StateSolveNonlinear.cpp

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#include <polyfem/State.hpp>
 
#include <polyfem/assembler/Mass.hpp>
#include <polyfem/assembler/ViscousDamping.hpp>
 
#include <polyfem/solver/forms/BodyForm.hpp>
#include <polyfem/solver/forms/ContactForm.hpp>
#include <polyfem/solver/forms/ElasticForm.hpp>
#include <polyfem/solver/forms/FrictionForm.hpp>
#include <polyfem/solver/forms/InertiaForm.hpp>
#include <polyfem/solver/forms/LaggedRegForm.hpp>
#include <polyfem/solver/forms/RayleighDampingForm.hpp>
#include <polyfem/solver/forms/BCLagrangianForm.hpp>
 
#include <polyfem/solver/NLProblem.hpp>
#include <polyfem/solver/ALSolver.hpp>
#include <polyfem/solver/SolveData.hpp>
#include <polyfem/io/MshWriter.hpp>
#include <polyfem/io/OBJWriter.hpp>
#include <polyfem/io/OutData.hpp>
#include <polyfem/utils/MatrixUtils.hpp>
#include <polyfem/utils/Timer.hpp>
#include <polyfem/utils/JSONUtils.hpp>
#include <polyfem/utils/BoundarySampler.hpp>
 
#include <ipc/ipc.hpp>
 
namespace polyfem
{
    using namespace mesh;
    using namespace solver;
    using namespace time_integrator;
    using namespace io;
    using namespace utils;
 
    std::shared_ptr<polysolve::nonlinear::Solver> State::make_nl_solver(bool for_al) const
    {
        return polysolve::nonlinear::Solver::create(for_al ? args["solver"]["augmented_lagrangian"]["nonlinear"] : args["solver"]["nonlinear"], args["solver"]["linear"], units.characteristic_length(), logger());
    }
 
    void State::solve_transient_tensor_nonlinear(const int time_steps, const double t0, const double dt, Eigen::MatrixXd &sol)
    {
        init_nonlinear_tensor_solve(sol, t0 + dt);
 
        // Write the total energy to a CSV file
        int save_i = 0;
        EnergyCSVWriter energy_csv(resolve_output_path("energy.csv"), solve_data);
        RuntimeStatsCSVWriter stats_csv(resolve_output_path("stats.csv"), *this, t0, dt);
        const bool remesh_enabled = args["space"]["remesh"]["enabled"];
        // const double save_dt = remesh_enabled ? (dt / 3) : dt;
 
        // Save the initial solution
        energy_csv.write(save_i, sol);
        save_timestep(t0, save_i, t0, dt, sol, Eigen::MatrixXd()); // no pressure
        save_i++;
 
        if (optimization_enabled != solver::CacheLevel::None)
            cache_transient_adjoint_quantities(0, sol, Eigen::MatrixXd::Zero(mesh->dimension(), mesh->dimension()));
 
        for (int t = 1; t <= time_steps; ++t)
        {
            double forward_solve_time = 0, remeshing_time = 0, global_relaxation_time = 0;
 
            {
                POLYFEM_SCOPED_TIMER(forward_solve_time);
                solve_tensor_nonlinear(sol, t);
            }
 
            if (remesh_enabled)
            {
                energy_csv.write(save_i, sol);
                // save_timestep(t0 + dt * t, save_i, t0, save_dt, sol, Eigen::MatrixXd()); // no pressure
                save_i++;
 
                bool remesh_success;
                {
                    POLYFEM_SCOPED_TIMER(remeshing_time);
                    remesh_success = this->remesh(t0 + dt * t, dt, sol);
                }
 
                // Save the solution after remeshing
                energy_csv.write(save_i, sol);
                // save_timestep(t0 + dt * t, save_i, t0, save_dt, sol, Eigen::MatrixXd()); // no pressure
                save_i++;
 
                // Only do global relaxation if remeshing was successful
                if (remesh_success)
                {
                    POLYFEM_SCOPED_TIMER(global_relaxation_time);
                    solve_tensor_nonlinear(sol, t, false); // solve the scene again after remeshing
                }
            }
 
