NewtonSolver.H

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/* Copyright 2024 Justin Angus
 *
 * This file is part of WarpX.
 *
 * License: BSD-3-Clause-LBNL
 */
#ifndef NEWTON_SOLVER_H_
#define NEWTON_SOLVER_H_
 
#include "LinearSolverLibrary.H"
#include "NonlinearSolver.H"
#include "JacobianFunctionMF.H"
#include "Preconditioner.H"
#include "Utils/TextMsg.H"
 
#include <AMReX_ParmParse.H>
#include <AMReX_Config.H>
 
#include <vector>
#include <istream>
#include <filesystem>

 
template<class Vec, class Ops>
class NewtonSolver : public NonlinearSolver<Vec,Ops>
{
public:
 
    NewtonSolver() = default;
 
    ~NewtonSolver() override = default;
 
    // Prohibit Move and Copy operations
    NewtonSolver(const NewtonSolver&) = delete;
    NewtonSolver& operator=(const NewtonSolver&) = delete;
    NewtonSolver(NewtonSolver&&) noexcept = delete;
    NewtonSolver& operator=(NewtonSolver&&) noexcept = delete;
 
    void Define ( const Vec&  a_U,
                        Ops*  a_ops ) override;
 
    void Solve ( Vec&   a_U,
           const Vec&   a_b,
           amrex::Real  a_time,
           amrex::Real  a_dt,
           int          a_step) const override;
 
    void GetSolverParams ( amrex::Real&  a_rtol,
                           amrex::Real&  a_atol,
                           int&          a_maxits ) override
    {
        a_rtol = m_rtol;
        a_atol = m_atol;
        a_maxits = m_maxits;
    }
 
    inline void CurTime ( amrex::Real  a_time ) const
    {
        m_cur_time = a_time;
        m_linear_function->curTime( a_time );
    }
 
    inline void CurTimeStep ( amrex::Real  a_dt ) const
    {
        m_dt = a_dt;
        m_linear_function->curTimeStep( a_dt );
    }
 
    void PrintParams () const override
    {
        amrex::Print()     << "Newton verbose:             " << (this->m_verbose?"true":"false") << "\n";
        amrex::Print()     << "Newton max iterations:      " << m_maxits << "\n";
        amrex::Print()     << "Newton relative tolerance:  " << m_rtol << "\n";
        amrex::Print()     << "Newton absolute tolerance:  " << m_atol << "\n";
        amrex::Print()     << "Newton require convergence: " << (m_require_convergence?"true":"false") << "\n";
        auto linsol_name = amrex::getEnumNameString(m_linear_solver_type);
        amrex::Print()     << "Newton linear solver:       " << linsol_name << "\n";
        amrex::Print()     << "Linear solver (" << linsol_name << ") verbose:            " << m_linsol_verbose_int << "\n";
        amrex::Print()     << "Linear solver (" << linsol_name << ") restart length:     " << m_linsol_restart_length << "\n";
        amrex::Print()     << "Linear solver (" << linsol_name << ") max iterations:     " << m_linsol_maxits << "\n";
        amrex::Print()     << "Linear solver (" << linsol_name << ") relative tolerance: " << m_linsol_rtol << "\n";
        amrex::Print()     << "Linear solver (" << linsol_name << ") absolute tolerance: " << m_linsol_atol << "\n";
        amrex::Print()     << "Preconditioner type:      " << amrex::getEnumNameString(m_pc_type) << "\n";
 
        m_linear_function->printParams();
    }
 
private:

    mutable Vec m_dU, m_F, m_R;

    Ops* m_ops = nullptr;

    bool m_require_convergence = true;

    amrex::Real m_rtol = 1.0e-6;

    amrex::Real m_atol = 0.;

    int m_maxits = 100;

    mutable int m_total_iters = 0;

    amrex::Real m_linsol_rtol = 1.0e-4;

    amrex::Real m_linsol_atol = 0.;

    int m_linsol_maxits = 1000;

    mutable int m_total_linsol_iters = 0;

    int m_linsol_verbose_int = 2;

    int m_linsol_restart_length = 30;

