solid_mechanics_contact.hpp

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// Copyright (c) Lawrence Livermore National Security, LLC and
// other Smith Project Developers. See the top-level LICENSE file for
// details.
//
// SPDX-License-Identifier: (BSD-3-Clause)
 
#pragma once
 
#include <charconv>
#include <memory>
#include <optional>
#include <string_view>
#include <system_error>
#include <unordered_map>
#include <vector>
 
#include "smith/physics/solid_mechanics.hpp"
#include "smith/physics/contact/contact_data.hpp"
 
namespace smith {
 
template <int order, int dim, typename parameters = Parameters<>,
          typename parameter_indices = std::make_integer_sequence<int, parameters::n>>
class SolidMechanicsContact;
 
template <int order, int dim, typename... parameter_space, int... parameter_indices>
class SolidMechanicsContact<order, dim, Parameters<parameter_space...>,
                            std::integer_sequence<int, parameter_indices...>>
    : public SolidMechanics<order, dim, Parameters<parameter_space...>,
                            std::integer_sequence<int, parameter_indices...>> {
  using SolidMechanicsBase =
      SolidMechanics<order, dim, Parameters<parameter_space...>, std::integer_sequence<int, parameter_indices...>>;
 
 public:
  SolidMechanicsContact(const NonlinearSolverOptions nonlinear_opts, const LinearSolverOptions lin_opts,
                        const smith::TimesteppingOptions timestepping_opts, const std::string& physics_name,
                        std::shared_ptr<smith::Mesh> smith_mesh, std::vector<std::string> parameter_names = {},
                        int cycle = 0, double time = 0.0, bool checkpoint_to_disk = false, bool use_warm_start = true)
      : SolidMechanicsContact(std::make_unique<EquationSolver>(nonlinear_opts, lin_opts, smith_mesh->getComm()),
                              timestepping_opts, physics_name, smith_mesh, parameter_names, cycle, time,
                              checkpoint_to_disk, use_warm_start)
  {
  }
 
  SolidMechanicsContact(std::unique_ptr<smith::EquationSolver> solver,
                        const smith::TimesteppingOptions timestepping_opts, const std::string& physics_name,
                        std::shared_ptr<smith::Mesh> smith_mesh, std::vector<std::string> parameter_names = {},
                        int cycle = 0, double time = 0.0, bool checkpoint_to_disk = false, bool use_warm_start = true)
      : SolidMechanicsBase(std::move(solver), timestepping_opts, physics_name, smith_mesh, parameter_names, cycle, time,
                           checkpoint_to_disk, use_warm_start),
        contact_(BasePhysics::mfemParMesh())
  {
  }
 
  SolidMechanicsContact(const SolidMechanicsInputOptions& input_options, const std::string& physics_name,
                        std::shared_ptr<smith::Mesh> smith_mesh, int cycle = 0, double time = 0.0)
      : SolidMechanicsBase(input_options, physics_name, smith_mesh, cycle, time), contact_(BasePhysics::mfemParMesh())
  {
  }
 
  void resetStates(int cycle = 0, double time = 0.0) override
  {
    SolidMechanicsBase::resetStates(cycle, time);
    for (auto& [_, force] : contact_interaction_forces_) {
      if (force) {
        *force = 0.0;
      }
    }
    for (auto& [_, seed] : contact_interaction_force_adjoint_bcs_) {
      if (seed) {
        *seed = 0.0;
      }
    }
    contact_.reset();
    double dt = 0.0;
    mfem::Vector p(contact_.numPressureDofs());
    p = 0.0;
    contact_.updateForcesAndJacobian(cycle, time, dt, BasePhysics::shapeDisplacement(), displacement_, p);
    updateContactForceOutputs();
  }
 
  std::unique_ptr<mfem_ext::StdFunctionOperator> buildQuasistaticOperator() override
  {
    auto residual_fn = [this](const mfem::Vector& u, mfem::Vector& r) {
      const mfem::Vector u_blk(const_cast<mfem::Vector&>(u), 0, displacement_.Size());
      const mfem::Vector res = (*residual_)(time_, BasePhysics::shapeDisplacement(), u_blk, acceleration_,
                                            *parameters_[parameter_indices].state...);
 
