Assembler.hpp

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#pragma once
 
#include <polyfem/Units.hpp>
 
#include <polyfem/assembler/AssemblerData.hpp>
#include <polyfem/assembler/AssemblyValsCache.hpp>
 
#include <polyfem/utils/MatrixCache.hpp>
#include <polyfem/utils/ElasticityUtils.hpp>
#include <polyfem/utils/AutodiffTypes.hpp>
#include <polyfem/utils/Logger.hpp>
 
#include <functional>
 
// this casses are instantiated in the cpp, cannot be used with generic assembler
// without adding template instantiation
namespace polyfem::assembler
{
    // mixed formulation assembler
    class MixedAssembler
    {
    public:
        MixedAssembler();
        virtual ~MixedAssembler() = default;
 
        // this assembler takes two bases: psi_bases are the scalar ones, phi_bases are the tensor ones
        // both have the same geometric mapping
        void assemble(
            const bool is_volume,
            const int n_psi_basis,
            const int n_phi_basis,
            const std::vector<basis::ElementBases> &psi_bases,
            const std::vector<basis::ElementBases> &phi_bases,
            const std::vector<basis::ElementBases> &gbases,
            const AssemblyValsCache &psi_cache,
            const AssemblyValsCache &phi_cache,
            const double t,
            StiffnessMatrix &stiffness) const;
 
        virtual std::string name() const = 0;
 
        int size() const { return size_; }
        virtual void set_size(const int size) { size_ = size; }
 
    protected:
        int size_ = -1;
 
        virtual int rows() const = 0;
        virtual int cols() const = 0;
 
        virtual Eigen::Matrix<double, Eigen::Dynamic, 1, 0, 3, 1> assemble(const MixedAssemblerData &data) const = 0;
    };
 
    class Assembler
    {
    public:
        typedef std::pair<std::string, Eigen::MatrixXd> NamedMatrix;
        typedef std::function<double(const RowVectorNd &, const RowVectorNd &, double, int)> ParamFunc;
 
        virtual ~Assembler() = default;
 
        virtual std::string name() const = 0;
 
        int size() const { return size_; }
        virtual void set_size(const int size) { size_ = size; }
 
        // assembler stiffness matrix, is the mesh is volumetric, number of bases and bases (FE and geom)
        // gbases and bases can be the same (ie isoparametric)
        virtual void assemble(
            const bool is_volume,
            const int n_basis,
            const std::vector<basis::ElementBases> &bases,
            const std::vector<basis::ElementBases> &gbases,
            const AssemblyValsCache &cache,
            const double t,
            StiffnessMatrix &stiffness,
            const bool is_mass = false) const { log_and_throw_error("Assembler not implemented by {}!", name()); }
 
        // assemble energy
        virtual double assemble_energy(
            const bool is_volume,
            const std::vector<basis::ElementBases> &bases,
            const std::vector<basis::ElementBases> &gbases,
            const AssemblyValsCache &cache,
            const double t,
            const double dt,
            const Eigen::MatrixXd &displacement,
            const Eigen::MatrixXd &displacement_prev) const { log_and_throw_error("Assemble energy not implemented by {}!", name()); }
 
        virtual Eigen::VectorXd assemble_energy_per_element(
            const bool is_volume,
            const std::vector<basis::ElementBases> &bases,
            const std::vector<basis::ElementBases> &gbases,
            const AssemblyValsCache &cache,
            const double t,
            const double dt,
            const Eigen::MatrixXd &displacement,
            const Eigen::MatrixXd &displacement_prev) const { log_and_throw_error("Assemble energy not implemented by {}!", name()); }
 
        // assemble gradient of energy (rhs)
        virtual void assemble_gradient(
            const bool is_volume,
            const int n_basis,
            const std::vector<basis::ElementBases> &bases,
            const std::vector<basis::ElementBases> &gbases,
            const AssemblyValsCache &cache,
            const double t,
            const double dt,
            const Eigen::MatrixXd &displacement,
            const Eigen::MatrixXd &displacement_prev,
            Eigen::MatrixXd &rhs) const { log_and_throw_error("Assemble grad not implemented by {}!", name()); }
 
