AMReX_MLMG.H

Go to the documentation of this file.

#ifndef AMREX_ML_MG_H_
#define AMREX_ML_MG_H_
#include <AMReX_Config.H>
#include <AMReX_Enum.H>
 
#include <AMReX_MLLinOp.H>
#include <AMReX_MLCGSolver.H>
 
#include <functional>
#include <limits>
#include <optional>
 
namespace amrex {
 
// Norm used to evaluate the target convergence criteria
AMREX_ENUM(MLMGNormType, greater, bnorm, resnorm);
 
AMREX_ENUM(MultigridType, geometric, algebraic, hybrid);
 
template <typename MF>
class MLMGT
{
public:
 
    class error
        : public std::runtime_error
    {
    public :
        using std::runtime_error::runtime_error;
    };
 
    template <typename T> friend class MLCGSolverT;
    template <typename M> friend class GMRESMLMGT;
 
    using MFType = MF;
    using FAB = typename MLLinOpT<MF>::FAB;
    using RT  = typename MLLinOpT<MF>::RT;
 
    using BCMode   = typename MLLinOpT<MF>::BCMode;
    using Location = typename MLLinOpT<MF>::Location;
 
    using BottomSolver = amrex::BottomSolver;
    using MultigridType = amrex::MultigridType;
    enum class CFStrategy : int {none,ghostnodes};
 
    MLMGT (MLLinOpT<MF>& a_lp);
    ~MLMGT ();
 
    MLMGT (MLMGT<MF> const&) = delete;
    MLMGT (MLMGT<MF> &&) = delete;
    MLMGT<MF>& operator= (MLMGT<MF> const&) = delete;
    MLMGT<MF>& operator= (MLMGT<MF> &&) = delete;
 
    template <typename AMF>
    RT solve (const Vector<AMF*>& a_sol, const Vector<AMF const*>& a_rhs,
              RT a_tol_rel, RT a_tol_abs, const char* checkpoint_file = nullptr);
 
    template <typename AMF>
    RT solve (std::initializer_list<AMF*> a_sol,
              std::initializer_list<AMF const*> a_rhs,
              RT a_tol_rel, RT a_tol_abs, const char* checkpoint_file = nullptr);
 
    RT precond (Vector<MF*> const& a_sol, Vector<MF const*> const& a_rhs,
                RT a_tol_rel, RT a_tol_abs);
 
    template <typename AMF>
    void getGradSolution (const Vector<Array<AMF*,AMREX_SPACEDIM> >& a_grad_sol,
                          Location a_loc = Location::FaceCenter);
 
    template <typename AMF>
    void getGradSolution (std::initializer_list<Array<AMF*,AMREX_SPACEDIM>> a_grad_sol,
                          Location a_loc = Location::FaceCenter);
 
    template <typename AMF>
    void getFluxes (const Vector<Array<AMF*,AMREX_SPACEDIM> >& a_flux,
                    Location a_loc = Location::FaceCenter);
 
    template <typename AMF>
    void getFluxes (std::initializer_list<Array<AMF*,AMREX_SPACEDIM>> a_flux,
                    Location a_loc = Location::FaceCenter);
 
    template <typename AMF>
    void getFluxes (const Vector<Array<AMF*,AMREX_SPACEDIM> >& a_flux,
                    const Vector<AMF*> & a_sol,
                    Location a_loc = Location::FaceCenter);
 
    template <typename AMF>
    void getFluxes (std::initializer_list<Array<AMF*,AMREX_SPACEDIM>> a_flux,
                    std::initializer_list<AMF*>  a_sol,
                    Location a_loc = Location::FaceCenter);
 
    template <typename AMF>
    void getFluxes (const Vector<AMF*> & a_flux,
                    Location a_loc = Location::CellCenter);
 
    template <typename AMF>
    void getFluxes (std::initializer_list<AMF*> a_flux,
                    Location a_loc = Location::CellCenter);
 
    template <typename AMF>
    void getFluxes (const Vector<AMF*> & a_flux,
                    const Vector<AMF*> & a_sol,
                    Location a_loc = Location::CellCenter);
 
    template <typename AMF>
    void getFluxes (std::initializer_list<AMF*> a_flux,
                    std::initializer_list<AMF*> a_sol,
                    Location a_loc = Location::CellCenter);
 
    void compResidual (const Vector<MF*>& a_res, const Vector<MF*>& a_sol,
                       const Vector<MF const*>& a_rhs);
 
#ifdef AMREX_USE_EB
    void getEBFluxes (const Vector<MF*>& a_eb_flux);
    void getEBFluxes (const Vector<MF*>& a_eb_flux, const Vector<MF*> & a_sol);
#endif
 
    void apply (const Vector<MF*>& out, const Vector<MF*>& in);
 
    void applyPrecond (const Vector<MF*>& out, const Vector<MF*>& in);
 
    [[nodiscard]] int getVerbose () const { return verbose; }
    [[nodiscard]] int getBottomVerbose () const { return bottom_verbose; }
 
    void incPrintIdentation ();
    void decPrintIdentation ();
 
    void setThrowException (bool t) noexcept { throw_exception = t; }
    void setVerbose (int v) noexcept { verbose = v; }
    void setMaxIter (int n) noexcept { max_iters = n; }
    void setMaxFmgIter (int n) noexcept { max_fmg_iters = n; }
    void setFixedIter (int nit) noexcept { do_fixed_number_of_iters = nit; }
    void setPrecondIter (int nit) noexcept { max_precond_iters = nit; }
 
    void setPreSmooth (int n) noexcept { nu1 = n; }
    void setPostSmooth (int n) noexcept { nu2 = n; }
    void setFinalSmooth (int n) noexcept { nuf = n; }
    void setBottomSmooth (int n) noexcept { nub = n; }
 
    void setBottomSolver (BottomSolver s) noexcept { bottom_solver = s; }
    [[nodiscard]] BottomSolver getBottomSolver () const noexcept { return bottom_solver; }
 
    void setMultigridType (MultigridType t) noexcept { multigrid_type = t; }
    [[nodiscard]] MultigridType getMultigridType () const noexcept { return multigrid_type; }
    [[nodiscard]] bool usedAlgMG () const noexcept { return m_algmg_active; }
 
    void setAlgMGOptions (std::function<void(AlgMG<RT>&)> f) {
        m_algmg_options = std::move(f);
        m_algmg_bottom.reset();
        m_algmg_level0.reset();
    }
 
    void setHybridStallCriterion (int window, RT rate) noexcept {
        hybrid_stall_window = window; hybrid_stall_rate = rate;
    }
    void setHybridDivergenceFactor (RT f) noexcept { hybrid_divergence_factor = f; }
    void setCFStrategy (CFStrategy a_cf_strategy) noexcept {cf_strategy = a_cf_strategy;}
    void setBottomVerbose (int v) noexcept { bottom_verbose = v; }
    void setBottomMaxIter (int n) noexcept { bottom_maxiter = n; }
    void setBottomTolerance (RT t) noexcept { bottom_reltol = t; }
    void setBottomToleranceAbs (RT t) noexcept { bottom_abstol = t;}
    [[nodiscard]] RT getBottomToleranceAbs () const noexcept{ return bottom_abstol; }
 
    [[deprecated("Use MLMG::setConvergenceNormType() instead.")]]
    void setAlwaysUseBNorm (int flag) noexcept;
 
    void setConvergenceNormType (MLMGNormType norm) noexcept { norm_type = norm; }
 
    void setFinalFillBC (int flag) noexcept { final_fill_bc = flag; }
 
    [[nodiscard]] int numAMRLevels () const noexcept { return namrlevs; }
 
    void setNSolve (int flag) noexcept { do_nsolve = flag; }
    void setNSolveGridSize (int s) noexcept { nsolve_grid_size = s; }
 
    void setNoGpuSync (bool do_not_sync) noexcept { do_no_sync_gpu = do_not_sync; }
 
#if defined(AMREX_USE_HYPRE) && (AMREX_SPACEDIM > 1)
    void setHypreInterface (Hypre::Interface f) noexcept {
        // must use ij interface for EB
#ifndef AMREX_USE_EB
        hypre_interface = f;
#else
        amrex::ignore_unused(f);
#endif
    }
 
    void setHypreOptionsNamespace(const std::string& prefix) noexcept
    {
        hypre_options_namespace = prefix;
    }
 
    void setHypreOldDefault (bool l) noexcept {hypre_old_default = l;}
    void setHypreRelaxType (int n) noexcept {hypre_relax_type = n;}
    void setHypreRelaxOrder (int n) noexcept {hypre_relax_order = n;}
    void setHypreNumSweeps (int n) noexcept {hypre_num_sweeps = n;}
    void setHypreStrongThreshold (Real t) noexcept {hypre_strong_threshold = t;}
#endif
 
    void prepareForFluxes (Vector<MF const*> const& a_sol);
 
    template <typename AMF>
    void prepareForSolve (Vector<AMF*> const& a_sol, Vector<AMF const*> const& a_rhs);
 
    void prepareForNSolve ();
 
    void prepareLinOp ();
 
    void preparePrecond ();
 
    void oneIter (int iter);
 
    void miniCycle (int amrlev);
 
    void mgVcycle (int amrlev, int mglev);
    void mgFcycle ();
 
    void bottomSolve ();
    void NSolve (MLMGT<MF>& a_solver, MF& a_sol, MF& a_rhs);
    void actualBottomSolve ();
 
    void postCG (int ret, int niters = -1);
 
    void computeMLResidual (int amrlevmax);
    void computeResidual (int alev);
    void computeResWithCrseSolFineCor (int calev, int falev);
    void computeResWithCrseCorFineCor (int falev);
    void interpCorrection (int alev);
    void interpCorrection (int alev, int mglev);
    void addInterpCorrection (int alev, int mglev);
 
    void computeResOfCorrection (int amrlev, int mglev);
 
    RT ResNormInf (int alev, bool local = false);
    RT MLResNormInf (int alevmax, bool local = false);
    RT MLRhsNormInf (bool local = false);
 
    void makeSolvable ();
    void makeSolvable (int amrlev, int mglev, MF& mf);
 
#if defined(AMREX_USE_HYPRE) && (AMREX_SPACEDIM > 1)
    template <class TMF=MF>
    requires (std::same_as<TMF,MultiFab>)
    void bottomSolveWithHypre (MF& x, const MF& b);
#endif
 
#if defined(AMREX_USE_PETSC) && (AMREX_SPACEDIM > 1)
    template <class TMF=MF>
    requires (std::same_as<TMF,MultiFab>)
    void bottomSolveWithPETSc (MF& x, const MF& b);
#endif
 
    int bottomSolveWithCG (MF& x, const MF& b, typename MLCGSolverT<MF>::Type type);
 
    template <class TMF=MF>
    requires (std::same_as<TMF,MultiFab>)
    void bottomSolveWithAlgMG (MF& x, const MF& b);
 
    template <class TMF=MF>
    requires (std::same_as<TMF,MultiFab>)
    void algmgLevel0Solve ();
 
    template <class TMF=MF>
    requires (std::same_as<TMF,MultiFab>)
    void configureAlgMG (MLAlgMG& s, bool singular, bool with_options);
 
    template <class TMF=MF>
    requires (std::same_as<TMF,MultiFab>)
    void algmgSolve (MLAlgMG& s, MF& x, MF const& b);
 
    [[nodiscard]] bool hybridShouldSwitch (Vector<RT> const& norms, RT max_norm,
                                           RT best_norm, std::string& reason) const;
 
    [[nodiscard]] RT getInitRHS () const noexcept { return m_rhsnorm0; }
    // Initial composite residual
    [[nodiscard]] RT getInitResidual () const noexcept { return m_init_resnorm0; }
    // Final composite residual
    [[nodiscard]] RT getFinalResidual () const noexcept { return m_final_resnorm0; }
    // Residuals on the *finest* AMR level after each iteration
    [[nodiscard]] Vector<RT> const& getResidualHistory () const noexcept { return m_iter_fine_resnorm0; }
    [[nodiscard]] int getNumIters () const noexcept { return m_iter_fine_resnorm0.size(); }
    [[nodiscard]] Vector<int> const& getNumCGIters () const noexcept { return m_niters_cg; }
 
