OutData.cpp

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#include "OutData.hpp"
 
#include "Evaluator.hpp"
 
#include <polyfem/State.hpp>
 
#include <polyfem/assembler/ElementAssemblyValues.hpp>
#include <polyfem/assembler/AssemblyValues.hpp>
#include <polyfem/assembler/MatParams.hpp>
#include <polyfem/assembler/Mass.hpp>
 
#include <polyfem/basis/ElementBases.hpp>
 
#include <polyfem/mesh/MeshUtils.hpp>
#include <polyfem/mesh/mesh2D/Mesh2D.hpp>
#include <polyfem/mesh/mesh3D/Mesh3D.hpp>
 
#include <polyfem/time_integrator/ImplicitTimeIntegrator.hpp>
 
#include <polyfem/solver/forms/SmoothContactForm.hpp>
#include <polyfem/solver/forms/FrictionForm.hpp>
#include <polyfem/solver/NLProblem.hpp>
#include <polyfem/solver/forms/BodyForm.hpp>
#include <polyfem/solver/forms/BodyForm.hpp>
#include <polyfem/solver/forms/BarrierContactForm.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/lagrangian/AugmentedLagrangianForm.hpp>
 
#include <polyfem/utils/EdgeSampler.hpp>
#include <polyfem/utils/Logger.hpp>
#include <polyfem/utils/par_for.hpp>
#include <polyfem/utils/BoundarySampler.hpp>
#include <polyfem/utils/Timer.hpp>
#include <polyfem/utils/MaybeParallelFor.hpp>
#include <polyfem/utils/getRSS.h>
 
#include <polyfem/autogen/auto_p_bases.hpp>
#include <polyfem/autogen/auto_q_bases.hpp>
#include <polyfem/autogen/prism_bases.hpp>
 
#include <paraviewo/VTMWriter.hpp>
#include <paraviewo/PVDWriter.hpp>
 
#include <SimpleBVH/BVH.hpp>
 
#include <igl/write_triangle_mesh.h>
#include <igl/edges.h>
#include <igl/facet_adjacency_matrix.h>
#include <igl/connected_components.h>
 
#include <ipc/ipc.hpp>
 
#include <filesystem>
 
namespace polyfem::io
{
    using CellType = paraviewo::CellType;
    using CellElement = paraviewo::CellElement;
 
    namespace
    {
        void compute_traction_forces(const State &state, const Eigen::MatrixXd &solution, const double t, Eigen::MatrixXd &traction_forces, bool skip_dirichlet = true)
        {
            int actual_dim = 1;
            if (!state.problem->is_scalar())
                actual_dim = state.mesh->dimension();
            else
                return;
 
            const std::vector<basis::ElementBases> &bases = state.bases;
            const std::vector<basis::ElementBases> &gbases = state.geom_bases();
 
            Eigen::MatrixXd uv, samples, gtmp, rhs_fun, deform_mat, trafo;
            Eigen::VectorXi global_primitive_ids;
            Eigen::MatrixXd points, normals;
            Eigen::VectorXd weights;
            polyfem::assembler::ElementAssemblyValues vals;
 
            traction_forces.setZero(state.n_bases * actual_dim, 1);
 
            for (const auto &lb : state.total_local_boundary)
            {
                const int e = lb.element_id();
                bool has_samples = utils::BoundarySampler::boundary_quadrature(lb, state.n_boundary_samples(), *state.mesh, false, uv, points, normals, weights, global_primitive_ids);
 
                if (!has_samples)
                    continue;
 
                const basis::ElementBases &gbs = gbases[e];
                const basis::ElementBases &bs = bases[e];
 
                vals.compute(e, state.mesh->is_volume(), points, bs, gbs);
 
                for (int n = 0; n < normals.rows(); ++n)
                {
                    trafo = vals.jac_it[n].inverse();
 
                    if (solution.size() > 0)
                    {
                        assert(actual_dim == 2 || actual_dim == 3);
                        deform_mat.resize(actual_dim, actual_dim);
                        deform_mat.setZero();
                        for (const auto &b : vals.basis_values)
                        {
                            for (const auto &g : b.global)
                            {
                                for (int d = 0; d < actual_dim; ++d)
                                {
                                    deform_mat.row(d) += solution(g.index * actual_dim + d) * b.grad.row(n);
                                }
                            }
                        }
 
                        trafo += deform_mat;
                    }
 
                    normals.row(n) = normals.row(n) * trafo.inverse();
                    normals.row(n).normalize();
                }
 
                std::vector<assembler::Assembler::NamedMatrix> tensor_flat;
                state.assembler->compute_tensor_value(assembler::OutputData(t, e, bs, gbs, points, solution), tensor_flat);
 
                for (long n = 0; n < vals.basis_values.size(); ++n)
                {
                    const polyfem::assembler::AssemblyValues &v = vals.basis_values[n];
 
                    const int g_index = v.global[0].index * actual_dim;
 
                    for (int q = 0; q < points.rows(); ++q)
                    {
                        // TF computed only from cauchy stress
                        assert(tensor_flat[0].first == "cauchy_stess");
                        assert(tensor_flat[0].second.row(q).size() == actual_dim * actual_dim);
 
                        Eigen::MatrixXd stress_tensor = utils::unflatten(tensor_flat[0].second.row(q), actual_dim);
 
                        traction_forces.block(g_index, 0, actual_dim, 1) += stress_tensor * normals.row(q).transpose() * v.val(q) * weights(q);
                    }
                }
            }
        }
    } // namespace
 
    void OutGeometryData::extract_boundary_mesh(
        const mesh::Mesh &mesh,
        const int n_bases,
        const std::vector<basis::ElementBases> &bases,
        const std::vector<mesh::LocalBoundary> &total_local_boundary,
        Eigen::MatrixXd &node_positions,
        Eigen::MatrixXi &boundary_edges,
        Eigen::MatrixXi &boundary_triangles,
        std::vector<Eigen::Triplet<double>> &displacement_map_entries)
    {
        using namespace polyfem::mesh;
 
        displacement_map_entries.clear();
 
        if (mesh.is_volume())
        {
            if (mesh.has_poly())
            {
                logger().warn("Skipping as the mesh has polygons");
                return;
            }
 
            const bool is_simplicial = mesh.is_simplicial();
 
            node_positions.resize(n_bases + (is_simplicial ? 0 : mesh.n_faces()), 3);
            node_positions.setZero();
            const Mesh3D &mesh3d = dynamic_cast<const Mesh3D &>(mesh);
 
            std::vector<std::tuple<int, int, int>> tris;
 
            std::vector<bool> visited_node(n_bases, false);
 
            std::stringstream print_warning;
 
            for (const LocalBoundary &lb : total_local_boundary)
            {
                const basis::ElementBases &b = bases[lb.element_id()];
 
                for (int j = 0; j < lb.size(); ++j)
                {
                    const int eid = lb.global_primitive_id(j);
                    const int lid = lb[j];
                    const Eigen::VectorXi nodes = b.local_nodes_for_primitive(eid, mesh3d);
 
                    if (mesh.is_cube(lb.element_id()))
                    {
                        assert(!is_simplicial);
                        assert(!mesh.has_poly());
                        std::vector<int> loc_nodes;
                        RowVectorNd bary = RowVectorNd::Zero(3);
 
                        for (long n = 0; n < nodes.size(); ++n)
                        {
                            auto &bs = b.bases[nodes(n)];
                            const auto &glob = bs.global();
                            if (glob.size() != 1)
                                continue;
 
                            int gindex = glob.front().index;
                            node_positions.row(gindex) = glob.front().node;
                            bary += glob.front().node;
                            loc_nodes.push_back(gindex);
                        }
 
                        if (loc_nodes.size() != 4)
                        {
                            logger().trace("skipping element {} since it is not Q1", eid);
                            continue;
                        }
 
                        bary /= 4;
 
                        const int new_node = n_bases + eid;
                        node_positions.row(new_node) = bary;
                        tris.emplace_back(loc_nodes[1], loc_nodes[0], new_node);
                        tris.emplace_back(loc_nodes[2], loc_nodes[1], new_node);
                        tris.emplace_back(loc_nodes[3], loc_nodes[2], new_node);
                        tris.emplace_back(loc_nodes[0], loc_nodes[3], new_node);
 
                        for (int q = 0; q < 4; ++q)
                        {
                            if (!visited_node[loc_nodes[q]])
                                displacement_map_entries.emplace_back(loc_nodes[q], loc_nodes[q], 1);
 
                            visited_node[loc_nodes[q]] = true;
                            displacement_map_entries.emplace_back(new_node, loc_nodes[q], 0.25);
                        }
 
                        continue;
                    }
                    else if (mesh.is_prism(lb.element_id()))
                    {
                        assert(!is_simplicial);
                        assert(!mesh.has_poly());
                        std::vector<int> loc_nodes;
                        RowVectorNd bary = RowVectorNd::Zero(3);
 
                        for (long n = 0; n < nodes.size(); ++n)
                        {
                            auto &bs = b.bases[nodes(n)];
                            const auto &glob = bs.global();
                            if (glob.size() != 1)
                                continue;
 
                            int gindex = glob.front().index;
                            node_positions.row(gindex) = glob.front().node;
                            bary += glob.front().node;
                            loc_nodes.push_back(gindex);
                        }
 
                        auto update_mapping = [&displacement_map_entries, &visited_node](const std::vector<int> &loc_nodes) {
                            for (int k = 0; k < loc_nodes.size(); ++k)
                            {
                                if (!visited_node[loc_nodes[k]])
                                    displacement_map_entries.emplace_back(loc_nodes[k], loc_nodes[k], 1);
 
                                visited_node[loc_nodes[k]] = true;
                            }
                        };
 
                        if (loc_nodes.size() == 3)
                        {
                            tris.emplace_back(loc_nodes[0], loc_nodes[1], loc_nodes[2]);
 
                            update_mapping(loc_nodes);
                        }
                        else if (loc_nodes.size() == 6)
                        {
                            tris.emplace_back(loc_nodes[0], loc_nodes[3], loc_nodes[5]);
                            tris.emplace_back(loc_nodes[3], loc_nodes[1], loc_nodes[4]);
                            tris.emplace_back(loc_nodes[4], loc_nodes[2], loc_nodes[5]);
                            tris.emplace_back(loc_nodes[3], loc_nodes[4], loc_nodes[5]);
 
                            update_mapping(loc_nodes);
                        }
                        else if (loc_nodes.size() == 10)
                        {
                            tris.emplace_back(loc_nodes[0], loc_nodes[3], loc_nodes[8]);
                            tris.emplace_back(loc_nodes[3], loc_nodes[4], loc_nodes[9]);
                            tris.emplace_back(loc_nodes[4], loc_nodes[1], loc_nodes[5]);
                            tris.emplace_back(loc_nodes[5], loc_nodes[6], loc_nodes[9]);
                            tris.emplace_back(loc_nodes[6], loc_nodes[2], loc_nodes[7]);
                            tris.emplace_back(loc_nodes[7], loc_nodes[8], loc_nodes[9]);
                            tris.emplace_back(loc_nodes[8], loc_nodes[3], loc_nodes[9]);
                            tris.emplace_back(loc_nodes[9], loc_nodes[4], loc_nodes[5]);
                            tris.emplace_back(loc_nodes[6], loc_nodes[7], loc_nodes[9]);
                            update_mapping(loc_nodes);
                        }
                        else if (loc_nodes.size() == 15)
                        {
                            tris.emplace_back(loc_nodes[0], loc_nodes[3], loc_nodes[11]);
                            tris.emplace_back(loc_nodes[3], loc_nodes[4], loc_nodes[12]);
                            tris.emplace_back(loc_nodes[3], loc_nodes[12], loc_nodes[11]);
                            tris.emplace_back(loc_nodes[12], loc_nodes[10], loc_nodes[11]);
                            tris.emplace_back(loc_nodes[4], loc_nodes[5], loc_nodes[13]);
                            tris.emplace_back(loc_nodes[4], loc_nodes[13], loc_nodes[12]);
                            tris.emplace_back(loc_nodes[12], loc_nodes[13], loc_nodes[14]);
                            tris.emplace_back(loc_nodes[12], loc_nodes[14], loc_nodes[10]);
                            tris.emplace_back(loc_nodes[14], loc_nodes[9], loc_nodes[10]);
                            tris.emplace_back(loc_nodes[5], loc_nodes[1], loc_nodes[6]);
                            tris.emplace_back(loc_nodes[5], loc_nodes[6], loc_nodes[13]);
                            tris.emplace_back(loc_nodes[6], loc_nodes[7], loc_nodes[13]);
                            tris.emplace_back(loc_nodes[13], loc_nodes[7], loc_nodes[14]);
                            tris.emplace_back(loc_nodes[7], loc_nodes[8], loc_nodes[14]);
                            tris.emplace_back(loc_nodes[14], loc_nodes[8], loc_nodes[9]);
                            tris.emplace_back(loc_nodes[8], loc_nodes[2], loc_nodes[9]);
                            update_mapping(loc_nodes);
                        }
                        else if (loc_nodes.size() == 4)
                        {
                            bary /= 4;
 
                            const int new_node = n_bases + eid;
                            node_positions.row(new_node) = bary;
                            tris.emplace_back(loc_nodes[1], loc_nodes[0], new_node);
                            tris.emplace_back(loc_nodes[2], loc_nodes[1], new_node);
                            tris.emplace_back(loc_nodes[3], loc_nodes[2], new_node);
                            tris.emplace_back(loc_nodes[0], loc_nodes[3], new_node);
 
                            update_mapping(loc_nodes);
                        }
                        else
                        {
                            logger().trace("skipping element {} since it is not linear, it has {} nodes", eid, loc_nodes.size());
                            continue;
                        }
 
                        continue;
                    }
 
                    if (!mesh.is_simplex(lb.element_id()))
                    {
                        logger().trace("skipping element {} since it is not a simplex or hex", eid);
                        continue;
                    }
 
                    assert(mesh.is_simplex(lb.element_id()));
 
                    std::vector<int> loc_nodes;
 
                    bool is_follower = false;
                    if (!mesh3d.is_conforming())
                    {
                        for (long n = 0; n < nodes.size(); ++n)
                        {
                            auto &bs = b.bases[nodes(n)];
                            const auto &glob = bs.global();
                            if (glob.size() != 1)
                            {
                                is_follower = true;
                                break;
                            }
                        }
                    }
 
                    if (is_follower)
                        continue;
 
                    for (long n = 0; n < nodes.size(); ++n)
                    {
                        const basis::Basis &bs = b.bases[nodes(n)];
                        const std::vector<basis::Local2Global> &glob = bs.global();
                        if (glob.size() != 1)
                            continue;
 