        // assemble hessian of energy (grad)
        virtual void assemble_hessian(
            const bool is_volume,
            const int n_basis,
            const bool project_to_psd,
            const std::vector<basis::ElementBases> &bases,
            const std::vector<basis::ElementBases> &gbases,
            const AssemblyValsCache &cache,
            const double t,
            const double dt,
            const Eigen::MatrixXd &displacement,
            const Eigen::MatrixXd &displacement_prev,
            utils::MatrixCache &mat_cache,
            StiffnessMatrix &grad) const { log_and_throw_error("Assemble hessian not implemented by {}!", name()); }
 
        // plotting (eg von mises), assembler is the name of the formulation
        virtual void compute_scalar_value(
            const OutputData &data,
            std::vector<NamedMatrix> &result) const {}
 
        // computes tensor, assembler is the name of the formulation
        virtual void compute_tensor_value(
            const OutputData &data,
            std::vector<NamedMatrix> &result) const
        {
        }
 
        // computes tensor, assembler is the name of the formulation
        virtual void compute_stiffness_value(
            const double t,
            const assembler::ElementAssemblyValues &vals,
            const Eigen::MatrixXd &local_pts,
            const Eigen::MatrixXd &displacement,
            Eigen::MatrixXd &tensor) const { log_and_throw_error("Not implemented!"); }
 
        virtual void compute_dstress_dmu_dlambda(
            const OptAssemblerData &data,
            Eigen::MatrixXd &dstress_dmu,
            Eigen::MatrixXd &dstress_dlambda) const { log_and_throw_adjoint_error("Not implemented!"); }
 
        virtual void compute_stress_grad_multiply_mat(
            const OptAssemblerData &data,
            const Eigen::MatrixXd &mat,
            Eigen::MatrixXd &stress,
            Eigen::MatrixXd &result) const { log_and_throw_adjoint_error("Not implemented!"); }
 
        virtual void compute_stress_grad_multiply_stress(
            const OptAssemblerData &data,
            Eigen::MatrixXd &stress,
            Eigen::MatrixXd &result) const
        {
            Eigen::MatrixXd unused;
            compute_stress_grad_multiply_mat(data, Eigen::MatrixXd::Zero(data.grad_u_i.rows(), data.grad_u_i.cols()), stress, unused);
            compute_stress_grad_multiply_mat(data, stress, unused, result);
        }
 
        virtual void compute_stress_grad_multiply_vect(
            const OptAssemblerData &data,
            const Eigen::MatrixXd &vect,
            Eigen::MatrixXd &stress,
            Eigen::MatrixXd &result) const { log_and_throw_error("Not implemented!"); }
 
        virtual void compute_stress_grad(
            const OptAssemblerData &data,
            const Eigen::MatrixXd &prev_grad_u_i,
            Eigen::MatrixXd &stress,
            Eigen::MatrixXd &result) const { log_and_throw_adjoint_error("Not implemented!"); }
        virtual void compute_stress_prev_grad(
            const OptAssemblerData &data,
            const Eigen::MatrixXd &prev_grad_u_i,
            Eigen::MatrixXd &result) const { log_and_throw_adjoint_error("Not implemented!"); }
 
        virtual std::map<std::string, ParamFunc> parameters() const = 0;
        virtual VectorNd compute_rhs(const AutodiffHessianPt &pt) const { log_and_throw_error("Rhs not supported by {}!", name()); }
 
        virtual Eigen::Matrix<AutodiffScalarGrad, Eigen::Dynamic, 1, 0, 3, 1> kernel(const int dim, const AutodiffGradPt &rvect, const AutodiffScalarGrad &r) const { log_and_throw_error("Kernel not supported by {}!", name()); }
 
        void set_materials(const std::vector<int> &body_ids, const json &body_params, const Units &units, const std::string &root_path);
        virtual void add_multimaterial(const int index, const json &params, const Units &units, const std::string &root_path) {}
 