    MLLinOpT<MF>& getLinOp () { return linop; }
 
private:
 
    bool precond_mode = false;
    bool throw_exception = false;
    int verbose = 1;
 
    int max_iters = 200;
    int do_fixed_number_of_iters = 0;
    int max_precond_iters = 1;
 
    int nu1 = 2;       
    int nu2 = 2;       
    int nuf = 8;       
    int nub = 0;       
 
    int max_fmg_iters = 0;
 
    BottomSolver bottom_solver = BottomSolver::Default;
    CFStrategy cf_strategy     = CFStrategy::none;
    int  bottom_verbose        = 0;
    int  bottom_maxiter        = 200;
    RT bottom_reltol = std::is_same<RT,double>() ? RT(1.e-4) : RT(1.e-3);
    RT bottom_abstol = RT(-1.0);
 
    MLMGNormType norm_type = MLMGNormType::greater;
 
    MultigridType multigrid_type = MultigridType::geometric;
    bool m_algmg_active = false;         
    int hybrid_stall_window = 4;
    RT hybrid_stall_rate = RT(0.8);
    RT hybrid_divergence_factor = RT(10.0);
    std::function<void(AlgMG<RT>&)> m_algmg_options;
    std::unique_ptr<MLAlgMG> m_algmg_bottom;
    std::unique_ptr<MLAlgMG> m_algmg_level0;
 
    int final_fill_bc = 0;
 
    MLLinOpT<MF>& linop;
    int ncomp;
    int namrlevs;
    int finest_amr_lev;
 
    bool linop_prepared = false;
    Long solve_called = 0;
 
    int do_nsolve = false;
    int nsolve_grid_size = 16;
    std::unique_ptr<MLLinOpT<MF>> ns_linop;
    std::unique_ptr<MLMGT<MF>> ns_mlmg;
    std::unique_ptr<MF> ns_sol;
    std::unique_ptr<MF> ns_rhs;
 
    std::string print_ident;
 
    bool do_no_sync_gpu = false;
 
#if defined(AMREX_USE_HYPRE) && (AMREX_SPACEDIM > 1)
    // Hypre::Interface hypre_interface = Hypre::Interface::structed;
    // Hypre::Interface hypre_interface = Hypre::Interface::semi_structed;
    Hypre::Interface hypre_interface = Hypre::Interface::ij;
 
    std::unique_ptr<Hypre> hypre_solver;
    std::unique_ptr<MLMGBndryT<MF>> hypre_bndry;
    std::unique_ptr<HypreNodeLap> hypre_node_solver;
 
    std::string hypre_options_namespace = "hypre";
    bool hypre_old_default = HypreDefaults::old_default;
    int hypre_relax_type = HypreDefaults::relax_type;
    int hypre_relax_order = HypreDefaults::relax_order;
    int hypre_num_sweeps = 2;  // Sweeps on each level
    Real hypre_strong_threshold = 0.25; // HYPRE default is 0.25
#endif
 
#if defined(AMREX_USE_PETSC) && (AMREX_SPACEDIM > 1)
    std::unique_ptr<PETScABecLap> petsc_solver;
    std::unique_ptr<MLMGBndryT<MF>> petsc_bndry;
#endif
 
    Vector<MF> sol;      
    Vector<MF> rhs;      
 
    Vector<int> sol_is_alias;
 
    Vector<Vector<MF> > res;     
    Vector<Vector<MF> > cor;     
    Vector<Vector<MF> > cor_hold;
    Vector<Vector<MF> > rescor;  
 
    enum timer_types { solve_time=0, iter_time, bottom_time, ntimers };
    Vector<double> timer;
 
    RT m_rhsnorm0 = RT(-1.0);
    RT m_init_resnorm0 = RT(-1.0);
    RT m_final_resnorm0 = RT(-1.0);
    Vector<int> m_niters_cg;
    Vector<RT> m_iter_fine_resnorm0; // Residual for each iteration at the finest level
 
    void checkPoint (const Vector<MultiFab*>& a_sol,
                     const Vector<MultiFab const*>& a_rhs,
                     RT a_tol_rel, RT a_tol_abs, const char* a_file_name) const;
 
};
 
template <typename MF>
MLMGT<MF>::MLMGT (MLLinOpT<MF>& a_lp)
    : linop(a_lp), ncomp(a_lp.getNComp()), namrlevs(a_lp.NAMRLevels()),
      finest_amr_lev(a_lp.NAMRLevels()-1)
{}
 
template <typename MF> MLMGT<MF>::~MLMGT () = default;
 
template <typename MF>
void
MLMGT<MF>::setAlwaysUseBNorm (int flag) noexcept
{
    if (flag) {
        norm_type = MLMGNormType::bnorm;
    } else {
        norm_type = MLMGNormType::greater;
    }
}
 
template <typename MF>
template <typename AMF>
auto
MLMGT<MF>::solve (std::initializer_list<AMF*> a_sol,
                  std::initializer_list<AMF const*> a_rhs,
                  RT a_tol_rel, RT a_tol_abs, const char* checkpoint_file) -> RT
{
    return solve(Vector<AMF*>(std::move(a_sol)),
                 Vector<AMF const*>(std::move(a_rhs)),
                 a_tol_rel, a_tol_abs, checkpoint_file);
}
 
template <typename MF>
template <typename AMF>
auto
MLMGT<MF>::solve (const Vector<AMF*>& a_sol, const Vector<AMF const*>& a_rhs,
                  RT a_tol_rel, RT a_tol_abs, const char* checkpoint_file) -> RT
{
    BL_PROFILE("MLMG::solve()");
 
    // If requested with setNoGpuSync(true), run the whole solve in a
    // single-stream, no-implicit-sync region.  The RAII objects restore the
    // previous state (also when an exception is thrown), and SyncAtExitOnly
    // synchronizes the GPU streams on exit unless the caller was already in
    // a NoSync region.  The order matters:
    // no_sync_region is destroyed last, i.e., after the single stream region
    // has been popped, so that all streams are synchronized.
    std::optional<Gpu::SyncAtExitOnly> no_sync_region;
    std::optional<Gpu::SingleStreamRegion> single_stream_region;
    if (do_no_sync_gpu) {
        no_sync_region.emplace();
        single_stream_region.emplace();
    }
 
    if constexpr (std::is_same<AMF,MultiFab>()) {
        if (checkpoint_file != nullptr) {
            checkPoint(a_sol, a_rhs, a_tol_rel, a_tol_abs, checkpoint_file);
        }
    }
 
    if ((bottom_solver == BottomSolver::custom) && !linop.supportCustomBottomSolver()) {
        bottom_solver = BottomSolver::Default;
    }
 
    if (bottom_solver == BottomSolver::Default) {
        bottom_solver = linop.getDefaultBottomSolver();
    }
 
    // The assembled EB stencils support at most third order.
    bool eb_linop = false;
#ifdef AMREX_USE_EB
    if constexpr (IsFabArray_v<AMF>) {
        eb_linop = dynamic_cast<EBFArrayBoxFactory const*>(linop.Factory(0)) != nullptr;
    }
#endif
    amrex::ignore_unused(eb_linop);
 
#if (defined(AMREX_USE_HYPRE) || defined(AMREX_USE_PETSC)) && (AMREX_SPACEDIM > 1)
    if constexpr (IsFabArray_v<AMF>) {
        if (bottom_solver == BottomSolver::hypre || bottom_solver == BottomSolver::petsc) {
            if (eb_linop) {
                linop.setMaxOrder(std::min(3, linop.getMaxOrder()));
            }
#ifdef AMREX_USE_HYPRE
            else if (bottom_solver == BottomSolver::hypre && hypre_interface != Hypre::Interface::ij) {
                linop.setMaxOrder(std::min(3, linop.getMaxOrder())); // 4 needs the IJ interface
            }
#endif
        }
    }
#endif
    if (bottom_solver == BottomSolver::algmg || multigrid_type != MultigridType::geometric) {
        AMREX_ALWAYS_ASSERT_WITH_MESSAGE(linop.supportsAlgMG() && ncomp == 1,
            "MLMG: AlgMG is not available for this operator (single-component cell and nodal operators only)");
        // The algebraic correction has zero ghost cells.
        AMREX_ALWAYS_ASSERT_WITH_MESSAGE(cf_strategy != CFStrategy::ghostnodes || linop.getNGrow() == 0,
            "MLMG: AlgMG does not support the ghostnodes strategy with ghost cells");
        // The matrix must match the operator.
        if (eb_linop) {
            linop.setMaxOrder(std::min(3, linop.getMaxOrder()));
        }
    }
 
    bool is_nsolve = linop.m_parent;
 
    m_algmg_active = (multigrid_type == MultigridType::algebraic);
    const bool hybrid = (multigrid_type == MultigridType::hybrid) && !is_nsolve;
    AMREX_ALWAYS_ASSERT_WITH_MESSAGE(!(do_nsolve && multigrid_type != MultigridType::geometric),
                                     "MLMG: NSolve requires the geometric multigrid type");
    AMREX_ALWAYS_ASSERT_WITH_MESSAGE(!(hybrid && do_fixed_number_of_iters != 0),
        "MLMG: the hybrid multigrid type needs a convergence test; as a preconditioner or with a fixed number of iterations use geometric or algebraic");
 
    auto solve_start_time = amrex::second();
 
    RT& composite_norminf = m_final_resnorm0;
 
    m_niters_cg.clear();
    m_iter_fine_resnorm0.clear();
 
    prepareForSolve(a_sol, a_rhs);
 
    computeMLResidual(finest_amr_lev);
 
    bool local = true;
    RT resnorm0 = MLResNormInf(finest_amr_lev, local);
    RT rhsnorm0 = MLRhsNormInf(local);
    if (!is_nsolve) {
        ParallelAllReduce::Max<RT>({resnorm0, rhsnorm0}, ParallelContext::CommunicatorSub());
 
        if (verbose >= 1)
        {
            amrex::Print() << print_ident << "MLMG: Initial rhs               = " << rhsnorm0 << "\n"
                           << print_ident << "MLMG: Initial residual (resid0) = " << resnorm0 << "\n";
        }
    }
 
    m_init_resnorm0 = resnorm0;
    m_rhsnorm0 = rhsnorm0;
 
    if (!is_nsolve && !amrex::isfinite(std::max(resnorm0, rhsnorm0))) {
        if ( throw_exception ) {
            throw error("MLMG: rhs or initial residual is not finite.");
        } else {
            amrex::Abort("MLMG: rhs or initial residual is not finite");
        }
    }
 
    RT max_norm = resnorm0;
    std::string norm_name = "resid0";
    switch (norm_type) {
        case MLMGNormType::greater:
            if (rhsnorm0 >= resnorm0) {
                norm_name = "bnorm";
                max_norm = rhsnorm0;
            } else {
                norm_name = "resid0";
                max_norm = resnorm0;
            }
            break;
        case MLMGNormType::bnorm:
            norm_name = "bnorm";
            max_norm = rhsnorm0;
            break;
        case MLMGNormType::resnorm:
            norm_name = "resid0";
            max_norm = resnorm0;
            break;
    }
 
    const RT res_target = std::max(a_tol_abs, std::max(a_tol_rel,std::numeric_limits<RT>::epsilon())*max_norm);
 
    if (!is_nsolve && resnorm0 <= res_target) {
        composite_norminf = resnorm0;
        if (verbose >= 1) {
            amrex::Print() << print_ident << "MLMG: No iterations needed\n";
        }
    } else {
        auto iter_start_time = amrex::second();
        bool converged = false;
 
        // Hybrid: keep the best iterate so far, starting with the initial guess.
        // The switch tests use the residual MLMG reports: the finest level
        // until it converges, then the composite one.
        Vector<MF> best_sol;
        Vector<RT> hybrid_norms;
        bool hybrid_composite = false; // the reported residual became the composite one
        RT best_norm = resnorm0;
        if (hybrid) {
            if (namrlevs > 1) { best_norm = ResNormInf(finest_amr_lev); }
            best_sol.resize(namrlevs);
            for (int alev = 0; alev < namrlevs; ++alev) {
                const IntVect ng = nGrowVect(sol[alev]);
                best_sol[alev] = linop.make(alev, 0, ng);
                LocalCopy(best_sol[alev], sol[alev], 0, 0, ncomp, ng);
            }
        }
 
        int niters = do_fixed_number_of_iters ? do_fixed_number_of_iters : max_iters;
        for (int iter = 0; iter < niters; ++iter)
        {
            oneIter(iter);
 
            converged = false;
 