            // Always save the solution for consistency
            energy_csv.write(save_i, sol);
            save_timestep(t0 + dt * t, t, t0, dt, sol, Eigen::MatrixXd()); // no pressure
            save_i++;
 
            if (optimization_enabled != solver::CacheLevel::None)
            {
                cache_transient_adjoint_quantities(t, sol, Eigen::MatrixXd::Zero(mesh->dimension(), mesh->dimension()));
            }
 
            {
                POLYFEM_SCOPED_TIMER("Update quantities");
 
                solve_data.time_integrator->update_quantities(sol);
 
                solve_data.nl_problem->update_quantities(t0 + (t + 1) * dt, sol);
 
                solve_data.update_dt();
                solve_data.update_barrier_stiffness(sol);
            }
 
            logger().info("{}/{}  t={}", t, time_steps, t0 + dt * t);
 
            const std::string rest_mesh_path = args["output"]["data"]["rest_mesh"].get<std::string>();
            if (!rest_mesh_path.empty())
            {
                Eigen::MatrixXd V;
                Eigen::MatrixXi F;
                build_mesh_matrices(V, F);
                io::MshWriter::write(
                    resolve_output_path(fmt::format(args["output"]["data"]["rest_mesh"], t)),
                    V, F, mesh->get_body_ids(), mesh->is_volume(), /*binary=*/true);
            }
 
            const std::string &state_path = resolve_output_path(fmt::format(args["output"]["data"]["state"], t));
            if (!state_path.empty())
                solve_data.time_integrator->save_state(state_path);
 
            // save restart file
            save_restart_json(t0, dt, t);
            if (remesh_enabled)
                stats_csv.write(t, forward_solve_time, remeshing_time, global_relaxation_time, sol);
        }
    }
 
    void State::init_nonlinear_tensor_solve(Eigen::MatrixXd &sol, const double t, const bool init_time_integrator)
    {
        assert(sol.cols() == 1);
        assert(!assembler->is_linear() || is_contact_enabled()); // non-linear
        assert(!problem->is_scalar());                           // tensor
        assert(mixed_assembler == nullptr);
 
        if (optimization_enabled != solver::CacheLevel::None)
        {
            if (initial_sol_update.size() == ndof())
                sol = initial_sol_update;
            else
                initial_sol_update = sol;
        }
 
        // --------------------------------------------------------------------
        // Check for initial intersections
        if (is_contact_enabled())
        {
            POLYFEM_SCOPED_TIMER("Check for initial intersections");
 
            const Eigen::MatrixXd displaced = collision_mesh.displace_vertices(
                utils::unflatten(sol, mesh->dimension()));
 
            if (ipc::has_intersections(collision_mesh, displaced, args["solver"]["contact"]["CCD"]["broad_phase"]))
            {
                OBJWriter::write(
                    resolve_output_path("intersection.obj"), displaced,
                    collision_mesh.edges(), collision_mesh.faces());
                log_and_throw_error("Unable to solve, initial solution has intersections!");
            }
        }
 
        // --------------------------------------------------------------------
        // Initialize time integrator
        if (problem->is_time_dependent())
        {
            if (init_time_integrator)
            {
                POLYFEM_SCOPED_TIMER("Initialize time integrator");
                solve_data.time_integrator = ImplicitTimeIntegrator::construct_time_integrator(args["time"]["integrator"]);
 
                Eigen::MatrixXd solution, velocity, acceleration;
                initial_solution(solution); // Reload this because we need all previous solutions
                solution.col(0) = sol;      // Make sure the current solution is the same as `sol`
                assert(solution.rows() == sol.size());
                initial_velocity(velocity);
                assert(velocity.rows() == sol.size());
                initial_acceleration(acceleration);
                assert(acceleration.rows() == sol.size());
 
                if (optimization_enabled != solver::CacheLevel::None)
                {
                    if (initial_vel_update.size() == ndof())
                        velocity = initial_vel_update;
                    else
                        initial_vel_update = velocity;
                }
 
                const double dt = args["time"]["dt"];
                solve_data.time_integrator->init(solution, velocity, acceleration, dt);
            }
            assert(solve_data.time_integrator != nullptr);
        }
        else
        {
            solve_data.time_integrator = nullptr;
        }
 
