MGPoissonSolver.cpp

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//
// Class MGPoissonSolver
//   This class contains methods for solving Poisson's equation for the
//   space charge portion of the calculation.
//
//   A smoothed aggregation based AMG preconditioned iterative solver for space charge
//   \see FFTPoissonSolver
//   \warning This solver is in an EXPERIMENTAL STAGE. For reliable simulations use the FFTPoissonSolver
//
// Copyright (c) 2008,        Yves Ineichen, ETH Zürich,
//               2013 - 2015, Tülin Kaman, Paul Scherrer Institut, Villigen PSI, Switzerland
//               2017 - 2020, Paul Scherrer Institut, Villigen PSI, Switzerland
// All rights reserved
//
// Implemented as part of the master thesis
// "A Parallel Multigrid Solver for Beam Dynamics"
// and the paper
// "A fast parallel Poisson solver on irregular domains applied to beam dynamics simulations"
// (https://doi.org/10.1016/j.jcp.2010.02.022)
//
// In 2020, the code was ported to the second generation Trilinos packages,
// i.e., Epetra --> Tpetra, ML --> MueLu. See also issue #507.
//
// This file is part of OPAL.
//
// OPAL is free software: you can redistribute it and/or modify
// it under the terms of the GNU General Public License as published by
// the Free Software Foundation, either version 3 of the License, or
// (at your option) any later version.
//
// You should have received a copy of the GNU General Public License
// along with OPAL. If not, see <https://www.gnu.org/licenses/>.
//
 
//#define DBG_STENCIL
 
#include "Solvers/MGPoissonSolver.h"
 
#include "Structure/BoundaryGeometry.h"
#include "ArbitraryDomain.h"
#include "EllipticDomain.h"
#include "BoxCornerDomain.h"
#include "RectangularDomain.h"
 
#include "Track/Track.h"
#include "Physics/Physics.h"
#include "Utilities/OpalException.h"
#include "Attributes/Attributes.h"
#include "ValueDefinitions/RealVariable.h"
#include "AbstractObjects/OpalData.h"
#include "Utilities/Options.h"
 
#include <Tpetra_Import.hpp>
#include <BelosTpetraAdapter.hpp>
 
#ifdef DBG_STENCIL
    #include "TpetraExt_MatrixMatrix.hpp"
#endif
 
#include "Teuchos_CommandLineProcessor.hpp"
 
#include "BelosLinearProblem.hpp"
#include "BelosRCGSolMgr.hpp"
#include "BelosBlockCGSolMgr.hpp"
#include "BelosBiCGStabSolMgr.hpp"
#include "BelosBlockGmresSolMgr.hpp"
#include "BelosGCRODRSolMgr.hpp"
 
#include <MueLu_CreateTpetraPreconditioner.hpp>
 
#include <algorithm>
 
using Teuchos::RCP;
using Teuchos::rcp;
using Physics::c;
 
MGPoissonSolver::MGPoissonSolver ( PartBunch *beam,
                                   Mesh_t *mesh,
                                   FieldLayout_t *fl,
                                   std::vector<BoundaryGeometry *> geometries,
                                   std::string itsolver,
                                   std::string interpl,
                                   double tol,
                                   int maxiters,
                                   std::string precmode)
    : isMatrixfilled_m(false)
    , useLeftPrec_m(true)
    , geometries_m(geometries)
    , tol_m(tol)
    , maxiters_m(maxiters)
    , comm_mp(new Comm_t(Ippl::getComm()))
    , itsBunch_m(beam)
    , mesh_m(mesh)
    , layout_m(fl)
{
 
    domain_m = layout_m->getDomain();
 
    for (int i = 0; i < 3; i++) {
        hr_m[i] = mesh_m->get_meshSpacing(i);
        orig_nr_m[i] = domain_m[i].length();
    }
 
    precmode_m = STD_PREC;
    if (precmode == "HIERARCHY") precmode_m = REUSE_HIERARCHY;
    else if (precmode == "REUSE") precmode_m = REUSE_PREC;
 
    repartFreq_m = 1000;
    if (Ippl::Info->getOutputLevel() > 3) {
        verbose_m = true;
    } else {
        verbose_m = false;
    }
    // Find CURRENT geometry
    currentGeometry = geometries_m[0];
    if ( (currentGeometry->getFilename()).empty() ) {
        if (currentGeometry->getTopology() == Topology::ELLIPTIC){
            bp_m = std::unique_ptr<IrregularDomain>(
                new EllipticDomain(currentGeometry, orig_nr_m, hr_m, interpl));
 