            // Test convergence on the fine amr level
            computeResidual(finest_amr_lev);
 
            if (is_nsolve) { continue; }
 
            RT fine_norminf = ResNormInf(finest_amr_lev);
            m_iter_fine_resnorm0.push_back(fine_norminf);
            composite_norminf = fine_norminf;
            if (verbose >= 2) {
                amrex::Print() << print_ident << "MLMG: Iteration " << std::setw(3) << iter+1 << " Fine resid/"
                               << norm_name << " = " << fine_norminf/max_norm << "\n";
            }
            bool fine_converged = (fine_norminf <= res_target);
 
            if (namrlevs == 1 && fine_converged) {
                converged = true;
            } else if (fine_converged) {
                // finest level is converged, but we still need to test the coarse levels
                computeMLResidual(finest_amr_lev-1);
                RT crse_norminf = MLResNormInf(finest_amr_lev-1);
                if (verbose >= 2) {
                    amrex::Print() << print_ident << "MLMG: Iteration " << std::setw(3) << iter+1
                                   << " Crse resid/" << norm_name << " = "
                                   << crse_norminf/max_norm << "\n";
                }
                converged = (crse_norminf <= res_target);
                composite_norminf = std::max(fine_norminf, crse_norminf);
            } else {
                converged = false;
            }
 
            if (converged) {
                if (verbose >= 1) {
                    amrex::Print() << print_ident << "MLMG: Final Iter. " << iter+1
                                   << " resid, resid/" << norm_name << " = "
                                   << composite_norminf << ", "
                                   << composite_norminf/max_norm << "\n";
                }
                break;
            } else {
                if (hybrid && !m_algmg_active) {
                    if (fine_converged && !hybrid_composite) {
                        // The reported residual now includes the coarse levels:
                        // restart the comparisons from this iterate.
                        hybrid_composite = true;
                        hybrid_norms.clear();
                        best_norm = composite_norminf;
                        for (int alev = 0; alev < namrlevs; ++alev) {
                            LocalCopy(best_sol[alev], sol[alev], 0, 0, ncomp, nGrowVect(sol[alev]));
                        }
                    }
                    hybrid_norms.push_back(composite_norminf);
                    std::string reason;
                    bool do_switch = hybridShouldSwitch(hybrid_norms, max_norm,
                                                        best_norm, reason);
                    if (!do_switch && iter+1 == niters) {
                        do_switch = true;
                        reason = "not converged";
                    }
                    if (do_switch) {
                        if (verbose >= 1) {
                            amrex::Print() << print_ident << "MLMG: " << reason << " after "
                                           << iter+1 << " iterations, switching to AlgMG on AMR level 0\n";
                        }
                        if (!amrex::isfinite(composite_norminf) || composite_norminf > best_norm) {
                            for (int alev = 0; alev < namrlevs; ++alev) {
                                LocalCopy(sol[alev], best_sol[alev], 0, 0, ncomp, nGrowVect(sol[alev]));
                            }
                            computeResidual(finest_amr_lev);
                            composite_norminf = best_norm;
                            if (verbose >= 2) {
                                amrex::Print() << print_ident << "MLMG: restarting from the best iterate, resid/"
                                               << norm_name << " = " << best_norm/max_norm << "\n";
                            }
                        }
                        m_algmg_active = true;
                        niters = iter + 1 + max_iters;
                        continue;
                    }
                    if (composite_norminf < best_norm) {
                        best_norm = composite_norminf;
                        for (int alev = 0; alev < namrlevs; ++alev) {
                            LocalCopy(best_sol[alev], sol[alev], 0, 0, ncomp, nGrowVect(sol[alev]));
                        }
                    }
                }
                if (composite_norminf > RT(1.e20)*max_norm || !amrex::isfinite(composite_norminf))
                {
                    if (verbose > 0) {
                        amrex::Print() << print_ident << "MLMG: Failing to converge after " << iter+1 << " iterations."
                                       << " resid, resid/" << norm_name << " = "
                                       << composite_norminf << ", "
                                       << composite_norminf/max_norm << "\n";
                    }
 
                    if ( throw_exception ) {
                        throw error("MLMG blew up.");
                    } else {
                        amrex::Abort("MLMG failing so lets stop here");
                    }
                }
            }
        }
 
        if (!converged && do_fixed_number_of_iters == 0) {
            if (verbose > 0) {
                amrex::Print() << print_ident << "MLMG: Failed to converge after " << niters << " iterations."
                               << " resid, resid/" << norm_name << " = "
                               << composite_norminf << ", "
                               << composite_norminf/max_norm << "\n";
            }
 
            if ( throw_exception ) {
                throw error("MLMG failed to converge.");
            } else {
                amrex::Abort("MLMG failed.");
            }
        }
        timer[iter_time] = amrex::second() - iter_start_time;
    }
 
    linop.postSolve(GetVecOfPtrs(sol));
 
    IntVect ng_back = final_fill_bc ? IntVect(1) : IntVect(0);
    if (linop.hasHiddenDimension()) {
        ng_back[linop.hiddenDirection()] = 0;
    }
    for (int alev = 0; alev < namrlevs; ++alev)
    {
        if (!sol_is_alias[alev]) {
            LocalCopy(*a_sol[alev], sol[alev], 0, 0, ncomp, ng_back);
        }
    }
 
    timer[solve_time] = amrex::second() - solve_start_time;
    if (verbose >= 1) {
        ParallelReduce::Max<double>(timer.data(), timer.size(), 0,
                                    ParallelContext::CommunicatorSub());
        if (ParallelContext::MyProcSub() == 0)
        {
            amrex::AllPrint() << print_ident << "MLMG: Timers: Solve = " << timer[solve_time]
                              << " Iter = " << timer[iter_time]
                              << " Bottom = " << timer[bottom_time] << "\n";
        }
    }
 
    ++solve_called;
 
    return composite_norminf;
}
 
template <typename MF>
auto
MLMGT<MF>::precond (const Vector<MF*>& a_sol, const Vector<MF const*>& a_rhs,
                    RT a_tol_rel, RT a_tol_abs) -> RT
{
    precond_mode = true;
    std::swap(max_precond_iters, do_fixed_number_of_iters);
    linop.beginPrecondBC();
 
    auto r = solve(a_sol, a_rhs, a_tol_rel, a_tol_abs);
 
    linop.endPrecondBC();
    std::swap(max_precond_iters, do_fixed_number_of_iters);
    precond_mode = false;
 
    return r;
}
 
template <typename MF>
void
MLMGT<MF>::prepareForFluxes (Vector<MF const*> const& a_sol)
{
    for (int alev = finest_amr_lev; alev >= 0; --alev) {
        const MF* crse_bcdata = (alev > 0) ? a_sol[alev-1] : nullptr;
        linop.prepareForFluxes(alev, crse_bcdata);
    }
}
 
template <typename MF>
template <typename AMF>
void
MLMGT<MF>::getGradSolution (const Vector<Array<AMF*,AMREX_SPACEDIM> >& a_grad_sol, Location a_loc)
{
    BL_PROFILE("MLMG::getGradSolution()");
    for (int alev = 0; alev <= finest_amr_lev; ++alev) {
        if constexpr (std::is_same<AMF,MF>()) {
            linop.compGrad(alev, a_grad_sol[alev], sol[alev], a_loc);
        } else {
            Array<MF,AMREX_SPACEDIM> grad_sol;
            for (int idim = 0; idim < AMREX_SPACEDIM; ++idim) {
                auto const& amf = *(a_grad_sol[alev][idim]);
                grad_sol[idim].define(boxArray(amf), DistributionMap(amf), ncomp, 0);
            }
            linop.compGrad(alev, GetArrOfPtrs(grad_sol), sol[alev], a_loc);
            for (int idim = 0; idim < AMREX_SPACEDIM; ++idim) {
                LocalCopy(*a_grad_sol[alev][idim], grad_sol[idim], 0, 0, ncomp, IntVect(0));
            }
        }
    }
}
 
template <typename MF>
template <typename AMF>
void
MLMGT<MF>::getGradSolution (std::initializer_list<Array<AMF*,AMREX_SPACEDIM>> a_grad_sol, Location a_loc)
{
    getGradSolution(Vector<Array<AMF*,AMREX_SPACEDIM>>(std::move(a_grad_sol)), a_loc);
}
 
template <typename MF>
template <typename AMF>
void
MLMGT<MF>::getFluxes (const Vector<Array<AMF*,AMREX_SPACEDIM> >& a_flux,
                      Location a_loc)
{
    if (!linop.isCellCentered()) {
        amrex::Abort("Calling wrong getFluxes for nodal solver");
    }
 
    AMREX_ASSERT(sol.size() == a_flux.size());
 
    if constexpr (std::is_same<AMF,MF>()) {
        getFluxes(a_flux, GetVecOfPtrs(sol), a_loc);
    } else {
        Vector<Array<MF,AMREX_SPACEDIM>> fluxes(namrlevs);
        for (int ilev = 0; ilev < namrlevs; ++ilev) {
            for (int idim = 0; idim < AMREX_SPACEDIM; ++idim) {
                auto const& amf = *(a_flux[ilev][idim]);
                fluxes[ilev][idim].define(boxArray(amf), DistributionMap(amf), ncomp, 0);
            }
        }
        getFluxes(GetVecOfArrOfPtrs(fluxes), GetVecOfPtrs(sol), a_loc);
        for (int ilev = 0; ilev < namrlevs; ++ilev) {
            for (int idim = 0; idim < AMREX_SPACEDIM; ++idim) {
                LocalCopy(*a_flux[ilev][idim], fluxes[ilev][idim], 0, 0, ncomp, IntVect(0));
            }
        }
    }
}
 
template <typename MF>
template <typename AMF>
void
MLMGT<MF>::getFluxes (std::initializer_list<Array<AMF*,AMREX_SPACEDIM>> a_flux,
                      Location a_loc)
{
    getFluxes(Vector<Array<AMF*,AMREX_SPACEDIM>>(std::move(a_flux)), a_loc);
}
 
template <typename MF>
template <typename AMF>
void
MLMGT<MF>::getFluxes (const Vector<Array<AMF*,AMREX_SPACEDIM> >& a_flux,
                      const Vector<AMF*>& a_sol, Location a_loc)
{
    BL_PROFILE("MLMG::getFluxes()");
 
    if (!linop.isCellCentered()) {
       amrex::Abort("Calling wrong getFluxes for nodal solver");
    }
 
    if constexpr (std::is_same<AMF,MF>()) {
        linop.getFluxes(a_flux, a_sol, a_loc);
    } else {
        Vector<Array<MF,AMREX_SPACEDIM>> fluxes(namrlevs);
        for (int ilev = 0; ilev < namrlevs; ++ilev) {
            for (int idim = 0; idim < AMREX_SPACEDIM; ++idim) {
                auto const& amf = *(a_flux[ilev][idim]);
                fluxes[ilev][idim].define(boxArray(amf), DistributionMap(amf), ncomp, 0);
            }
            LocalCopy(sol[ilev], *a_sol[ilev], 0, 0, ncomp, nGrowVect(sol[ilev]));
        }
        linop.getFluxes(GetVecOfArrOfPtrs(fluxes), GetVecOfPtrs(sol), a_loc);
        for (int ilev = 0; ilev < namrlevs; ++ilev) {
            for (int idim = 0; idim < AMREX_SPACEDIM; ++idim) {
                LocalCopy(*a_flux[ilev][idim], fluxes[ilev][idim], 0, 0, ncomp, IntVect(0));
            }
        }
    }
}
 
template <typename MF>
template <typename AMF>
void
MLMGT<MF>::getFluxes (std::initializer_list<Array<AMF*,AMREX_SPACEDIM>> a_flux,
                      std::initializer_list<AMF*> a_sol, Location a_loc)
{
    getFluxes(Vector<Array<AMF*,AMREX_SPACEDIM>>(std::move(a_flux)),
              Vector<AMF*>(std::move(a_sol)), a_loc);
}
 