                        int gindex = glob.front().index;
                        node_positions.row(gindex) = glob.front().node;
                        loc_nodes.push_back(gindex);
                    }
 
                    if (loc_nodes.size() == 3)
                    {
                        tris.emplace_back(loc_nodes[0], loc_nodes[1], loc_nodes[2]);
                    }
                    else if (loc_nodes.size() == 6)
                    {
                        tris.emplace_back(loc_nodes[0], loc_nodes[3], loc_nodes[5]);
                        tris.emplace_back(loc_nodes[3], loc_nodes[1], loc_nodes[4]);
                        tris.emplace_back(loc_nodes[4], loc_nodes[2], loc_nodes[5]);
                        tris.emplace_back(loc_nodes[3], loc_nodes[4], loc_nodes[5]);
                    }
                    else if (loc_nodes.size() == 10)
                    {
                        tris.emplace_back(loc_nodes[0], loc_nodes[3], loc_nodes[8]);
                        tris.emplace_back(loc_nodes[3], loc_nodes[4], loc_nodes[9]);
                        tris.emplace_back(loc_nodes[4], loc_nodes[1], loc_nodes[5]);
                        tris.emplace_back(loc_nodes[5], loc_nodes[6], loc_nodes[9]);
                        tris.emplace_back(loc_nodes[6], loc_nodes[2], loc_nodes[7]);
                        tris.emplace_back(loc_nodes[7], loc_nodes[8], loc_nodes[9]);
                        tris.emplace_back(loc_nodes[8], loc_nodes[3], loc_nodes[9]);
                        tris.emplace_back(loc_nodes[9], loc_nodes[4], loc_nodes[5]);
                        tris.emplace_back(loc_nodes[6], loc_nodes[7], loc_nodes[9]);
                    }
                    else if (loc_nodes.size() == 15)
                    {
                        tris.emplace_back(loc_nodes[0], loc_nodes[3], loc_nodes[11]);
                        tris.emplace_back(loc_nodes[3], loc_nodes[4], loc_nodes[12]);
                        tris.emplace_back(loc_nodes[3], loc_nodes[12], loc_nodes[11]);
                        tris.emplace_back(loc_nodes[12], loc_nodes[10], loc_nodes[11]);
                        tris.emplace_back(loc_nodes[4], loc_nodes[5], loc_nodes[13]);
                        tris.emplace_back(loc_nodes[4], loc_nodes[13], loc_nodes[12]);
                        tris.emplace_back(loc_nodes[12], loc_nodes[13], loc_nodes[14]);
                        tris.emplace_back(loc_nodes[12], loc_nodes[14], loc_nodes[10]);
                        tris.emplace_back(loc_nodes[14], loc_nodes[9], loc_nodes[10]);
                        tris.emplace_back(loc_nodes[5], loc_nodes[1], loc_nodes[6]);
                        tris.emplace_back(loc_nodes[5], loc_nodes[6], loc_nodes[13]);
                        tris.emplace_back(loc_nodes[6], loc_nodes[7], loc_nodes[13]);
                        tris.emplace_back(loc_nodes[13], loc_nodes[7], loc_nodes[14]);
                        tris.emplace_back(loc_nodes[7], loc_nodes[8], loc_nodes[14]);
                        tris.emplace_back(loc_nodes[14], loc_nodes[8], loc_nodes[9]);
                        tris.emplace_back(loc_nodes[8], loc_nodes[2], loc_nodes[9]);
                    }
                    else
                    {
                        print_warning << loc_nodes.size() << " ";
                        // assert(false);
                    }
 
                    if (!is_simplicial)
                    {
                        for (int k = 0; k < loc_nodes.size(); ++k)
                        {
                            if (!visited_node[loc_nodes[k]])
                                displacement_map_entries.emplace_back(loc_nodes[k], loc_nodes[k], 1);
 
                            visited_node[loc_nodes[k]] = true;
                        }
                    }
                }
            }
 
            if (print_warning.str().size() > 0)
                logger().warn("Skipping faces as theys have {} nodes, boundary export supported up to p4", print_warning.str());
 
            boundary_triangles.resize(tris.size(), 3);
            for (int i = 0; i < tris.size(); ++i)
            {
                boundary_triangles.row(i) << std::get<0>(tris[i]), std::get<2>(tris[i]), std::get<1>(tris[i]);
            }
 
            if (boundary_triangles.rows() > 0)
            {
                igl::edges(boundary_triangles, boundary_edges);
            }
        }
        else
        {
            node_positions.resize(n_bases, 2);
            node_positions.setZero();
            const Mesh2D &mesh2d = dynamic_cast<const Mesh2D &>(mesh);
 
            std::vector<std::pair<int, int>> edges;
 
            for (const LocalBoundary &lb : total_local_boundary)
            {
                const basis::ElementBases &b = bases[lb.element_id()];
 
                for (int j = 0; j < lb.size(); ++j)
                {
                    const int eid = lb.global_primitive_id(j);
                    const int lid = lb[j];
                    const Eigen::VectorXi nodes = b.local_nodes_for_primitive(eid, mesh2d);
 
                    int prev_node = -1;
 
                    for (long n = 0; n < nodes.size(); ++n)
                    {
                        const basis::Basis &bs = b.bases[nodes(n)];
                        const std::vector<basis::Local2Global> &glob = bs.global();
                        if (glob.size() != 1)
                            continue;
 
                        int gindex = glob.front().index;
                        node_positions.row(gindex) = glob.front().node.head<2>();
 
                        if (prev_node >= 0)
                            edges.emplace_back(prev_node, gindex);
 
                        prev_node = gindex;
                    }
                }
            }
 
            boundary_triangles.resize(0, 0);
            boundary_edges.resize(edges.size(), 2);
            for (int i = 0; i < edges.size(); ++i)
            {
                boundary_edges.row(i) << edges[i].first, edges[i].second;
            }
        }
    }
 
    void OutGeometryData::build_vis_boundary_mesh(
        const mesh::Mesh &mesh,
        const std::vector<basis::ElementBases> &bases,
        const std::vector<basis::ElementBases> &gbases,
        const std::vector<mesh::LocalBoundary> &total_local_boundary,
        const Eigen::MatrixXd &solution,
        const int problem_dim,
        Eigen::MatrixXd &boundary_vis_vertices,
        Eigen::MatrixXd &boundary_vis_local_vertices,
        Eigen::MatrixXi &boundary_vis_elements,
        Eigen::MatrixXi &boundary_vis_elements_ids,
        Eigen::MatrixXi &boundary_vis_primitive_ids,
        Eigen::MatrixXd &boundary_vis_normals,
        Eigen::MatrixXd &displaced_boundary_vis_normals) const
    {
        using namespace polyfem::mesh;
 
        std::vector<Eigen::MatrixXd> lv, vertices, allnormals, displaced_allnormals;
        std::vector<int> el_ids, global_primitive_ids;
        Eigen::MatrixXd uv, local_pts, tmp_n, normals, displaced_normals, trafo, deform_mat;
        assembler::ElementAssemblyValues vals;
        const auto &sampler = ref_element_sampler;
        const int n_samples = sampler.num_samples();
        int size = 0;
 
        std::vector<std::pair<int, int>> edges;
        std::vector<std::tuple<int, int, int>> tris;
 
        for (auto it = total_local_boundary.begin(); it != total_local_boundary.end(); ++it)
        {
            const auto &lb = *it;
            const auto &gbs = gbases[lb.element_id()];
            const auto &bs = bases[lb.element_id()];
 
            for (int k = 0; k < lb.size(); ++k)
            {
                switch (lb.type())
                {
                case BoundaryType::TRI_LINE:
                    utils::BoundarySampler::normal_for_tri_edge(lb[k], tmp_n);
                    utils::BoundarySampler::sample_parametric_tri_edge(lb[k], n_samples, uv, local_pts);
                    break;
                case BoundaryType::QUAD_LINE:
                    utils::BoundarySampler::normal_for_quad_edge(lb[k], tmp_n);
                    utils::BoundarySampler::sample_parametric_quad_edge(lb[k], n_samples, uv, local_pts);
                    break;
                case BoundaryType::QUAD:
                    utils::BoundarySampler::normal_for_quad_face(lb[k], tmp_n);
                    utils::BoundarySampler::sample_parametric_quad_face(lb[k], n_samples, uv, local_pts);
                    break;
                case BoundaryType::TRI:
                    utils::BoundarySampler::normal_for_tri_face(lb[k], tmp_n);
                    utils::BoundarySampler::sample_parametric_tri_face(lb[k], n_samples, uv, local_pts);
                    break;
                case BoundaryType::PRISM:
                    utils::BoundarySampler::normal_for_prism_face(lb[k], tmp_n);
                    utils::BoundarySampler::sample_parametric_prism_face(lb[k], n_samples, uv, local_pts);
                    break;
                case BoundaryType::POLYGON:
                    utils::BoundarySampler::normal_for_polygon_edge(lb.element_id(), lb.global_primitive_id(k), mesh, tmp_n);
                    utils::BoundarySampler::sample_polygon_edge(lb.element_id(), lb.global_primitive_id(k), n_samples, mesh, uv, local_pts);
                    break;
                case BoundaryType::POLYHEDRON:
                    assert(false);
                    break;
                case BoundaryType::INVALID:
                    assert(false);
                    break;
                default:
                    assert(false);
                }
 
                vertices.emplace_back();
                lv.emplace_back(local_pts);
                el_ids.push_back(lb.element_id());
                global_primitive_ids.push_back(lb.global_primitive_id(k));
                gbs.eval_geom_mapping(local_pts, vertices.back());
                vals.compute(lb.element_id(), mesh.is_volume(), local_pts, bs, gbs);
                const int tris_start = tris.size();
 
                if (mesh.is_volume())
                {
                    const bool prism_quad = lb.type() == BoundaryType::PRISM && lb[k] >= 2;
                    const bool prism_tri = lb.type() == BoundaryType::PRISM && lb[k] < 2;
 
                    if (lb.type() == BoundaryType::QUAD || prism_quad)
                    {
                        const auto map = [n_samples, size](int i, int j) { return j * n_samples + i + size; };
 
                        for (int j = 0; j < n_samples - 1; ++j)
                        {
                            for (int i = 0; i < n_samples - 1; ++i)
                            {
                                tris.emplace_back(map(i, j), map(i + 1, j), map(i, j + 1));
                                tris.emplace_back(map(i + 1, j + 1), map(i, j + 1), map(i + 1, j));
                            }
                        }
                    }
                    else if (lb.type() == BoundaryType::TRI || prism_tri)
                    {
                        int index = 0;
                        std::vector<int> mapp(n_samples * n_samples, -1);
                        for (int j = 0; j < n_samples; ++j)
                        {
                            for (int i = 0; i < n_samples - j; ++i)
                            {
                                mapp[j * n_samples + i] = index;
                                ++index;
                            }
                        }
                        const auto map = [mapp, n_samples](int i, int j) {
                            if (j * n_samples + i >= mapp.size())
                                return -1;
                            return mapp[j * n_samples + i];
                        };
 
                        for (int j = 0; j < n_samples - 1; ++j)
                        {
                            for (int i = 0; i < n_samples - j; ++i)
                            {
                                if (map(i, j) >= 0 && map(i + 1, j) >= 0 && map(i, j + 1) >= 0)
                                    tris.emplace_back(map(i, j) + size, map(i + 1, j) + size, map(i, j + 1) + size);
 
                                if (map(i + 1, j + 1) >= 0 && map(i, j + 1) >= 0 && map(i + 1, j) >= 0)
                                    tris.emplace_back(map(i + 1, j + 1) + size, map(i, j + 1) + size, map(i + 1, j) + size);
                            }
                        }
                    }
                    else
                    {
                        assert(false);
                    }
                }
                else
                {
                    for (int i = 0; i < vertices.back().rows() - 1; ++i)
                        edges.emplace_back(i + size, i + size + 1);
                }
 
                normals.resize(vals.jac_it.size(), tmp_n.cols());
                displaced_normals.resize(vals.jac_it.size(), tmp_n.cols());
 
                for (int n = 0; n < vals.jac_it.size(); ++n)
                {
                    trafo = vals.jac_it[n].inverse();
 
                    if (problem_dim == 2 || problem_dim == 3)
                    {
 
                        if (solution.size() > 0)
                        {
                            deform_mat.resize(problem_dim, problem_dim);
                            deform_mat.setZero();
                            for (const auto &b : vals.basis_values)
                                for (const auto &g : b.global)
                                    for (int d = 0; d < problem_dim; ++d)
                                        deform_mat.row(d) += solution(g.index * problem_dim + d) * b.grad.row(n);
 
                            trafo += deform_mat;
                        }
                    }
 
                    normals.row(n) = tmp_n * vals.jac_it[n];
                    normals.row(n).normalize();
 
                    displaced_normals.row(n) = tmp_n * trafo.inverse();
                    displaced_normals.row(n).normalize();
                }
 
                allnormals.push_back(normals);
                displaced_allnormals.push_back(displaced_normals);
 
                tmp_n.setZero();
                for (int n = 0; n < vals.jac_it.size(); ++n)
                {
                    tmp_n += normals.row(n);
                }
 
                if (mesh.is_volume())
                {
                    Eigen::Vector3d e1 = vertices.back().row(std::get<1>(tris.back()) - size) - vertices.back().row(std::get<0>(tris.back()) - size);
                    Eigen::Vector3d e2 = vertices.back().row(std::get<2>(tris.back()) - size) - vertices.back().row(std::get<0>(tris.back()) - size);
 
                    Eigen::Vector3d n = e1.cross(e2);
                    Eigen::Vector3d nn = tmp_n.transpose();
 
                    if (n.dot(nn) < 0)
                    {
                        for (int i = tris_start; i < tris.size(); ++i)
                        {
                            tris[i] = std::tuple<int, int, int>(std::get<0>(tris[i]), std::get<2>(tris[i]), std::get<1>(tris[i]));
                        }
                    }
                }
 
                size += vertices.back().rows();
            }
        }
 
        boundary_vis_vertices.resize(size, vertices.front().cols());
        boundary_vis_local_vertices.resize(size, vertices.front().cols());
        boundary_vis_elements_ids.resize(size, 1);
        boundary_vis_primitive_ids.resize(size, 1);
        boundary_vis_normals.resize(size, vertices.front().cols());
        displaced_boundary_vis_normals.resize(size, vertices.front().cols());
 
        if (mesh.is_volume())
            boundary_vis_elements.resize(tris.size(), 3);
        else
            boundary_vis_elements.resize(edges.size(), 2);
 
        int index = 0;
        int ii = 0;
        for (const auto &v : vertices)
        {
            boundary_vis_vertices.block(index, 0, v.rows(), v.cols()) = v;
            boundary_vis_local_vertices.block(index, 0, v.rows(), v.cols()) = lv[ii];
            boundary_vis_elements_ids.block(index, 0, v.rows(), 1).setConstant(el_ids[ii]);
            boundary_vis_primitive_ids.block(index, 0, v.rows(), 1).setConstant(global_primitive_ids[ii++]);
            index += v.rows();
        }
 
        index = 0;
        for (const auto &n : allnormals)
        {
            boundary_vis_normals.block(index, 0, n.rows(), n.cols()) = n;
            index += n.rows();
        }
 
        index = 0;
        for (const auto &n : displaced_allnormals)
        {
            displaced_boundary_vis_normals.block(index, 0, n.rows(), n.cols()) = n;
            index += n.rows();
        }
 
        index = 0;
        if (mesh.is_volume())
        {
            for (const auto &t : tris)
            {
                boundary_vis_elements.row(index) << std::get<0>(t), std::get<1>(t), std::get<2>(t);
                ++index;
            }
        }
        else
        {
            for (const auto &e : edges)
            {
                boundary_vis_elements.row(index) << e.first, e.second;
                ++index;
            }
        }
    }
 
    void OutGeometryData::build_vis_mesh(
        const mesh::Mesh &mesh,
        const Eigen::VectorXi &disc_orders,
        const std::vector<basis::ElementBases> &gbases,
        const std::map<int, Eigen::MatrixXd> &polys,
        const std::map<int, std::pair<Eigen::MatrixXd, Eigen::MatrixXi>> &polys_3d,
        const bool boundary_only,
        Eigen::MatrixXd &points,
        Eigen::MatrixXi &tets,
        Eigen::MatrixXi &el_id,
        Eigen::MatrixXd &discr) const
    {
        const auto &sampler = ref_element_sampler;
 
        const auto &current_bases = gbases;
        int tet_total_size = 0;
        int pts_total_size = 0;
 
        Eigen::MatrixXd vis_pts_poly;
        Eigen::MatrixXi vis_faces_poly, vis_edges_poly;
 
        for (size_t i = 0; i < current_bases.size(); ++i)
        {
            const auto &bs = current_bases[i];
 
            if (boundary_only && mesh.is_volume() && !mesh.is_boundary_element(i))
                continue;
 
            if (mesh.is_simplex(i))
            {
                tet_total_size += sampler.simplex_volume().rows();
                pts_total_size += sampler.simplex_points().rows();
            }
            else if (mesh.is_cube(i))
            {
                tet_total_size += sampler.cube_volume().rows();
                pts_total_size += sampler.cube_points().rows();
            }
            else if (mesh.is_prism(i))
            {
                tet_total_size += sampler.prism_volume().rows();
                pts_total_size += sampler.prism_points().rows();
            }
            else
            {
                if (mesh.is_volume())
                {
                    sampler.sample_polyhedron(polys_3d.at(i).first, polys_3d.at(i).second, vis_pts_poly, vis_faces_poly, vis_edges_poly);
 
                    tet_total_size += vis_faces_poly.rows();
                    pts_total_size += vis_pts_poly.rows();
                }
                else
                {
                    sampler.sample_polygon(polys.at(i), vis_pts_poly, vis_faces_poly, vis_edges_poly);
 
                    tet_total_size += vis_faces_poly.rows();
                    pts_total_size += vis_pts_poly.rows();
                }
            }
        }
 
        points.resize(pts_total_size, mesh.dimension());
        tets.resize(tet_total_size, mesh.is_volume() ? 4 : 3);
 
        el_id.resize(pts_total_size, 1);
        discr.resize(pts_total_size, 1);
 