        } else if (currentGeometry->getTopology() == Topology::BOXCORNER) {
            bp_m = std::unique_ptr<IrregularDomain>(
                new BoxCornerDomain(currentGeometry->getA(),
                                    currentGeometry->getB(),
                                    currentGeometry->getC(),
                                    currentGeometry->getL1(),
                                    currentGeometry->getL2(),
                                    orig_nr_m, hr_m, interpl));
            bp_m->compute(itsBunch_m->get_hr(), layout_m->getLocalNDIndex());
        } else if (currentGeometry->getTopology() == Topology::RECTANGULAR) {
            bp_m = std::unique_ptr<IrregularDomain>(
                new RectangularDomain(currentGeometry->getA(),
                                      currentGeometry->getB(),
                                      orig_nr_m, hr_m));
        }
    } else {
        NDIndex<3> localId = layout_m->getLocalNDIndex();
        if (localId[0].length() != domain_m[0].length() ||
            localId[1].length() != domain_m[1].length()) {
            throw OpalException("MGPoissonSolver::MGPoissonSolver",
                                "The class ArbitraryDomain only works with parallelization\n"
                                "in z-direction.\n"
                                "Please set PARFFTX=FALSE, PARFFTY=FALSE, PARFFTT=TRUE in \n"
                                "the definition of the field solver in the input file.\n");
        }
        Vector_t hr = (currentGeometry->getmaxcoords() -
                       currentGeometry->getmincoords()) / orig_nr_m;
        bp_m = std::unique_ptr<IrregularDomain>(
            new ArbitraryDomain(currentGeometry, orig_nr_m, hr, interpl));
    }
 
    map_p = Teuchos::null;
    A = Teuchos::null;
    LHS = Teuchos::null;
    RHS = Teuchos::null;
    prec_mp = Teuchos::null;
 
    numBlocks_m = Options::numBlocks;
    recycleBlocks_m = Options::recycleBlocks;
    nLHS_m = Options::nLHS;
    setupMueLuList();
    setupBelosList();
    problem_mp = rcp(new Belos::LinearProblem<TpetraScalar_t,
                                              TpetraMultiVector_t,
                                              TpetraOperator_t>);
    // setup Belos solver
    if (itsolver == "CG") {
        if (numBlocks_m == 0 || recycleBlocks_m == 0) {
            solver_mp = rcp(new Belos::BlockCGSolMgr<TpetraScalar_t,
                                                     TpetraMultiVector_t,
                                                     TpetraOperator_t>());
        } else {
            solver_mp = rcp(new Belos::RCGSolMgr<TpetraScalar_t,
                                                 TpetraMultiVector_t,
                                                 TpetraOperator_t>());
        }
    } else if (itsolver == "BICGSTAB") {
        useLeftPrec_m = false;
        solver_mp = rcp(new Belos::BiCGStabSolMgr<TpetraScalar_t,
                                                  TpetraMultiVector_t,
                                                  TpetraOperator_t>());
    } else if (itsolver == "GMRES") {
        if (numBlocks_m == 0 || recycleBlocks_m == 0) {
            solver_mp = rcp(new Belos::BlockGmresSolMgr<TpetraScalar_t,
                                                        TpetraMultiVector_t,
                                                        TpetraOperator_t>());
        } else {
            solver_mp = rcp(new Belos::GCRODRSolMgr<TpetraScalar_t,
                                                    TpetraMultiVector_t,
                                                    TpetraOperator_t>());
        }
    }
 
    solver_mp->setParameters(rcp(&belosList, false));
 
 
    //all timers used here
    FunctionTimer1_m = IpplTimings::getTimer("BGF-IndexCoordMap");
    FunctionTimer2_m = IpplTimings::getTimer("computeMap");
    FunctionTimer3_m = IpplTimings::getTimer("IPPL to RHS");
    FunctionTimer4_m = IpplTimings::getTimer("ComputeStencil");
    FunctionTimer5_m = IpplTimings::getTimer("MueLu");
    FunctionTimer6_m = IpplTimings::getTimer("Setup");
    FunctionTimer7_m = IpplTimings::getTimer("CG");
    FunctionTimer8_m = IpplTimings::getTimer("LHS to IPPL");
}
 
void MGPoissonSolver::deletePtr() {
    map_p  = Teuchos::null;
    A      = Teuchos::null;
    LHS    = Teuchos::null;
    RHS    = Teuchos::null;
    prec_mp = Teuchos::null;
    isMatrixfilled_m = false;
}
 