      // NOTE this copy is required as the sundials solvers do not allow move assignments because of their memory
      // tracking strategy
      // See https://github.com/mfem/mfem/issues/3531
      mfem::Vector r_blk(r, 0, displacement_.Size());
      r_blk = res;
 
      contact_.residualFunction(BasePhysics::shapeDisplacement(), u, r);
      r_blk.SetSubVector(bcs_.allEssentialTrueDofs(), 0.0);
    };
    // This if-block below breaks up building the Jacobian operator depending if there is Lagrange multiplier
    // enforcement or not
    if (contact_.haveLagrangeMultipliers()) {
      // The quasistatic operator has blocks if any of the contact interactions are enforced using Lagrange multipliers.
      // Jacobian operator is an mfem::BlockOperator
      J_offsets_ = mfem::Array<int>({0, displacement_.Size(), displacement_.Size() + contact_.numPressureDofs()});
      return std::make_unique<mfem_ext::StdFunctionOperator>(
          displacement_.space().TrueVSize() + contact_.numPressureDofs(), residual_fn,
          // gradient of residual function
          [this](const mfem::Vector& u) -> mfem::Operator& {
            const mfem::Vector u_blk(const_cast<mfem::Vector&>(u), 0, displacement_.Size());
            auto [r, drdu] = (*residual_)(time_, BasePhysics::shapeDisplacement(), differentiate_wrt(u_blk),
                                          acceleration_, *parameters_[parameter_indices].state...);
 
            // create block operator holding jacobian contributions
            J_constraint_ = contact_.jacobianFunction(assemble(drdu));
 
            // take ownership of blocks
            J_constraint_->owns_blocks = false;
            J_ = std::unique_ptr<mfem::HypreParMatrix>(
                static_cast<mfem::HypreParMatrix*>(&J_constraint_->GetBlock(0, 0)));
            J_12_ = std::unique_ptr<mfem::HypreParMatrix>(
                static_cast<mfem::HypreParMatrix*>(&J_constraint_->GetBlock(0, 1)));
            J_21_ = std::unique_ptr<mfem::HypreParMatrix>(
                static_cast<mfem::HypreParMatrix*>(&J_constraint_->GetBlock(1, 0)));
            J_22_ = std::unique_ptr<mfem::HypreParMatrix>(
                static_cast<mfem::HypreParMatrix*>(&J_constraint_->GetBlock(1, 1)));
 
            // eliminate bcs and compute eliminated blocks
            J_e_ = bcs_.eliminateAllEssentialDofsFromMatrix(*J_);
            J_e_21_ = std::unique_ptr<mfem::HypreParMatrix>(J_21_->EliminateCols(bcs_.allEssentialTrueDofs()));
            J_12_->EliminateRows(bcs_.allEssentialTrueDofs());
 
            // create block operator for constraints
            J_constraint_e_ = std::make_unique<mfem::BlockOperator>(J_offsets_);
            J_constraint_e_->SetBlock(0, 0, J_e_.get());
            J_constraint_e_->SetBlock(1, 0, J_e_21_.get());
 
            J_operator_ = J_constraint_.get();
            return *J_constraint_;
          });
    } else {
      // If all of the contact interactions are penalty, then there will be no blocks. Jacobian operator is a single
      // mfem::HypreParMatrix
      return std::make_unique<mfem_ext::StdFunctionOperator>(
          displacement_.space().TrueVSize(), residual_fn, [this](const mfem::Vector& u) -> mfem::Operator& {
            auto [r, drdu] = (*residual_)(time_, BasePhysics::shapeDisplacement(), differentiate_wrt(u), acceleration_,
                                          *parameters_[parameter_indices].state...);
 
            // get 11-block holding Jacobian contributions
            auto block_J = contact_.jacobianFunction(assemble(drdu));
            block_J->owns_blocks = false;
            J_ = std::unique_ptr<mfem::HypreParMatrix>(static_cast<mfem::HypreParMatrix*>(&block_J->GetBlock(0, 0)));
 
            J_e_ = bcs_.eliminateAllEssentialDofsFromMatrix(*J_);
 