template <typename MF>
template <typename AMF>
void
MLMGT<MF>::getFluxes (const Vector<AMF*> & a_flux, Location a_loc)
{
    AMREX_ASSERT(sol.size() == a_flux.size());
    if constexpr (std::is_same<AMF,MF>()) {
        getFluxes(a_flux, GetVecOfPtrs(sol), a_loc);
    } else {
        Vector<MF> fluxes(namrlevs);
        for (int ilev = 0; ilev < namrlevs; ++ilev) {
            auto const& amf = *a_flux[ilev];
            fluxes[ilev].define(boxArray(amf), DistributionMap(amf), AMREX_SPACEDIM, 0);
        }
        getFluxes(GetVecOfPtrs(fluxes), GetVecOfPtrs(sol), a_loc);
        for (int ilev = 0; ilev < namrlevs; ++ilev) {
            LocalCopy(*a_flux[ilev], fluxes[ilev], 0, 0, AMREX_SPACEDIM, IntVect(0));
        }
    }
}
 
template <typename MF>
template <typename AMF>
void
MLMGT<MF>::getFluxes (std::initializer_list<AMF*> a_flux, Location a_loc)
{
    getFluxes(Vector<AMF*>(std::move(a_flux)), a_loc);
}
 
template <typename MF>
template <typename AMF>
void
MLMGT<MF>::getFluxes (const Vector<AMF*> & a_flux,
                      const Vector<AMF*>& a_sol, Location /*a_loc*/)
{
    AMREX_ASSERT(nComp(*a_flux[0]) >= AMREX_SPACEDIM);
 
    if constexpr (! std::is_same<AMF,MF>()) {
        for (int alev = 0; alev < namrlevs; ++alev) {
            LocalCopy(sol[alev], *a_sol[alev], 0, 0, ncomp, nGrowVect(sol[alev]));
        }
    }
 
    if (linop.isCellCentered())
    {
        Vector<Array<MF,AMREX_SPACEDIM> > ffluxes(namrlevs);
        for (int alev = 0; alev < namrlevs; ++alev) {
            for (int idim = 0; idim < AMREX_SPACEDIM; ++idim) {
                const int mglev = 0;
                int nghost = 0;
                if (cf_strategy == CFStrategy::ghostnodes) { nghost = linop.getNGrow(alev); }
                ffluxes[alev][idim].define(amrex::convert(linop.m_grids[alev][mglev],
                                                          IntVect::TheDimensionVector(idim)),
                                           linop.m_dmap[alev][mglev], ncomp, nghost, MFInfo(),
                                           *linop.m_factory[alev][mglev]);
            }
        }
        if constexpr (std::is_same<AMF,MF>()) {
            getFluxes(amrex::GetVecOfArrOfPtrs(ffluxes), a_sol, Location::FaceCenter);
        } else {
            getFluxes(amrex::GetVecOfArrOfPtrs(ffluxes), GetVecOfPtrs(sol), Location::FaceCenter);
        }
        for (int alev = 0; alev < namrlevs; ++alev) {
#ifdef AMREX_USE_EB
            EB_average_face_to_cellcenter(*a_flux[alev], 0, amrex::GetArrOfConstPtrs(ffluxes[alev]));
#else
            average_face_to_cellcenter(*a_flux[alev], 0, amrex::GetArrOfConstPtrs(ffluxes[alev]));
#endif
        }
 
    } else {
        if constexpr (std::is_same<AMF,MF>()) {
            linop.getFluxes(a_flux, a_sol);
        } else {
            Vector<MF> fluxes(namrlevs);
            for (int ilev = 0; ilev < namrlevs; ++ilev) {
                auto const& amf = *a_flux[ilev];
                fluxes[ilev].define(boxArray(amf), DistributionMap(amf), AMREX_SPACEDIM, 0);
            }
            linop.getFluxes(GetVecOfPtrs(fluxes), GetVecOfPtrs(sol));
            for (int ilev = 0; ilev < namrlevs; ++ilev) {
                LocalCopy(*a_flux[ilev], fluxes[ilev], 0, 0, AMREX_SPACEDIM, IntVect(0));
            }
        }
    }
}
 
template <typename MF>
template <typename AMF>
void
MLMGT<MF>::getFluxes (std::initializer_list<AMF*> a_flux,
                      std::initializer_list<AMF*> a_sol, Location a_loc)
{
    getFluxes(Vector<AMF*>(std::move(a_flux)),
              Vector<AMF*>(std::move(a_sol)), a_loc);
}
 
#ifdef AMREX_USE_EB
template <typename MF>
void
MLMGT<MF>::getEBFluxes (const Vector<MF*>& a_eb_flux)
{
    if (!linop.isCellCentered()) {
       amrex::Abort("getEBFluxes is for cell-centered only");
    }
 
    AMREX_ASSERT(sol.size() == a_eb_flux.size());
    getEBFluxes(a_eb_flux, GetVecOfPtrs(sol));
}
 
template <typename MF>
void
MLMGT<MF>::getEBFluxes (const Vector<MF*>& a_eb_flux, const Vector<MF*>& a_sol)
{
    BL_PROFILE("MLMG::getEBFluxes()");
 
    if (!linop.isCellCentered()) {
       amrex::Abort("getEBFluxes is for cell-centered only");
    }
 
    linop.getEBFluxes(a_eb_flux, a_sol);
}
#endif
 
template <typename MF>
void
MLMGT<MF>::compResidual (const Vector<MF*>& a_res, const Vector<MF*>& a_sol,
                         const Vector<MF const*>& a_rhs)
{
    BL_PROFILE("MLMG::compResidual()");
 
    IntVect ng_sol(1);
    if (linop.hasHiddenDimension()) { ng_sol[linop.hiddenDirection()] = 0; }
 
    sol.resize(namrlevs);
    sol_is_alias.resize(namrlevs,true);
    for (int alev = 0; alev < namrlevs; ++alev)
    {
        if (cf_strategy == CFStrategy::ghostnodes || nGrowVect(*a_sol[alev]) == ng_sol)
        {
            sol[alev] = linop.makeAlias(*a_sol[alev]);
            sol_is_alias[alev] = true;
        }
        else
        {
            if (sol_is_alias[alev])
            {
                sol[alev] = linop.make(alev, 0, ng_sol);
                sol_is_alias[alev] = false;
            }
            LocalCopy(sol[alev], *a_sol[alev], 0, 0, ncomp, IntVect(0));
        }
    }
 
    prepareLinOp();
 
 
    for (int alev = finest_amr_lev; alev >= 0; --alev) {
        const MF* crse_bcdata = (alev > 0) ? &(sol[alev-1]) : nullptr;
        const MF* prhs = a_rhs[alev];
#if (AMREX_SPACEDIM != 3)
        int nghost = (cf_strategy == CFStrategy::ghostnodes) ? linop.getNGrow(alev) : 0;
        MF rhstmp(boxArray(*prhs), DistributionMap(*prhs), ncomp, nghost,
                  MFInfo(), *linop.Factory(alev));
        LocalCopy(rhstmp, *prhs, 0, 0, ncomp, IntVect(nghost));
        linop.applyMetricTerm(alev, 0, rhstmp);
        linop.unimposeNeumannBC(alev, rhstmp);
        linop.applyInhomogNeumannTerm(alev, rhstmp);
        prhs = &rhstmp;
#endif
        linop.solutionResidual(alev, *a_res[alev], sol[alev], *prhs, crse_bcdata);
        if (alev < finest_amr_lev) {
            linop.reflux(alev, *a_res[alev], sol[alev], *prhs,
                         *a_res[alev+1], sol[alev+1], *a_rhs[alev+1]);
            if (linop.isCellCentered()) {
#ifdef AMREX_USE_EB
                EB_average_down(*a_res[alev+1], *a_res[alev], 0, ncomp, linop.AMRRefRatioVect(alev));
#else
                average_down(*a_res[alev+1], *a_res[alev], 0, ncomp, linop.AMRRefRatioVect(alev));
#endif
            }
        }
    }
 
 
#if (AMREX_SPACEDIM != 3)
    for (int alev = 0; alev <= finest_amr_lev; ++alev) {
        linop.unapplyMetricTerm(alev, 0, *a_res[alev]);
    }
#endif
}
 
template <typename MF>
void
MLMGT<MF>::apply (const Vector<MF*>& out, const Vector<MF*>& a_in)
{
    BL_PROFILE("MLMG::apply()");
 
    Vector<MF*> in(namrlevs);
    Vector<MF> in_raii(namrlevs);
    Vector<MF> rh(namrlevs);
    int nghost = 0;
    IntVect ng_sol(1);
    if (linop.hasHiddenDimension()) { ng_sol[linop.hiddenDirection()] = 0; }
 
    for (int alev = 0; alev < namrlevs; ++alev)
    {
        if (cf_strategy == CFStrategy::ghostnodes)
        {
            nghost = linop.getNGrow(alev);
            in[alev] = a_in[alev];
        }
        else if (nGrowVect(*a_in[alev]) == ng_sol)
        {
            in[alev] = a_in[alev];
        }
        else
        {
            IntVect ng = ng_sol;
            if (cf_strategy == CFStrategy::ghostnodes) { ng = IntVect(nghost); }
            in_raii[alev] = linop.make(alev, 0, ng,
                                       MFInfo().SetArena(The_Async_Arena()));
            LocalCopy(in_raii[alev], *a_in[alev], 0, 0, ncomp, IntVect(nghost));
            in[alev] = &(in_raii[alev]);
        }
        rh[alev] = linop.make(alev, 0, IntVect(nghost),
                              MFInfo().SetArena(The_Async_Arena()));
        setVal(rh[alev], RT(0.0));
    }
 
    prepareLinOp();
 
    for (int alev = 0; alev < namrlevs; ++alev) {
        linop.applyInhomogNeumannTerm(alev, rh[alev]);
    }
 
 
    for (int alev = finest_amr_lev; alev >= 0; --alev) {
        const MF* crse_bcdata = (alev > 0) ? in[alev-1] : nullptr;
        linop.solutionResidual(alev, *out[alev], *in[alev], rh[alev], crse_bcdata);
        if (alev < finest_amr_lev) {
            linop.reflux(alev, *out[alev], *in[alev], rh[alev],
                         *out[alev+1], *in[alev+1], rh[alev+1]);
            if (linop.isCellCentered()) {
                if constexpr (IsMultiFabLike_v<MF>) {
#ifdef AMREX_USE_EB
                    EB_average_down(*out[alev+1], *out[alev], 0, nComp(*out[alev]), linop.AMRRefRatioVect(alev));
#else
                    average_down(*out[alev+1], *out[alev], 0, nComp(*out[alev]), linop.AMRRefRatioVect(alev));
#endif
                } else {
                    amrex::Abort("MLMG: TODO average_down for non-MultiFab");
                }
            }
        }
    }
 
#if (AMREX_SPACEDIM != 3)
    for (int alev = 0; alev <= finest_amr_lev; ++alev) {
        linop.unapplyMetricTerm(alev, 0, *out[alev]);
    }
#endif
 
    for (int alev = 0; alev <= finest_amr_lev; ++alev) {
        if (cf_strategy == CFStrategy::ghostnodes) { nghost = linop.getNGrow(alev); }
        Scale(*out[alev], RT(-1), 0, nComp(*out[alev]), nghost);
    }
}
 
template <typename MF>
void
MLMGT<MF>::applyPrecond (const Vector<MF*>& out, const Vector<MF*>& in)
{
    precond_mode = true;
    linop.beginPrecondBC();
    apply(out, in);
    linop.endPrecondBC();
    precond_mode = false;
}
 
template <typename MF>
template <typename AMF>
void
MLMGT<MF>::prepareForSolve (Vector<AMF*> const& a_sol, Vector<AMF const*> const& a_rhs)
{
    BL_PROFILE("MLMG::prepareForSolve()");
 
    AMREX_ASSERT(namrlevs <= a_sol.size());
    AMREX_ASSERT(namrlevs <= a_rhs.size());
 
    timer.assign(ntimers, 0.0);
 