MGPoissonSolver::~MGPoissonSolver() {
    deletePtr ();
    solver_mp = Teuchos::null;
    problem_mp = Teuchos::null;
}
 
void MGPoissonSolver::computePotential(Field_t& /*rho*/, Vector_t /*hr*/, double /*zshift*/) {
    throw OpalException("MGPoissonSolver", "not implemented yet");
}
 
void MGPoissonSolver::computeMap(NDIndex<3> localId) {
    if (itsBunch_m->getLocalTrackStep()%repartFreq_m == 0){
        deletePtr();
        IPPLToMap3D(localId);
 
        extrapolateLHS();
    }
}
 
void MGPoissonSolver::extrapolateLHS() {
// Aitken-Neville
// Pi0 (x) := yi , i = 0 : n
// Pik (x) := (x − xi ) Pi+1,k−1(x) − (x − xi+k ) Pi,k−1(x) /(xi+k − xi )
// k = 1, . . . , n, i = 0, . . . , n − k.
    //we also have to redistribute LHS
 
    if (Teuchos::is_null(LHS)){
        LHS = rcp(new TpetraVector_t(map_p));
        LHS->putScalar(1.0);
    } else {
        RCP<TpetraVector_t> tmplhs = rcp(new TpetraVector_t(map_p));
        Tpetra::Import<> importer(map_p, LHS->getMap());
        tmplhs->doImport(*LHS, importer, Tpetra::CombineMode::ADD);
        LHS = tmplhs;
    }
 
    //...and all previously saved LHS
    std::deque< TpetraVector_t >::iterator it = OldLHS.begin();
    if (!OldLHS.empty()) {
        int n = OldLHS.size();
        for (int i = 0; i < n; ++i) {
            TpetraVector_t tmplhs = TpetraVector_t(map_p);
            Tpetra::Import<> importer(map_p, it->getMap());
            tmplhs.doImport(*it, importer, Tpetra::CombineMode::ADD);
            *it = tmplhs;
            ++it;
        }
    }
 
    // extrapolate last OldLHS.size LHS to get a new start vector
    it = OldLHS.begin();
    if (nLHS_m == 0 || OldLHS.size()==0)
        LHS->putScalar(1.0);
    else if (OldLHS.size() == 1)
        *LHS = *it;
    else if (OldLHS.size() == 2)
        LHS->update(2.0, *it++, -1.0, *it, 0.0);
    else if (OldLHS.size() > 2) {
        int n = OldLHS.size();
        P_mp = rcp(new TpetraMultiVector_t(map_p, nLHS_m, false));
        for (int i = 0; i < n; ++i) {
           *(P_mp->getVectorNonConst(i)) = *it++;
        }
        for (int k = 1; k < n; ++k) {
           for (int i = 0; i < n - k; ++i) {
              P_mp->getVectorNonConst(i)->update(-(i + 1) / (float)k, *(P_mp->getVector(i + 1)), (i + k + 1) / (float)k);
           }
        }
        *LHS = *(P_mp->getVector(0));
     } else
        throw OpalException("MGPoissonSolver",
                            "Invalid number of old LHS: " + std::to_string(OldLHS.size()));
}
 
 
// given a charge-density field rho and a set of mesh spacings hr,
// compute the electric field and put in eg by solving the Poisson's equation
// XXX: use matrix stencil in computation directly (no Tpetra, define operators
// on IPPL GRID)
void MGPoissonSolver::computePotential(Field_t &rho, Vector_t hr) {
 
    Inform msg("OPAL ", INFORM_ALL_NODES);
    nr_m[0] = orig_nr_m[0];
    nr_m[1] = orig_nr_m[1];
    nr_m[2] = orig_nr_m[2];
 
    bp_m->setNr(nr_m);
 
    NDIndex<3> localId = layout_m->getLocalNDIndex();
 