            J_operator_ = J_.get();
            return *J_;
          });
    }
  }
 
  void addContactInteraction(int interaction_id, const std::set<int>& bdry_attr_surf1,
                             const std::set<int>& bdry_attr_surf2, ContactOptions contact_opts)
  {
    SLIC_ERROR_ROOT_IF(!is_quasistatic_, "Contact can only be applied to quasistatic problems.");
    SLIC_ERROR_ROOT_IF(order > 1, "Contact can only be applied to linear (order = 1) meshes.");
 
    // Disallow duplicates for this physics module. Tribol ids are global, so reusing the same interaction_id is an
    // error even if ContactData rejects it later.
    SLIC_ERROR_ROOT_IF(
        contact_interaction_forces_.find(interaction_id) != contact_interaction_forces_.end(),
        std::format("Contact interaction id {} already exists for physics module '{}'.", interaction_id, name_));
 
    // Register with Tribol via ContactData (includes global uniqueness check).
    contact_.addContactInteraction(interaction_id, bdry_attr_surf1, bdry_attr_surf2, contact_opts);
 
    const auto interaction_force_name = detail::addPrefix(name_, std::format("contact_force_{}", interaction_id));
    auto interaction_force_dual =
        std::make_unique<FiniteElementDual>(StateManager::newDual(displacement_.space(), interaction_force_name));
    *interaction_force_dual = 0.0;
    duals_.push_back(interaction_force_dual.get());
    contact_interaction_forces_.emplace(interaction_id, std::move(interaction_force_dual));
 
    const auto force_adjoint_bcs_name =
        detail::addPrefix(name_, std::format("contact_force_adjoint_bcs_{}", interaction_id));
    auto force_adjoint_bcs = std::make_unique<FiniteElementState>(displacement_.space(), force_adjoint_bcs_name);
    *force_adjoint_bcs = 0.0;
    this->dual_adjoints_.push_back(force_adjoint_bcs.get());
    contact_interaction_force_adjoint_bcs_.emplace(interaction_id, std::move(force_adjoint_bcs));
  }
 
  std::vector<std::string> dualNames() const override
  {
    auto dual_names = SolidMechanicsBase::dualNames();
#ifdef SMITH_USE_TRIBOL
    for (const auto& interaction : contact_.getContactInteractions()) {
      dual_names.push_back(std::format("contact_force_{}", interaction.getInteractionId()));
    }
#endif
    return dual_names;
  }
 
  const FiniteElementDual& dual(const std::string& dual_name) const override
  {
    const auto interaction_id = parseContactInteractionForceId(dual_name);
    if (interaction_id.has_value()) {
      auto it = contact_interaction_forces_.find(*interaction_id);
      if (it != contact_interaction_forces_.end()) {
        return *it->second;
      }
    }
 
    return SolidMechanicsBase::dual(dual_name);
  }
 
  const FiniteElementState& dualAdjoint(const std::string& dual_name) const override
  {
    const auto interaction_id = parseContactInteractionForceId(dual_name);
    if (interaction_id.has_value()) {
      auto it = contact_interaction_force_adjoint_bcs_.find(*interaction_id);
      if (it != contact_interaction_force_adjoint_bcs_.end()) {
        return *it->second;
      }
    }
 
    return SolidMechanicsBase::dualAdjoint(dual_name);
  }
 
  FiniteElementDual loadCheckpointedDual(const std::string& dual_name, int cycle) override
  {
    if (parseContactInteractionForceId(dual_name).has_value()) {
      SLIC_ERROR_ROOT_IF(contact_.haveLagrangeMultipliers(),
                         "Checkpointed retrieval of contact forces is not supported for Lagrange multiplier contact.");
 
      const FiniteElementState checkpointed_displacement = this->loadCheckpointedState("displacement", cycle);
      double dt = this->getCheckpointedTimestep(cycle);
      contact_.updateForcesAndJacobian(cycle, time_, dt, BasePhysics::shapeDisplacement(), checkpointed_displacement);
      updateContactForceOutputs();
 
      const auto interaction_id = parseContactInteractionForceId(dual_name);
      SLIC_ERROR_ROOT_IF(
          !interaction_id.has_value(),
          std::format("Requested checkpointed dual '{}' does not exist in physics module '{}'.", dual_name, name_));
      auto it = contact_interaction_forces_.find(*interaction_id);
      SLIC_ERROR_ROOT_IF(
          it == contact_interaction_forces_.end(),
          std::format("Requested checkpointed dual '{}' does not exist in physics module '{}'.", dual_name, name_));
      return *it->second;
    }
 