        Eigen::MatrixXd mapped, tmp;
        int tet_index = 0, pts_index = 0;
 
        for (size_t i = 0; i < current_bases.size(); ++i)
        {
            const auto &bs = current_bases[i];
 
            if (boundary_only && mesh.is_volume() && !mesh.is_boundary_element(i))
                continue;
 
            if (mesh.is_simplex(i))
            {
                bs.eval_geom_mapping(sampler.simplex_points(), mapped);
 
                tets.block(tet_index, 0, sampler.simplex_volume().rows(), tets.cols()) = sampler.simplex_volume().array() + pts_index;
                tet_index += sampler.simplex_volume().rows();
 
                points.block(pts_index, 0, mapped.rows(), points.cols()) = mapped;
                discr.block(pts_index, 0, mapped.rows(), 1).setConstant(disc_orders(i));
                el_id.block(pts_index, 0, mapped.rows(), 1).setConstant(i);
                pts_index += mapped.rows();
            }
            else if (mesh.is_cube(i))
            {
                bs.eval_geom_mapping(sampler.cube_points(), mapped);
 
                tets.block(tet_index, 0, sampler.cube_volume().rows(), tets.cols()) = sampler.cube_volume().array() + pts_index;
                tet_index += sampler.cube_volume().rows();
 
                points.block(pts_index, 0, mapped.rows(), points.cols()) = mapped;
                discr.block(pts_index, 0, mapped.rows(), 1).setConstant(disc_orders(i));
                el_id.block(pts_index, 0, mapped.rows(), 1).setConstant(i);
                pts_index += mapped.rows();
            }
            else if (mesh.is_prism(i))
            {
                bs.eval_geom_mapping(sampler.prism_points(), mapped);
 
                tets.block(tet_index, 0, sampler.prism_volume().rows(), tets.cols()) = sampler.prism_volume().array() + pts_index;
                tet_index += sampler.prism_volume().rows();
 
                points.block(pts_index, 0, mapped.rows(), points.cols()) = mapped;
                discr.block(pts_index, 0, mapped.rows(), 1).setConstant(disc_orders(i));
                el_id.block(pts_index, 0, mapped.rows(), 1).setConstant(i);
                pts_index += mapped.rows();
            }
            else
            {
                if (mesh.is_volume())
                {
                    sampler.sample_polyhedron(polys_3d.at(i).first, polys_3d.at(i).second, vis_pts_poly, vis_faces_poly, vis_edges_poly);
                    bs.eval_geom_mapping(vis_pts_poly, mapped);
 
                    tets.block(tet_index, 0, vis_faces_poly.rows(), tets.cols()) = vis_faces_poly.array() + pts_index;
                    tet_index += vis_faces_poly.rows();
 
                    points.block(pts_index, 0, mapped.rows(), points.cols()) = mapped;
                    discr.block(pts_index, 0, mapped.rows(), 1).setConstant(-1);
                    el_id.block(pts_index, 0, mapped.rows(), 1).setConstant(i);
                    pts_index += mapped.rows();
                }
                else
                {
                    sampler.sample_polygon(polys.at(i), vis_pts_poly, vis_faces_poly, vis_edges_poly);
                    bs.eval_geom_mapping(vis_pts_poly, mapped);
 
                    tets.block(tet_index, 0, vis_faces_poly.rows(), tets.cols()) = vis_faces_poly.array() + pts_index;
                    tet_index += vis_faces_poly.rows();
 
                    points.block(pts_index, 0, mapped.rows(), points.cols()) = mapped;
                    discr.block(pts_index, 0, mapped.rows(), 1).setConstant(-1);
                    el_id.block(pts_index, 0, mapped.rows(), 1).setConstant(i);
                    pts_index += mapped.rows();
                }
            }
        }
 
        assert(pts_index == points.rows());
        assert(tet_index == tets.rows());
    }
 
    void OutGeometryData::build_high_order_vis_mesh(
        const mesh::Mesh &mesh,
        const Eigen::VectorXi &disc_orders,
        const Eigen::VectorXi &disc_ordersq,
        const std::vector<basis::ElementBases> &bases,
        Eigen::MatrixXd &points,
        std::vector<CellElement> &elements,
        Eigen::MatrixXi &el_id,
        Eigen::MatrixXd &discr) const
    {
        // if (!mesh)
        // {
        //  logger().error("Load the mesh first!");
        //  return;
        // }
        // if (n_bases <= 0)
        // {
        //  logger().error("Build the bases first!");
        //  return;
        // }
        // assert(mesh.is_linear());
 
        std::vector<RowVectorNd> nodes;
        int pts_total_size = 0;
        elements.resize(bases.size());
        Eigen::MatrixXd ref_pts;
 
        for (size_t i = 0; i < bases.size(); ++i)
        {
            const auto &bs = bases[i];
            if (mesh.is_volume())
            {
                if (mesh.is_simplex(i))
                    autogen::p_nodes_3d(disc_orders(i), ref_pts);
                else if (mesh.is_cube(i))
                    autogen::q_nodes_3d(disc_orders(i), ref_pts);
                else if (mesh.is_prism(i))
                {
                    int max_order = std::max(disc_orders(i), disc_ordersq(i));
                    autogen::prism_nodes_3d(max_order, max_order, ref_pts);
                }
                else
                    continue;
            }
            else
            {
                if (mesh.is_simplex(i))
                    autogen::p_nodes_2d(disc_orders(i), ref_pts);
                else if (mesh.is_cube(i))
                    autogen::q_nodes_2d(disc_orders(i), ref_pts);
                else
                {
                    const int n_v = static_cast<const mesh::Mesh2D &>(mesh).n_face_vertices(i);
                    ref_pts.resize(n_v, 2);
                }
            }
 
            pts_total_size += ref_pts.rows();
        }
 
        points.resize(pts_total_size, mesh.dimension());
 
        el_id.resize(pts_total_size, 1);
        discr.resize(pts_total_size, 1);
 
        Eigen::MatrixXd mapped;
        int pts_index = 0;
 
        std::string error_msg = "";
 
        for (size_t i = 0; i < bases.size(); ++i)
        {
            const auto &bs = bases[i];
            if (mesh.is_volume())
            {
                if (mesh.is_simplex(i))
                    autogen::p_nodes_3d(disc_orders(i), ref_pts);
                else if (mesh.is_cube(i))
                    autogen::q_nodes_3d(disc_orders(i), ref_pts);
                else if (mesh.is_prism(i))
                {
                    int max_order = std::max(disc_orders(i), disc_ordersq(i));
                    autogen::prism_nodes_3d(max_order, max_order, ref_pts);
                }
                else
                    continue;
            }
            else
            {
                if (mesh.is_simplex(i))
                    autogen::p_nodes_2d(disc_orders(i), ref_pts);
                else if (mesh.is_cube(i))
                    autogen::q_nodes_2d(disc_orders(i), ref_pts);
                else
                    continue;
            }
 
            bs.eval_geom_mapping(ref_pts, mapped);
 
            for (int j = 0; j < mapped.rows(); ++j)
            {
                points.row(pts_index) = mapped.row(j);
                el_id(pts_index) = i;
                discr(pts_index) = disc_orders(i);
                elements[i].vertices.push_back(pts_index);
 
                pts_index++;
            }
 
            if (mesh.is_simplex(i))
            {
                if (mesh.is_volume())
                {
                    const int n_nodes = elements[i].vertices.size();
                    if (disc_orders(i) >= 3)
                    {
                        std::swap(elements[i].vertices[16], elements[i].vertices[17]);
                        std::swap(elements[i].vertices[17], elements[i].vertices[18]);
                        std::swap(elements[i].vertices[18], elements[i].vertices[19]);
                    }
                    if (disc_orders(i) > 4)
                        error_msg = "Saving high-order meshes not implemented for P5+ elements!";
                }
                else
                {
                    if (disc_orders(i) == 4)
                    {
                        const int n_nodes = elements[i].vertices.size();
                        std::swap(elements[i].vertices[n_nodes - 1], elements[i].vertices[n_nodes - 2]);
                    }
                    if (disc_orders(i) > 4)
                        error_msg = "Saving high-order meshes not implemented for P5+ elements!";
                }
            }
            else if (disc_orders(i) > 1)
                error_msg = "Saving high-order meshes not implemented for Q2+ elements!";
        }
 
        if (!error_msg.empty())
            logger().warn(error_msg);
 
        for (size_t i = 0; i < bases.size(); ++i)
        {
            if (mesh.is_volume() || !mesh.is_polytope(i))
                continue;
 
            const auto &mesh2d = static_cast<const mesh::Mesh2D &>(mesh);
            const int n_v = mesh2d.n_face_vertices(i);
 
            for (int j = 0; j < n_v; ++j)
            {
                points.row(pts_index) = mesh2d.point(mesh2d.face_vertex(i, j));
                el_id(pts_index) = i;
                discr(pts_index) = disc_orders(i);
                elements[i].vertices.push_back(pts_index);
 
                pts_index++;
            }
        }
 
        for (size_t i = 0; i < bases.size(); ++i)
        {
            if (!mesh.is_volume())
            {
                if (elements[i].vertices.size() == 1)
                    elements[i].ctype = CellType::Vertex;
                else if (elements[i].vertices.size() == 2)
                    elements[i].ctype = CellType::Line;
                else if (mesh.is_simplex(i))
                    elements[i].ctype = CellType::Triangle;
                else if (mesh.is_cube(i))
                    elements[i].ctype = CellType::Quadrilateral;
                else
                    elements[i].ctype = CellType::Polygon;
            }
            else
            {
                if (mesh.is_simplex(i))
                    elements[i].ctype = CellType::Tetrahedron;
                else if (mesh.is_cube(i))
                    elements[i].ctype = CellType::Hexahedron;
                else if (mesh.is_prism(i))
                    elements[i].ctype = CellType::Wedge;
            }
        }
 
        assert(pts_index == points.rows());
    }
 
    void OutGeometryData::export_data(
        const State &state,
        const Eigen::MatrixXd &sol,
        const Eigen::MatrixXd &pressure,
        const bool is_time_dependent,
        const double tend_in,
        const double dt,
        const ExportOptions &opts,
        const std::string &vis_mesh_path,
        const std::string &nodes_path,
        const std::string &solution_path,
        const std::string &stress_path,
        const std::string &mises_path,
        const bool is_contact_enabled) const
    {
        if (!state.mesh)
        {
            logger().error("Load the mesh first!");
            return;
        }
        const int n_bases = state.n_bases;
        const std::vector<basis::ElementBases> &bases = state.bases;
        const std::vector<basis::ElementBases> &gbases = state.geom_bases();
        const mesh::Mesh &mesh = *state.mesh;
        const Eigen::VectorXi &in_node_to_node = state.in_node_to_node;
        const Eigen::MatrixXd &rhs = state.rhs;
        const assembler::Problem &problem = *state.problem;
 
        if (n_bases <= 0)
        {
            logger().error("Build the bases first!");
            return;
        }
        // if (rhs.size() <= 0)
        // {
        //  logger().error("Assemble the rhs first!");
        //  return;
        // }
        if (sol.size() <= 0)
        {
            logger().error("Solve the problem first!");
            return;
        }
 
        if (!solution_path.empty())
        {
            logger().info("Saving solution to {}", solution_path);
 
            std::ofstream out(solution_path);
            out.precision(100);
            out << std::scientific;
            if (opts.reorder_output)
            {
                int problem_dim = (problem.is_scalar() ? 1 : mesh.dimension());
                Eigen::VectorXi reordering(n_bases);
                reordering.setConstant(-1);
 
                for (int i = 0; i < in_node_to_node.size(); ++i)
                {
                    reordering[in_node_to_node[i]] = i;
                }
                Eigen::MatrixXd tmp_sol = utils::unflatten(sol, problem_dim);
                Eigen::MatrixXd tmp(tmp_sol.rows(), tmp_sol.cols());
 
                for (int i = 0; i < reordering.size(); ++i)
                {
                    if (reordering[i] < 0)
                        continue;
 
                    tmp.row(reordering[i]) = tmp_sol.row(i);
                }
 
                for (int i = 0; i < tmp.rows(); ++i)
                {
                    for (int j = 0; j < tmp.cols(); ++j)
                        out << tmp(i, j) << " ";
 
                    out << std::endl;
                }
            }
            else
                out << sol << std::endl;
            out.close();
        }
 
        double tend = tend_in;
        if (tend <= 0)
            tend = 1;
 
        if (!vis_mesh_path.empty() && !is_time_dependent)
        {
            save_vtu(
                vis_mesh_path, state, sol, pressure,
                tend, dt, opts,
                is_contact_enabled);
        }
        if (!nodes_path.empty())
        {
            Eigen::MatrixXd nodes(n_bases, mesh.dimension());
            for (const basis::ElementBases &eb : bases)
            {
                for (const basis::Basis &b : eb.bases)
                {
                    // for(const auto &lg : b.global())
                    for (size_t ii = 0; ii < b.global().size(); ++ii)
                    {
                        const auto &lg = b.global()[ii];
                        nodes.row(lg.index) = lg.node;
                    }
                }
            }
            std::ofstream out(nodes_path);
            out.precision(100);
            out << nodes;
            out.close();
        }
        if (!stress_path.empty())
        {
            Eigen::MatrixXd result;
            Eigen::VectorXd mises;
            Evaluator::compute_stress_at_quadrature_points(
                mesh, problem.is_scalar(),
                bases, gbases, state.disc_orders, state.disc_ordersq, *state.assembler,
                sol, tend, result, mises);
            std::ofstream out(stress_path);
            out.precision(20);
            out << result;
        }
        if (!mises_path.empty())
        {
            Eigen::MatrixXd result;
            Eigen::VectorXd mises;
            Evaluator::compute_stress_at_quadrature_points(
                mesh, problem.is_scalar(),
                bases, gbases, state.disc_orders, state.disc_ordersq, *state.assembler,
                sol, tend, result, mises);
            std::ofstream out(mises_path);
            out.precision(20);
            out << mises;
        }
    }
 
    bool OutGeometryData::ExportOptions::export_field(const std::string &field) const
    {
        return fields.empty() || std::find(fields.begin(), fields.end(), field) != fields.end();
    }
 