        virtual void update_lame_params(const Eigen::MatrixXd &lambdas, const Eigen::MatrixXd &mus)
        {
            log_and_throw_error("Not implemented!");
        }
 
        virtual bool is_linear() const = 0;
        virtual bool is_solution_displacement() const { return false; }
        virtual bool is_fluid() const { return false; }
        virtual bool is_tensor() const { return false; }
 
    protected:
        int size_ = -1;
    };
 
    class MixedNLAssembler : virtual public Assembler
    {
    public:
        using SolutionSplitter = std::function<void(
            const Eigen::MatrixXd &x,
            Eigen::MatrixXd &x_phi,
            Eigen::MatrixXd &x_psi)>;
 
        using Assembler::assemble_energy;
        using Assembler::assemble_energy_per_element;
        using Assembler::assemble_gradient;
        using Assembler::assemble_hessian;
 
        virtual ~MixedNLAssembler() = default;
 
        double assemble_energy(
            const bool is_volume,
            const int n_psi_basis,
            const int n_phi_basis,
            const std::vector<basis::ElementBases> &psi_bases,
            const std::vector<basis::ElementBases> &phi_bases,
            const std::vector<basis::ElementBases> &gbases,
            const AssemblyValsCache &psi_cache,
            const AssemblyValsCache &phi_cache,
            const double t,
            const double dt,
            const Eigen::MatrixXd &x,
            const Eigen::MatrixXd &x_prev,
            const SolutionSplitter &split_solution) const;
 
        Eigen::VectorXd assemble_energy_per_element(
            const bool is_volume,
            const int n_psi_basis,
            const int n_phi_basis,
            const std::vector<basis::ElementBases> &psi_bases,
            const std::vector<basis::ElementBases> &phi_bases,
            const std::vector<basis::ElementBases> &gbases,
            const AssemblyValsCache &psi_cache,
            const AssemblyValsCache &phi_cache,
            const double t,
            const double dt,
            const Eigen::MatrixXd &x,
            const Eigen::MatrixXd &x_prev,
            const SolutionSplitter &split_solution) const;
 
        void assemble_gradient(
            const bool is_volume,
            const int n_psi_basis,
            const int n_phi_basis,
            const std::vector<basis::ElementBases> &psi_bases,
            const std::vector<basis::ElementBases> &phi_bases,
            const std::vector<basis::ElementBases> &gbases,
            const AssemblyValsCache &psi_cache,
            const AssemblyValsCache &phi_cache,
            const double t,
            const double dt,
            const Eigen::MatrixXd &x,
            const Eigen::MatrixXd &x_prev,
            const SolutionSplitter &split_solution,
            Eigen::MatrixXd &grad) const;
 
        void assemble_hessian(
            const bool is_volume,
            const int n_psi_basis,
            const int n_phi_basis,
            const bool project_to_psd,
            const std::vector<basis::ElementBases> &psi_bases,
            const std::vector<basis::ElementBases> &phi_bases,
            const std::vector<basis::ElementBases> &gbases,
            const AssemblyValsCache &psi_cache,
            const AssemblyValsCache &phi_cache,
            const double t,
            const double dt,
            const Eigen::MatrixXd &x,
            const Eigen::MatrixXd &x_prev,
            const SolutionSplitter &split_solution,
            utils::MatrixCache &mat_cache,
            StiffnessMatrix &hessian) const;
 
        bool is_linear() const override { return false; }
 
    protected:
        virtual int rows() const = 0;
        virtual int cols() const = 0;
 
        virtual double compute_energy(const MixedNonLinearAssemblerData &data) const = 0;
        virtual Eigen::VectorXd compute_gradient(const MixedNonLinearAssemblerData &data) const = 0;
        virtual Eigen::MatrixXd compute_hessian(const MixedNonLinearAssemblerData &data) const = 0;
    };
 
    class LinearAssembler : virtual public Assembler
    {
    public:
        LinearAssembler();
        virtual ~LinearAssembler() = default;
 
        void assemble(
            const bool is_volume,
            const int n_basis,
            const std::vector<basis::ElementBases> &bases,
            const std::vector<basis::ElementBases> &gbases,
            const AssemblyValsCache &cache,
            const double t,
            StiffnessMatrix &stiffness,
            const bool is_mass = false) const override;
 
        virtual bool is_linear() const override { return true; }
 
        virtual Eigen::Matrix<double, Eigen::Dynamic, 1, 0, 9, 1> assemble(const LinearAssemblerData &data) const = 0;
    };
 