    PreconditionerType m_pc_type = PreconditionerType::none;
 
    mutable amrex::Real m_cur_time, m_dt;

    std::unique_ptr<JacobianFunctionMF<Vec,Ops>> m_linear_function;

    LinearSolverType m_linear_solver_type = LinearSolverType::amrex_gmres;

    std::unique_ptr<LinearSolver<Vec,JacobianFunctionMF<Vec,Ops>>> m_linear_solver;
 
    void ParseParameters ();

    void EvalResidual ( Vec&         a_F,
                  const Vec&         a_U,
                  const Vec&         a_b,
                        amrex::Real  a_time,
                        int          a_iter ) const;
 
};
 
template <class Vec, class Ops>
void NewtonSolver<Vec,Ops>::Define ( const Vec&  a_U,
                                     Ops*        a_ops )
{
    BL_PROFILE("NewtonSolver::Define()");
    WARPX_ALWAYS_ASSERT_WITH_MESSAGE(
        !this->m_is_defined,
        "Newton nonlinear solver object is already defined!");
 
    ParseParameters();
 
    m_dU.Define(a_U);
    m_F.Define(a_U); // residual function F(U) = U - b - R(U) = 0
    m_R.Define(a_U); // right hand side function R(U)
 
    m_ops = a_ops;
 
    m_linear_function = std::make_unique<JacobianFunctionMF<Vec,Ops>>();
    m_linear_function->define(m_F, m_ops, m_pc_type);
    this->m_usePC = m_linear_function->usePreconditioner();
 
    if (m_linear_solver_type == LinearSolverType::amrex_gmres) {
        m_linear_solver = std::make_unique<AMReXGMRES<Vec,JacobianFunctionMF<Vec,Ops>>>();
    } else if (m_linear_solver_type == LinearSolverType::petsc_ksp) {
#ifdef AMREX_USE_PETSC
        m_linear_solver = std::make_unique<PETScKSP<Vec,JacobianFunctionMF<Vec,Ops>>>();
#else
        WARPX_ABORT_WITH_MESSAGE("NewtonSolver::Define(): must compile with PETSc to use petsc_ksp (AMREX_USE_PETSC must be defined)");
#endif
    } else {
        WARPX_ABORT_WITH_MESSAGE("NewtonSolver::Define(): invalid linear solver type");
    }
    m_linear_solver->define(*m_linear_function);
    m_linear_solver->setVerbose( m_linsol_verbose_int );
    m_linear_solver->setRestartLength( m_linsol_restart_length );
    m_linear_solver->setMaxIters( m_linsol_maxits );
 
    this->m_is_defined = true;
 
    // Create diagnostic file and write header
    if (amrex::ParallelDescriptor::IOProcessor()
        && !this->m_diagnostic_file.empty()
        && !amrex::FileExists(this->m_diagnostic_file)) {
 
        std::filesystem::path const diagnostic_path(this->m_diagnostic_file);
        std::filesystem::path const diagnostic_dir = diagnostic_path.parent_path();
        if (!diagnostic_dir.empty()) {
            std::filesystem::create_directories(diagnostic_dir);
        }
 
        std::ofstream diagnostic_file{this->m_diagnostic_file, std::ofstream::out | std::ofstream::trunc};
        int c = 0;
        diagnostic_file << "#";
        diagnostic_file << "[" << c++ << "]step()";
        diagnostic_file << " ";
        diagnostic_file << "[" << c++ << "]time(s)";
        diagnostic_file << " ";
        diagnostic_file << "[" << c++ << "]iters";
        diagnostic_file << " ";
        diagnostic_file << "[" << c++ << "]total_iters";
        diagnostic_file << " ";
        diagnostic_file << "[" << c++ << "]norm_abs";
        diagnostic_file << " ";
        diagnostic_file << "[" << c++ << "]norm_rel";
        diagnostic_file << " ";
        diagnostic_file << "[" << c++ << "]gmres_iters";
        diagnostic_file << " ";
        diagnostic_file << "[" << c++ << "]gmres_total_iters";
        diagnostic_file << " ";
        diagnostic_file << "[" << c++ << "]gmres_last_res";
        diagnostic_file << "\n";
        diagnostic_file.close();
    }
}
 
