GlobalLinSysPETScStaticCond.cpp

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///////////////////////////////////////////////////////////////////////////////
//
// File: GlobalLinSysPETScStaticCond.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
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// DEALINGS IN THE SOFTWARE.
//
// Description: GlobalLinSys definition
//
///////////////////////////////////////////////////////////////////////////////
 
#include <boost/core/ignore_unused.hpp>
 
#include <MultiRegions/GlobalLinSysPETScStaticCond.h>
 
#include <petscksp.h>
#include <petscmat.h>
#include <petscsys.h>
 
using namespace std;
 
namespace Nektar
{
namespace MultiRegions
{
/**
 * @class GlobalLinSysPETSc
 *
 * Solves a linear system using single- or multi-level static
 * condensation.
 */
 
/**
 * Registers the class with the Factory.
 */
string GlobalLinSysPETScStaticCond::className =
    GetGlobalLinSysFactory().RegisterCreatorFunction(
        "PETScStaticCond", GlobalLinSysPETScStaticCond::create,
        "PETSc static condensation.");
 
string GlobalLinSysPETScStaticCond::className2 =
    GetGlobalLinSysFactory().RegisterCreatorFunction(
        "PETScMultiLevelStaticCond", GlobalLinSysPETScStaticCond::create,
        "PETSc 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.
 */
GlobalLinSysPETScStaticCond::GlobalLinSysPETScStaticCond(
    const GlobalLinSysKey &pKey, const std::weak_ptr<ExpList> &pExpList,
    const std::shared_ptr<AssemblyMap> &pLocToGloMap)
    : GlobalLinSys(pKey, pExpList, pLocToGloMap),
      GlobalLinSysPETSc(pKey, pExpList, pLocToGloMap),
      GlobalLinSysStaticCond(pKey, pExpList, pLocToGloMap)
{
    ASSERTL1((pKey.GetGlobalSysSolnType() == ePETScStaticCond) ||
                 (pKey.GetGlobalSysSolnType() == ePETScMultiLevelStaticCond),
             "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");
}
 
/**
 *
 */
GlobalLinSysPETScStaticCond::GlobalLinSysPETScStaticCond(
    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),
      GlobalLinSysPETSc(pKey, pExpList, pLocToGloMap),
      GlobalLinSysStaticCond(pKey, pExpList, pLocToGloMap)
{
    m_schurCompl = pSchurCompl;
    m_BinvD      = pBinvD;
    m_C          = pC;
    m_invD       = pInvD;
    m_precon     = pPrecon;
}
 
/**
 *
 */
GlobalLinSysPETScStaticCond::~GlobalLinSysPETScStaticCond()
{
}
 
void GlobalLinSysPETScStaticCond::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);
}
 
/**
 * 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 GlobalLinSysPETScStaticCond::v_AssembleSchurComplement(
    AssemblyMapSharedPtr pLocToGloMap)
{
    int i, j, n, cnt, gid1, gid2, loc_lda;
    NekDouble sign1, sign2, value;
 
    const int nDirDofs = pLocToGloMap->GetNumGlobalDirBndCoeffs();
 
    DNekScalBlkMatSharedPtr SchurCompl = m_schurCompl;
    DNekScalBlkMatSharedPtr BinvD      = m_BinvD;
    DNekScalBlkMatSharedPtr C          = m_C;
    DNekScalBlkMatSharedPtr invD       = m_invD;
    DNekScalMatSharedPtr loc_mat;
 
    // Build precon again if we in multi-level static condensation (a
    // bit of a hack)
    if (m_linSysKey.GetGlobalSysSolnType() == ePETScMultiLevelStaticCond)
    {
        m_precon = CreatePrecon(m_locToGloMap.lock());
        m_precon->BuildPreconditioner();
    }
 
    // CALCULATE REORDERING MAPPING
    CalculateReordering(pLocToGloMap->GetGlobalToUniversalBndMap(),
                        pLocToGloMap->GetGlobalToUniversalBndMapUnique(),
                        pLocToGloMap);
 
    // SET UP VECTORS AND MATRIX
    SetUpMatVec(pLocToGloMap->GetNumGlobalBndCoeffs(), nDirDofs);
 
    // SET UP SCATTER OBJECTS
    SetUpScatter();
 
    // CONSTRUCT KSP OBJECT
    SetUpSolver(pLocToGloMap->GetIterativeTolerance());
 
    // If we are using the matrix multiplication shell don't try to
    // populate the matrix.
    if (m_matMult == ePETScMatMultShell)
    {
        return;
    }
 
    // POPULATE MATRIX
    for (n = cnt = 0; n < m_schurCompl->GetNumberOfBlockRows(); ++n)
    {
        loc_mat = m_schurCompl->GetBlock(n, n);
        loc_lda = loc_mat->GetRows();
 
        for (i = 0; i < loc_lda; ++i)
        {
            gid1  = pLocToGloMap->GetLocalToGlobalBndMap(cnt + i) - nDirDofs;
            sign1 = pLocToGloMap->GetLocalToGlobalBndSign(cnt + i);
            if (gid1 >= 0)
            {
                int gid1ro = m_reorderedMap[gid1];
                for (j = 0; j < loc_lda; ++j)
                {
                    gid2 = pLocToGloMap->GetLocalToGlobalBndMap(cnt + j) -
                           nDirDofs;
                    sign2 = pLocToGloMap->GetLocalToGlobalBndSign(cnt + j);
                    if (gid2 >= 0)
                    {
                        int gid2ro = m_reorderedMap[gid2];
                        value      = sign1 * sign2 * (*loc_mat)(i, j);
                        MatSetValue(m_matrix, gid1ro, gid2ro, value,
                                    ADD_VALUES);
                    }
                }
            }
        }
        cnt += loc_lda;
    }
 