    IntVect ng_rhs(0);
    IntVect ng_sol(1);
    if (linop.hasHiddenDimension()) { ng_sol[linop.hiddenDirection()] = 0; }
 
    linop.setPrintIndentation(print_ident);
    if (!linop_prepared) {
        linop.prepareForSolve();
        AMREX_ASSERT(!linop.m_mg_deferred || linop.m_mg_built);
        linop_prepared = true;
    } else if (linop.needsUpdate()) {
        linop.update();
 
        m_algmg_bottom.reset();
        m_algmg_level0.reset();
 
#if defined(AMREX_USE_HYPRE) && (AMREX_SPACEDIM > 1)
        hypre_solver.reset();
        hypre_bndry.reset();
        hypre_node_solver.reset();
#endif
 
#if defined(AMREX_USE_PETSC) && (AMREX_SPACEDIM > 1)
        petsc_solver.reset();
        petsc_bndry.reset();
#endif
    }
 
    sol.resize(namrlevs);
    sol_is_alias.resize(namrlevs,false);
    for (int alev = 0; alev < namrlevs; ++alev)
    {
        if (cf_strategy == CFStrategy::ghostnodes)
        {
            if constexpr (std::is_same<AMF,MF>()) {
                sol[alev] = linop.makeAlias(*a_sol[alev]);
                sol_is_alias[alev] = true;
            } else {
                amrex::Abort("Type conversion not supported for CFStrategy::ghostnodes");
            }
        }
        else
        {
            bool alias_made = false;
            if (nGrowVect(*a_sol[alev]) == ng_sol) {
                if constexpr (std::is_same<AMF,MF>()) {
                    sol[alev] = linop.makeAlias(*a_sol[alev]);
                    sol_is_alias[alev] = true;
                    alias_made = true;
                }
            }
            if (!alias_made) {
                if (sol_is_alias[alev] || !solve_called) {
                    sol[alev] = linop.make(alev, 0, ng_sol);
                    sol_is_alias[alev] = false;
                }
                LocalCopy(sol[alev], *a_sol[alev], 0, 0, ncomp, IntVect(0));
                setBndry(sol[alev], RT(0.0), 0, ncomp);
            }
        }
    }
 
    rhs.resize(namrlevs);
    for (int alev = 0; alev < namrlevs; ++alev)
    {
        if (cf_strategy == CFStrategy::ghostnodes) { ng_rhs = IntVect(linop.getNGrow(alev)); }
        if (!solve_called) {
            rhs[alev] = linop.make(alev, 0, ng_rhs);
        }
        LocalCopy(rhs[alev], *a_rhs[alev], 0, 0, ncomp, ng_rhs);
        linop.applyMetricTerm(alev, 0, rhs[alev]);
        linop.unimposeNeumannBC(alev, rhs[alev]);
        linop.applyInhomogNeumannTerm(alev, rhs[alev]);
        linop.applyOverset(alev, rhs[alev]);
        if ( ! precond_mode) {
            bool r = linop.scaleRHS(alev, &(rhs[alev]));
            amrex::ignore_unused(r);
        }
 
#ifdef AMREX_USE_EB
        const auto *factory = dynamic_cast<EBFArrayBoxFactory const*>(linop.Factory(alev));
        if (factory && !factory->isAllRegular()) {
            if constexpr (std::is_same<MF,MultiFab>()) {
                EB_set_covered(rhs[alev], 0, ncomp, 0, RT(0.0));
                EB_set_covered(sol[alev], 0, ncomp, 0, RT(0.0));
            } else {
                amrex::Abort("TODO: MLMG with EB only works with MultiFab");
            }
        }
#endif
    }
 
    for (int falev = finest_amr_lev; falev > 0; --falev)
    {
        linop.averageDownSolutionRHS(falev-1, sol[falev-1], rhs[falev-1], sol[falev], rhs[falev]);
    }
 
    // enforce solvability if appropriate
    if (linop.isSingular(0) && linop.getEnforceSingularSolvable())
    {
        makeSolvable();
    }
 
    IntVect ng = linop.getNGrowVectRestriction();
    if (cf_strategy == CFStrategy::ghostnodes) { ng = ng_rhs; }
    if (!solve_called) {
        linop.make(res, ng);
        linop.make(rescor, ng);
    }
    for (int alev = 0; alev <= finest_amr_lev; ++alev)
    {
        const int nmglevs = linop.NMGLevels(alev);
        for (int mglev = 0; mglev < nmglevs; ++mglev)
        {
            setVal(res   [alev][mglev], RT(0.0));
            setVal(rescor[alev][mglev], RT(0.0));
        }
    }
 
    if (cf_strategy != CFStrategy::ghostnodes) { ng = ng_sol; }
    cor.resize(namrlevs);
    for (int alev = 0; alev <= finest_amr_lev; ++alev)
    {
        const int nmglevs = linop.NMGLevels(alev);
        cor[alev].resize(nmglevs);
        for (int mglev = 0; mglev < nmglevs; ++mglev)
        {
            if (!solve_called) {
                IntVect _ng = ng;
                if (cf_strategy == CFStrategy::ghostnodes) { _ng=IntVect(linop.getNGrow(alev,mglev)); }
                cor[alev][mglev] = linop.make(alev, mglev, _ng);
            }
            setVal(cor[alev][mglev], RT(0.0));
        }
    }
 
    cor_hold.resize(std::max(namrlevs-1,1));
    {
        const int alev = 0;
        const int nmglevs = linop.NMGLevels(alev);
        cor_hold[alev].resize(nmglevs);
        for (int mglev = 0; mglev < nmglevs-1; ++mglev)
        {
            if (!solve_called) {
                IntVect _ng = ng;
                if (cf_strategy == CFStrategy::ghostnodes) { _ng=IntVect(linop.getNGrow(alev,mglev)); }
                cor_hold[alev][mglev] = linop.make(alev, mglev, _ng);
            }
            setVal(cor_hold[alev][mglev], RT(0.0));
        }
    }
    for (int alev = 1; alev < finest_amr_lev; ++alev)
    {
        cor_hold[alev].resize(1);
        if (!solve_called) {
            IntVect _ng = ng;
            if (cf_strategy == CFStrategy::ghostnodes) { _ng=IntVect(linop.getNGrow(alev)); }
            cor_hold[alev][0] = linop.make(alev, 0, _ng);
        }
        setVal(cor_hold[alev][0], RT(0.0));
    }
 
    if (linop.m_parent // no embedded N-Solve
        || !linop.supportNSolve())
    {
        do_nsolve = false;
    }
 
    if (do_nsolve && ns_linop == nullptr)
    {
        prepareForNSolve();
    }
 
    if (verbose >= 2) {
        amrex::Print() << print_ident << "MLMG: # of AMR levels: " << namrlevs << "\n"
                       << print_ident << "      # of MG levels on the coarsest AMR level: " << linop.NMGLevels(0)
                       << "\n";
        if (ns_linop) {
            amrex::Print() << print_ident << "      # of MG levels in N-Solve: " << ns_linop->NMGLevels(0) << "\n"
                           << print_ident << "      # of grids in N-Solve: " << ns_linop->m_grids[0][0].size() << "\n";
        }
    }
}
 
template <typename MF>
void
MLMGT<MF>::prepareLinOp ()
{
    linop.setPrintIndentation(print_ident);
    if (!linop_prepared) {
        linop.prepareForSolve();
        AMREX_ASSERT(!linop.m_mg_deferred || linop.m_mg_built);
        linop_prepared = true;
    } else if (linop.needsUpdate()) {
        linop.update();
 
        m_algmg_bottom.reset();
        m_algmg_level0.reset();
 
#if defined(AMREX_USE_HYPRE) && (AMREX_SPACEDIM > 1)
        hypre_solver.reset();
        hypre_bndry.reset();
        hypre_node_solver.reset();
#endif
 
#if defined(AMREX_USE_PETSC) && (AMREX_SPACEDIM > 1)
        petsc_solver.reset();
        petsc_bndry.reset();
#endif
    }
}
 
template <typename MF>
void
MLMGT<MF>::preparePrecond ()
{
    prepareLinOp();
    linop.preparePrecond();
}
 
template <typename MF>
void
MLMGT<MF>::prepareForNSolve ()
{
    if constexpr (IsMultiFabLike_v<MF>) {
        ns_linop = linop.makeNLinOp(nsolve_grid_size);
 
        int nghost = 0;
        if (cf_strategy == CFStrategy::ghostnodes) { nghost = linop.getNGrow(); }
 
        const BoxArray& ba = (*ns_linop).m_grids[0][0];
        const DistributionMapping& dm =(*ns_linop).m_dmap[0][0];
 
        int ng = 1;
        if (cf_strategy == CFStrategy::ghostnodes) { ng = nghost; }
        ns_sol = std::make_unique<MF>(ba, dm, ncomp, ng, MFInfo(), *(ns_linop->Factory(0,0)));
        ng = 0;
        if (cf_strategy == CFStrategy::ghostnodes) { ng = nghost; }
        ns_rhs = std::make_unique<MF>(ba, dm, ncomp, ng, MFInfo(), *(ns_linop->Factory(0,0)));
        setVal(*ns_sol, RT(0.0));
        setVal(*ns_rhs, RT(0.0));
 
        ns_linop->setLevelBC(0, ns_sol.get());
 
        ns_mlmg = std::make_unique<MLMGT<MF>>(*ns_linop);
        ns_mlmg->setVerbose(0);
        ns_mlmg->setFixedIter(1);
        ns_mlmg->setMaxFmgIter(20);
        ns_mlmg->setBottomSolver(BottomSolver::smoother);
    }
}
 
// in  : Residual (res) on the finest AMR level
// out : sol on all AMR levels
template <typename MF>
void MLMGT<MF>::oneIter (int iter)
{
    BL_PROFILE("MLMG::oneIter()");
 
    for (int alev = finest_amr_lev; alev > 0; --alev)
    {
        miniCycle(alev);
 
        IntVect nghost(0);
        if (cf_strategy == CFStrategy::ghostnodes) { nghost = IntVect(linop.getNGrow(alev)); }
        LocalAdd(sol[alev], cor[alev][0], 0, 0, ncomp, nghost);
 
        // compute residual for the coarse AMR level
        computeResWithCrseSolFineCor(alev-1,alev);
 
        if (alev != finest_amr_lev) {
            std::swap(cor_hold[alev][0], cor[alev][0]); // save it for the up cycle
        }
    }
 
    // coarsest amr level
    {
        // enforce solvability if appropriate
        if (linop.isSingular(0) && linop.getEnforceSingularSolvable())
        {
            makeSolvable(0,0,res[0][0]);
        }
 
        if (m_algmg_active) {
            if constexpr (std::is_same<MF,MultiFab>()) {
                algmgLevel0Solve();
            } else {
                amrex::Abort("MLMG: AlgMG is only supported for MultiFab");
            }
        } else if (iter < max_fmg_iters) {
            mgFcycle();
        } else {
            mgVcycle(0, 0);
        }
 
        IntVect nghost(0);
        if (cf_strategy == CFStrategy::ghostnodes) { nghost = IntVect(linop.getNGrow(0)); }
        LocalAdd(sol[0], cor[0][0], 0, 0, ncomp, nghost);
    }
 
    for (int alev = 1; alev <= finest_amr_lev; ++alev)
    {
        // (Fine AMR correction) = I(Coarse AMR correction)
        interpCorrection(alev);
        // Known overset cells must not receive the interpolated correction.
        linop.applyOverset(alev, cor[alev][0]);
 
        IntVect nghost(0);
        if (cf_strategy == CFStrategy::ghostnodes) { nghost = IntVect(linop.getNGrow(alev)); }
        LocalAdd(sol[alev], cor[alev][0], 0, 0, ncomp, nghost);
 
        if (alev != finest_amr_lev) {
            LocalAdd(cor_hold[alev][0], cor[alev][0], 0, 0, ncomp, nghost);
        }
 
        // Update fine AMR level correction
        computeResWithCrseCorFineCor(alev);
 
        miniCycle(alev);
 
