StateSolveLinear.cpp

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#include <polyfem/State.hpp>
 
#include <polyfem/assembler/Mass.hpp>
#include <polyfem/assembler/AssemblerUtils.hpp>
 
#include <polyfem/time_integrator/ImplicitTimeIntegrator.hpp>
#include <polyfem/time_integrator/BDF.hpp>
 
#include <polyfem/solver/forms/BodyForm.hpp>
#include <polyfem/solver/forms/ElasticForm.hpp>
#include <polyfem/solver/forms/InertiaForm.hpp>
#include <polysolve/linear/FEMSolver.hpp>
 
#include <polyfem/utils/Timer.hpp>
 
#include <unsupported/Eigen/SparseExtra>
#include <polyfem/io/Evaluator.hpp>
 
namespace polyfem
{
    using namespace mesh;
    using namespace time_integrator;
    using namespace utils;
    using namespace solver;
    using namespace io;
 
    void State::build_stiffness_mat(StiffnessMatrix &stiffness)
    {
        igl::Timer timer;
        timer.start();
        logger().info("Assembling stiffness mat...");
        assert(assembler->is_linear());
 
        if (mixed_assembler != nullptr)
        {
 
            StiffnessMatrix velocity_stiffness, mixed_stiffness, pressure_stiffness;
            assembler->assemble(mesh->is_volume(), n_bases, bases, geom_bases(), ass_vals_cache, 0, velocity_stiffness);
            mixed_assembler->assemble(mesh->is_volume(), n_pressure_bases, n_bases, pressure_bases, bases, geom_bases(), pressure_ass_vals_cache, ass_vals_cache, 0, mixed_stiffness);
            pressure_assembler->assemble(mesh->is_volume(), n_pressure_bases, pressure_bases, geom_bases(), pressure_ass_vals_cache, 0, pressure_stiffness);
 
            const int problem_dim = problem->is_scalar() ? 1 : mesh->dimension();
 
            assembler::AssemblerUtils::merge_mixed_matrices(n_bases, n_pressure_bases, problem_dim, use_avg_pressure ? assembler->is_fluid() : false,
                                                            velocity_stiffness, mixed_stiffness, pressure_stiffness,
                                                            stiffness);
        }
        else
        {
            assembler->assemble(mesh->is_volume(), n_bases, bases, geom_bases(), ass_vals_cache, 0, stiffness);
        }
 
        timer.stop();
        timings.assembling_stiffness_mat_time = timer.getElapsedTime();
        logger().info(" took {}s", timings.assembling_stiffness_mat_time);
 
        stats.nn_zero = stiffness.nonZeros();
        stats.num_dofs = stiffness.rows();
        stats.mat_size = (long long)stiffness.rows() * (long long)stiffness.cols();
        logger().info("sparsity: {}/{}", stats.nn_zero, stats.mat_size);
 
        const std::string full_mat_path = args["output"]["data"]["full_mat"];
        if (!full_mat_path.empty())
        {
            Eigen::saveMarket(stiffness, full_mat_path);
        }
    }
 
    void State::solve_linear(
        const std::unique_ptr<polysolve::linear::Solver> &solver,
        StiffnessMatrix &A,
        Eigen::VectorXd &b,
        const bool compute_spectrum,
        Eigen::MatrixXd &sol, Eigen::MatrixXd &pressure)
    {
        assert(assembler->is_linear() && !is_contact_enabled());
        assert(solve_data.rhs_assembler != nullptr);
 
        const int problem_dim = problem->is_scalar() ? 1 : mesh->dimension();
        const int full_size = A.rows();
        int precond_num = problem_dim * n_bases;
 
        std::vector<int> boundary_nodes_tmp;
        if (has_periodic_bc())
        {
            boundary_nodes_tmp = periodic_bc->full_to_periodic(boundary_nodes);
            precond_num = periodic_bc->full_to_periodic(A);
            Eigen::MatrixXd tmp = periodic_bc->full_to_periodic(b, true);
            b = tmp;
        }
        else
            boundary_nodes_tmp = boundary_nodes;
 