        // --------------------------------------------------------------------
        // Initialize forms
 
        damping_assembler = std::make_shared<assembler::ViscousDamping>();
        set_materials(*damping_assembler);
 
        elasticity_pressure_assembler = build_pressure_assembler();
 
        // for backward solve
        damping_prev_assembler = std::make_shared<assembler::ViscousDampingPrev>();
        set_materials(*damping_prev_assembler);
 
        const std::vector<std::shared_ptr<Form>> forms = solve_data.init_forms(
            // General
            units,
            mesh->dimension(), t,
            // Elastic form
            n_bases, bases, geom_bases(), *assembler, ass_vals_cache, mass_ass_vals_cache,
            // Body form
            n_pressure_bases, boundary_nodes, local_boundary,
            local_neumann_boundary,
            n_boundary_samples(), rhs, sol, mass_matrix_assembler->density(),
            // Pressure form
            local_pressure_boundary, local_pressure_cavity, elasticity_pressure_assembler,
            // Inertia form
            args.value("/time/quasistatic"_json_pointer, true), mass,
            damping_assembler->is_valid() ? damping_assembler : nullptr,
            // Lagged regularization form
            args["solver"]["advanced"]["lagged_regularization_weight"],
            args["solver"]["advanced"]["lagged_regularization_iterations"],
            // Augmented lagrangian form
            obstacle.ndof(),
            // Contact form
            args["contact"]["enabled"], args["contact"]["periodic"].get<bool>() ? periodic_collision_mesh : collision_mesh, args["contact"]["dhat"],
            avg_mass, args["contact"]["use_convergent_formulation"],
            args["solver"]["contact"]["barrier_stiffness"],
            args["solver"]["contact"]["CCD"]["broad_phase"],
            args["solver"]["contact"]["CCD"]["tolerance"],
            args["solver"]["contact"]["CCD"]["max_iterations"],
            optimization_enabled == solver::CacheLevel::Derivatives,
            // Homogenization
            macro_strain_constraint,
            // Periodic contact
            args["contact"]["periodic"], periodic_collision_mesh_to_basis,
            // Friction form
            args["contact"]["friction_coefficient"],
            args["contact"]["epsv"],
            args["solver"]["contact"]["friction_iterations"],
            // Rayleigh damping form
            args["solver"]["rayleigh_damping"]);
 
        for (const auto &form : forms)
            form->set_output_dir(output_dir);
 
        if (solve_data.contact_form != nullptr)
            solve_data.contact_form->save_ccd_debug_meshes = args["output"]["advanced"]["save_ccd_debug_meshes"];
 
        // --------------------------------------------------------------------
        // Initialize nonlinear problems
 
        const int ndof = n_bases * mesh->dimension();
        solve_data.nl_problem = std::make_shared<NLProblem>(
            ndof, boundary_nodes, local_boundary, n_boundary_samples(),
            *solve_data.rhs_assembler, periodic_bc, t, forms);
        solve_data.nl_problem->init(sol);
        solve_data.nl_problem->update_quantities(t, sol);
        // --------------------------------------------------------------------
 
        stats.solver_info = json::array();
    }
 
    void State::solve_tensor_nonlinear(Eigen::MatrixXd &sol, const int t, const bool init_lagging)
    {
        assert(solve_data.nl_problem != nullptr);
        NLProblem &nl_problem = *(solve_data.nl_problem);
 
        assert(sol.size() == rhs.size());
 
        if (nl_problem.uses_lagging())
        {
            if (init_lagging)
            {
                POLYFEM_SCOPED_TIMER("Initializing lagging");
                nl_problem.init_lagging(sol); // TODO: this should be u_prev projected
            }
            logger().info("Lagging iteration 1:");
        }
 
        // ---------------------------------------------------------------------
 
        // Save the subsolve sequence for debugging
        int subsolve_count = 0;
        save_subsolve(subsolve_count, t, sol, Eigen::MatrixXd()); // no pressure
 
        // ---------------------------------------------------------------------
 
        std::shared_ptr<polysolve::nonlinear::Solver> nl_solver = make_nl_solver(true);
 