        LocalAdd(sol[alev], cor[alev][0], 0, 0, ncomp, nghost);
 
        if (alev != finest_amr_lev) {
            LocalAdd(cor[alev][0], cor_hold[alev][0], 0, 0, ncomp, nghost);
        }
    }
 
    linop.averageDownAndSync(sol);
}
 
template <typename MF>
void
MLMGT<MF>::miniCycle (int amrlev)
{
    BL_PROFILE("MLMG::miniCycle()");
    const int mglev = 0;
    mgVcycle(amrlev, mglev);
}
 
// in   : Residual (res)
// out  : Correction (cor) from bottom to this function's local top
template <typename MF>
void
MLMGT<MF>::mgVcycle (int amrlev, int mglev_top)
{
    BL_PROFILE("MLMG::mgVcycle()");
 
    const int mglev_bottom = linop.NMGLevels(amrlev) - 1;
 
    for (int mglev = mglev_top; mglev < mglev_bottom; ++mglev)
    {
        BL_PROFILE_VAR("MLMG::mgVcycle_down::"+std::to_string(mglev), blp_mgv_down_lev);
 
        if (verbose >= 4)
        {
            RT norm = norminf(res[amrlev][mglev],0,ncomp,IntVect(0));
            amrex::Print() << print_ident << "AT LEVEL "  << amrlev << " " << mglev
                           << "   DN: Norm before smooth " << norm << "\n";
        }
 
        setVal(cor[amrlev][mglev], RT(0.0));
        bool skip_fillboundary = true;
        linop.smooth(amrlev, mglev, cor[amrlev][mglev], res[amrlev][mglev], skip_fillboundary, nu1);
 
        // rescor = res - L(cor)
        computeResOfCorrection(amrlev, mglev);
 
        if (verbose >= 4)
        {
            RT norm = norminf(rescor[amrlev][mglev],0,ncomp,IntVect(0));
            amrex::Print() << print_ident << "AT LEVEL "  << amrlev << " " << mglev
                           << "   DN: Norm after  smooth " << norm << "\n";
        }
 
        // res_crse = R(rescor_fine); this provides res/b to the level below
        linop.restriction(amrlev, mglev+1, res[amrlev][mglev+1], rescor[amrlev][mglev]);
    }
 
    BL_PROFILE_VAR("MLMG::mgVcycle_bottom", blp_bottom);
    if (amrlev == 0)
    {
        if (verbose >= 4)
        {
            RT norm = norminf(res[amrlev][mglev_bottom],0,ncomp,IntVect(0));
            amrex::Print() << print_ident << "AT LEVEL "  << amrlev << " " << mglev_bottom
                           << "   DN: Norm before bottom " << norm << "\n";
        }
        bottomSolve();
        if (verbose >= 4)
        {
            computeResOfCorrection(amrlev, mglev_bottom);
            RT norm = norminf(rescor[amrlev][mglev_bottom],0,ncomp,IntVect(0));
            amrex::Print() << print_ident << "AT LEVEL "  << amrlev << " " << mglev_bottom
                           << "   UP: Norm after  bottom " << norm << "\n";
        }
    }
    else
    {
        if (verbose >= 4)
        {
            RT norm = norminf(res[amrlev][mglev_bottom],0,ncomp,IntVect(0));
            amrex::Print() << print_ident << "AT LEVEL "  << amrlev << " " << mglev_bottom
                           << "       Norm before smooth " << norm << "\n";
        }
        setVal(cor[amrlev][mglev_bottom], RT(0.0));
        bool skip_fillboundary = true;
        linop.smooth(amrlev, mglev_bottom, cor[amrlev][mglev_bottom],
            res[amrlev][mglev_bottom], skip_fillboundary, nu1);
        if (verbose >= 4)
        {
            computeResOfCorrection(amrlev, mglev_bottom);
            RT norm = norminf(rescor[amrlev][mglev_bottom],0,ncomp,IntVect(0));
            amrex::Print() << print_ident << "AT LEVEL "  << amrlev  << " " << mglev_bottom
                           << "       Norm after  smooth " << norm << "\n";
        }
    }
    BL_PROFILE_VAR_STOP(blp_bottom);
 
    for (int mglev = mglev_bottom-1; mglev >= mglev_top; --mglev)
    {
        BL_PROFILE_VAR("MLMG::mgVcycle_up::"+std::to_string(mglev), blp_mgv_up_lev);
        // cor_fine += I(cor_crse)
        addInterpCorrection(amrlev, mglev);
        if (verbose >= 4)
        {
            computeResOfCorrection(amrlev, mglev);
            RT norm = norminf(rescor[amrlev][mglev],0,ncomp,IntVect(0));
            amrex::Print() << print_ident << "AT LEVEL "  << amrlev << " " << mglev
                           << "   UP: Norm before smooth " << norm << "\n";
        }
        linop.smooth(amrlev, mglev, cor[amrlev][mglev], res[amrlev][mglev], false, nu2);
 
        if (cf_strategy == CFStrategy::ghostnodes) { computeResOfCorrection(amrlev, mglev); }
 
        if (verbose >= 4)
        {
            computeResOfCorrection(amrlev, mglev);
            RT norm = norminf(rescor[amrlev][mglev],0,ncomp,IntVect(0));
            amrex::Print() << print_ident << "AT LEVEL "  << amrlev << " " << mglev
                           << "   UP: Norm after  smooth " << norm << "\n";
        }
    }
}
 
// FMG cycle on the coarsest AMR level.
// in:  Residual on the top MG level (i.e., 0)
// out: Correction (cor) on all MG levels
template <typename MF>
void
MLMGT<MF>::mgFcycle ()
{
    BL_PROFILE("MLMG::mgFcycle()");
 
#ifdef AMREX_USE_EB
   auto* pf = linop.Factory(0);
   auto is_all_regular = [pf] () {
        const auto *const f = dynamic_cast<EBFArrayBoxFactory const*>(pf);
        if (f) {
            return f->isAllRegular();
        } else {
            return true;
        }
    };
    amrex::ignore_unused(pf, is_all_regular);
    AMREX_ASSERT(linop.isCellCentered() || is_all_regular());
#endif
 
    const int amrlev = 0;
    const int mg_bottom_lev = linop.NMGLevels(amrlev) - 1;
    IntVect nghost(0);
    if (cf_strategy == CFStrategy::ghostnodes) { nghost = IntVect(linop.getNGrow(amrlev)); }
 
    for (int mglev = 1; mglev <= mg_bottom_lev; ++mglev)
    {
        linop.avgDownResMG(mglev, res[amrlev][mglev], res[amrlev][mglev-1]);
    }
 
    bottomSolve();
 
    for (int mglev = mg_bottom_lev-1; mglev >= 0; --mglev)
    {
        // cor_fine = I(cor_crse)
        interpCorrection(amrlev, mglev);
 
        // rescor = res - L(cor)
        computeResOfCorrection(amrlev, mglev);
        // res = rescor; this provides b to the vcycle below
        LocalCopy(res[amrlev][mglev], rescor[amrlev][mglev], 0, 0, ncomp, nghost);
 
        // save cor; do v-cycle; add the saved to cor
        std::swap(cor[amrlev][mglev], cor_hold[amrlev][mglev]);
        mgVcycle(amrlev, mglev);
        LocalAdd(cor[amrlev][mglev], cor_hold[amrlev][mglev], 0, 0, ncomp, nghost);
    }
}
 
// At the true bottom of the coarsest AMR level.
// in  : Residual (res) as b
// out : Correction (cor) as x
template <typename MF>
void
MLMGT<MF>::bottomSolve ()
{
    if (do_nsolve)
    {
        NSolve(*ns_mlmg, *ns_sol, *ns_rhs);
    }
    else
    {
        actualBottomSolve();
    }
}
 
template <typename MF>
void
MLMGT<MF>::NSolve (MLMGT<MF>& a_solver, MF& a_sol, MF& a_rhs)
{
    BL_PROFILE("MLMG::NSolve()");
 
    setVal(a_sol, RT(0.0));
 
    MF const& res_bottom = res[0].back();
    if (BoxArray::SameRefs(boxArray(a_rhs),boxArray(res_bottom)) &&
        DistributionMapping::SameRefs(DistributionMap(a_rhs),DistributionMap(res_bottom)))
    {
        LocalCopy(a_rhs, res_bottom, 0, 0, ncomp, IntVect(0));
    } else {
        setVal(a_rhs, RT(0.0));
        ParallelCopy(a_rhs, res_bottom, 0, 0, ncomp);
    }
 
    a_solver.solve(Vector<MF*>{&a_sol}, Vector<MF const*>{&a_rhs},
                   RT(-1.0), RT(-1.0));
 
    linop.copyNSolveSolution(cor[0].back(), a_sol);
}
 
template <typename MF>
void
MLMGT<MF>::postCG (int ret, int niters)
{
    if (niters >= 0) {
        m_niters_cg.push_back(niters);
    }
 
    const int amrlev = 0;
    const int mglev = linop.NMGLevels(amrlev) - 1;
    auto& x = cor[amrlev][mglev];
    auto& b = res[amrlev][mglev];
    const int n = (ret==0) ? nub : nuf;
    linop.smooth(amrlev, mglev, x, b, false, n);
}
 
template <typename MF>
void
MLMGT<MF>::actualBottomSolve ()
{
    BL_PROFILE("MLMG::actualBottomSolve()");
 
    if (!linop.isBottomActive()) { return; }
 
    auto bottom_start_time = amrex::second();
 
    ParallelContext::push(linop.BottomCommunicator());
    struct PopGuard { ~PopGuard () { ParallelContext::pop(); } } pop_guard; // NOLINT(cppcoreguidelines-special-member-functions)
 
    const int amrlev = 0;
    const int mglev = linop.NMGLevels(amrlev) - 1;
    auto& x = cor[amrlev][mglev];
    auto& b = res[amrlev][mglev];
 
    setVal(x, RT(0.0));
 
    if (bottom_solver == BottomSolver::smoother)
    {
        bool skip_fillboundary = true;
        linop.smooth(amrlev, mglev, x, b, skip_fillboundary, nuf);
    }
    else
    {
        MF* bottom_b = &b;
        MF raii_b;
        if (linop.isBottomSingular() && linop.getEnforceSingularSolvable())
        {
            const IntVect ng = nGrowVect(b);
            raii_b = linop.make(amrlev, mglev, ng,
                                MFInfo().SetArena(The_Async_Arena()));
            LocalCopy(raii_b, b, 0, 0, ncomp, ng);
            bottom_b = &raii_b;
 
            makeSolvable(amrlev,mglev,*bottom_b);
        }
 
        if (bottom_solver == BottomSolver::hypre)
        {
#if defined(AMREX_USE_HYPRE) && (AMREX_SPACEDIM > 1)
            if constexpr (std::is_same<MF,MultiFab>()) {
                bottomSolveWithHypre(x, *bottom_b);
            } else
#endif
            {
                amrex::Abort("Using Hypre as bottom solver not supported in this case");
            }
        }
        else if (bottom_solver == BottomSolver::petsc)
        {
#if defined(AMREX_USE_PETSC) && (AMREX_SPACEDIM > 1)
            if constexpr (std::is_same<MF,MultiFab>()) {
                bottomSolveWithPETSc(x, *bottom_b);
            } else
#endif
            {
                amrex::Abort("Using PETSc as bottom solver not supported in this case");
            }
        }
        else if (bottom_solver == BottomSolver::algmg)
        {
            if constexpr (std::is_same<MF,MultiFab>()) {
                bottomSolveWithAlgMG(x, *bottom_b);
            } else {
                amrex::Abort("MLMG: AlgMG is only supported for MultiFab");
            }
        }
        else if (bottom_solver == BottomSolver::custom && linop.supportCustomBottomSolver())
        {
            linop.customBottomSolve(this, x, *bottom_b, bottom_reltol, bottom_abstol,
                                    bottom_maxiter);
        }
        else
        {
            typename MLCGSolverT<MF>::Type cg_type;
            if (bottom_solver == BottomSolver::cg ||
                bottom_solver == BottomSolver::cgbicg) {
                cg_type = MLCGSolverT<MF>::Type::CG;
            } else {
                cg_type = MLCGSolverT<MF>::Type::BiCGStab;
            }
 