    IpplTimings::startTimer(FunctionTimer1_m);
    // Compute boundary intersections (only do on the first step)
    if (!itsBunch_m->getLocalTrackStep())
        bp_m->compute(hr, localId);
    IpplTimings::stopTimer(FunctionTimer1_m);
 
    // Define the Map
    INFOMSG(level3 << "* Computing Map..." << endl);
    IpplTimings::startTimer(FunctionTimer2_m);
    computeMap(localId);
    IpplTimings::stopTimer(FunctionTimer2_m);
    INFOMSG(level3 << "* Done." << endl);
 
    // Allocate the RHS with the new Tpetra Map
    if (Teuchos::is_null(RHS))
        RHS = rcp(new TpetraVector_t(map_p));
    RHS->putScalar(0.0);
 
    // get charge densities from IPPL field and store in Tpetra vector (RHS)
    if (verbose_m) {
        Ippl::Comm->barrier();
        msg << "* Node:" << Ippl::myNode() << ", Filling RHS..." << endl;
        Ippl::Comm->barrier();
    }
    IpplTimings::startTimer(FunctionTimer3_m);
    int id = 0;
    float scaleFactor = itsBunch_m->getdT();
 
 
    if (verbose_m) {
        msg << "* Node:" << Ippl::myNode() << ", Rho for final element: "
            << rho[localId[0].last()][localId[1].last()][localId[2].last()].get()
            << endl;
 
        Ippl::Comm->barrier();
        msg << "* Node:" << Ippl::myNode() << ", Local nx*ny*nz = "
            <<  localId[2].last() *  localId[0].last() *  localId[1].last()
            << endl;
        msg << "* Node:" << Ippl::myNode()
            << ", Number of reserved local elements in RHS: "
            << RHS->getLocalLength() << endl;
        msg << "* Node:" << Ippl::myNode()
            << ", Number of reserved global elements in RHS: "
            << RHS->getGlobalLength() << endl;
        Ippl::Comm->barrier();
    }
    for (int idz = localId[2].first(); idz <= localId[2].last(); idz++) {
        for (int idy = localId[1].first(); idy <= localId[1].last(); idy++) {
            for (int idx = localId[0].first(); idx <= localId[0].last(); idx++) {
                NDIndex<3> l(Index(idx, idx), Index(idy, idy), Index(idz, idz));
                if (bp_m->isInside(idx, idy, idz))
                        RHS->replaceGlobalValue(bp_m->getIdx(idx, idy, idz),
                                                4.0 * M_PI * rho.localElement(l) / scaleFactor);
            }
        }
    }
 
    IpplTimings::stopTimer(FunctionTimer3_m);
    if (verbose_m) {
        Ippl::Comm->barrier();
        msg << "* Node:" << Ippl::myNode()
            << ", Number of Local Inside Points " << id << endl;
        msg << "* Node:" << Ippl::myNode() << ", Done." << endl;
        Ippl::Comm->barrier();
    }
    // build discretization matrix
    INFOMSG(level3 << "* Building Discretization Matrix..." << endl);
    IpplTimings::startTimer(FunctionTimer4_m);
#if defined(__clang__)
# pragma clang diagnostic push
# pragma clang diagnostic warning "-Wdeprecated-declarations"
#endif
    if (Teuchos::is_null(A))
        A = rcp(new TpetraCrsMatrix_t(map_p,  7));
#if defined(__clang__)
# pragma clang diagnostic pop
#endif
    ComputeStencil(hr, RHS);
    IpplTimings::stopTimer(FunctionTimer4_m);
    INFOMSG(level3 << "* Done." << endl);
 
#ifdef DBG_STENCIL
    Tpetra::MatrixMarket::Writer<TpetraCrsMatrix_t>::writeSparseFile(
        "DiscrStencil.dat", A);
#endif
 
    INFOMSG(level3 << "* Computing Preconditioner..." << endl);
    IpplTimings::startTimer(FunctionTimer5_m);
    if (Teuchos::is_null(prec_mp)) {
        Teuchos::RCP<TpetraOperator_t> At = Teuchos::rcp_dynamic_cast<TpetraOperator_t>(A);
        prec_mp = MueLu::CreateTpetraPreconditioner(At, MueLuList_m);
    }
 
    switch (precmode_m) {
        case REUSE_PREC:
        case REUSE_HIERARCHY: {
            MueLu::ReuseTpetraPreconditioner(A, *prec_mp);
            break;
        }
        case STD_PREC:
        default: {
            Teuchos::RCP<TpetraOperator_t> At = Teuchos::rcp_dynamic_cast<TpetraOperator_t>(A);
            prec_mp = MueLu::CreateTpetraPreconditioner(At, MueLuList_m);
            break;
        }
    }
    IpplTimings::stopTimer(FunctionTimer5_m);
    INFOMSG(level3 << "* Done." << endl);
 