template <class Vec, class Ops>
void NewtonSolver<Vec,Ops>::ParseParameters ()
{
    const amrex::ParmParse pp_newton("newton");
    pp_newton.query("verbose",             this->m_verbose);
    pp_newton.query("linear_solver",       m_linear_solver_type);
    pp_newton.query("absolute_tolerance",  m_atol);
    pp_newton.query("relative_tolerance",  m_rtol);
    pp_newton.query("max_iterations",      m_maxits);
    pp_newton.query("require_convergence", m_require_convergence);
    pp_newton.query("diagnostic_file",     this->m_diagnostic_file);
    pp_newton.query("diagnostic_interval", this->m_diagnostic_interval);
 
    const amrex::ParmParse pp_l(amrex::getEnumNameString(m_linear_solver_type));
    pp_l.query("verbose_int",         m_linsol_verbose_int);
    pp_l.query("restart_length",      m_linsol_restart_length);
    pp_l.query("absolute_tolerance",  m_linsol_atol);
    pp_l.query("relative_tolerance",  m_linsol_rtol);
    pp_l.query("max_iterations",      m_linsol_maxits);
 
    /* backward compatibility */
    const amrex::ParmParse pp_gmres("gmres");
    pp_gmres.query("verbose_int",         m_linsol_verbose_int);
    pp_gmres.query("restart_length",      m_linsol_restart_length);
    pp_gmres.query("absolute_tolerance",  m_linsol_atol);
    pp_gmres.query("relative_tolerance",  m_linsol_rtol);
    pp_gmres.query("max_iterations",      m_linsol_maxits);
 
    const amrex::ParmParse pp_jac("jacobian");
    pp_jac.query("pc_type", m_pc_type);
}
 
template <class Vec, class Ops>
void NewtonSolver<Vec,Ops>::Solve ( Vec&         a_U,
                              const Vec&         a_b,
                                    amrex::Real  a_time,
                                    amrex::Real  a_dt,
                                    int          a_step) const
{
    BL_PROFILE("NewtonSolver::Solve()");
    WARPX_ALWAYS_ASSERT_WITH_MESSAGE(
        this->m_is_defined,
        "NewtonSolver::Solve() called on undefined object");
    using namespace amrex::literals;
 
    //
    // Newton routine to solve nonlinear equation of form:
    // F(U) = U - b - R(U) = 0
    //
 
    CurTime(a_time);
    CurTimeStep(a_dt);
 
    amrex::Real norm_abs = 0.;
    amrex::Real norm0 = 1._rt;
    amrex::Real norm_rel = 0.;
 
    int iter;
    int linear_solver_iters = 0;
    for (iter = 0; iter < m_maxits;) {
 
        // Compute residual: F(U) = U - b - R(U)
        EvalResidual(m_F, a_U, a_b, a_time, iter);
 
        // Compute norm of the residual
        norm_abs = m_F.norm2();
        if (iter == 0) {
            if (norm_abs > 0.) { norm0 = norm_abs; }
            else { norm0 = 1._rt; }
        }
        norm_rel = norm_abs/norm0;
 
        // Check for convergence criteria
        if (this->m_verbose || iter == m_maxits) {
            amrex::Print() << "Newton: iteration = " << std::setw(3) << iter <<  ", norm = "
                           << std::scientific << std::setprecision(5) << norm_abs << " (abs.), "
                           << std::scientific << std::setprecision(5) << norm_rel << " (rel.)" << "\n";
        }
 
        if (norm_abs < m_atol) {
            if (this->m_verbose) {
                amrex::Print() << "Newton: exiting at iteration = " << std::setw(3) << iter
                               << ". Satisfied absolute tolerance " << m_atol << "\n";
            }
            break;
        }
 
        if (norm_rel < m_rtol) {
            if (this->m_verbose) {
                amrex::Print() << "Newton: exiting at iteration = " << std::setw(3) << iter
                               << ". Satisfied relative tolerance " << m_rtol << "\n";
            }
            break;
        }
 