            int ret = bottomSolveWithCG(x, *bottom_b, cg_type);
 
            if (ret != 0 && (bottom_solver == BottomSolver::cgbicg ||
                             bottom_solver == BottomSolver::bicgcg))
            {
                if (bottom_solver == BottomSolver::cgbicg) {
                    cg_type = MLCGSolverT<MF>::Type::BiCGStab; // switch to bicg
                } else {
                    cg_type = MLCGSolverT<MF>::Type::CG; // switch to cg
                }
                if (ret == 9) {
                    // if ret != 9 && ret != 0, x has been set to zero in bottomSolveWithCG
                    setVal(x, RT(0));
                }
                ret = bottomSolveWithCG(x, *bottom_b, cg_type);
                if (ret == 0) { // switch permanently
                    if (cg_type == MLCGSolverT<MF>::Type::CG) {
                        bottom_solver = BottomSolver::cg;
                    } else {
                        bottom_solver = BottomSolver::bicgstab;
                    }
                }
            }
 
            postCG(ret);
        }
    }
 
    if (! timer.empty()) {
        timer[bottom_time] += amrex::second() - bottom_start_time;
    }
}
 
template <typename MF>
int
MLMGT<MF>::bottomSolveWithCG (MF& x, const MF& b, typename MLCGSolverT<MF>::Type type)
{
    MLCGSolverT<MF> cg_solver(linop);
    cg_solver.setSolver(type);
    cg_solver.setVerbose(bottom_verbose);
    cg_solver.setPrintIndentation(print_ident);
    cg_solver.setMaxIter(bottom_maxiter);
    cg_solver.setInitSolnZeroed(true);
    if (cf_strategy == CFStrategy::ghostnodes) { cg_solver.setNGhost(linop.getNGrow()); }
 
    int ret = cg_solver.solve(x, b, bottom_reltol, bottom_abstol);
    if (ret != 0 && verbose > 1) {
        amrex::Print() << print_ident << "MLMG: Bottom solve failed.\n";
    }
    m_niters_cg.push_back(cg_solver.getNumIters());
 
    if (ret != 0 && ret != 9) {
        setVal(x, RT(0));
    }
 
    return ret;
}
 
// Compute multi-level Residual (res) up to amrlevmax.
template <typename MF>
void
MLMGT<MF>::computeMLResidual (int amrlevmax)
{
    BL_PROFILE("MLMG::computeMLResidual()");
 
    const int mglev = 0;
    for (int alev = amrlevmax; alev >= 0; --alev) {
        const MF* crse_bcdata = (alev > 0) ? &(sol[alev-1]) : nullptr;
        linop.solutionResidual(alev, res[alev][mglev], sol[alev], rhs[alev], crse_bcdata);
        if (alev < finest_amr_lev) {
            linop.reflux(alev, res[alev][mglev], sol[alev], rhs[alev],
                         res[alev+1][mglev], sol[alev+1], rhs[alev+1]);
        }
    }
}
 
// Compute single AMR level residual without masking.
template <typename MF>
void
MLMGT<MF>::computeResidual (int alev)
{
    BL_PROFILE("MLMG::computeResidual()");
    const MF* crse_bcdata = (alev > 0) ? &(sol[alev-1]) : nullptr;
    linop.solutionResidual(alev, res[alev][0], sol[alev], rhs[alev], crse_bcdata);
}
 
// Compute coarse AMR level composite residual with coarse solution and fine correction
template <typename MF>
void
MLMGT<MF>::computeResWithCrseSolFineCor (int calev, int falev)
{
    BL_PROFILE("MLMG::computeResWithCrseSolFineCor()");
 
    IntVect nghost(0);
    if (cf_strategy == CFStrategy::ghostnodes) {
        nghost = IntVect(std::min(linop.getNGrow(falev),linop.getNGrow(calev)));
    }
 
    MF&       crse_sol = sol[calev];
    const MF& crse_rhs = rhs[calev];
    MF&       crse_res = res[calev][0];
 
    MF&       fine_sol = sol[falev];
    const MF& fine_rhs = rhs[falev];
    MF&       fine_cor = cor[falev][0];
    MF&       fine_res = res[falev][0];
    MF&    fine_rescor = rescor[falev][0];
 
    const MF* crse_bcdata = (calev > 0) ? &(sol[calev-1]) : nullptr;
    linop.solutionResidual(calev, crse_res, crse_sol, crse_rhs, crse_bcdata);
 
    linop.correctionResidual(falev, 0, fine_rescor, fine_cor, fine_res, BCMode::Homogeneous);
    LocalCopy(fine_res, fine_rescor, 0, 0, ncomp, nghost);
 
    linop.reflux(calev, crse_res, crse_sol, crse_rhs, fine_res, fine_sol, fine_rhs);
 
    linop.avgDownResAmr(calev, crse_res, fine_res);
}
 
// Compute fine AMR level residual fine_res = fine_res - L(fine_cor) with coarse providing BC.
template <typename MF>
void
MLMGT<MF>::computeResWithCrseCorFineCor (int falev)
{
    BL_PROFILE("MLMG::computeResWithCrseCorFineCor()");
 
    IntVect nghost(0);
    if (cf_strategy == CFStrategy::ghostnodes) {
        nghost = IntVect(linop.getNGrow(falev));
    }
 
    const MF& crse_cor = cor[falev-1][0];
 
    MF& fine_cor    = cor   [falev][0];
    MF& fine_res    = res   [falev][0];
    MF& fine_rescor = rescor[falev][0];
 
    // fine_rescor = fine_res - L(fine_cor)
    linop.correctionResidual(falev, 0, fine_rescor, fine_cor, fine_res,
                             BCMode::Inhomogeneous, &crse_cor);
    LocalCopy(fine_res, fine_rescor, 0, 0, ncomp, nghost);
}
 
// Interpolate correction from coarse to fine AMR level.
template <typename MF>
void
MLMGT<MF>::interpCorrection (int alev)
{
    BL_PROFILE("MLMG::interpCorrection_1");
 
    IntVect nghost(0);
    if (cf_strategy == CFStrategy::ghostnodes) {
        nghost = IntVect(linop.getNGrow(alev));
    }
 
    MF & crse_cor = cor[alev-1][0];
    MF & fine_cor = cor[alev  ][0];
 
    const Geometry& crse_geom = linop.Geom(alev-1,0);
 
    int ng_src = 0;
    int ng_dst = linop.isCellCentered() ? 1 : 0;
    if (cf_strategy == CFStrategy::ghostnodes)
    {
        ng_src = linop.getNGrow(alev-1);
        ng_dst = linop.getNGrow(alev-1);
        if constexpr (IsMultiFabLike_v<MF>) {
            crse_cor.FillBoundary(0, ncomp, IntVect(ng_src), crse_geom.periodicity());
        } else {
            amrex::Abort("MLMG: CFStrategy::ghostnodes not supported for non-MultiFab like types");
        }
    }
 
    MF cfine = linop.makeCoarseAmr(alev, IntVect(ng_dst),
                                   MFInfo().SetArena(The_Async_Arena()));
    setVal(cfine, RT(0.0));
    ParallelCopy(cfine, crse_cor, 0, 0, ncomp, IntVect(ng_src), IntVect(ng_dst),
                 crse_geom.periodicity());
 
    linop.interpolationAmr(alev, fine_cor, cfine, nghost); // NOLINT(readability-suspicious-call-argument)
}
 
// Interpolate correction between MG levels
// inout: Correction (cor) on coarse MG lev.  (out due to FillBoundary)
// out  : Correction (cor) on fine MG lev.
template <typename MF>
void
MLMGT<MF>::interpCorrection (int alev, int mglev)
{
    BL_PROFILE("MLMG::interpCorrection_2");
 
    MF& crse_cor = cor[alev][mglev+1];
    MF& fine_cor = cor[alev][mglev  ];
    linop.interpAssign(alev, mglev, fine_cor, crse_cor);
}
 
// (Fine MG level correction) += I(Coarse MG level correction)
template <typename MF>
void
MLMGT<MF>::addInterpCorrection (int alev, int mglev)
{
    BL_PROFILE("MLMG::addInterpCorrection()");
 
    const MF& crse_cor = cor[alev][mglev+1];
    MF&       fine_cor = cor[alev][mglev  ];
 
    MF cfine;
    const MF* cmf;
 
    if (linop.isMFIterSafe(alev, mglev, mglev+1))
    {
        cmf = &crse_cor;
    }
    else
    {
        cfine = linop.makeCoarseMG(alev, mglev, IntVect(0),
                                   MFInfo().SetArena(The_Async_Arena()));
        ParallelCopy(cfine, crse_cor, 0, 0, ncomp);
        cmf = &cfine;
    }
 
    linop.interpolation(alev, mglev, fine_cor, *cmf);
}
 
// Compute rescor = res - L(cor)
// in   : res
// inout: cor (out due to FillBoundary in linop.correctionResidual)
// out  : rescor
template <typename MF>
void
MLMGT<MF>::computeResOfCorrection (int amrlev, int mglev)
{
    BL_PROFILE("MLMG:computeResOfCorrection()");
    MF      & x =    cor[amrlev][mglev];
    const MF& b =    res[amrlev][mglev];
    MF      & r = rescor[amrlev][mglev];
    linop.correctionResidual(amrlev, mglev, r, x, b, BCMode::Homogeneous);
}
 
// Compute single-level masked inf-norm of Residual (res).
template <typename MF>
auto
MLMGT<MF>::ResNormInf (int alev, bool local) -> RT
{
    BL_PROFILE("MLMG::ResNormInf()");
    return linop.normInf(alev, res[alev][0], local);
}
 
// Computes multi-level masked inf-norm of Residual (res).
template <typename MF>
auto
MLMGT<MF>::MLResNormInf (int alevmax, bool local) -> RT
{
    BL_PROFILE("MLMG::MLResNormInf()");
    RT r = RT(0.0);
    for (int alev = 0; alev <= alevmax; ++alev)
    {
        r = std::max(r, ResNormInf(alev,true));
    }
    if (!local) { ParallelAllReduce::Max(r, ParallelContext::CommunicatorSub()); }
    return r;
}
 
// Compute multi-level masked inf-norm of RHS (rhs).
template <typename MF>
auto
MLMGT<MF>::MLRhsNormInf (bool local) -> RT
{
    BL_PROFILE("MLMG::MLRhsNormInf()");
    RT r = RT(0.0);
    for (int alev = 0; alev <= finest_amr_lev; ++alev) {
        auto t = linop.normInf(alev, rhs[alev], true);
        r = std::max(r, t);
    }
    if (!local) { ParallelAllReduce::Max(r, ParallelContext::CommunicatorSub()); }
    return r;
}
 
template <typename MF>
void
MLMGT<MF>::makeSolvable ()
{
    auto const& offset = linop.getSolvabilityOffset(0, 0, rhs[0]);
    if (verbose >= 4) {
        for (int c = 0; c < ncomp; ++c) {
            amrex::Print() << print_ident << "MLMG: Subtracting " << offset[c] << " from rhs component "
                           << c << "\n";
        }
    }
    for (int alev = 0; alev < namrlevs; ++alev) {
        linop.fixSolvabilityByOffset(alev, 0, rhs[alev], offset);
    }
}
 
template <typename MF>
void
MLMGT<MF>::makeSolvable (int amrlev, int mglev, MF& mf)
{
    auto const& offset = linop.getSolvabilityOffset(amrlev, mglev, mf);
    if (verbose >= 4) {
        for (int c = 0; c < ncomp; ++c) {
            amrex::Print() << print_ident << "MLMG: Subtracting " << offset[c]
                           << " from mf component c = " << c
                           << " on level (" << amrlev << ", " << mglev << ")\n";
        }
    }
    linop.fixSolvabilityByOffset(amrlev, mglev, mf, offset);
}
 
template <typename MF>
template <class TMF>
requires (std::same_as<TMF,MultiFab>)
void
MLMGT<MF>::configureAlgMG (MLAlgMG& s, bool singular, bool with_options)
{
    // Dependent type: AlgMG stays a forward declaration in this header.
    AlgMG<RT>& a = s.solver();
    a.setVerbose(bottom_verbose);
    a.setPrintIndentation(print_ident + "    ");
    a.setThrowException(throw_exception);
    // Settings that select the setup (singular flag, Krylov type, the user's
    // options) are applied once per assembled matrix. Reapplying them on
    // every solve could toggle a value against the callback and redo the
    // expensive AlgMG setup each time.
    if (with_options) {
        a.setSingular(singular);
        a.setKrylovSolver(AlgMG<RT>::KrylovSolver::bicgstab);
        if (m_algmg_options) { m_algmg_options(a); }
    }
}
 
template <typename MF>
template <class TMF>
requires (std::same_as<TMF,MultiFab>)
void
MLMGT<MF>::algmgSolve (MLAlgMG& s, MF& x, MF const& b)
{
    // As a preconditioner MLMG must be a fixed linear operation: one V-cycle.
    if (precond_mode) {
        s.applyVcycle(x, b);
    } else {
        try {
            s.solve(x, b, bottom_reltol, std::max(bottom_abstol, RT(0)), bottom_maxiter);
        } catch (std::runtime_error const& e) {
            throw error(e.what());
        }
    }
}
 
template <typename MF>
template <class TMF>
requires (std::same_as<TMF,MultiFab>)
void
MLMGT<MF>::bottomSolveWithAlgMG (MF& x, const MF& b)
{
    const int amrlev = 0;
    const int mglev  = linop.NMGLevels(amrlev) - 1;
 
