Ai, m_Aj, m_Ar, vComm);
    if (m_verbose)
    {
        Xxt::nektar_crs_stats(m_crsData);
    }
}
 
GlobalLinSysStaticCondSharedPtr GlobalLinSysXxtStaticCond::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)
{
    GlobalLinSysXxtStaticCondSharedPtr sys =
        MemoryManager<GlobalLinSysXxtStaticCond>::AllocateSharedPtr(
            mkey, pExpList, pSchurCompl, pBinvD, pC, pInvD, l2gMap);
    sys->Initialise(l2gMap);
    return sys;
}
} // namespace MultiRegions
} // namespace Nektar