    OutGeometryData::ExportOptions::ExportOptions(const json &args, const bool is_mesh_linear, const bool mesh_has_prisms, const bool is_problem_scalar)
    {
        fields = args["output"]["paraview"]["fields"];
 
        volume = args["output"]["paraview"]["volume"];
        surface = args["output"]["paraview"]["surface"];
        wire = args["output"]["paraview"]["wireframe"];
        points = args["output"]["paraview"]["points"];
        contact_forces = args["output"]["paraview"]["options"]["contact_forces"] && !is_problem_scalar;
        friction_forces = args["output"]["paraview"]["options"]["friction_forces"] && !is_problem_scalar;
        normal_adhesion_forces = args["output"]["paraview"]["options"]["normal_adhesion_forces"] && !is_problem_scalar;
        tangential_adhesion_forces = args["output"]["paraview"]["options"]["tangential_adhesion_forces"] && !is_problem_scalar;
 
        if (args["output"]["paraview"]["options"]["force_high_order"])
            use_sampler = false;
        else
            use_sampler = !(is_mesh_linear && args["output"]["paraview"]["high_order_mesh"]);
        boundary_only = use_sampler && args["output"]["advanced"]["vis_boundary_only"];
        material_params = args["output"]["paraview"]["options"]["material"];
        body_ids = args["output"]["paraview"]["options"]["body_ids"];
        sol_on_grid = args["output"]["advanced"]["sol_on_grid"] > 0;
        velocity = args["output"]["paraview"]["options"]["velocity"];
        acceleration = args["output"]["paraview"]["options"]["acceleration"];
        forces = args["output"]["paraview"]["options"]["forces"] && !is_problem_scalar;
        jacobian_validity = args["output"]["paraview"]["options"]["jacobian_validity"] && !is_problem_scalar;
 
        scalar_values = args["output"]["paraview"]["options"]["scalar_values"];
        tensor_values = args["output"]["paraview"]["options"]["tensor_values"] && !is_problem_scalar;
        discretization_order = args["output"]["paraview"]["options"]["discretization_order"];
        nodes = args["output"]["paraview"]["options"]["nodes"] && !is_problem_scalar;
 
        use_spline = args["space"]["basis_type"] == "Spline";
 
        reorder_output = args["output"]["data"]["advanced"]["reorder_nodes"];
 
        use_hdf5 = args["output"]["paraview"]["options"]["use_hdf5"];
    }
 
    void OutGeometryData::save_vtu(
        const std::string &path,
        const State &state,
        const Eigen::MatrixXd &sol,
        const Eigen::MatrixXd &pressure,
        const double t,
        const double dt,
        const ExportOptions &opts,
        const bool is_contact_enabled) const
    {
        if (!state.mesh)
        {
            logger().error("Load the mesh first!");
            return;
        }
        const mesh::Mesh &mesh = *state.mesh;
        const Eigen::MatrixXd &rhs = state.rhs;
 
        if (state.n_bases <= 0)
        {
            logger().error("Build the bases first!");
            return;
        }
        // if (rhs.size() <= 0)
        // {
        //  logger().error("Assemble the rhs first!");
        //  return;
        // }
        if (sol.size() <= 0)
        {
            logger().error("Solve the problem first!");
            return;
        }
 
        const bool save_contact = is_contact_enabled && (opts.contact_forces || opts.friction_forces);
 
        logger().info("Saving vtu to {}; volume={}, surface={}, contact={}, points={}, wireframe={}",
                      path, opts.volume, opts.surface, save_contact, opts.points, opts.wire);
 
        const std::filesystem::path fs_path(path);
        const std::string path_stem = fs_path.stem().string();
        const std::string base_path = (fs_path.parent_path() / path_stem).string();
 
        if (opts.volume)
        {
            save_volume(base_path + opts.file_extension(), state, sol, pressure, t, dt, opts);
        }
 
        if (opts.surface)
        {
            save_surface(base_path + "_surf" + opts.file_extension(), state, sol, pressure, t, dt, opts,
                         is_contact_enabled);
        }
 
        if (is_contact_enabled && (opts.contact_forces || opts.friction_forces || opts.normal_adhesion_forces || opts.tangential_adhesion_forces))
        {
            save_contact_surface(base_path + "_surf" + opts.file_extension(), state, sol, pressure, t, dt, opts,
                                 is_contact_enabled);
        }
 
        if (opts.wire)
        {
            save_wire(base_path + "_wire" + opts.file_extension(), state, sol, t, opts);
        }
 
        if (opts.points)
        {
            save_points(base_path + "_points" + opts.file_extension(), state, sol, opts);
        }
 
        paraviewo::VTMWriter vtm(t);
        if (opts.volume)
            vtm.add_dataset("Volume", "data", path_stem + opts.file_extension());
        if (opts.surface)
            vtm.add_dataset("Surface", "data", path_stem + "_surf" + opts.file_extension());
        if (is_contact_enabled && (opts.contact_forces || opts.friction_forces || opts.normal_adhesion_forces || opts.tangential_adhesion_forces))
            vtm.add_dataset("Contact", "data", path_stem + "_surf_contact" + opts.file_extension());
        if (opts.wire)
            vtm.add_dataset("Wireframe", "data", path_stem + "_wire" + opts.file_extension());
        if (opts.points)
            vtm.add_dataset("Points", "data", path_stem + "_points" + opts.file_extension());
        vtm.save(base_path + ".vtm");
    }
 
    void OutGeometryData::save_volume(
        const std::string &path,
        const State &state,
        const Eigen::MatrixXd &sol,
        const Eigen::MatrixXd &pressure,
        const double t,
        const double dt,
        const ExportOptions &opts) const
    {
        const Eigen::VectorXi &disc_orders = state.disc_orders;
        const Eigen::VectorXi &disc_ordersq = state.disc_ordersq;
        const auto &density = state.mass_matrix_assembler->density();
        const std::vector<basis::ElementBases> &bases = state.bases;
        const std::vector<basis::ElementBases> &pressure_bases = state.pressure_bases;
        const std::vector<basis::ElementBases> &gbases = state.geom_bases();
        const std::map<int, Eigen::MatrixXd> &polys = state.polys;
        const std::map<int, std::pair<Eigen::MatrixXd, Eigen::MatrixXi>> &polys_3d = state.polys_3d;
        const assembler::Assembler &assembler = *state.assembler;
        const std::shared_ptr<time_integrator::ImplicitTimeIntegrator> time_integrator = state.solve_data.time_integrator;
        const mesh::Mesh &mesh = *state.mesh;
        const mesh::Obstacle &obstacle = state.obstacle;
        const assembler::Problem &problem = *state.problem;
 
        Eigen::MatrixXd points;
        Eigen::MatrixXi tets;
        Eigen::MatrixXi el_id;
        Eigen::MatrixXd discr;
        std::vector<CellElement> elements;
 
        if (opts.use_sampler)
            build_vis_mesh(mesh, disc_orders, gbases,
                           state.polys, state.polys_3d, opts.boundary_only,
                           points, tets, el_id, discr);
        else
            build_high_order_vis_mesh(mesh, disc_orders, disc_ordersq, bases,
                                      points, elements, el_id, discr);
 
        Eigen::MatrixXd fun, exact_fun, err, node_fun;
 
        if (opts.sol_on_grid)
        {
            const int problem_dim = problem.is_scalar() ? 1 : mesh.dimension();
            Eigen::MatrixXd tmp, tmp_grad;
            Eigen::MatrixXd tmp_p, tmp_grad_p;
            Eigen::MatrixXd res(grid_points_to_elements.size(), problem_dim);
            res.setConstant(std::numeric_limits<double>::quiet_NaN());
            Eigen::MatrixXd res_grad(grid_points_to_elements.size(), problem_dim * problem_dim);
            res_grad.setConstant(std::numeric_limits<double>::quiet_NaN());
 
            Eigen::MatrixXd res_p(grid_points_to_elements.size(), 1);
            res_p.setConstant(std::numeric_limits<double>::quiet_NaN());
            Eigen::MatrixXd res_grad_p(grid_points_to_elements.size(), problem_dim);
            res_grad_p.setConstant(std::numeric_limits<double>::quiet_NaN());
 
            for (int i = 0; i < grid_points_to_elements.size(); ++i)
            {
                const int el_id = grid_points_to_elements(i);
                if (el_id < 0)
                    continue;
                assert(mesh.is_simplex(el_id));
                const Eigen::MatrixXd bc = grid_points_bc.row(i);
                Eigen::MatrixXd pt(1, bc.cols() - 1);
                for (int d = 1; d < bc.cols(); ++d)
                    pt(d - 1) = bc(d);
                Evaluator::interpolate_at_local_vals(
                    mesh, problem.is_scalar(), bases, gbases,
                    el_id, pt, sol, tmp, tmp_grad);
 
                res.row(i) = tmp;
                res_grad.row(i) = tmp_grad;
 
                if (state.mixed_assembler != nullptr)
                {
                    Evaluator::interpolate_at_local_vals(
                        mesh, 1, pressure_bases, gbases,
                        el_id, pt, pressure, tmp_p, tmp_grad_p);
                    res_p.row(i) = tmp_p;
                    res_grad_p.row(i) = tmp_grad_p;
                }
            }
 
            std::ofstream os(path + "_sol.txt");
            os << res;
 
            std::ofstream osg(path + "_grad.txt");
            osg << res_grad;
 
            std::ofstream osgg(path + "_grid.txt");
            osgg << grid_points;
 
            if (state.mixed_assembler != nullptr)
            {
                std::ofstream osp(path + "_p_sol.txt");
                osp << res_p;
 
                std::ofstream osgp(path + "_p_grad.txt");
                osgp << res_grad_p;
            }
        }
 
        Eigen::Vector<bool, -1> validity;
        if (opts.jacobian_validity)
            Evaluator::mark_flipped_cells(
                mesh, gbases, bases, state.disc_orders,
                state.polys, state.polys_3d, ref_element_sampler,
                points.rows(), sol, validity, opts.use_sampler, opts.boundary_only);
 
        Evaluator::interpolate_function(
            mesh, problem.is_scalar(), bases, disc_orders, disc_ordersq,
            state.polys, state.polys_3d, ref_element_sampler,
            points.rows(), sol, fun, opts.use_sampler, opts.boundary_only);
 
        {
            Eigen::MatrixXd tmp = Eigen::VectorXd::LinSpaced(sol.size(), 0, sol.size() - 1);
 
            Evaluator::interpolate_function(
                mesh, problem.is_scalar(), bases, disc_orders, disc_ordersq,
                state.polys, state.polys_3d, ref_element_sampler,
                points.rows(), tmp, node_fun, opts.use_sampler, opts.boundary_only);
        }
 
        if (obstacle.n_vertices() > 0)
        {
            fun.conservativeResize(fun.rows() + obstacle.n_vertices(), fun.cols());
            node_fun.conservativeResize(node_fun.rows() + obstacle.n_vertices(), node_fun.cols());
            node_fun.bottomRows(obstacle.n_vertices()).setZero();
            // obstacle.update_displacement(t, fun);
            // NOTE: Assuming the obstacle displacement is the last part of the solution
            fun.bottomRows(obstacle.n_vertices()) = utils::unflatten(sol.bottomRows(obstacle.ndof()), fun.cols());
        }
 
        if (problem.has_exact_sol())
        {
            problem.exact(points, t, exact_fun);
            err = (fun - exact_fun).eval().rowwise().norm();
 
            if (obstacle.n_vertices() > 0)
            {
                exact_fun.conservativeResize(exact_fun.rows() + obstacle.n_vertices(), exact_fun.cols());
                // obstacle.update_displacement(t, exact_fun);
                exact_fun.bottomRows(obstacle.n_vertices()) = utils::unflatten(sol.bottomRows(obstacle.ndof()), fun.cols());
 
                err.conservativeResize(err.rows() + obstacle.n_vertices(), 1);
                err.bottomRows(obstacle.n_vertices()).setZero();
            }
        }
 
        std::shared_ptr<paraviewo::ParaviewWriter> tmpw;
        if (opts.use_hdf5)
            tmpw = std::make_shared<paraviewo::HDF5VTUWriter>();
        else
            tmpw = std::make_shared<paraviewo::VTUWriter>();
        paraviewo::ParaviewWriter &writer = *tmpw;
 
        if (validity.size() && opts.export_field("validity"))
            writer.add_field("validity", validity.cast<double>());
 
        if (opts.nodes && opts.export_field("nodes"))
            writer.add_field("nodes", node_fun);
 
        if (problem.is_time_dependent())
        {
            bool is_time_integrator_valid = time_integrator != nullptr;
 
            if (opts.velocity || opts.export_field("velocity"))
            {
                const Eigen::VectorXd velocity =
                    is_time_integrator_valid ? (time_integrator->v_prev()) : Eigen::VectorXd::Zero(sol.size());
                save_volume_vector_field(state, points, opts, "velocity", velocity, writer);
            }
 
            if (opts.acceleration || opts.export_field("acceleration"))
            {
                const Eigen::VectorXd acceleration =
                    is_time_integrator_valid ? (time_integrator->a_prev()) : Eigen::VectorXd::Zero(sol.size());
                save_volume_vector_field(state, points, opts, "acceleration", acceleration, writer);
            }
        }
 
        if (opts.forces)
        {
            const double s = state.solve_data.time_integrator
                                 ? state.solve_data.time_integrator->acceleration_scaling()
                                 : 1;
 
            for (const auto &[name, form] : state.solve_data.named_forms())
            {
                // NOTE: Assumes this form will be null for the entire sim
                if (form == nullptr)
                    continue;
 
                Eigen::VectorXd force;
                if (form->enabled())
                {
                    form->first_derivative(sol, force);
                    force *= -1.0 / s; // Divide by acceleration scaling to get units of force
                }
                else
                {
                    force.setZero(sol.size());
                }
                if (opts.export_field(name + "_forces"))
                    save_volume_vector_field(state, points, opts, name + "_forces", force, writer);
            }
        }
 
        // if(problem->is_mixed())
        if (state.mixed_assembler != nullptr && opts.export_field("pressure"))
        {
            Eigen::MatrixXd interp_p;
            Evaluator::interpolate_function(
                mesh, 1, // FIXME: disc_orders should use pressure discr orders, works only with sampler
                pressure_bases, disc_orders, disc_ordersq, state.polys, state.polys_3d, ref_element_sampler,
                points.rows(), pressure, interp_p, opts.use_sampler, opts.boundary_only);
 
            if (obstacle.n_vertices() > 0)
            {
                interp_p.conservativeResize(interp_p.size() + obstacle.n_vertices(), 1);
                interp_p.bottomRows(obstacle.n_vertices()).setZero();
            }
 
            writer.add_field("pressure", interp_p);
        }
 
        if (obstacle.n_vertices() > 0)
        {
            discr.conservativeResize(discr.size() + obstacle.n_vertices(), 1);
            discr.bottomRows(obstacle.n_vertices()).setZero();
        }
 
        if (opts.discretization_order && opts.export_field("discr"))
            writer.add_field("discr", discr);
 
        if (problem.has_exact_sol())
        {
            if (opts.export_field("exact"))
                writer.add_field("exact", exact_fun);
            if (opts.export_field("error"))
                writer.add_field("error", err);
        }
 
        if (fun.cols() != 1 && (opts.scalar_values || opts.tensor_values || (!opts.use_spline && (opts.scalar_values || opts.tensor_values))))
        {
            std::vector<assembler::Assembler::NamedMatrix> vals, tvals;
            Evaluator::compute_scalar_value(
                mesh, problem.is_scalar(), bases, gbases,
                disc_orders, disc_ordersq, state.polys, state.polys_3d,
                *state.assembler,
                ref_element_sampler, points.rows(), sol, t, vals, opts.use_sampler, opts.boundary_only);
 
            for (auto &[_, v] : vals)
                utils::append_rows_of_zeros(v, obstacle.n_vertices());
 
            if (opts.scalar_values)
            {
                for (const auto &[name, v] : vals)
                {
                    if (opts.export_field(name))
                        writer.add_field(name, v);
                }
            }
 
            if (opts.tensor_values)
            {
                Evaluator::compute_tensor_value(
                    mesh, problem.is_scalar(), bases, gbases, disc_orders, disc_ordersq,
                    state.polys, state.polys_3d, *state.assembler, ref_element_sampler,
                    points.rows(), sol, t, tvals, opts.use_sampler, opts.boundary_only);
 
                for (auto &[_, v] : tvals)
                    utils::append_rows_of_zeros(v, obstacle.n_vertices());
 
                for (const auto &[name, v] : tvals)
                {
                    const int stride = mesh.dimension();
                    assert(v.cols() % stride == 0);
 
                    if (!opts.export_field(name))
                        continue;
 
                    for (int i = 0; i < v.cols(); i += stride)
                    {
                        const Eigen::MatrixXd tmp = v.middleCols(i, stride);
                        assert(tmp.cols() == stride);
 