    // setup preconditioned iterative solver
    // use old LHS solution as initial guess
    INFOMSG(level3 << "* Final Setup of Solver..." << endl);
    IpplTimings::startTimer(FunctionTimer6_m);
    problem_mp->setOperator(A);
    problem_mp->setLHS(LHS);
    problem_mp->setRHS(RHS);
 
    if (useLeftPrec_m)
        problem_mp->setLeftPrec(prec_mp);
    else
        problem_mp->setRightPrec(prec_mp);
 
    solver_mp->setProblem( problem_mp);
    if (!problem_mp->isProblemSet()) {
        if (problem_mp->setProblem() == false) {
            ERRORMSG("Belos::LinearProblem failed to set up correctly!" << endl);
        }
    }
    IpplTimings::stopTimer(FunctionTimer6_m);
    INFOMSG(level3 << "* Done." << endl);
 
    double time = MPI_Wtime();
 
    INFOMSG(level3 << "* Solving for Space Charge..." << endl);
    IpplTimings::startTimer(FunctionTimer7_m);
    solver_mp->solve();
 
    IpplTimings::stopTimer(FunctionTimer7_m);
    INFOMSG(level3 << "* Done." << endl);
 
    std::ofstream timings;
    if (true || verbose_m) {
        time = MPI_Wtime() - time;
        double minTime = 0, maxTime = 0, avgTime = 0;
        reduce(time, minTime, 1, std::less<double>());
        reduce(time, maxTime, 1, std::greater<double>());
        reduce(time, avgTime, 1, std::plus<double>());
        avgTime /= comm_mp->getSize();
        if (comm_mp->getRank() == 0) {
            char filename[256];  // common size supported by most file-systems
            snprintf(filename, sizeof(filename),
                     "timing_MX%d_MY%d_MZ%d_nProc%d_recB%d_numB%d_nLHS%d",
                    orig_nr_m[0], orig_nr_m[1], orig_nr_m[2],
                    comm_mp->getSize(), recycleBlocks_m, numBlocks_m, nLHS_m);
 
            timings.open(filename, std::ios::app);
            timings << solver_mp->getNumIters() << "\t"
                    //<< time <<" "<<
                    << minTime << "\t"
                    << maxTime << "\t"
                    << avgTime << "\t"
                    << numBlocks_m << "\t"
                    << recycleBlocks_m << "\t"
                    << nLHS_m << "\t"
                    //<< OldLHS.size() <<"\t"<<
                    << std::endl;
 
            timings.close();
        }
 
    }
    // Store new LHS in OldLHS
    if (nLHS_m > 1) OldLHS.push_front(*(LHS.get()));
    if (OldLHS.size() > nLHS_m) OldLHS.pop_back();
 
    //now transfer solution back to IPPL grid
    IpplTimings::startTimer(FunctionTimer8_m);
    id = 0;
    rho = 0.0;
    for (int idz = localId[2].first(); idz <= localId[2].last(); idz++) {
        for (int idy = localId[1].first(); idy <= localId[1].last(); idy++) {
            for (int idx = localId[0].first(); idx <= localId[0].last(); idx++) {
                  NDIndex<3> l(Index(idx, idx), Index(idy, idy), Index(idz, idz));
                  if (bp_m->isInside(idx, idy, idz))
                     rho.localElement(l) = LHS->getData()[id++] * scaleFactor;
            }
        }
    }
    IpplTimings::stopTimer(FunctionTimer8_m);
 
    if (itsBunch_m->getLocalTrackStep()+1 == (long long)Track::block->localTimeSteps.front()) {
        A = Teuchos::null;
        LHS = Teuchos::null;
        RHS = Teuchos::null;
        prec_mp = Teuchos::null;
    }
}
 