    // ASSEMBLE MATRIX
    MatAssemblyBegin(m_matrix, MAT_FINAL_ASSEMBLY);
    MatAssemblyEnd(m_matrix, MAT_FINAL_ASSEMBLY);
}
 
DNekScalBlkMatSharedPtr GlobalLinSysPETScStaticCond::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;
}
 
void GlobalLinSysPETScStaticCond::v_PreSolve(int scLevel,
                                             Array<OneD, NekDouble> &F_bnd)
{
    boost::ignore_unused(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();
        }
    }
}
 
/**
 * @brief Solve linear system using PETSc.
 *
 * The general strategy being a PETSc solve is to:
 *
 * - Copy values into the PETSc vector #m_b
 * - Solve the system #m_ksp and place result into #m_x.
 * - Scatter results back into #m_locVec using #m_ctx scatter object.
 * - Copy from #m_locVec to output array #pOutput.
 */
void GlobalLinSysPETScStaticCond::v_SolveLinearSystem(
    const int pNumRows, const Array<OneD, const NekDouble> &pInput,
    Array<OneD, NekDouble> &pOutput, const AssemblyMapSharedPtr &locToGloMap,
    const int pNumDir)
{
    const int nHomDofs = pNumRows - pNumDir;
 
    if (!m_precon && m_matMult == ePETScMatMultShell)
    {
        m_precon = CreatePrecon(locToGloMap);
        m_precon->BuildPreconditioner();
    }
 
    Array<OneD, NekDouble> Glo(pNumRows);
    locToGloMap->AssembleBnd(pInput, Glo);
 
    // Populate RHS vector from input
    VecSetValues(m_b, nHomDofs, &m_reorderedMap[0], &Glo[pNumDir],
                 INSERT_VALUES);
 
    // Assemble RHS vector
    VecAssemblyBegin(m_b);
    VecAssemblyEnd(m_b);
 
    // Do system solve
    KSPSolve(m_ksp, m_b, m_x);
 
    KSPConvergedReason reason;
    KSPGetConvergedReason(m_ksp, &reason);
    ASSERTL0(reason > 0, "PETSc solver diverged, reason is: " +
                             std::string(KSPConvergedReasons[reason]));
 
    // Scatter results to local vector
    VecScatterBegin(m_ctx, m_x, m_locVec, INSERT_VALUES, SCATTER_FORWARD);
    VecScatterEnd(m_ctx, m_x, m_locVec, INSERT_VALUES, SCATTER_FORWARD);
 
    // Copy results into output vector
    PetscScalar *tmp;
    VecGetArray(m_locVec, &tmp);
    Vmath::Vcopy(nHomDofs, tmp, 1, &Glo[pNumDir], 1);
    Vmath::Zero(pNumDir, Glo, 1);
    locToGloMap->GlobalToLocalBnd(Glo, pOutput);
    VecRestoreArray(m_locVec, &tmp);
}
 
void GlobalLinSysPETScStaticCond::v_BasisFwdTransform(
    Array<OneD, NekDouble> &pInOut)
{
    m_precon->DoTransformBasisToLowEnergy(pInOut);
}
 
void GlobalLinSysPETScStaticCond::v_CoeffsBwdTransform(
    Array<OneD, NekDouble> &pInOut)
{
    m_precon->DoTransformCoeffsFromLowEnergy(pInOut);
}
 
void GlobalLinSysPETScStaticCond::v_CoeffsFwdTransform(
    const Array<OneD, NekDouble> &pInput, Array<OneD, NekDouble> &pOutput)
{
    m_precon->DoTransformCoeffsToLowEnergy(pInput, pOutput);
}
 
/**
 * @brief Apply matrix-vector multiplication using local approach and
 * the assembly map.
 *
 * @param input   Vector input.
 * @param output  Result of multiplication.
 *
 * @todo This can possibly be made faster by using the sparse
 *       block-matrix multiplication code from the iterative elastic
 *       systems.
 */
void GlobalLinSysPETScStaticCond::v_DoMatrixMultiply(
    const Array<OneD, const NekDouble> &input, Array<OneD, NekDouble> &output)
{
    auto asmMap = m_locToGloMap.lock();
 
    int nLocBndDofs = asmMap->GetNumLocalBndCoeffs();
    int nDirDofs    = asmMap->GetNumGlobalDirBndCoeffs();
 
    NekVector<NekDouble> in(nLocBndDofs), out(nLocBndDofs);
    asmMap->GlobalToLocalBnd(input, in.GetPtr(), nDirDofs);
    out = (*m_schurCompl) * in;
    asmMap->AssembleBnd(out.GetPtr(), output, nDirDofs);
}
 
GlobalLinSysStaticCondSharedPtr GlobalLinSysPETScStaticCond::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)
{
    GlobalLinSysPETScStaticCondSharedPtr sys =
        MemoryManager<GlobalLinSysPETScStaticCond>::AllocateSharedPtr(
            mkey, pExpList, pSchurCompl, pBinvD, pC, pInvD, l2gMap, m_precon);
    sys->Initialise(l2gMap);
    return sys;
}
} // namespace MultiRegions
} // namespace Nektar