        Eigen::VectorXd x;
        if (optimization_enabled == solver::CacheLevel::Derivatives)
        {
            auto A_tmp = A;
            prefactorize(*solver, A, boundary_nodes_tmp, precond_num, args["output"]["data"]["stiffness_mat"]);
            dirichlet_solve_prefactorized(*solver, A_tmp, b, boundary_nodes_tmp, x);
        }
        else
        {
            stats.spectrum = dirichlet_solve(
                *solver, A, b, boundary_nodes_tmp, x, precond_num, args["output"]["data"]["stiffness_mat"], compute_spectrum,
                assembler->is_fluid(), use_avg_pressure);
        }
        if (has_periodic_bc())
        {
            sol = periodic_bc->periodic_to_full(full_size, x);
            if (args["/boundary_conditions/periodic_boundary/force_zero_mean"_json_pointer].get<bool>())
            {
                Eigen::VectorXd integral = Evaluator::integrate_function(bases, geom_bases(), sol, mesh->dimension(), problem_dim);
                double area = Evaluator::integrate_function(bases, geom_bases(), Eigen::VectorXd::Ones(n_bases), mesh->dimension(), 1)(0);
                for (int d = 0; d < problem_dim; d++)
                    sol(Eigen::seqN(d, n_bases, problem_dim), 0).array() -= integral(d) / area;
            }
        }
        else
            sol = x; // Explicit copy because sol is a MatrixXd (with one column)
 
        solver->get_info(stats.solver_info);
 
        const auto error = (A * x - b).norm();
 
        if (error > 1e-4)
            logger().error("Solver error: {}", error);
        else
            logger().debug("Solver error: {}", error);
 
        if (mixed_assembler != nullptr)
            sol_to_pressure(sol, pressure);
    }
 
    void State::solve_linear(Eigen::MatrixXd &sol, Eigen::MatrixXd &pressure)
    {
        assert(!problem->is_time_dependent());
        assert(assembler->is_linear() && !is_contact_enabled());
 
        // --------------------------------------------------------------------
        if (lin_solver_cached)
            lin_solver_cached.reset();
 
        lin_solver_cached =
            polysolve::linear::Solver::create(args["solver"]["linear"], logger());
        logger().info("{}...", lin_solver_cached->name());
 
        // --------------------------------------------------------------------
 
        solve_data.rhs_assembler->set_bc(
            local_boundary, boundary_nodes, n_boundary_samples(),
            (assembler->name() != "Bilaplacian") ? local_neumann_boundary : std::vector<LocalBoundary>(), rhs);
 
        StiffnessMatrix A;
        build_stiffness_mat(A);
 
        Eigen::VectorXd b = rhs;
 
        // --------------------------------------------------------------------
 
        solve_linear(lin_solver_cached, A, b, args["output"]["advanced"]["spectrum"], sol, pressure);
    }
 
    void State::init_linear_solve(Eigen::MatrixXd &sol, const double t)
    {
        assert(sol.cols() == 1);
        assert(assembler->is_linear() && !is_contact_enabled()); // linear
 
        if (mixed_assembler != nullptr)
            return;
 
        const int ndof = n_bases * mesh->dimension();
 
        solve_data.elastic_form = std::make_shared<ElasticForm>(
            n_bases, bases, geom_bases(),
            *assembler, ass_vals_cache,
            t, problem->is_time_dependent() ? args["time"]["dt"].get<double>() : 0.0,
            mesh->is_volume());
 
        solve_data.body_form = std::make_shared<BodyForm>(
            ndof, n_pressure_bases,
            boundary_nodes, local_boundary, local_neumann_boundary, n_boundary_samples(),
            rhs, *solve_data.rhs_assembler,
            mass_matrix_assembler->density(),
            /*is_formulation_mixed=*/false, problem->is_time_dependent());
        solve_data.body_form->update_quantities(t, sol);
 
        solve_data.inertia_form = nullptr;
        solve_data.damping_form = nullptr;
        if (problem->is_time_dependent())
        {
            solve_data.time_integrator = time_integrator::ImplicitTimeIntegrator::construct_time_integrator(args["time"]["integrator"]);
            solve_data.inertia_form = std::make_shared<InertiaForm>(mass, *solve_data.time_integrator);
        }
 
        solve_data.contact_form = nullptr;
        solve_data.friction_form = nullptr;
 
        // Initialize time integrator
        if (problem->is_time_dependent() && assembler->is_tensor())
        {
            POLYFEM_SCOPED_TIMER("Initialize 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());
 
            const double dt = args["time"]["dt"];
            solve_data.time_integrator->init(solution, velocity, acceleration, dt);
        }
        solve_data.update_dt();
    }
 
    void State::solve_transient_linear(const int time_steps, const double t0, const double dt, Eigen::MatrixXd &sol, Eigen::MatrixXd &pressure)
    {
        assert(sol.cols() == 1);
        assert(problem->is_time_dependent());
        assert(assembler->is_linear() && !is_contact_enabled());
        assert(solve_data.rhs_assembler != nullptr);
 
        const bool is_scalar_or_mixed = problem->is_scalar() || mixed_assembler != nullptr;
 
