PeriodicContactForceDerivative.cpp

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#include "PeriodicContactForceDerivative.hpp"
 
#include <Eigen/Core>
#include <polyfem/solver/forms/PeriodicContactForm.hpp>
#include <polyfem/State.hpp>
#include <polyfem/optimization/parametrization/PeriodicMeshToMesh.hpp>
#include <polyfem/utils/MatrixUtils.hpp>
#include <polyfem/utils/Types.hpp>
#include <ipc/collisions/normal/normal_collisions.hpp>
 
namespace polyfem::solver
{
    void PeriodicContactForceDerivative::force_shape_derivative(
        const PeriodicContactForm &form,
        const State &state,
        const PeriodicMeshToMesh &periodic_mesh_map,
        const Eigen::VectorXd &periodic_mesh_representation,
        const ipc::NormalCollisions &contact_set,
        const Eigen::VectorXd &solution,
        const Eigen::VectorXd &adjoint_sol,
        Eigen::VectorXd &term)
    {
        const int dim = form.collision_mesh_.dim();
        const Eigen::MatrixXd displaced_surface = form.compute_displaced_surface(form.single_to_tiled(solution));
 
        Eigen::VectorXd tiled_term;
 
        {
            StiffnessMatrix dq_h = form.collision_mesh_.to_full_dof(form.barrier_potential().shape_derivative(contact_set, form.collision_mesh_, displaced_surface));
            tiled_term = dq_h.transpose() * form.single_to_tiled(adjoint_sol);
        }
 
        {
            Eigen::VectorXd force;
            force = form.barrier_potential().gradient(contact_set, form.collision_mesh_, displaced_surface);
            force = form.collision_mesh_.to_full_dof(force);
            Eigen::MatrixXd adjoint_affine = utils::unflatten(adjoint_sol.tail(dim * dim), dim);
            for (int k = 0; k < form.collision_mesh_.num_vertices(); k++)
            {
                const int k_full = form.collision_mesh_.to_full_vertex_id(k);
                tiled_term.segment(k_full * dim, dim) += adjoint_affine.transpose() * force.segment(k_full * dim, dim);
            }
        }
 
        {
            StiffnessMatrix hessian_full;
            form.BarrierContactForm::second_derivative_unweighted(form.single_to_tiled(solution), hessian_full);
            Eigen::VectorXd tmp = form.single_to_tiled(adjoint_sol).transpose() * hessian_full;
            Eigen::MatrixXd sol_affine = utils::unflatten(solution.tail(dim * dim), dim);
            for (int k = 0; k < form.collision_mesh_.num_vertices(); k++)
            {
                const int k_full = form.collision_mesh_.to_full_vertex_id(k);
                tiled_term.segment(k_full * dim, dim) += sol_affine.transpose() * tmp.segment(k_full * dim, dim);
            }
        }
 
        // chain rule from tiled to periodic
        Eigen::VectorXd unit_term;
        Eigen::MatrixXd affine_term;
        affine_term.setZero(dim, dim);
        unit_term.setZero(tiled_term.size());
        Eigen::MatrixXd affine = utils::unflatten(periodic_mesh_representation.tail(dim * dim), dim).transpose();
        for (int k = 0; k < form.collision_mesh_.num_vertices(); k++)
        {
            const int k_full = form.collision_mesh_.to_full_vertex_id(k);
            affine_term += tiled_term.segment(k_full * dim, dim) * form.collision_mesh_.rest_positions().row(k);
            unit_term.segment(k_full * dim, dim) += affine.transpose() * tiled_term.segment(k_full * dim, dim);
        }
 
        Eigen::VectorXd single_term = state.basis_nodes_to_gbasis_nodes * form.proj.topRows(dim * form.n_single_dof_) * unit_term;
        single_term = utils::flatten(utils::unflatten(single_term, dim)(state.primitive_to_node(), Eigen::all));
 
        term.setZero(periodic_mesh_representation.size());
        for (int i = 0; i < state.n_geom_bases; i++)
            term.segment(periodic_mesh_map.full_to_periodic(i) * dim, dim).array() += single_term.segment(i * dim, dim).array();
        term.tail(dim * dim) = Eigen::Map<Eigen::VectorXd>(affine_term.data(), dim * dim, 1);
 
        term *= form.weight();
    }
} // namespace polyfem::solver