        if (norm_abs > 100._rt*norm0) {
            amrex::Print() << "Newton: exiting at iteration = " << std::setw(3) << iter
                           << ". SOLVER DIVERGED! relative tolerance = " << m_rtol << "\n";
            std::stringstream convergenceMsg;
            convergenceMsg << "Newton: exiting at iteration " << std::setw(3) << iter <<
                              ". SOLVER DIVERGED! absolute norm = " << norm_abs <<
                              " has increased by 100X from that after first iteration.";
            WARPX_ABORT_WITH_MESSAGE(convergenceMsg.str());
        }
 
        // Solve linear system for Newton step [Jac]*dU = F
        m_dU.zero();
        m_linear_solver->solve( m_dU, m_F, m_linsol_rtol, m_linsol_atol );
        linear_solver_iters += m_linear_solver->getNumIters();
 
        // Update solution
        a_U -= m_dU;
 
        iter++;
        if (iter >= m_maxits) {
            if (this->m_verbose) {
                amrex::Print() << "Newton: exiting at iter = " << std::setw(3) << iter
                               << ". Maximum iteration reached: iter = " << m_maxits << "\n";
            }
            break;
        }
 
    }
 
    // Update total iteration count
    m_total_iters += iter;
    m_total_linsol_iters += linear_solver_iters;
 
    if (m_rtol > 0. && iter == m_maxits) {
       std::stringstream convergenceMsg;
       convergenceMsg << "Newton solver failed to converge after " << iter <<
                         " iterations. Relative norm is " << norm_rel <<
                         " and the relative tolerance is " << m_rtol <<
                         ". Absolute norm is " << norm_abs <<
                         " and the absolute tolerance is " << m_atol;
       if (this->m_verbose) { amrex::Print() << convergenceMsg.str() << "\n"; }
       if (m_require_convergence) {
           WARPX_ABORT_WITH_MESSAGE(convergenceMsg.str());
       } else {
           ablastr::warn_manager::WMRecordWarning("NewtonSolver", convergenceMsg.str());
       }
    }
 
    if (!this->m_diagnostic_file.empty() && amrex::ParallelDescriptor::IOProcessor() &&
        ((a_step+1)%this->m_diagnostic_interval==0 || a_step==0)) {
        std::ofstream diagnostic_file{this->m_diagnostic_file, std::ofstream::out | std::ofstream::app};
        diagnostic_file << std::setprecision(14);
        diagnostic_file << a_step+1;
        diagnostic_file << " ";
        diagnostic_file << a_time + a_dt;
        diagnostic_file << " ";
        diagnostic_file << iter;
        diagnostic_file << " ";
        diagnostic_file << m_total_iters;
        diagnostic_file << " ";
        diagnostic_file << norm_abs;
        diagnostic_file << " ";
        diagnostic_file << norm_rel;
        diagnostic_file << " ";
        diagnostic_file << linear_solver_iters;
        diagnostic_file << " ";
        diagnostic_file << m_total_linsol_iters;
        diagnostic_file << " ";
        diagnostic_file << m_linear_solver->getResidualNorm();
        diagnostic_file << "\n";
        diagnostic_file.close();
    }
 
}
 
template <class Vec, class Ops>
void NewtonSolver<Vec,Ops>::EvalResidual ( Vec&         a_F,
                                     const Vec&         a_U,
                                     const Vec&         a_b,
                                           amrex::Real  a_time,
                                           int          a_iter ) const
{
    BL_PROFILE("NewtonSolver::EvalResidual()");
    m_ops->ComputeRHS( m_R, a_U, a_time, a_iter, false );
 
    // set base U and R(U) for matrix-free Jacobian action calculation
    m_linear_function->setBaseSolution(a_U);
    m_linear_function->setBaseRHS(m_R);
 
    // update preconditioner
    m_linear_function->updatePreCondMat(a_U);
 
    // Compute residual: F(U) = U - b - R(U)
    a_F.Copy(a_U);
    a_F -= m_R;
    a_F -= a_b;
 
}
 
#endif