                        const int ii = (i / stride) + 1;
                        writer.add_field(fmt::format("{:s}_{:d}", name, ii), tmp);
                    }
                }
            }
 
            if (!opts.use_spline && (opts.scalar_values || opts.tensor_values))
            {
                Evaluator::average_grad_based_function(
                    mesh, problem.is_scalar(), state.n_bases, bases, gbases,
                    disc_orders, disc_ordersq, state.polys, state.polys_3d, *state.assembler,
                    ref_element_sampler, t, points.rows(), sol, vals, tvals,
                    opts.use_sampler, opts.boundary_only);
 
                if (obstacle.n_vertices() > 0)
                {
                    for (auto &v : vals)
                    {
                        v.second.conservativeResize(v.second.size() + obstacle.n_vertices(), 1);
                        v.second.bottomRows(obstacle.n_vertices()).setZero();
                    }
                }
 
                if (opts.scalar_values)
                {
                    for (const auto &v : vals)
                    {
                        if (opts.export_field(fmt::format("{:s}_avg", v.first)))
                            writer.add_field(fmt::format("{:s}_avg", v.first), v.second);
                    }
                }
                if (opts.tensor_values)
                {
                    for (const auto &v : tvals)
                    {
                        const int stride = mesh.dimension();
                        assert(v.second.cols() % stride == 0);
 
                        if (!opts.export_field(fmt::format("{:s}_avg", v.first)))
                            continue;
 
                        for (int i = 0; i < v.second.cols(); i += stride)
                        {
                            const Eigen::MatrixXd tmp = v.second.middleCols(i, stride);
                            assert(tmp.cols() == stride);
 
                            const int ii = (i / stride) + 1;
                            writer.add_field(
                                fmt::format("{:s}_avg_{:d}", v.first, ii), tmp);
                        }
                    }
                }
            }
        }
 
        if (opts.material_params)
        {
            const auto &params = assembler.parameters();
 
            std::map<std::string, Eigen::MatrixXd> param_val;
            for (const auto &[p, _] : params)
                param_val[p] = Eigen::MatrixXd(points.rows(), 1);
            Eigen::MatrixXd rhos(points.rows(), 1);
 
            Eigen::MatrixXd local_pts;
            Eigen::MatrixXi vis_faces_poly, vis_edges_poly;
 
            int index = 0;
            const auto &sampler = ref_element_sampler;
            for (int e = 0; e < int(bases.size()); ++e)
            {
                const basis::ElementBases &gbs = gbases[e];
                const basis::ElementBases &bs = bases[e];
 
                if (opts.use_sampler)
                {
                    if (mesh.is_simplex(e))
                        local_pts = sampler.simplex_points();
                    else if (mesh.is_cube(e))
                        local_pts = sampler.cube_points();
                    else if (mesh.is_prism(e))
                        local_pts = sampler.prism_points();
                    else
                    {
                        if (mesh.is_volume())
                            sampler.sample_polyhedron(polys_3d.at(e).first, polys_3d.at(e).second, local_pts, vis_faces_poly, vis_edges_poly);
                        else
                            sampler.sample_polygon(polys.at(e), local_pts, vis_faces_poly, vis_edges_poly);
                    }
                }
                else
                {
                    if (mesh.is_volume())
                    {
                        if (mesh.is_simplex(e))
                            autogen::p_nodes_3d(disc_orders(e), local_pts);
                        else if (mesh.is_cube(e))
                            autogen::q_nodes_3d(disc_orders(e), local_pts);
                        else if (mesh.is_prism(e))
                            autogen::prism_nodes_3d(disc_orders(e), disc_ordersq(e), local_pts);
                        else
                            continue;
                    }
                    else
                    {
                        if (mesh.is_simplex(e))
                            autogen::p_nodes_2d(disc_orders(e), local_pts);
                        else if (mesh.is_cube(e))
                            autogen::q_nodes_2d(disc_orders(e), local_pts);
                        else
                        {
                            const auto &mesh2d = static_cast<const mesh::Mesh2D &>(mesh);
                            const int n_v = mesh2d.n_face_vertices(e);
                            local_pts.resize(n_v, 2);
 
                            for (int j = 0; j < n_v; ++j)
                            {
                                local_pts.row(j) = mesh2d.point(mesh2d.face_vertex(e, j));
                            }
                        }
                    }
                }
 
                assembler::ElementAssemblyValues vals;
                vals.compute(e, mesh.is_volume(), local_pts, bs, gbs);
 
                for (int j = 0; j < vals.val.rows(); ++j)
                {
                    for (const auto &[p, func] : params)
                        param_val.at(p)(index) = func(local_pts.row(j), vals.val.row(j), t, e);
 
                    rhos(index) = density(local_pts.row(j), vals.val.row(j), t, e);
 
                    ++index;
                }
            }
 
            assert(index == points.rows());
 
            if (obstacle.n_vertices() > 0)
            {
                for (auto &[_, tmp] : param_val)
                {
                    tmp.conservativeResize(tmp.size() + obstacle.n_vertices(), 1);
                    tmp.bottomRows(obstacle.n_vertices()).setZero();
                }
 
                rhos.conservativeResize(rhos.size() + obstacle.n_vertices(), 1);
                rhos.bottomRows(obstacle.n_vertices()).setZero();
            }
            for (const auto &[p, tmp] : param_val)
            {
                if (opts.export_field(p))
                    writer.add_field(p, tmp);
            }
            if (opts.export_field("rho"))
                writer.add_field("rho", rhos);
        }
 
        if (opts.body_ids || opts.export_field("body_ids"))
        {
 
            Eigen::MatrixXd ids(points.rows(), 1);
 
            for (int i = 0; i < points.rows(); ++i)
            {
                ids(i) = mesh.get_body_id(el_id(i));
            }
 
            if (obstacle.n_vertices() > 0)
            {
                ids.conservativeResize(ids.size() + obstacle.n_vertices(), 1);
                ids.bottomRows(obstacle.n_vertices()).setZero();
            }
 
            writer.add_field("body_ids", ids);
        }
 
        // if (opts.export_field("rhs"))
        // {
        //  interpolate_function(pts_index, rhs, fun, opts.boundary_only);
        //  writer.add_field("rhs", fun);
        // }
 
        if (fun.cols() != 1 && state.mixed_assembler == nullptr && opts.export_field("traction_force"))
        {
            Eigen::MatrixXd traction_forces, traction_forces_fun;
            compute_traction_forces(state, sol, t, traction_forces, false);
 
            Evaluator::interpolate_function(
                mesh, problem.is_scalar(), bases, disc_orders, disc_ordersq,
                state.polys, state.polys_3d, ref_element_sampler,
                points.rows(), traction_forces, traction_forces_fun, opts.use_sampler, opts.boundary_only);
 
            if (obstacle.n_vertices() > 0)
            {
                traction_forces_fun.conservativeResize(traction_forces_fun.rows() + obstacle.n_vertices(), traction_forces_fun.cols());
                traction_forces_fun.bottomRows(obstacle.n_vertices()).setZero();
            }
 
            writer.add_field("traction_force", traction_forces_fun);
        }
 
        if (fun.cols() != 1 && state.mixed_assembler == nullptr && opts.export_field("gradient_of_elastic_potential"))
        {
            try
            {
                Eigen::VectorXd potential_grad;
                Eigen::MatrixXd potential_grad_fun;
                if (state.solve_data.elastic_form)
                    state.solve_data.elastic_form->first_derivative(sol, potential_grad);
 
                Evaluator::interpolate_function(
                    mesh, problem.is_scalar(), bases, disc_orders, disc_ordersq,
                    state.polys, state.polys_3d, ref_element_sampler,
                    points.rows(), potential_grad, potential_grad_fun, opts.use_sampler, opts.boundary_only);
 
                if (obstacle.n_vertices() > 0)
                {
                    potential_grad_fun.conservativeResize(potential_grad_fun.rows() + obstacle.n_vertices(), potential_grad_fun.cols());
                    potential_grad_fun.bottomRows(obstacle.n_vertices()).setZero();
                }
 
                writer.add_field("gradient_of_elastic_potential", potential_grad_fun);
            }
            catch (std::exception &)
            {
            }
        }
 
        if (fun.cols() != 1 && state.mixed_assembler == nullptr && opts.export_field("gradient_of_contact_potential"))
        {
            try
            {
                Eigen::VectorXd potential_grad;
                Eigen::MatrixXd potential_grad_fun;
                if (state.solve_data.contact_form && state.solve_data.contact_form->weight() > 0)
                {
                    state.solve_data.contact_form->first_derivative(sol, potential_grad);
                    potential_grad *= -state.solve_data.contact_form->barrier_stiffness() / state.solve_data.contact_form->weight();
 
                    Evaluator::interpolate_function(
                        mesh, problem.is_scalar(), bases, state.disc_orders, state.disc_ordersq,
                        state.polys, state.polys_3d, ref_element_sampler,
                        points.rows(), potential_grad, potential_grad_fun, opts.use_sampler, opts.boundary_only);
 
                    if (obstacle.n_vertices() > 0)
                    {
                        potential_grad_fun.conservativeResize(potential_grad_fun.rows() + obstacle.n_vertices(), potential_grad_fun.cols());
                        potential_grad_fun.bottomRows(obstacle.n_vertices()).setZero();
                    }
 
                    writer.add_field("gradient_of_contact_potential", potential_grad_fun);
                }
            }
            catch (std::exception &)
            {
            }
        }
 
        // Write the solution last so it is the default for warp-by-vector
        writer.add_field("solution", fun);
 
        if (obstacle.n_vertices() > 0)
        {
            const int orig_p = points.rows();
            points.conservativeResize(points.rows() + obstacle.n_vertices(), points.cols());
            points.bottomRows(obstacle.n_vertices()) = obstacle.v();
 
            if (elements.empty())
            {
                for (int i = 0; i < tets.rows(); ++i)
                {
                    elements.emplace_back();
                    elements.back().ctype = CellType::Tetrahedron;
                    for (int j = 0; j < tets.cols(); ++j)
                        elements.back().vertices.push_back(tets(i, j));
                }
            }
 
            for (int i = 0; i < obstacle.get_face_connectivity().rows(); ++i)
            {
                elements.emplace_back();
                elements.back().ctype = CellType::Tetrahedron;
                for (int j = 0; j < obstacle.get_face_connectivity().cols(); ++j)
                    elements.back().vertices.push_back(obstacle.get_face_connectivity()(i, j) + orig_p);
            }
 
            for (int i = 0; i < obstacle.get_edge_connectivity().rows(); ++i)
            {
                elements.emplace_back();
                elements.back().ctype = CellType::Tetrahedron;
                for (int j = 0; j < obstacle.get_edge_connectivity().cols(); ++j)
                    elements.back().vertices.push_back(obstacle.get_edge_connectivity()(i, j) + orig_p);
            }
 
            for (int i = 0; i < obstacle.get_vertex_connectivity().size(); ++i)
            {
                elements.emplace_back();
                elements.back().ctype = CellType::Tetrahedron;
                elements.back().vertices.push_back(obstacle.get_vertex_connectivity()(i) + orig_p);
            }
        }
 
        if (elements.empty())
            writer.write_mesh(path, points, tets, mesh.is_volume() ? CellType::Tetrahedron : CellType::Triangle);
        else
            writer.write_mesh(path, points, elements);
    }
 
    void OutGeometryData::save_volume_vector_field(
        const State &state,
        const Eigen::MatrixXd &points,
        const ExportOptions &opts,
        const std::string &name,
        const Eigen::VectorXd &field,
        paraviewo::ParaviewWriter &writer) const
    {
        Eigen::MatrixXd inerpolated_field;
        Evaluator::interpolate_function(
            *state.mesh, state.problem->is_scalar(), state.bases, state.disc_orders, state.disc_ordersq,
            state.polys, state.polys_3d, ref_element_sampler,
            points.rows(), field, inerpolated_field, opts.use_sampler, opts.boundary_only);
 
        if (state.obstacle.n_vertices() > 0)
        {
            inerpolated_field.conservativeResize(
                inerpolated_field.rows() + state.obstacle.n_vertices(), inerpolated_field.cols());
            inerpolated_field.bottomRows(state.obstacle.n_vertices()) =
                utils::unflatten(field.tail(state.obstacle.ndof()), inerpolated_field.cols());
        }
        if (opts.export_field(name))
            writer.add_field(name, inerpolated_field);
    }
 
    void OutGeometryData::save_surface(
        const std::string &export_surface,
        const State &state,
        const Eigen::MatrixXd &sol,
        const Eigen::MatrixXd &pressure,
        const double t,
        const double dt_in,
        const ExportOptions &opts,
        const bool is_contact_enabled) const
    {
 
        const Eigen::VectorXi &disc_orders = state.disc_orders;
        const auto &density = state.mass_matrix_assembler->density();
        const std::vector<basis::ElementBases> &bases = state.bases;
        const std::vector<basis::ElementBases> &pressure_bases = state.pressure_bases;
        const std::vector<basis::ElementBases> &gbases = state.geom_bases();
        const assembler::Assembler &assembler = *state.assembler;
        const assembler::Problem &problem = *state.problem;
        const mesh::Mesh &mesh = *state.mesh;
        int problem_dim = (problem.is_scalar() ? 1 : mesh.dimension());
 
        Eigen::MatrixXd boundary_vis_vertices;
        Eigen::MatrixXd boundary_vis_local_vertices;
        Eigen::MatrixXi boundary_vis_elements;
        Eigen::MatrixXi boundary_vis_elements_ids;
        Eigen::MatrixXi boundary_vis_primitive_ids;
        Eigen::MatrixXd boundary_vis_normals;
        Eigen::MatrixXd displaced_boundary_vis_normals;
 
        build_vis_boundary_mesh(mesh, bases, gbases, state.total_local_boundary, sol, problem_dim,
                                boundary_vis_vertices, boundary_vis_local_vertices, boundary_vis_elements,
                                boundary_vis_elements_ids, boundary_vis_primitive_ids, boundary_vis_normals,
                                displaced_boundary_vis_normals);
 
        Eigen::MatrixXd fun, interp_p, discr, vect, b_sidesets;
 
        Eigen::MatrixXd lsol, lp, lgrad, lpgrad;
 
        int actual_dim = 1;
        if (!problem.is_scalar())
            actual_dim = mesh.dimension();
 
        discr.resize(boundary_vis_vertices.rows(), 1);
        fun.resize(boundary_vis_vertices.rows(), actual_dim);
        interp_p.resize(boundary_vis_vertices.rows(), 1);
        vect.resize(boundary_vis_vertices.rows(), mesh.dimension());
 
        b_sidesets.resize(boundary_vis_vertices.rows(), 1);
        b_sidesets.setZero();
 
        for (int i = 0; i < boundary_vis_vertices.rows(); ++i)
        {
            const auto s_id = mesh.get_boundary_id(boundary_vis_primitive_ids(i));
            if (s_id > 0)
            {
                b_sidesets(i) = s_id;
            }
 
            const int el_index = boundary_vis_elements_ids(i);
            Evaluator::interpolate_at_local_vals(
                mesh, problem.is_scalar(), bases, gbases,
                el_index, boundary_vis_local_vertices.row(i), sol, lsol, lgrad);
            assert(lsol.size() == actual_dim);
            if (state.mixed_assembler != nullptr)
            {
                Evaluator::interpolate_at_local_vals(
                    mesh, 1, pressure_bases, gbases,
                    el_index, boundary_vis_local_vertices.row(i), pressure, lp, lpgrad);
                assert(lp.size() == 1);
                interp_p(i) = lp(0);
            }
 
            discr(i) = disc_orders(el_index);
            for (int j = 0; j < actual_dim; ++j)
            {
                fun(i, j) = lsol(j);
            }
 
            if (actual_dim == 1)
            {
                assert(lgrad.size() == mesh.dimension());
                for (int j = 0; j < mesh.dimension(); ++j)
                {
                    vect(i, j) = lgrad(j);
                }
            }
            else
            {
                assert(lgrad.size() == actual_dim * actual_dim);
                std::vector<assembler::Assembler::NamedMatrix> tensor_flat;
                const basis::ElementBases &gbs = gbases[el_index];
                const basis::ElementBases &bs = bases[el_index];
                assembler.compute_tensor_value(assembler::OutputData(t, el_index, bs, gbs, boundary_vis_local_vertices.row(i), sol), tensor_flat);
                // TF computed only from cauchy stress
                assert(tensor_flat[0].first == "cauchy_stess");
                assert(tensor_flat[0].second.size() == actual_dim * actual_dim);
 