    return SolidMechanicsBase::loadCheckpointedDual(dual_name, cycle);
  }
 
  void computeContactSubspaceTransferOperator()
  {
    // compute contact dof --> displacement dof prolongation operator
    // if not previously computed
    if (!contact_dof_prolongation_) {
      contact_dof_prolongation_ = contact_.contactSubspaceTransferOperator();
    }
  }
 
  void completeSetup() override
  {
    double dt = 0.0;
    mfem::Vector p = pressure();
    contact_.updateForcesAndJacobian(cycle_, time_, dt, BasePhysics::shapeDisplacement(), displacement_, p);
    updateContactForceOutputs();
 
    SolidMechanicsBase::completeSetup();
  }
 
  mfem::HypreParVector pressure() const { return contact_.mergedPressures(); }
 
#ifdef SMITH_USE_TRIBOL
  const ContactInteraction& contactInteraction(int interaction_id) const
  {
    for (const auto& interaction : contact_.getContactInteractions()) {
      if (interaction.getInteractionId() == interaction_id) {
        return interaction;
      }
    }
    SLIC_ERROR_ROOT(std::format("No contact interaction found with interaction_id={}", interaction_id));
    return contact_.getContactInteractions().front();
  }
#endif
 
 protected:
  bool trySetDualAdjointBc(const std::string& dual_name, const smith::FiniteElementState& bc) override
  {
    const auto interaction_id = parseContactInteractionForceId(dual_name);
    if (interaction_id.has_value()) {
      auto it = contact_interaction_force_adjoint_bcs_.find(*interaction_id);
      SLIC_ERROR_ROOT_IF(it == contact_interaction_force_adjoint_bcs_.end(),
                         std::format("No contact force adjoint BC registered for interaction_id={}", *interaction_id));
      *it->second = bc;
      return true;
    }
 
    // No match found for dual_name in SolidMechanicsContact. Try the base class.
    return SolidMechanicsBase::trySetDualAdjointBc(dual_name, bc);
  }
 
  std::optional<int> parseContactInteractionForceId(std::string_view dual_name) const
  {
    constexpr std::string_view prefix = "contact_force_";
    const std::string normalized_name = detail::removePrefix(this->name_, std::string(dual_name));
    const std::string_view normalized_name_view{normalized_name};
 
    if (normalized_name_view.substr(0, prefix.size()) != prefix) {
      return std::nullopt;
    }
 
    return parseInteractionId(normalized_name_view.substr(prefix.size()));
  }
 
  static std::optional<int> parseInteractionId(std::string_view id_str)
  {
    int interaction_id = -1;
    const auto* begin = id_str.data();
    const auto* end = id_str.data() + id_str.size();
    auto [ptr, ec] = std::from_chars(begin, end, interaction_id);
    if (ec != std::errc{} || ptr != end) {
      return std::nullopt;
    }
    return interaction_id;
  }
 
  void quasiStaticSolve(double dt) override
  {
    // warm start must be called prior to the time update so that the previous Jacobians can be used consistently
    // throughout. warm start for contact needs to include the previous stiffness terms associated with contact
    // otherwise the system will interpenetrate instantly on warm-starting.
    warmStartDisplacementContact(dt);
    time_ += dt;
 
    // In general, the solution vector is a stacked (block) vector:
    //  | displacement     |
    //  | contact pressure |
    // Contact pressure is only active when solving a contact problem with Lagrange multipliers.
    mfem::Vector augmented_solution(displacement_.Size() + contact_.numPressureDofs());
    augmented_solution.SetVector(displacement_, 0);
    augmented_solution.SetVector(contact_.mergedPressures(), displacement_.Size());
 