 
void MGPoissonSolver::IPPLToMap3D(NDIndex<3> localId) {
 
    int NumMyElements = 0;
    std::vector<TpetraGlobalOrdinal_t> MyGlobalElements;
 
    for (int idz = localId[2].first(); idz <= localId[2].last(); idz++) {
        for (int idy = localId[1].first(); idy <= localId[1].last(); idy++) {
            for (int idx = localId[0].first(); idx <= localId[0].last(); idx++) {
                if (bp_m->isInside(idx, idy, idz)) {
                    MyGlobalElements.push_back(bp_m->getIdx(idx, idy, idz));
                    NumMyElements++;
                }
            }
        }
    }
 
    int indexbase = 0;
    map_p = Teuchos::rcp(new TpetraMap_t(Teuchos::OrdinalTraits<Tpetra::global_size_t>::invalid(),
                                         &MyGlobalElements[0], NumMyElements, indexbase, comm_mp));
}
 
void MGPoissonSolver::ComputeStencil(Vector_t /*hr*/, Teuchos::RCP<TpetraVector_t> RHS) {
 
    A->resumeFill();
    A->setAllToScalar(0.0);
 
#if defined(__clang__)
# pragma clang diagnostic push
# pragma clang diagnostic warning "-Wdeprecated-declarations"
#endif
    int NumMyElements = map_p->getLocalNumElements();
#if defined(__clang__)
# pragma clang diagnostic pop
#endif
 
    auto MyGlobalElements = map_p->getMyGlobalIndices();
 
    std::vector<TpetraScalar_t> Values(6);
    std::vector<TpetraGlobalOrdinal_t> Indices(6);
 
    IrregularDomain::StencilValue_t value;
    IrregularDomain::StencilIndex_t index;
 
    for (int i = 0 ; i < NumMyElements ; i++) {
 
        int NumEntries = 0;
 
        double scaleFactor=1.0;
 
        bp_m->getBoundaryStencil(MyGlobalElements[i], value, scaleFactor);
        RHS->scale(scaleFactor);
 
        bp_m->getNeighbours(MyGlobalElements[i], index);
        if (index.east != -1) {
            Indices[NumEntries]  = index.east;
            Values[NumEntries++] = value.east;
        }
        if (index.west != -1) {
            Indices[NumEntries]  = index.west;
            Values[NumEntries++] = value.west;
        }
        if (index.south != -1) {
            Indices[NumEntries]  = index.south;
            Values[NumEntries++] = value.south;
        }
        if (index.north != -1) {
            Indices[NumEntries]  = index.north;
            Values[NumEntries++] = value.north;
        }
        if (index.front != -1) {
            Indices[NumEntries]  = index.front;
            Values[NumEntries++] = value.front;
        }
        if (index.back != -1) {
            Indices[NumEntries]  = index.back;
            Values[NumEntries++] = value.back;
        }
 
        // if matrix has already been filled (fillComplete()) we can only
        // replace entries
 
        if (isMatrixfilled_m) {
            // off-diagonal entries
            A->replaceGlobalValues(MyGlobalElements[i], NumEntries, &Values[0], &Indices[0]);
            // diagonal entry
            A->replaceGlobalValues(MyGlobalElements[i], 1, &value.center, &MyGlobalElements[i]);
        } else {
            // off-diagonal entries
            A->insertGlobalValues(MyGlobalElements[i], NumEntries, &Values[0], &Indices[0]);
            // diagonal entry
            A->insertGlobalValues(MyGlobalElements[i], 1, &value.center, &MyGlobalElements[i]);
        }
    }
 
    RCP<ParameterList_t> params = Teuchos::parameterList();
    params->set ("Optimize Storage", true);
    A->fillComplete(params);
    isMatrixfilled_m = true;
}
 
void MGPoissonSolver::printLoadBalanceStats() {
 
    //compute some load balance statistics
    
#if defined(__clang__)
# pragma clang diagnostic push
# pragma clang diagnostic warning "-Wdeprecated-declarations"
#endif
    size_t myNumPart = map_p->getLocalNumElements();
    size_t NumPart = map_p->getGlobalNumElements() * 1.0 / comm_mp->getSize();
#if defined(__clang__)
# pragma clang diagnostic pop
#endif
    double imbalance = 1.0;
    if (myNumPart >= NumPart)
        imbalance += (myNumPart - NumPart) / NumPart;
    else
        imbalance += (NumPart - myNumPart) / NumPart;
 