    AMREX_ALWAYS_ASSERT_WITH_MESSAGE(ncomp == 1, "MLMG: AlgMG needs ncomp == 1");
 
    bool const fresh = (m_algmg_bottom == nullptr);
    if (fresh) { m_algmg_bottom = linop.makeAlgMG(mglev); }
    configureAlgMG(*m_algmg_bottom, linop.isBottomSingular(), fresh);
    algmgSolve(*m_algmg_bottom, x, b);
 
    if (linop.isSingular(amrlev) && linop.getEnforceSingularSolvable()) {
        makeSolvable(amrlev, mglev, x);
    }
}
 
template <typename MF>
template <class TMF>
requires (std::same_as<TMF,MultiFab>)
void
MLMGT<MF>::algmgLevel0Solve ()
{
    BL_PROFILE("MLMG::algmgLevel0Solve()");
 
    auto t0 = amrex::second();
 
    AMREX_ALWAYS_ASSERT_WITH_MESSAGE(ncomp == 1, "MLMG: AlgMG needs ncomp == 1");
 
    bool const fresh = (m_algmg_level0 == nullptr);
    if (fresh) { m_algmg_level0 = linop.makeAlgMG(0); }
    configureAlgMG(*m_algmg_level0, linop.isSingular(0), fresh);
    algmgSolve(*m_algmg_level0, cor[0][0], res[0][0]);
 
    // Known overset cells must not receive a correction; the matrix rows
    // there are identities with a zero rhs, so this is a safety pass.
    linop.applyOverset(0, cor[0][0]);
 
    if (linop.isSingular(0) && linop.getEnforceSingularSolvable()) {
        makeSolvable(0, 0, cor[0][0]);
    }
 
    if (! timer.empty()) {
        timer[bottom_time] += amrex::second() - t0;
    }
}
 
template <typename MF>
bool
MLMGT<MF>::hybridShouldSwitch (Vector<RT> const& norms, RT max_norm,
                               RT best_norm, std::string& reason) const
{
    RT const rnorm = norms.back();
    if (!amrex::isfinite(rnorm)) {
        reason = "non-finite residual";
        return true;
    }
    if (rnorm > RT(1.e20)*max_norm ||
        rnorm > hybrid_divergence_factor*best_norm) {
        reason = "diverging";
        return true;
    }
    const int w = hybrid_stall_window;
    if (w > 0 && int(norms.size()) > w) {
        const RT r_old = norms[norms.size()-1-w];
        if (rnorm > std::pow(hybrid_stall_rate, RT(w)) * r_old) {
            reason = "stalling";
            return true;
        }
    }
    return false;
}
 
#if defined(AMREX_USE_HYPRE) && (AMREX_SPACEDIM > 1)
template <typename MF>
template <class TMF>
requires (std::same_as<TMF,MultiFab>)
void
MLMGT<MF>::bottomSolveWithHypre (MF& x, const MF& b)
{
    const int amrlev = 0;
    const int mglev  = linop.NMGLevels(amrlev) - 1;
 
    AMREX_ALWAYS_ASSERT_WITH_MESSAGE(ncomp == 1, "bottomSolveWithHypre doesn't work with ncomp > 1");
 
    if (linop.isCellCentered())
    {
        if (hypre_solver == nullptr)  // We should reuse the setup
        {
            hypre_solver = linop.makeHypre(hypre_interface);
 
            hypre_solver->setVerbose(bottom_verbose);
            if (hypre_interface == amrex::Hypre::Interface::ij) {
                hypre_solver->setHypreOptionsNamespace(hypre_options_namespace);
            } else {
                hypre_solver->setHypreOldDefault(hypre_old_default);
                hypre_solver->setHypreRelaxType(hypre_relax_type);
                hypre_solver->setHypreRelaxOrder(hypre_relax_order);
                hypre_solver->setHypreNumSweeps(hypre_num_sweeps);
                hypre_solver->setHypreStrongThreshold(hypre_strong_threshold);
            }
 
            const BoxArray& ba = linop.m_grids[amrlev].back();
            const DistributionMapping& dm = linop.m_dmap[amrlev].back();
            const Geometry& geom = linop.m_geom[amrlev].back();
 
            hypre_bndry = std::make_unique<MLMGBndryT<MF>>(ba, dm, ncomp, geom);
            hypre_bndry->setHomogValues();
            const Real* dx = linop.m_geom[0][0].CellSize();
            IntVect crse_ratio = linop.m_coarse_data_crse_ratio.allGT(0) ? linop.m_coarse_data_crse_ratio : IntVect(1);
            RealVect bclocation(AMREX_D_DECL(0.5*dx[0]*crse_ratio[0],
                                             0.5*dx[1]*crse_ratio[1],
                                             0.5*dx[2]*crse_ratio[2]));
            hypre_bndry->setLOBndryConds(linop.m_lobc, linop.m_hibc, IntVect(-1), bclocation,
                                         linop.m_coarse_fine_bc_type);
        }
 
        // IJ interface understands absolute tolerance API of HYPRE
        amrex::Real hypre_abstol =
            (hypre_interface == amrex::Hypre::Interface::ij)
            ? bottom_abstol : Real(-1.0);
        hypre_solver->solve(
            x, b, bottom_reltol, hypre_abstol, bottom_maxiter, *hypre_bndry,
            linop.getMaxOrder());
    }
    else
    {
        if (hypre_node_solver == nullptr)
        {
            hypre_node_solver =
                linop.makeHypreNodeLap(bottom_verbose, hypre_options_namespace);
        }
        hypre_node_solver->solve(x, b, bottom_reltol, bottom_abstol, bottom_maxiter);
    }
 
    // For singular problems there may be a large constant added to all values of the solution
    // For precision reasons we enforce that the average of the correction from HYPRE is 0
    if (linop.isSingular(amrlev) && linop.getEnforceSingularSolvable())
    {
        makeSolvable(amrlev, mglev, x);
    }
}
#endif
 
#if defined(AMREX_USE_PETSC) && (AMREX_SPACEDIM > 1)
template <typename MF>
template <class TMF>
requires (std::same_as<TMF,MultiFab>)
void
MLMGT<MF>::bottomSolveWithPETSc (MF& x, const MF& b)
{
    AMREX_ALWAYS_ASSERT_WITH_MESSAGE(ncomp == 1, "bottomSolveWithPETSc doesn't work with ncomp > 1");
 
    if(petsc_solver == nullptr)
    {
        petsc_solver = linop.makePETSc();
        petsc_solver->setVerbose(bottom_verbose);
 
        const BoxArray& ba = linop.m_grids[0].back();
        const DistributionMapping& dm = linop.m_dmap[0].back();
        const Geometry& geom = linop.m_geom[0].back();
 
        petsc_bndry = std::make_unique<MLMGBndryT<MF>>(ba, dm, ncomp, geom);
        petsc_bndry->setHomogValues();
        const Real* dx = linop.m_geom[0][0].CellSize();
        auto crse_ratio = linop.m_coarse_data_crse_ratio.allGT(0) ? linop.m_coarse_data_crse_ratio : IntVect(1);
        RealVect bclocation(AMREX_D_DECL(0.5*dx[0]*crse_ratio[0],
                                         0.5*dx[1]*crse_ratio[1],
                                         0.5*dx[2]*crse_ratio[2]));
        petsc_bndry->setLOBndryConds(linop.m_lobc, linop.m_hibc, IntVect(-1), bclocation,
                                     linop.m_coarse_fine_bc_type);
    }
    petsc_solver->solve(x, b, bottom_reltol, Real(-1.), bottom_maxiter, *petsc_bndry,
                        linop.getMaxOrder());
}
#endif
 
template <typename MF>
void
MLMGT<MF>::checkPoint (const Vector<MultiFab*>& a_sol,
                       const Vector<MultiFab const*>& a_rhs,
                       RT a_tol_rel, RT a_tol_abs, const char* a_file_name) const
{
    std::string file_name(a_file_name);
    UtilCreateCleanDirectory(file_name, false);
 
    if (ParallelContext::IOProcessorSub())
    {
        std::string HeaderFileName(std::string(a_file_name)+"/Header");
        std::ofstream HeaderFile;
        HeaderFile.open(HeaderFileName.c_str(), std::ofstream::out   |
                                                std::ofstream::trunc |
                                                std::ofstream::binary);
        if( ! HeaderFile.good()) {
            FileOpenFailed(HeaderFileName);
        }
 
        HeaderFile.precision(17);
 
        std::string norm_name = getEnumNameString(norm_type);
 
        HeaderFile << linop.name() << "\n"
                   << "a_tol_rel = " << a_tol_rel << "\n"
                   << "a_tol_abs = " << a_tol_abs << "\n"
                   << "verbose = " << verbose << "\n"
                   << "max_iters = " << max_iters << "\n"
                   << "nu1 = " << nu1 << "\n"
                   << "nu2 = " << nu2 << "\n"
                   << "nuf = " << nuf << "\n"
                   << "nub = " << nub << "\n"
                   << "max_fmg_iters = " << max_fmg_iters << "\n"
                   << "bottom_solver = " << static_cast<int>(bottom_solver) << "\n"
                   << "bottom_verbose = " << bottom_verbose << "\n"
                   << "bottom_maxiter = " << bottom_maxiter << "\n"
                   << "bottom_reltol = " << bottom_reltol << "\n"
                   << "convergence_norm = " << norm_name << "\n"
                   << "namrlevs = " << namrlevs << "\n"
                   << "finest_amr_lev = " << finest_amr_lev << "\n"
                   << "linop_prepared = " << linop_prepared << "\n"
                   << "solve_called = " << solve_called << "\n";
 
        for (int ilev = 0; ilev <= finest_amr_lev; ++ilev) {
            UtilCreateCleanDirectory(file_name+"/Level_"+std::to_string(ilev), false);
        }
    }
 
    ParallelContext::BarrierSub();
 
    for (int ilev = 0; ilev <= finest_amr_lev; ++ilev) {
        VisMF::Write(*a_sol[ilev], file_name+"/Level_"+std::to_string(ilev)+"/sol");
        VisMF::Write(*a_rhs[ilev], file_name+"/Level_"+std::to_string(ilev)+"/rhs");
    }
 
    linop.checkPoint(file_name+"/linop");
}
 
template <typename MF>
void
MLMGT<MF>::incPrintIdentation ()
{
    print_ident.resize(print_ident.size()+4, ' ');
}
 
template <typename MF>
void
MLMGT<MF>::decPrintIdentation ()
{
    if (print_ident.size() > 4) {
        print_ident.resize(print_ident.size()-4, ' ');
    } else {
        print_ident.clear();
    }
}
 
extern template class MLMGT<MultiFab>;
 
using MLMG = MLMGT<MultiFab>;
 
}
 
#endif