    // solve the non-linear system resid = 0 and pressure * gap = 0
    nonlin_solver_->solve(augmented_solution);
    displacement_.Set(1.0, mfem::Vector(augmented_solution, 0, displacement_.Size()));
    updateContactForceOutputs();
  }
 
  void warmStartDisplacementContact(double dt)
  {
    SMITH_MARK_FUNCTION;
 
    du_ = 0.0;
    for (auto& bc : bcs_.essentials()) {
      // apply the future boundary conditions, but use the most recent Jacobians stiffness.
      bc.setDofs(du_, time_ + dt);
    }
 
    auto& constrained_dofs = bcs_.allEssentialTrueDofs();
    for (int i = 0; i < constrained_dofs.Size(); i++) {
      int j = constrained_dofs[i];
      du_[j] -= displacement_(j);
    }
 
    auto amgf_prec = dynamic_cast<mfem::AMGFSolver*>(&nonlin_solver_->preconditioner());
    if (amgf_prec) {
      // compute contact_dof_prolongation
      computeContactSubspaceTransferOperator();
      // set AMGF subspace transfer operator
      amgf_prec->SetFilteredSubspaceTransferOperator(*(contact_dof_prolongation_.get()));
      // set the filteredsubspace solver component of AMGF
      // better solution: retrieve print level from .preconditioner_print_level from linear_solver_options
      int filter_solver_print_level = 0;
      filter_solver_ =
          std::make_unique<StrumpackSolver>(filter_solver_print_level, contact_dof_prolongation_->GetComm());
      amgf_prec->SetFilteredSubspaceSolver(*filter_solver_.get());
 
      auto& lin_solver = nonlin_solver_->linearSolver();
      auto iterative_solver = dynamic_cast<mfem::IterativeSolver*>(&lin_solver);
      SLIC_WARNING_ROOT_IF(!iterative_solver,
                           "AMGFContact should only be used as a preconditioner for an iterative solver");
    }
 
    if (use_warm_start_) {
      // Update the system residual
      mfem::Vector augmented_residual(displacement_.Size() + contact_.numPressureDofs());
      augmented_residual = 0.0;
      const mfem::Vector res = (*residual_)(time_ + dt, BasePhysics::shapeDisplacement(), displacement_, acceleration_,
                                            *parameters_[parameter_indices].state...);
 
      mfem::Vector augmented_solution(displacement_.space().TrueVSize() + contact_.numPressureDofs());
      augmented_solution = 0.0;
      mfem::Vector du(augmented_solution, 0, displacement_.space().TrueVSize());
      du = displacement_;
      mfem::Vector p_blk(augmented_solution, displacement_.Size(), contact_.numPressureDofs());
 
      // Perform a single update for the warm start evaluation.
      // Note: we use time_ to match the previous Jacobian evaluation point.
      contact_.updateForcesAndJacobian(cycle_, time_, dt, BasePhysics::shapeDisplacement(), displacement_, p_blk);
 
      mfem::Vector r_blk(augmented_residual, 0, displacement_.space().TrueVSize());
      r_blk = res;
      r_blk += contact_.forces();
 
      mfem::Vector g_blk(augmented_residual, displacement_.Size(), contact_.numPressureDofs());
      g_blk.Set(1.0, contact_.mergedGaps(true));
 
      r_blk.SetSubVector(bcs_.allEssentialTrueDofs(), 0.0);
 
      // use the most recently evaluated Jacobian
      auto [_, drdu] = (*residual_)(time_, BasePhysics::shapeDisplacement(), differentiate_wrt(displacement_),
                                    acceleration_, *parameters_[parameter_indices].previous_state...);
 
      if (contact_.haveLagrangeMultipliers()) {
        J_offsets_ = mfem::Array<int>({0, displacement_.Size(), displacement_.Size() + contact_.numPressureDofs()});
        J_constraint_ = contact_.jacobianFunction(assemble(drdu));
 
        // take ownership of blocks
        J_constraint_->owns_blocks = false;
        J_ = std::unique_ptr<mfem::HypreParMatrix>(static_cast<mfem::HypreParMatrix*>(&J_constraint_->GetBlock(0, 0)));
        J_12_ =
            std::unique_ptr<mfem::HypreParMatrix>(static_cast<mfem::HypreParMatrix*>(&J_constraint_->GetBlock(0, 1)));
        J_21_ =
            std::unique_ptr<mfem::HypreParMatrix>(static_cast<mfem::HypreParMatrix*>(&J_constraint_->GetBlock(1, 0)));
        J_22_ =
            std::unique_ptr<mfem::HypreParMatrix>(static_cast<mfem::HypreParMatrix*>(&J_constraint_->GetBlock(1, 1)));
 