        // --------------------------------------------------------------------
 
        auto solver =
            polysolve::linear::Solver::create(args["solver"]["linear"], logger());
        logger().info("{}...", solver->name());
 
        // --------------------------------------------------------------------
 
        std::shared_ptr<ImplicitTimeIntegrator> time_integrator;
        if (is_scalar_or_mixed)
        {
            time_integrator = std::make_shared<BDF>();
            time_integrator->set_parameters(args["time"]);
            time_integrator->init(sol, Eigen::VectorXd::Zero(sol.size()), Eigen::VectorXd::Zero(sol.size()), dt);
        }
        else
        {
            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());
 
            time_integrator = ImplicitTimeIntegrator::construct_time_integrator(args["time"]["integrator"]);
            time_integrator->init(solution, velocity, acceleration, dt);
        }
 
        // --------------------------------------------------------------------
 
        const int n_b_samples = n_boundary_samples();
 
        if (optimization_enabled != solver::CacheLevel::None)
        {
            log_and_throw_adjoint_error("Transient linear problems are not differentiable yet!");
            cache_transient_adjoint_quantities(0, sol, Eigen::MatrixXd::Zero(mesh->dimension(), mesh->dimension()));
        }
 
        Eigen::MatrixXd current_rhs = rhs;
 
        StiffnessMatrix stiffness;
        build_stiffness_mat(stiffness);
 
        // --------------------------------------------------------------------
        // TODO rebuild stiffnes if material are time dept
        for (int t = 1; t <= time_steps; ++t)
        {
            const double time = t0 + t * dt;
 
            StiffnessMatrix A;
            Eigen::VectorXd b;
            bool compute_spectrum = args["output"]["advanced"]["spectrum"];
 
            if (is_scalar_or_mixed)
            {
                solve_data.rhs_assembler->compute_energy_grad(
                    local_boundary, boundary_nodes, mass_matrix_assembler->density(), n_b_samples, local_neumann_boundary, rhs, time,
                    current_rhs);
 
                solve_data.rhs_assembler->set_bc(
                    local_boundary, boundary_nodes, n_b_samples, local_neumann_boundary, current_rhs, sol, time);
 
                if (mixed_assembler != nullptr)
                {
                    // divergence free
                    int fluid_offset = use_avg_pressure ? (assembler->is_fluid() ? 1 : 0) : 0;
                    current_rhs
                        .block(
                            current_rhs.rows() - n_pressure_bases - use_avg_pressure, 0,
                            n_pressure_bases + use_avg_pressure, current_rhs.cols())
                        .setZero();
                }
 
                std::shared_ptr<BDF> bdf = std::dynamic_pointer_cast<BDF>(time_integrator);
                A = mass / bdf->beta_dt() + stiffness;
                b = (mass * bdf->weighted_sum_x_prevs()) / bdf->beta_dt();
                for (int i : boundary_nodes)
                    b[i] = 0;
                b += current_rhs;
 
                compute_spectrum &= t == time_steps;
            }
            else
            {
                solve_data.rhs_assembler->assemble(mass_matrix_assembler->density(), current_rhs, time);
 
                current_rhs *= -1;
 
                solve_data.rhs_assembler->set_bc(
                    std::vector<LocalBoundary>(), std::vector<int>(), n_b_samples, local_neumann_boundary, current_rhs, sol, time);
 
                current_rhs *= time_integrator->acceleration_scaling();
                current_rhs += mass * time_integrator->x_tilde();
 
                solve_data.rhs_assembler->set_bc(
                    local_boundary, boundary_nodes, n_b_samples, std::vector<LocalBoundary>(), current_rhs, sol, time);
 
                A = stiffness * time_integrator->acceleration_scaling() + mass;
                b = current_rhs;
 
                compute_spectrum &= t == 1;
            }
 
            solve_linear(solver, A, b, compute_spectrum, sol, pressure);
 
            if (optimization_enabled != solver::CacheLevel::None)
            {
                log_and_throw_adjoint_error("Transient linear problems are not differentiable yet!");
                cache_transient_adjoint_quantities(t, sol, Eigen::MatrixXd::Zero(mesh->dimension(), mesh->dimension()));
            }
 
            time_integrator->update_quantities(sol);
 
            save_timestep(time, t, t0, dt, sol, pressure);
            logger().info("{}/{}  t={}", t, time_steps, time);
        }
 
        time_integrator->save_state(resolve_output_path(args["output"]["data"]["state"]));
    }
} // namespace polyfem