                Eigen::Map<Eigen::MatrixXd> tensor(tensor_flat[0].second.data(), actual_dim, actual_dim);
                vect.row(i) = displaced_boundary_vis_normals.row(i) * tensor;
 
                double area = 0;
                if (mesh.is_volume())
                {
                    if (mesh.is_simplex(el_index))
                        area = mesh.tri_area(boundary_vis_primitive_ids(i));
                    else if (mesh.is_cube(el_index))
                        area = mesh.quad_area(boundary_vis_primitive_ids(i));
                    else if (mesh.is_prism(el_index))
                    {
                        const int tmp = boundary_vis_primitive_ids(i);
                        area = mesh.n_face_vertices(tmp) == 4 ? mesh.quad_area(tmp) : mesh.tri_area(tmp);
                    }
                }
                else
                    area = mesh.edge_length(boundary_vis_primitive_ids(i));
 
                vect.row(i) *= area;
            }
        }
 
        std::shared_ptr<paraviewo::ParaviewWriter> tmpw;
        if (opts.use_hdf5)
            tmpw = std::make_shared<paraviewo::HDF5VTUWriter>();
        else
            tmpw = std::make_shared<paraviewo::VTUWriter>();
        paraviewo::ParaviewWriter &writer = *tmpw;
 
        if (opts.export_field("normals"))
            writer.add_field("normals", boundary_vis_normals);
        if (opts.export_field("displaced_normals"))
            writer.add_field("displaced_normals", displaced_boundary_vis_normals);
        if (state.mixed_assembler != nullptr && opts.export_field("pressure"))
            writer.add_field("pressure", interp_p);
        if (opts.export_field("discr"))
            writer.add_field("discr", discr);
        if (opts.export_field("sidesets"))
            writer.add_field("sidesets", b_sidesets);
 
        if (actual_dim == 1 && opts.export_field("solution_grad"))
            writer.add_field("solution_grad", vect);
        else if (opts.export_field("traction_force"))
        {
            writer.add_field("traction_force", vect);
        }
 
        if (opts.material_params)
        {
            const auto &params = assembler.parameters();
 
            std::map<std::string, Eigen::MatrixXd> param_val;
            for (const auto &[p, _] : params)
                param_val[p] = Eigen::MatrixXd(boundary_vis_vertices.rows(), 1);
            Eigen::MatrixXd rhos(boundary_vis_vertices.rows(), 1);
 
            for (int i = 0; i < boundary_vis_vertices.rows(); ++i)
            {
                double lambda, mu;
 
                for (const auto &[p, func] : params)
                    param_val.at(p)(i) = func(boundary_vis_local_vertices.row(i), boundary_vis_vertices.row(i), t, boundary_vis_elements_ids(i));
 
                rhos(i) = density(boundary_vis_local_vertices.row(i), boundary_vis_vertices.row(i), t, boundary_vis_elements_ids(i));
            }
 
            for (const auto &[p, tmp] : param_val)
            {
                if (opts.export_field(p))
                    writer.add_field(p, tmp);
            }
            if (opts.export_field("rho"))
                writer.add_field("rho", rhos);
        }
 
        if (opts.body_ids || opts.export_field("body_ids"))
        {
 
            Eigen::MatrixXd ids(boundary_vis_vertices.rows(), 1);
 
            for (int i = 0; i < boundary_vis_vertices.rows(); ++i)
            {
                ids(i) = mesh.get_body_id(boundary_vis_elements_ids(i));
            }
 
            writer.add_field("body_ids", ids);
        }
 
        // Write the solution last so it is the default for warp-by-vector
        writer.add_field("solution", fun);
        writer.write_mesh(export_surface, boundary_vis_vertices, boundary_vis_elements, mesh.is_volume() ? CellType::Triangle : CellType::Line);
    }
 
    void OutGeometryData::save_contact_surface(
        const std::string &export_surface,
        const State &state,
        const Eigen::MatrixXd &sol,
        const Eigen::MatrixXd &pressure,
        const double t,
        const double dt_in,
        const ExportOptions &opts,
        const bool is_contact_enabled) const
    {
        const mesh::Mesh &mesh = *state.mesh;
        const ipc::CollisionMesh &collision_mesh = state.collision_mesh;
        const double dhat = state.args["contact"]["dhat"];
        const double friction_coefficient = state.args["contact"]["friction_coefficient"];
        const double epsv = state.args["contact"]["epsv"];
        const double dhat_a = state.args["contact"]["adhesion"]["dhat_a"];
        const double dhat_p = state.args["contact"]["adhesion"]["dhat_p"];
        const double Y = state.args["contact"]["adhesion"]["adhesion_strength"];
        const double epsa = state.args["contact"]["adhesion"]["epsa"];
        const double tangential_adhesion_coefficient = state.args["contact"]["adhesion"]["tangential_adhesion_coefficient"];
        const std::shared_ptr<solver::ContactForm> &contact_form = state.solve_data.contact_form;
        const std::shared_ptr<solver::FrictionForm> &friction_form = state.solve_data.friction_form;
        const std::shared_ptr<solver::NormalAdhesionForm> &normal_adhesion_form = state.solve_data.normal_adhesion_form;
        const std::shared_ptr<solver::TangentialAdhesionForm> &tangential_adhesion_form = state.solve_data.tangential_adhesion_form;
 
        std::shared_ptr<paraviewo::ParaviewWriter> tmpw;
        if (opts.use_hdf5)
            tmpw = std::make_shared<paraviewo::HDF5VTUWriter>();
        else
            tmpw = std::make_shared<paraviewo::VTUWriter>();
        paraviewo::ParaviewWriter &writer = *tmpw;
 
        const int problem_dim = mesh.dimension();
        const Eigen::MatrixXd full_displacements = utils::unflatten(sol, problem_dim);
        const Eigen::MatrixXd surface_displacements = collision_mesh.map_displacements(full_displacements);
 
        const Eigen::MatrixXd displaced_surface = collision_mesh.displace_vertices(full_displacements);
 
        ipc::NormalCollisions collision_set;
        // collision_set.set_use_convergent_formulation(state.args["contact"]["use_convergent_formulation"]);
        if (state.args["contact"]["use_convergent_formulation"])
        {
            collision_set.set_use_area_weighting(state.args["contact"]["use_area_weighting"]);
            collision_set.set_use_improved_max_approximator(state.args["contact"]["use_improved_max_operator"]);
        }
 
        collision_set.build(
            collision_mesh, displaced_surface, dhat,
            /*dmin=*/0, ipc::create_broad_phase(state.args["solver"]["contact"]["CCD"]["broad_phase"]));
 
        ipc::BarrierPotential barrier_potential(dhat);
        if (state.args["contact"]["use_convergent_formulation"])
        {
            barrier_potential.set_use_physical_barrier(state.args["contact"]["use_physical_barrier"]);
        }
 
        const double barrier_stiffness = contact_form != nullptr ? contact_form->barrier_stiffness() : 1;
 
        if (opts.contact_forces || opts.export_field("contact_forces"))
        {
            Eigen::MatrixXd forces = -barrier_stiffness * barrier_potential.gradient(collision_set, collision_mesh, displaced_surface);
 
            Eigen::MatrixXd forces_reshaped = utils::unflatten(forces, problem_dim);
 
            assert(forces_reshaped.rows() == surface_displacements.rows());
            assert(forces_reshaped.cols() == surface_displacements.cols());
            writer.add_field("contact_forces", forces_reshaped);
        }
 
        if (contact_form && state.args["contact"]["use_gcp_formulation"] && state.args["contact"]["use_adaptive_dhat"] && opts.export_field("adaptive_dhat"))
        {
            const auto form = std::dynamic_pointer_cast<solver::SmoothContactForm>(contact_form);
            assert(form);
            const auto &set = form->collision_set();
 
            if (problem_dim == 2)
            {
                Eigen::VectorXd dhats(collision_mesh.num_edges());
                dhats.setConstant(dhat);
                for (int e = 0; e < dhats.size(); e++)
                    dhats(e) = set.get_edge_dhat(e);
 
                writer.add_cell_field("dhat", dhats);
            }
            else
            {
                Eigen::VectorXd fdhats(collision_mesh.num_faces());
                fdhats.setConstant(dhat);
                for (int e = 0; e < fdhats.size(); e++)
                    fdhats(e) = set.get_face_dhat(e);
 
                writer.add_cell_field("dhat_face", fdhats);
 
                Eigen::VectorXd vdhats(collision_mesh.num_vertices());
                vdhats.setConstant(dhat);
                for (int i = 0; i < vdhats.size(); i++)
                    vdhats(i) = set.get_vert_dhat(i);
 
                writer.add_field("dhat_vert", vdhats);
            }
        }
 
        if (opts.friction_forces || opts.export_field("friction_forces"))
        {
            ipc::TangentialCollisions friction_collision_set;
            friction_collision_set.build(
                collision_mesh, displaced_surface, collision_set,
                barrier_potential, barrier_stiffness, friction_coefficient);
 
            ipc::FrictionPotential friction_potential(epsv);
 
            Eigen::MatrixXd velocities;
            if (state.solve_data.time_integrator != nullptr)
                velocities = state.solve_data.time_integrator->v_prev();
            else
                velocities = sol;
            velocities = collision_mesh.map_displacements(utils::unflatten(velocities, collision_mesh.dim()));
 
            Eigen::MatrixXd forces = -friction_potential.gradient(
                friction_collision_set, collision_mesh, velocities);
 
            Eigen::MatrixXd forces_reshaped = utils::unflatten(forces, problem_dim);
 
            assert(forces_reshaped.rows() == surface_displacements.rows());
            assert(forces_reshaped.cols() == surface_displacements.cols());
            writer.add_field("friction_forces", forces_reshaped);
        }
 
        ipc::NormalCollisions adhesion_collision_set;
        adhesion_collision_set.build(
            collision_mesh, displaced_surface, dhat_a,
            /*dmin=*/0, ipc::create_broad_phase(state.args["solver"]["contact"]["CCD"]["broad_phase"]));
 
        ipc::NormalAdhesionPotential normal_adhesion_potential(dhat_p, dhat_a, Y, 1);
 
        if (opts.normal_adhesion_forces || opts.export_field("normal_adhesion_forces"))
        {
            Eigen::MatrixXd forces = -1 * normal_adhesion_potential.gradient(adhesion_collision_set, collision_mesh, displaced_surface);
 
            Eigen::MatrixXd forces_reshaped = utils::unflatten(forces, problem_dim);
 
            assert(forces_reshaped.rows() == surface_displacements.rows());
            assert(forces_reshaped.cols() == surface_displacements.cols());
            writer.add_field("normal_adhesion_forces", forces_reshaped);
        }
 
        if (opts.tangential_adhesion_forces || opts.export_field("tangential_adhesion_forces"))
        {
            ipc::TangentialCollisions tangential_collision_set;
            tangential_collision_set.build(
                collision_mesh, displaced_surface, adhesion_collision_set,
                normal_adhesion_potential, 1, tangential_adhesion_coefficient);
 
            ipc::TangentialAdhesionPotential tangential_adhesion_potential(epsa);
 
            Eigen::MatrixXd velocities;
            if (state.solve_data.time_integrator != nullptr)
                velocities = state.solve_data.time_integrator->v_prev();
            else
                velocities = sol;
            velocities = collision_mesh.map_displacements(utils::unflatten(velocities, collision_mesh.dim()));
 
            Eigen::MatrixXd forces = -tangential_adhesion_potential.gradient(
                tangential_collision_set, collision_mesh, velocities);
 
            Eigen::MatrixXd forces_reshaped = utils::unflatten(forces, problem_dim);
 
            assert(forces_reshaped.rows() == surface_displacements.rows());
            assert(forces_reshaped.cols() == surface_displacements.cols());
            writer.add_field("tangential_adhesion_forces", forces_reshaped);
        }
 
        assert(collision_mesh.rest_positions().rows() == surface_displacements.rows());
        assert(collision_mesh.rest_positions().cols() == surface_displacements.cols());
 
        // Write the solution last so it is the default for warp-by-vector
        writer.add_field("solution", surface_displacements);
 
        writer.write_mesh(
            export_surface.substr(0, export_surface.length() - 4) + "_contact.vtu",
            collision_mesh.rest_positions(),
            problem_dim == 3 ? collision_mesh.faces() : collision_mesh.edges(),
            problem_dim == 3 ? CellType::Triangle : CellType::Line);
    }
 
    void OutGeometryData::save_wire(
        const std::string &name,
        const State &state,
        const Eigen::MatrixXd &sol,
        const double t,
        const ExportOptions &opts) const
    {
        const std::vector<basis::ElementBases> &gbases = state.geom_bases();
        const mesh::Mesh &mesh = *state.mesh;
        const assembler::Problem &problem = *state.problem;
 
        const auto &sampler = ref_element_sampler;
 
        Eigen::MatrixXi vis_faces_poly, vis_edges_poly;
        Eigen::MatrixXd vis_pts_poly;
 
        const auto &current_bases = gbases;
        int seg_total_size = 0;
        int pts_total_size = 0;
        int faces_total_size = 0;
 
        for (size_t i = 0; i < current_bases.size(); ++i)
        {
            const auto &bs = current_bases[i];
 
            if (mesh.is_simplex(i))
            {
                pts_total_size += sampler.simplex_points().rows();
                seg_total_size += sampler.simplex_edges().rows();
                faces_total_size += sampler.simplex_faces().rows();
            }
            else if (mesh.is_cube(i))
            {
                pts_total_size += sampler.cube_points().rows();
                seg_total_size += sampler.cube_edges().rows();
                faces_total_size += sampler.cube_faces().rows();
            }
            else if (mesh.is_prism(i))
            {
                pts_total_size += sampler.prism_points().rows();
                seg_total_size += sampler.prism_edges().rows();
                faces_total_size += sampler.prism_faces().rows();
            }
            else
            {
                if (mesh.is_volume())
                    sampler.sample_polyhedron(state.polys_3d.at(i).first, state.polys_3d.at(i).second, vis_pts_poly, vis_faces_poly, vis_edges_poly);
                else
                    sampler.sample_polygon(state.polys.at(i), vis_pts_poly, vis_faces_poly, vis_edges_poly);
 
                pts_total_size += vis_pts_poly.rows();
                seg_total_size += vis_edges_poly.rows();
                faces_total_size += vis_faces_poly.rows();
            }
        }
 
        Eigen::MatrixXd points(pts_total_size, mesh.dimension());
        Eigen::MatrixXi edges(seg_total_size, 2);
        Eigen::MatrixXi faces(faces_total_size, 3);
        points.setZero();
 