        J_e_ = bcs_.eliminateAllEssentialDofsFromMatrix(*J_);
        J_e_21_ = std::unique_ptr<mfem::HypreParMatrix>(J_21_->EliminateCols(bcs_.allEssentialTrueDofs()));
        J_12_->EliminateRows(bcs_.allEssentialTrueDofs());
 
        J_operator_ = J_constraint_.get();
      } else {
        // get 11-block holding jacobian contributions
        auto block_J = contact_.jacobianFunction(assemble(drdu));
        block_J->owns_blocks = false;
        J_ = std::unique_ptr<mfem::HypreParMatrix>(static_cast<mfem::HypreParMatrix*>(&block_J->GetBlock(0, 0)));
 
        J_e_ = bcs_.eliminateAllEssentialDofsFromMatrix(*J_);
 
        J_operator_ = J_.get();
      }
 
      augmented_residual *= -1.0;
 
      du = du_;
      mfem::EliminateBC(*J_, *J_e_, constrained_dofs, du, r_blk);
      for (int i = 0; i < constrained_dofs.Size(); i++) {
        int j = constrained_dofs[i];
        r_blk[j] = du[j];
      }
 
      auto& lin_solver = nonlin_solver_->linearSolver();
      lin_solver.SetOperator(*J_operator_);
      lin_solver.Mult(augmented_residual, augmented_solution);
 
      du_ = du;
    }
 
    displacement_ += du_;
  }
 
  void quasiStaticAdjointSolve(double dt) override
  {
    SLIC_ERROR_ROOT_IF(contact_.haveLagrangeMultipliers(),
                       "Lagrange multiplier contact does not currently support sensitivities/adjoints.");
 
    contact_.updateForcesAndJacobian(cycle_, time_, dt, BasePhysics::shapeDisplacement(), displacement_);
 
    auto [_, drdu] = (*residual_)(time_, BasePhysics::shapeDisplacement(), differentiate_wrt(displacement_),
                                  acceleration_, *parameters_[parameter_indices].state...);
 
    auto block_J = contact_.jacobianFunction(assemble(drdu));
    block_J->owns_blocks = false;
    auto jacobian = std::unique_ptr<mfem::HypreParMatrix>(static_cast<mfem::HypreParMatrix*>(&block_J->GetBlock(0, 0)));
    auto J_T = std::unique_ptr<mfem::HypreParMatrix>(jacobian->Transpose());
 
    // If a QoI depends on per-interaction contact force duals, the dual-adjoint seeds define an additional contribution
    // to the adjoint load:
    //   dJ/du += (df_i/du)^T * dJ/df_i
    // Following SolidMechanics::setAdjointLoad() sign convention, displacement_adjoint_load_ stores the negative of the
    // provided dJ/du, so we subtract these contributions here.
#ifdef SMITH_USE_TRIBOL
    if (!contact_interaction_force_adjoint_bcs_.empty()) {
      FiniteElementDual contact_force_load(displacement_.space(), "contact_force_dual_adjoint_load");
      contact_force_load = 0.0;
 
      for (const auto& [interaction_id, force_seed] : contact_interaction_force_adjoint_bcs_) {
        if (!force_seed) {
          continue;
        }
 
        // Only apply if the seed is nonzero.
        if (force_seed->Norml2() == 0.0) {
          continue;
        }
 
        const auto interaction_J = contactInteraction(interaction_id).jacobianContribution();
        auto* J00 = dynamic_cast<mfem::HypreParMatrix*>(&interaction_J->GetBlock(0, 0));
        SLIC_ERROR_ROOT_IF(!J00, "Expected HypreParMatrix (0,0) block for contact interaction Jacobian.");
 