        ALSolver al_solver(
            solve_data.al_lagr_form, solve_data.al_pen_form,
            args["solver"]["augmented_lagrangian"]["initial_weight"],
            args["solver"]["augmented_lagrangian"]["scaling"],
            args["solver"]["augmented_lagrangian"]["max_weight"],
            args["solver"]["augmented_lagrangian"]["eta"],
            [&](const Eigen::VectorXd &x) {
                this->solve_data.update_barrier_stiffness(sol);
            });
 
        al_solver.post_subsolve = [&](const double al_weight) {
            stats.solver_info.push_back(
                {{"type", al_weight > 0 ? "al" : "rc"},
                 {"t", t}, // TODO: null if static?
                 {"info", nl_solver->info()}});
            if (al_weight > 0)
                stats.solver_info.back()["weight"] = al_weight;
            save_subsolve(++subsolve_count, t, sol, Eigen::MatrixXd()); // no pressure
        };
 
        Eigen::MatrixXd prev_sol = sol;
        al_solver.solve_al(nl_solver, nl_problem, sol);
 
        nl_solver = make_nl_solver(false);
        al_solver.solve_reduced(nl_solver, nl_problem, sol);
 
        // ---------------------------------------------------------------------
 
        // TODO: Make this more general
        const double lagging_tol = args["solver"]["contact"].value("friction_convergence_tol", 1e-2) * units.characteristic_length();
 
        if (optimization_enabled != solver::CacheLevel::Derivatives)
        {
            // Lagging loop (start at 1 because we already did an iteration above)
            bool lagging_converged = !nl_problem.uses_lagging();
            for (int lag_i = 1; !lagging_converged; lag_i++)
            {
                Eigen::VectorXd tmp_sol = nl_problem.full_to_reduced(sol);
 
                // Update the lagging before checking for convergence
                nl_problem.update_lagging(tmp_sol, lag_i);
 
                // Check if lagging converged
                Eigen::VectorXd grad;
                nl_problem.gradient(tmp_sol, grad);
                const double delta_x_norm = (prev_sol - sol).lpNorm<Eigen::Infinity>();
                logger().debug("Lagging convergence grad_norm={:g} tol={:g} (||Δx||={:g})", grad.norm(), lagging_tol, delta_x_norm);
                if (grad.norm() <= lagging_tol)
                {
                    logger().info(
                        "Lagging converged in {:d} iteration(s) (grad_norm={:g} tol={:g})",
                        lag_i, grad.norm(), lagging_tol);
                    lagging_converged = true;
                    break;
                }
 
                if (delta_x_norm <= 1e-12)
                {
                    logger().warn(
                        "Lagging produced tiny update between iterations {:d} and {:d} (grad_norm={:g} grad_tol={:g} ||Δx||={:g} Δx_tol={:g}); stopping early",
                        lag_i - 1, lag_i, grad.norm(), lagging_tol, delta_x_norm, 1e-6);
                    lagging_converged = false;
                    break;
                }
 
                // Check for convergence first before checking if we can continue
                if (lag_i >= nl_problem.max_lagging_iterations())
                {
                    logger().warn(
                        "Lagging failed to converge with {:d} iteration(s) (grad_norm={:g} tol={:g})",
                        lag_i, grad.norm(), lagging_tol);
                    lagging_converged = false;
                    break;
                }
 
                // Solve the problem with the updated lagging
                logger().info("Lagging iteration {:d}:", lag_i + 1);
                nl_problem.init(sol);
                solve_data.update_barrier_stiffness(sol);
                nl_solver->minimize(nl_problem, tmp_sol);
                prev_sol = sol;
                sol = nl_problem.reduced_to_full(tmp_sol);
 
                // Save the subsolve sequence for debugging and info
                stats.solver_info.push_back(
                    {{"type", "rc"},
                     {"t", t}, // TODO: null if static?
                     {"lag_i", lag_i},
                     {"info", nl_solver->info()}});
                save_subsolve(++subsolve_count, t, sol, Eigen::MatrixXd()); // no pressure
            }
        }
    }
} // namespace polyfem