        Eigen::MatrixXd mapped, tmp;
        int seg_index = 0, pts_index = 0, face_index = 0;
        for (size_t i = 0; i < current_bases.size(); ++i)
        {
            const auto &bs = current_bases[i];
 
            if (mesh.is_simplex(i))
            {
                bs.eval_geom_mapping(sampler.simplex_points(), mapped);
                edges.block(seg_index, 0, sampler.simplex_edges().rows(), edges.cols()) = sampler.simplex_edges().array() + pts_index;
                seg_index += sampler.simplex_edges().rows();
 
                faces.block(face_index, 0, sampler.simplex_faces().rows(), 3) = sampler.simplex_faces().array() + pts_index;
                face_index += sampler.simplex_faces().rows();
 
                points.block(pts_index, 0, mapped.rows(), points.cols()) = mapped;
                pts_index += mapped.rows();
            }
            else if (mesh.is_cube(i))
            {
                bs.eval_geom_mapping(sampler.cube_points(), mapped);
                edges.block(seg_index, 0, sampler.cube_edges().rows(), edges.cols()) = sampler.cube_edges().array() + pts_index;
                seg_index += sampler.cube_edges().rows();
 
                faces.block(face_index, 0, sampler.cube_faces().rows(), 3) = sampler.cube_faces().array() + pts_index;
                face_index += sampler.cube_faces().rows();
 
                points.block(pts_index, 0, mapped.rows(), points.cols()) = mapped;
                pts_index += mapped.rows();
            }
            else if (mesh.is_prism(i))
            {
                bs.eval_geom_mapping(sampler.prism_points(), mapped);
                edges.block(seg_index, 0, sampler.prism_edges().rows(), edges.cols()) = sampler.prism_edges().array() + pts_index;
                seg_index += sampler.prism_edges().rows();
 
                faces.block(face_index, 0, sampler.prism_faces().rows(), 3) = sampler.prism_faces().array() + pts_index;
                face_index += sampler.prism_faces().rows();
 
                points.block(pts_index, 0, mapped.rows(), points.cols()) = mapped;
                pts_index += mapped.rows();
            }
            else
            {
                if (mesh.is_volume())
                    sampler.sample_polyhedron(state.polys_3d.at(i).first, state.polys_3d.at(i).second, vis_pts_poly, vis_faces_poly, vis_edges_poly);
                else
                    sampler.sample_polygon(state.polys.at(i), vis_pts_poly, vis_faces_poly, vis_edges_poly);
 
                edges.block(seg_index, 0, vis_edges_poly.rows(), edges.cols()) = vis_edges_poly.array() + pts_index;
                seg_index += vis_edges_poly.rows();
 
                faces.block(face_index, 0, vis_faces_poly.rows(), 3) = vis_faces_poly.array() + pts_index;
                face_index += vis_faces_poly.rows();
 
                points.block(pts_index, 0, vis_pts_poly.rows(), points.cols()) = vis_pts_poly;
                pts_index += vis_pts_poly.rows();
            }
        }
 
        assert(pts_index == points.rows());
        assert(face_index == faces.rows());
 
        if (mesh.is_volume())
        {
            // reverse all faces
            for (long i = 0; i < faces.rows(); ++i)
            {
                const int v0 = faces(i, 0);
                const int v1 = faces(i, 1);
                const int v2 = faces(i, 2);
 
                int tmpc = faces(i, 2);
                faces(i, 2) = faces(i, 1);
                faces(i, 1) = tmpc;
            }
        }
        else
        {
            Eigen::Matrix2d mmat;
            for (long i = 0; i < faces.rows(); ++i)
            {
                const int v0 = faces(i, 0);
                const int v1 = faces(i, 1);
                const int v2 = faces(i, 2);
 
                mmat.row(0) = points.row(v2) - points.row(v0);
                mmat.row(1) = points.row(v1) - points.row(v0);
 
                if (mmat.determinant() > 0)
                {
                    int tmpc = faces(i, 2);
                    faces(i, 2) = faces(i, 1);
                    faces(i, 1) = tmpc;
                }
            }
        }
 
        Eigen::MatrixXd fun;
        Evaluator::interpolate_function(
            mesh, problem.is_scalar(), state.bases, state.disc_orders, state.disc_ordersq,
            state.polys, state.polys_3d, ref_element_sampler,
            pts_index, sol, fun, /*use_sampler*/ true, false);
 
        Eigen::MatrixXd exact_fun, err;
 
        if (problem.has_exact_sol())
        {
            problem.exact(points, t, exact_fun);
            err = (fun - exact_fun).eval().rowwise().norm();
        }
 
        std::shared_ptr<paraviewo::ParaviewWriter> tmpw;
        if (opts.use_hdf5)
            tmpw = std::make_shared<paraviewo::HDF5VTUWriter>();
        else
            tmpw = std::make_shared<paraviewo::VTUWriter>();
        paraviewo::ParaviewWriter &writer = *tmpw;
 
        if (problem.has_exact_sol())
        {
            if (opts.export_field("exact"))
                writer.add_field("exact", exact_fun);
            if (opts.export_field("error"))
                writer.add_field("error", err);
        }
 
        if (fun.cols() != 1)
        {
            std::vector<assembler::Assembler::NamedMatrix> scalar_val;
            Evaluator::compute_scalar_value(
                mesh, problem.is_scalar(), state.bases, gbases,
                state.disc_orders, state.disc_ordersq, state.polys, state.polys_3d,
                *state.assembler,
                ref_element_sampler, pts_index, sol, t, scalar_val, /*use_sampler*/ true, false);
            for (const auto &v : scalar_val)
            {
                if (opts.export_field(v.first))
                    writer.add_field(v.first, v.second);
            }
        }
        // Write the solution last so it is the default for warp-by-vector
        writer.add_field("solution", fun);
 
        writer.write_mesh(name, points, edges, CellType::Line);
    }
 
    void OutGeometryData::save_points(
        const std::string &path,
        const State &state,
        const Eigen::MatrixXd &sol,
        const ExportOptions &opts) const
    {
        const auto &dirichlet_nodes = state.dirichlet_nodes;
        const auto &dirichlet_nodes_position = state.dirichlet_nodes_position;
        const mesh::Mesh &mesh = *state.mesh;
        const assembler::Problem &problem = *state.problem;
 
        int actual_dim = 1;
        if (!problem.is_scalar())
            actual_dim = mesh.dimension();
 
        Eigen::MatrixXd fun(dirichlet_nodes_position.size(), actual_dim);
        Eigen::MatrixXd b_sidesets(dirichlet_nodes_position.size(), 1);
        b_sidesets.setZero();
        Eigen::MatrixXd points(dirichlet_nodes_position.size(), mesh.dimension());
        std::vector<CellElement> cells(dirichlet_nodes_position.size());
 
        for (int i = 0; i < dirichlet_nodes_position.size(); ++i)
        {
            const int n_id = dirichlet_nodes[i];
            const auto s_id = mesh.get_node_id(n_id);
            if (s_id > 0)
            {
                b_sidesets(i) = s_id;
            }
 
            for (int j = 0; j < actual_dim; ++j)
            {
                fun(i, j) = sol(n_id * actual_dim + j);
            }
 
            points.row(i) = dirichlet_nodes_position[i];
            cells[i].vertices.push_back(i);
            cells[i].ctype = CellType::Vertex;
        }
 
        std::shared_ptr<paraviewo::ParaviewWriter> tmpw;
        if (opts.use_hdf5)
            tmpw = std::make_shared<paraviewo::HDF5VTUWriter>();
        else
            tmpw = std::make_shared<paraviewo::VTUWriter>();
        paraviewo::ParaviewWriter &writer = *tmpw;
 
        if (opts.export_field("sidesets"))
            writer.add_field("sidesets", b_sidesets);
        // Write the solution last so it is the default for warp-by-vector
        writer.add_field("solution", fun);
        writer.write_mesh(path, points, cells);
    }
 
    void OutGeometryData::save_pvd(
        const std::string &name,
        const std::function<std::string(int)> &vtu_names,
        int time_steps, double t0, double dt, int skip_frame) const
    {
        paraviewo::PVDWriter::save_pvd(name, vtu_names, time_steps, t0, dt, skip_frame);
    }
 
    void OutGeometryData::init_sampler(const polyfem::mesh::Mesh &mesh, const double vismesh_rel_area)
    {
        ref_element_sampler.init(mesh.is_volume(), mesh.n_elements(), vismesh_rel_area);
    }
 
    void OutGeometryData::build_grid(const polyfem::mesh::Mesh &mesh, const double spacing)
    {
        if (spacing <= 0)
            return;
 
        RowVectorNd min, max;
        mesh.bounding_box(min, max);
        const RowVectorNd delta = max - min;
        const int nx = delta[0] / spacing + 1;
        const int ny = delta[1] / spacing + 1;
        const int nz = delta.cols() >= 3 ? (delta[2] / spacing + 1) : 1;
        const int n = nx * ny * nz;
 
        grid_points.resize(n, delta.cols());
        int index = 0;
        for (int i = 0; i < nx; ++i)
        {
            const double x = (delta[0] / (nx - 1)) * i + min[0];
 
            for (int j = 0; j < ny; ++j)
            {
                const double y = (delta[1] / (ny - 1)) * j + min[1];
 
                if (delta.cols() <= 2)
                {
                    grid_points.row(index++) << x, y;
                }
                else
                {
                    for (int k = 0; k < nz; ++k)
                    {
                        const double z = (delta[2] / (nz - 1)) * k + min[2];
                        grid_points.row(index++) << x, y, z;
                    }
                }
            }
        }
 
        assert(index == n);
 
        std::vector<std::array<Eigen::Vector3d, 2>> boxes;
        mesh.elements_boxes(boxes);
 
        SimpleBVH::BVH bvh;
        bvh.init(boxes);
 
        const double eps = 1e-6;
 
        grid_points_to_elements.resize(grid_points.rows(), 1);
        grid_points_to_elements.setConstant(-1);
 
        grid_points_bc.resize(grid_points.rows(), mesh.is_volume() ? 4 : 3);
 
        for (int i = 0; i < grid_points.rows(); ++i)
        {
            const Eigen::Vector3d min(
                grid_points(i, 0) - eps,
                grid_points(i, 1) - eps,
                (mesh.is_volume() ? grid_points(i, 2) : 0) - eps);
 
            const Eigen::Vector3d max(
                grid_points(i, 0) + eps,
                grid_points(i, 1) + eps,
                (mesh.is_volume() ? grid_points(i, 2) : 0) + eps);
 
            std::vector<unsigned int> candidates;
 
            bvh.intersect_box(min, max, candidates);
 
            for (const auto cand : candidates)
            {
                if (!mesh.is_simplex(cand))
                {
                    logger().warn("Element {} is not simplex, skipping", cand);
                    continue;
                }
 
                Eigen::MatrixXd coords;
                mesh.barycentric_coords(grid_points.row(i), cand, coords);
 
                for (int d = 0; d < coords.size(); ++d)
                {
                    if (fabs(coords(d)) < 1e-8)
                        coords(d) = 0;
                    else if (fabs(coords(d) - 1) < 1e-8)
                        coords(d) = 1;
                }
 
                if (coords.array().minCoeff() >= 0 && coords.array().maxCoeff() <= 1)
                {
                    grid_points_to_elements(i) = cand;
                    grid_points_bc.row(i) = coords;
                    break;
                }
            }
        }
    }
 
    void OutStatsData::compute_mesh_size(const polyfem::mesh::Mesh &mesh_in, const std::vector<polyfem::basis::ElementBases> &bases_in, const int n_samples, const bool use_curved_mesh_size)
    {
        Eigen::MatrixXd samples_simplex, samples_cube, mapped, p0, p1, p;
 
        mesh_size = 0;
        average_edge_length = 0;
        min_edge_length = std::numeric_limits<double>::max();
 
        if (!use_curved_mesh_size)
        {
            mesh_in.get_edges(p0, p1);
            p = p0 - p1;
            min_edge_length = p.rowwise().norm().minCoeff();
            average_edge_length = p.rowwise().norm().mean();
            mesh_size = p.rowwise().norm().maxCoeff();
 
            logger().info("hmin: {}", min_edge_length);
            logger().info("hmax: {}", mesh_size);
            logger().info("havg: {}", average_edge_length);
 
            return;
        }
 
        if (mesh_in.is_volume())
        {
            utils::EdgeSampler::sample_3d_simplex(n_samples, samples_simplex);
            utils::EdgeSampler::sample_3d_cube(n_samples, samples_cube);
        }
        else
        {
            utils::EdgeSampler::sample_2d_simplex(n_samples, samples_simplex);
            utils::EdgeSampler::sample_2d_cube(n_samples, samples_cube);
        }
 
        int n = 0;
        for (size_t i = 0; i < bases_in.size(); ++i)
        {
            if (mesh_in.is_polytope(i))
                continue;
            int n_edges;
 
            if (mesh_in.is_simplex(i))
            {
                n_edges = mesh_in.is_volume() ? 6 : 3;
                bases_in[i].eval_geom_mapping(samples_simplex, mapped);
            }
            else
            {
                n_edges = mesh_in.is_volume() ? 12 : 4;
                bases_in[i].eval_geom_mapping(samples_cube, mapped);
            }
 
            for (int j = 0; j < n_edges; ++j)
            {
                double current_edge = 0;
                for (int k = 0; k < n_samples - 1; ++k)
                {
                    p0 = mapped.row(j * n_samples + k);
                    p1 = mapped.row(j * n_samples + k + 1);
                    p = p0 - p1;
 
                    current_edge += p.norm();
                }
 
                mesh_size = std::max(current_edge, mesh_size);
                min_edge_length = std::min(current_edge, min_edge_length);
                average_edge_length += current_edge;
                ++n;
            }
        }
 
        average_edge_length /= n;
 
        logger().info("hmin: {}", min_edge_length);
        logger().info("hmax: {}", mesh_size);
        logger().info("havg: {}", average_edge_length);
    }
 
    void OutStatsData::reset()
    {
        sigma_avg = 0;
        sigma_max = 0;
        sigma_min = 0;
 
        n_flipped = 0;
    }
 
    void OutStatsData::count_flipped_elements(const polyfem::mesh::Mesh &mesh, const std::vector<polyfem::basis::ElementBases> &gbases)
    {
        using namespace mesh;
 
        logger().info("Counting flipped elements...");
        const auto &els_tag = mesh.elements_tag();
 
        // flipped_elements.clear();
        for (size_t i = 0; i < gbases.size(); ++i)
        {
            if (mesh.is_polytope(i))
                continue;
 
            polyfem::assembler::ElementAssemblyValues vals;
            if (!vals.is_geom_mapping_positive(mesh.is_volume(), gbases[i]))
            {
                ++n_flipped;
 
                static const std::vector<std::string> element_type_names{{
                    "Simplex",
                    "RegularInteriorCube",
                    "RegularBoundaryCube",
                    "SimpleSingularInteriorCube",
                    "MultiSingularInteriorCube",
                    "SimpleSingularBoundaryCube",
                    "InterfaceCube",
                    "MultiSingularBoundaryCube",
                    "BoundaryPolytope",
                    "InteriorPolytope",
                    "Undefined",
                }};
 
                log_and_throw_error("element {} is flipped, type {}", i, element_type_names[static_cast<int>(els_tag[i])]);
            }
        }
 
        logger().info(" done");
 
        // dynamic_cast<Mesh3D *>(mesh.get())->save({56}, 1, "mesh.HYBRID");
 
        // std::sort(flipped_elements.begin(), flipped_elements.end());
        // auto it = std::unique(flipped_elements.begin(), flipped_elements.end());
        // flipped_elements.resize(std::distance(flipped_elements.begin(), it));
    }
 
    void OutStatsData::compute_errors(
        const int n_bases,
        const std::vector<polyfem::basis::ElementBases> &bases,
        const std::vector<polyfem::basis::ElementBases> &gbases,
        const polyfem::mesh::Mesh &mesh,
        const assembler::Problem &problem,
        const double tend,
        const Eigen::MatrixXd &sol)
    {
        if (n_bases <= 0)
        {
            logger().error("Build the bases first!");
            return;
        }
        if (sol.size() <= 0)
        {
            logger().error("Solve the problem first!");
            return;
        }
 
        int actual_dim = 1;
        if (!problem.is_scalar())
            actual_dim = mesh.dimension();
 
        igl::Timer timer;
        timer.start();
        logger().info("Computing errors...");
        using std::max;
 
        const int n_el = int(bases.size());
 
        Eigen::MatrixXd v_exact, v_approx;
        Eigen::MatrixXd v_exact_grad(0, 0), v_approx_grad;
 
        l2_err = 0;
        h1_err = 0;
        grad_max_err = 0;
        h1_semi_err = 0;
        linf_err = 0;
        lp_err = 0;
        // double pred_norm = 0;
 
        static const int p = 8;
 