        FiniteElementDual tmp(displacement_.space(), "contact_force_dual_adjoint_load_tmp");
        tmp = 0.0;
        J00->MultTranspose(*force_seed, tmp);
        contact_force_load.Add(1.0, tmp);
      }
 
      displacement_adjoint_load_.Add(-1.0, contact_force_load);
    }
#endif
 
    auto J_e_T = bcs_.eliminateAllEssentialDofsFromMatrix(*J_T);
    auto& constrained_dofs = bcs_.allEssentialTrueDofs();
 
    mfem::EliminateBC(*J_T, *J_e_T, constrained_dofs, reactions_adjoint_bcs_, displacement_adjoint_load_);
    for (int i = 0; i < constrained_dofs.Size(); i++) {
      int j = constrained_dofs[i];
      displacement_adjoint_load_[j] = reactions_adjoint_bcs_[j];
    }
 
    auto& lin_solver = nonlin_solver_->linearSolver();
    lin_solver.SetOperator(*J_T);
    lin_solver.Mult(displacement_adjoint_load_, adjoint_displacement_);
  }
 
  const FiniteElementDual& computeTimestepShapeSensitivity() override
  {
    double dt = this->getCheckpointedTimestep(cycle_);
    contact_.updateForcesAndJacobian(cycle_ + 1, time_end_step_, dt, BasePhysics::shapeDisplacement(), displacement_);
 
    auto drdshape =
        smith::get<DERIVATIVE>((*residual_)(time_end_step_, differentiate_wrt(BasePhysics::shapeDisplacement()),
                                            displacement_, acceleration_, *parameters_[parameter_indices].state...));
 
    auto block_J = contact_.jacobianFunction(assemble(drdshape));
    block_J->owns_blocks = false;
    auto drdshape_mat =
        std::unique_ptr<mfem::HypreParMatrix>(static_cast<mfem::HypreParMatrix*>(&block_J->GetBlock(0, 0)));
 
    drdshape_mat->MultTranspose(adjoint_displacement_, shape_displacement_dual_);
 
    return BasePhysics::shapeDisplacementSensitivity();
  }
 
  void updateContactForceOutputs()
  {
#ifdef SMITH_USE_TRIBOL
    for (const auto& interaction : contact_.getContactInteractions()) {
      auto it = contact_interaction_forces_.find(interaction.getInteractionId());
      if (it != contact_interaction_forces_.end()) {
        const auto interaction_forces = interaction.forces();
        *it->second = interaction_forces;
      }
    }
#endif
  }
 
  using BasePhysics::bcs_;
  using BasePhysics::cycle_;
  using BasePhysics::duals_;
  using BasePhysics::is_quasistatic_;
  using BasePhysics::mesh_;
  using BasePhysics::name_;
  using BasePhysics::parameters_;
  using BasePhysics::states_;
  using BasePhysics::time_;
  using SolidMechanicsBase::acceleration_;
  using SolidMechanicsBase::adjoint_displacement_;
  using SolidMechanicsBase::d_residual_d_;
  using SolidMechanicsBase::DERIVATIVE;
  using SolidMechanicsBase::displacement_;
  using SolidMechanicsBase::displacement_adjoint_load_;
  using SolidMechanicsBase::du_;
  using SolidMechanicsBase::J_;
  using SolidMechanicsBase::J_e_;
  using SolidMechanicsBase::nonlin_solver_;
  using SolidMechanicsBase::reactions_adjoint_bcs_;
  using SolidMechanicsBase::residual_;
  using SolidMechanicsBase::residual_with_bcs_;
  using SolidMechanicsBase::shape_displacement_dual_;
  using SolidMechanicsBase::time_end_step_;
  using SolidMechanicsBase::use_warm_start_;
  using SolidMechanicsBase::warmStartDisplacement;
 
  mfem::Operator* J_operator_;
 
  std::unique_ptr<mfem::HypreParMatrix> J_21_;
 
  std::unique_ptr<mfem::HypreParMatrix> J_12_;
 
  std::unique_ptr<mfem::HypreParMatrix> J_22_;
 
  mfem::Array<int> J_offsets_;
 
  std::unique_ptr<mfem::BlockOperator> J_constraint_;
 
  std::unique_ptr<mfem::HypreParMatrix> J_e_21_;
 
  std::unique_ptr<mfem::BlockOperator> J_constraint_e_;
 
  ContactData contact_;
 
  std::unordered_map<int, std::unique_ptr<FiniteElementDual>> contact_interaction_forces_;
 
  std::unordered_map<int, std::unique_ptr<FiniteElementState>> contact_interaction_force_adjoint_bcs_;
 
  std::unique_ptr<mfem::HypreParMatrix> contact_dof_prolongation_;
 
  std::unique_ptr<mfem::Solver> filter_solver_;
};
 
}  // namespace smith