    double max = 0.0, min = 0.0, avg = 0.0;
    size_t minn = 0, maxn = 0;
    reduce(imbalance, min, 1, std::less<double>());
    reduce(imbalance, max, 1, std::greater<double>());
    reduce(imbalance, avg, 1, std::plus<double>());
    reduce(myNumPart, minn, 1, std::less<size_t>());
    reduce(myNumPart, maxn, 1, std::greater<size_t>());
 
    avg /= comm_mp->getSize();
    *gmsg << "LBAL min = " << min << ", max = " << max << ", avg = " << avg << endl;
    *gmsg << "min nr gridpoints = " << minn << ", max nr gridpoints = " << maxn << endl;
}
 
void MGPoissonSolver::setupBelosList() {
    belosList.set("Maximum Iterations", maxiters_m);
    belosList.set("Convergence Tolerance", tol_m);
 
    if (numBlocks_m != 0 && recycleBlocks_m != 0){//only set if solver==RCGSolMgr
        belosList.set("Num Blocks", numBlocks_m);               // Maximum number of blocks in Krylov space
        belosList.set("Num Recycled Blocks", recycleBlocks_m); // Number of vectors in recycle space
    }
    if (verbose_m) {
        belosList.set("Verbosity", Belos::Errors + Belos::Warnings +
                                   Belos::TimingDetails + Belos::FinalSummary +
                                   Belos::StatusTestDetails);
        belosList.set("Output Frequency", 1);
    } else
        belosList.set("Verbosity", Belos::Errors + Belos::Warnings);
}
 
 
void MGPoissonSolver::setupMueLuList() {
    MueLuList_m.set("problem: type", "Poisson-3D");
    MueLuList_m.set("verbosity", "none");
    MueLuList_m.set("number of equations", 1);
    MueLuList_m.set("max levels", 8);
    MueLuList_m.set("cycle type", "V");
 
    // heuristic for max coarse size depending on number of processors
    int coarsest_size = std::max(comm_mp->getSize() * 10, 1024);
    MueLuList_m.set("coarse: max size", coarsest_size);
 
    MueLuList_m.set("multigrid algorithm", "sa");
    MueLuList_m.set("sa: damping factor", 1.33);
    MueLuList_m.set("sa: use filtered matrix", true);
    MueLuList_m.set("filtered matrix: reuse eigenvalue", false);
 
    MueLuList_m.set("repartition: enable", false);
    MueLuList_m.set("repartition: rebalance P and R", false);
    MueLuList_m.set("repartition: partitioner", "zoltan2");
    MueLuList_m.set("repartition: min rows per proc", 800);
    MueLuList_m.set("repartition: start level", 2);
 
    MueLuList_m.set("smoother: type", "CHEBYSHEV");
    MueLuList_m.set("smoother: pre or post", "both");
    Teuchos::ParameterList smparms;
    smparms.set("chebyshev: degree", 3);
    smparms.set("chebyshev: assume matrix does not change", false);
    smparms.set("chebyshev: zero starting solution", true);
    smparms.set("relaxation: sweeps", 3);
    MueLuList_m.set("smoother: params", smparms);
 
    MueLuList_m.set("smoother: type", "CHEBYSHEV");
    MueLuList_m.set("smoother: pre or post", "both");
 
    MueLuList_m.set("coarse: type", "KLU2");
 
    MueLuList_m.set("aggregation: type", "uncoupled");
    MueLuList_m.set("aggregation: min agg size", 3);
    MueLuList_m.set("aggregation: max agg size", 27);
 
    MueLuList_m.set("transpose: use implicit", false);
 
    switch (precmode_m) {
        case REUSE_PREC:
            MueLuList_m.set("reuse: type", "full");
            break;
        case REUSE_HIERARCHY:
            MueLuList_m.set("sa: use filtered matrix", false);
            MueLuList_m.set("reuse: type", "tP");
            break;
        case STD_PREC:
        default:
            MueLuList_m.set("reuse: type", "none");
            break;
    }
}
 
Inform &MGPoissonSolver::print(Inform &os) const {
    os << "* *************** M G P o i s s o n S o l v e r ************************************ " << endl;
    os << "* h " << hr_m << '\n';
    os << "* ********************************************************************************** " << endl;
    return os;
}