        // Eigen::MatrixXd err_per_el(n_el, 5);
        polyfem::assembler::ElementAssemblyValues vals;
 
        for (int e = 0; e < n_el; ++e)
        {
            vals.compute(e, mesh.is_volume(), bases[e], gbases[e]);
 
            if (problem.has_exact_sol())
            {
                problem.exact(vals.val, tend, v_exact);
                problem.exact_grad(vals.val, tend, v_exact_grad);
            }
 
            v_approx.resize(vals.val.rows(), actual_dim);
            v_approx.setZero();
 
            v_approx_grad.resize(vals.val.rows(), mesh.dimension() * actual_dim);
            v_approx_grad.setZero();
 
            const int n_loc_bases = int(vals.basis_values.size());
 
            for (int i = 0; i < n_loc_bases; ++i)
            {
                const auto &val = vals.basis_values[i];
 
                for (size_t ii = 0; ii < val.global.size(); ++ii)
                {
                    for (int d = 0; d < actual_dim; ++d)
                    {
                        v_approx.col(d) += val.global[ii].val * sol(val.global[ii].index * actual_dim + d) * val.val;
                        v_approx_grad.block(0, d * val.grad_t_m.cols(), v_approx_grad.rows(), val.grad_t_m.cols()) += val.global[ii].val * sol(val.global[ii].index * actual_dim + d) * val.grad_t_m;
                    }
                }
            }
 
            const auto err = problem.has_exact_sol() ? (v_exact - v_approx).eval().rowwise().norm().eval() : (v_approx).eval().rowwise().norm().eval();
            const auto err_grad = problem.has_exact_sol() ? (v_exact_grad - v_approx_grad).eval().rowwise().norm().eval() : (v_approx_grad).eval().rowwise().norm().eval();
 
            // for(long i = 0; i < err.size(); ++i)
            // errors.push_back(err(i));
 
            linf_err = std::max(linf_err, err.maxCoeff());
            grad_max_err = std::max(linf_err, err_grad.maxCoeff());
 
            // {
            //  const auto &mesh3d = *dynamic_cast<Mesh3D *>(mesh.get());
            //  const auto v0 = mesh3d.point(mesh3d.cell_vertex(e, 0));
            //  const auto v1 = mesh3d.point(mesh3d.cell_vertex(e, 1));
            //  const auto v2 = mesh3d.point(mesh3d.cell_vertex(e, 2));
            //  const auto v3 = mesh3d.point(mesh3d.cell_vertex(e, 3));
 
            //  Eigen::Matrix<double, 6, 3> ee;
            //  ee.row(0) = v0 - v1;
            //  ee.row(1) = v1 - v2;
            //  ee.row(2) = v2 - v0;
 
            //  ee.row(3) = v0 - v3;
            //  ee.row(4) = v1 - v3;
            //  ee.row(5) = v2 - v3;
 
            //  Eigen::Matrix<double, 6, 1> en = ee.rowwise().norm();
 
            //  // Eigen::Matrix<double, 3*4, 1> alpha;
            //  // alpha(0) = angle3(e.row(0), -e.row(1));      alpha(1) = angle3(e.row(1), -e.row(2));     alpha(2) = angle3(e.row(2), -e.row(0));
            //  // alpha(3) = angle3(e.row(0), -e.row(4));      alpha(4) = angle3(e.row(4), e.row(3));      alpha(5) = angle3(-e.row(3), -e.row(0));
            //  // alpha(6) = angle3(-e.row(4), -e.row(1)); alpha(7) = angle3(e.row(1), -e.row(5));     alpha(8) = angle3(e.row(5), e.row(4));
            //  // alpha(9) = angle3(-e.row(2), -e.row(5)); alpha(10) = angle3(e.row(5), e.row(3));     alpha(11) = angle3(-e.row(3), e.row(2));
 
            //  const double S = (ee.row(0).cross(ee.row(1)).norm() + ee.row(0).cross(ee.row(4)).norm() + ee.row(4).cross(ee.row(1)).norm() + ee.row(2).cross(ee.row(5)).norm()) / 2;
            //  const double V = std::abs(ee.row(3).dot(ee.row(2).cross(-ee.row(0))))/6;
            //  const double rho = 3 * V / S;
            //  const double hp = en.maxCoeff();
            //  const int pp = disc_orders(e);
            //  const int p_ref = args["space"]["discr_order"];
 
            //  err_per_el(e, 0) = err.mean();
            //  err_per_el(e, 1) = err.maxCoeff();
            //  err_per_el(e, 2) = std::pow(hp, pp+1)/(rho/hp); // /std::pow(average_edge_length, p_ref+1) * (sqrt(6)/12);
            //  err_per_el(e, 3) = rho/hp;
            //  err_per_el(e, 4) = (vals.det.array() * vals.quadrature.weights.array()).sum();
 
            //  // pred_norm += (pow(std::pow(hp, pp+1)/(rho/hp),p) * vals.det.array() * vals.quadrature.weights.array()).sum();
            // }
 
            l2_err += (err.array() * err.array() * vals.det.array() * vals.quadrature.weights.array()).sum();
            h1_err += (err_grad.array() * err_grad.array() * vals.det.array() * vals.quadrature.weights.array()).sum();
            lp_err += (err.array().pow(p) * vals.det.array() * vals.quadrature.weights.array()).sum();
        }
 
        h1_semi_err = sqrt(fabs(h1_err));
        h1_err = sqrt(fabs(l2_err) + fabs(h1_err));
        l2_err = sqrt(fabs(l2_err));
 
        lp_err = pow(fabs(lp_err), 1. / p);
 
        // pred_norm = pow(fabs(pred_norm), 1./p);
 
        timer.stop();
        const double computing_errors_time = timer.getElapsedTime();
        logger().info(" took {}s", computing_errors_time);
 
        logger().info("-- L2 error: {}", l2_err);
        logger().info("-- Lp error: {}", lp_err);
        logger().info("-- H1 error: {}", h1_err);
        logger().info("-- H1 semi error: {}", h1_semi_err);
        // logger().info("-- Perd norm: {}", pred_norm);
 
        logger().info("-- Linf error: {}", linf_err);
        logger().info("-- grad max error: {}", grad_max_err);
 
        // {
        //  std::ofstream out("errs.txt");
        //  out<<err_per_el;
        //  out.close();
        // }
    }
 
    void OutStatsData::compute_mesh_stats(const polyfem::mesh::Mesh &mesh)
    {
        using namespace polyfem::mesh;
 
        simplex_count = 0;
        prism_count = 0;
        regular_count = 0;
        regular_boundary_count = 0;
        simple_singular_count = 0;
        multi_singular_count = 0;
        boundary_count = 0;
        non_regular_boundary_count = 0;
        non_regular_count = 0;
        undefined_count = 0;
        multi_singular_boundary_count = 0;
 
        const auto &els_tag = mesh.elements_tag();
 
        for (size_t i = 0; i < els_tag.size(); ++i)
        {
            const ElementType type = els_tag[i];
 
            switch (type)
            {
            case ElementType::SIMPLEX:
                simplex_count++;
                break;
            case ElementType::PRISM:
                prism_count++;
                break;
            case ElementType::REGULAR_INTERIOR_CUBE:
                regular_count++;
                break;
            case ElementType::REGULAR_BOUNDARY_CUBE:
                regular_boundary_count++;
                break;
            case ElementType::SIMPLE_SINGULAR_INTERIOR_CUBE:
                simple_singular_count++;
                break;
            case ElementType::MULTI_SINGULAR_INTERIOR_CUBE:
                multi_singular_count++;
                break;
            case ElementType::SIMPLE_SINGULAR_BOUNDARY_CUBE:
                boundary_count++;
                break;
            case ElementType::INTERFACE_CUBE:
            case ElementType::MULTI_SINGULAR_BOUNDARY_CUBE:
                multi_singular_boundary_count++;
                break;
            case ElementType::BOUNDARY_POLYTOPE:
                non_regular_boundary_count++;
                break;
            case ElementType::INTERIOR_POLYTOPE:
                non_regular_count++;
                break;
            case ElementType::UNDEFINED:
                undefined_count++;
                break;
            default:
                throw std::runtime_error("Unknown element type");
            }
        }
 
        logger().info("simplex_count: \t{}", simplex_count);
        logger().info("prism_count: \t{}", prism_count);
        logger().info("regular_count: \t{}", regular_count);
        logger().info("regular_boundary_count: \t{}", regular_boundary_count);
        logger().info("simple_singular_count: \t{}", simple_singular_count);
        logger().info("multi_singular_count: \t{}", multi_singular_count);
        logger().info("boundary_count: \t{}", boundary_count);
        logger().info("multi_singular_boundary_count: \t{}", multi_singular_boundary_count);
        logger().info("non_regular_count: \t{}", non_regular_count);
        logger().info("non_regular_boundary_count: \t{}", non_regular_boundary_count);
        logger().info("undefined_count: \t{}", undefined_count);
        logger().info("total count:\t {}", mesh.n_elements());
    }
 
    void OutStatsData::save_json(
        const nlohmann::json &args,
        const int n_bases, const int n_pressure_bases,
        const Eigen::MatrixXd &sol,
        const mesh::Mesh &mesh,
        const Eigen::VectorXi &disc_orders,
        const Eigen::VectorXi &disc_ordersq,
        const assembler::Problem &problem,
        const OutRuntimeData &runtime,
        const std::string &formulation,
        const bool isoparametric,
        const int sol_at_node_id,
        nlohmann::json &j)
    {
 
        j["args"] = args;
 
        j["geom_order"] = mesh.orders().size() > 0 ? mesh.orders().maxCoeff() : 1;
        j["geom_order_min"] = mesh.orders().size() > 0 ? mesh.orders().minCoeff() : 1;
        j["discr_order_min"] = disc_orders.minCoeff();
        j["discr_order_max"] = disc_orders.maxCoeff();
        j["discr_orderq_min"] = disc_ordersq.minCoeff();
        j["discr_orderq_max"] = disc_ordersq.maxCoeff();
        j["iso_parametric"] = isoparametric;
        j["problem"] = problem.name();
        j["mat_size"] = mat_size;
        j["num_bases"] = n_bases;
        j["num_pressure_bases"] = n_pressure_bases;
        j["num_non_zero"] = nn_zero;
        j["num_flipped"] = n_flipped;
        j["num_dofs"] = num_dofs;
        j["num_vertices"] = mesh.n_vertices();
        j["num_elements"] = mesh.n_elements();
 
        j["num_p1"] = (disc_orders.array() == 1).count();
        j["num_p2"] = (disc_orders.array() == 2).count();
        j["num_p3"] = (disc_orders.array() == 3).count();
        j["num_p4"] = (disc_orders.array() == 4).count();
        j["num_p5"] = (disc_orders.array() == 5).count();
 
        j["mesh_size"] = mesh_size;
        j["max_angle"] = max_angle;
 
        j["sigma_max"] = sigma_max;
        j["sigma_min"] = sigma_min;
        j["sigma_avg"] = sigma_avg;
 
        j["min_edge_length"] = min_edge_length;
        j["average_edge_length"] = average_edge_length;
 
        j["err_l2"] = l2_err;
        j["err_h1"] = h1_err;
        j["err_h1_semi"] = h1_semi_err;
        j["err_linf"] = linf_err;
        j["err_linf_grad"] = grad_max_err;
        j["err_lp"] = lp_err;
 
        j["spectrum"] = {spectrum(0), spectrum(1), spectrum(2), spectrum(3)};
        j["spectrum_condest"] = std::abs(spectrum(3)) / std::abs(spectrum(0));
 
        // j["errors"] = errors;
 
        j["time_building_basis"] = runtime.building_basis_time;
        j["time_loading_mesh"] = runtime.loading_mesh_time;
        j["time_computing_poly_basis"] = runtime.computing_poly_basis_time;
        j["time_assembling_stiffness_mat"] = runtime.assembling_stiffness_mat_time;
        j["time_assembling_mass_mat"] = runtime.assembling_mass_mat_time;
        j["time_assigning_rhs"] = runtime.assigning_rhs_time;
        j["time_solving"] = runtime.solving_time;
        // j["time_computing_errors"] = runtime.computing_errors_time;
 
        j["solver_info"] = solver_info;
 
        j["count_simplex"] = simplex_count;
        j["count_prism"] = prism_count;
        j["count_regular"] = regular_count;
        j["count_regular_boundary"] = regular_boundary_count;
        j["count_simple_singular"] = simple_singular_count;
        j["count_multi_singular"] = multi_singular_count;
        j["count_boundary"] = boundary_count;
        j["count_non_regular_boundary"] = non_regular_boundary_count;
        j["count_non_regular"] = non_regular_count;
        j["count_undefined"] = undefined_count;
        j["count_multi_singular_boundary"] = multi_singular_boundary_count;
 
        j["is_simplicial"] = mesh.n_elements() == simplex_count;
 
        j["peak_memory"] = getPeakRSS() / (1024 * 1024);
 
        const int actual_dim = problem.is_scalar() ? 1 : mesh.dimension();
 
        std::vector<double> mmin(actual_dim);
        std::vector<double> mmax(actual_dim);
 
        for (int d = 0; d < actual_dim; ++d)
        {
            mmin[d] = std::numeric_limits<double>::max();
            mmax[d] = -std::numeric_limits<double>::max();
        }
 
        for (int i = 0; i < sol.size(); i += actual_dim)
        {
            for (int d = 0; d < actual_dim; ++d)
            {
                mmin[d] = std::min(mmin[d], sol(i + d));
                mmax[d] = std::max(mmax[d], sol(i + d));
            }
        }
 
        std::vector<double> sol_at_node(actual_dim);
 
        if (sol_at_node_id >= 0)
        {
            const int node_id = sol_at_node_id;
 
            for (int d = 0; d < actual_dim; ++d)
            {
                sol_at_node[d] = sol(node_id * actual_dim + d);
            }
        }
 
        j["sol_at_node"] = sol_at_node;
        j["sol_min"] = mmin;
        j["sol_max"] = mmax;
 
#if defined(POLYFEM_WITH_CPP_THREADS)
        j["num_threads"] = utils::get_n_threads();
#elif defined(POLYFEM_WITH_TBB)
        j["num_threads"] = utils::get_n_threads();
#else
        j["num_threads"] = 1;
#endif
 
        j["formulation"] = formulation;
 
        logger().info("done");
    }
 
    EnergyCSVWriter::EnergyCSVWriter(const std::string &path, const solver::SolveData &solve_data)
        : file(path), solve_data(solve_data)
    {
        file << "i,";
        for (const auto &[name, _] : solve_data.named_forms())
        {
            file << name << ",";
        }
        file << "total_energy" << std::endl;
    }
 
    EnergyCSVWriter::~EnergyCSVWriter()
    {
        file.close();
    }
 
    void EnergyCSVWriter::write(const int i, const Eigen::MatrixXd &sol)
    {
        const double s = solve_data.time_integrator
                             ? solve_data.time_integrator->acceleration_scaling()
                             : 1;
        file << i << ",";
        for (const auto &[_, form] : solve_data.named_forms())
        {
            // Divide by acceleration scaling to get the energy (units of J)
            file << ((form && form->enabled()) ? form->value(sol) : 0) / s << ",";
        }
        file << solve_data.nl_problem->value(sol) / s << "\n";
        file.flush();
    }
 
    RuntimeStatsCSVWriter::RuntimeStatsCSVWriter(const std::string &path, const State &state, const double t0, const double dt)
        : file(path), state(state), t0(t0), dt(dt)
    {
        file << "step,time,forward,remeshing,global_relaxation,peak_mem,#V,#T" << std::endl;
    }
 
    RuntimeStatsCSVWriter::~RuntimeStatsCSVWriter()
    {
        file.close();
    }
 
    void RuntimeStatsCSVWriter::write(const int t, const double forward, const double remeshing, const double global_relaxation, const Eigen::MatrixXd &sol)
    {
        total_forward_solve_time += forward;
        total_remeshing_time += remeshing;
        total_global_relaxation_time += global_relaxation;
 
        // logger().debug(
        //  "Forward (cur, avg, total): {} s, {} s, {} s",
        //  forward, total_forward_solve_time / t, total_forward_solve_time);
        // logger().debug(
        //  "Remeshing (cur, avg, total): {} s, {} s, {} s",
        //  remeshing, total_remeshing_time / t, total_remeshing_time);
        // logger().debug(
        //  "Global relaxation (cur, avg, total): {} s, {} s, {} s",
        //  global_relaxation, total_global_relaxation_time / t, total_global_relaxation_time);
 
        const double peak_mem = getPeakRSS() / double(1 << 30);
        // logger().debug("Peak mem: {} GiB", peak_mem);
 
        file << fmt::format(
            "{},{},{},{},{},{},{},{}\n",
            t, t0 + dt * t, forward, remeshing, global_relaxation, peak_mem,
            state.n_bases, state.mesh->n_elements());
        file.flush();
    }
 
} // namespace polyfem::io