    // non-linear assembler (eg neohookean elasticity)
    class NLAssembler : virtual public Assembler
    {
    public:
        virtual ~NLAssembler() = default;
 
        // assemble energy
        double assemble_energy(
            const bool is_volume,
            const std::vector<basis::ElementBases> &bases,
            const std::vector<basis::ElementBases> &gbases,
            const AssemblyValsCache &cache,
            const double t,
            const double dt,
            const Eigen::MatrixXd &displacement,
            const Eigen::MatrixXd &displacement_prev) const override;
 
        // assemble the energy per element
        Eigen::VectorXd assemble_energy_per_element(
            const bool is_volume,
            const std::vector<basis::ElementBases> &bases,
            const std::vector<basis::ElementBases> &gbases,
            const AssemblyValsCache &cache,
            const double t,
            const double dt,
            const Eigen::MatrixXd &displacement,
            const Eigen::MatrixXd &displacement_prev) const override;
 
        // assemble gradient of energy (rhs)
        void assemble_gradient(
            const bool is_volume,
            const int n_basis,
            const std::vector<basis::ElementBases> &bases,
            const std::vector<basis::ElementBases> &gbases,
            const AssemblyValsCache &cache,
            const double t,
            const double dt,
            const Eigen::MatrixXd &displacement,
            const Eigen::MatrixXd &displacement_prev,
            Eigen::MatrixXd &rhs) const override;
 
        // assemble hessian of energy (grad)
        void assemble_hessian(
            const bool is_volume,
            const int n_basis,
            const bool project_to_psd,
            const std::vector<basis::ElementBases> &bases,
            const std::vector<basis::ElementBases> &gbases,
            const AssemblyValsCache &cache,
            const double t,
            const double dt,
            const Eigen::MatrixXd &displacement,
            const Eigen::MatrixXd &displacement_prev,
            utils::MatrixCache &mat_cache,
            StiffnessMatrix &grad) const override;
 
        virtual bool is_linear() const override { return false; }
 
        // energy, gradient, and hessian used in newton method
        virtual double compute_energy(const NonLinearAssemblerData &data) const = 0;
        virtual Eigen::VectorXd assemble_gradient(const NonLinearAssemblerData &data) const = 0;
        virtual Eigen::MatrixXd assemble_hessian(const NonLinearAssemblerData &data) const = 0;
    };
 
    class ElasticityAssembler : virtual public Assembler
    {
    public:
        ElasticityAssembler() {}
        virtual ~ElasticityAssembler() = default;
 
        void set_use_robust_jacobian();
 
        // plotting (eg von mises), assembler is the name of the formulation
        void compute_scalar_value(
            const OutputData &data,
            std::vector<NamedMatrix> &result) const override
        {
            result.clear();
            Eigen::MatrixXd tmp;
            compute_von_mises_stresses(data, tmp);
            result.emplace_back("von_mises", tmp);
        }
 
        // computes tensor, assembler is the name of the formulation
        void compute_tensor_value(
            const OutputData &data,
            std::vector<NamedMatrix> &result) const override
        {
            result.clear();
            Eigen::MatrixXd cauchy, pk1, pk2, F;
 
            compute_stress_tensor(data, ElasticityTensorType::CAUCHY, cauchy);
            compute_stress_tensor(data, ElasticityTensorType::PK1, pk1);
            compute_stress_tensor(data, ElasticityTensorType::PK2, pk2);
            compute_stress_tensor(data, ElasticityTensorType::F, F);
 
            result.emplace_back("cauchy_stess", cauchy);
            result.emplace_back("pk1_stess", pk1);
            result.emplace_back("pk2_stess", pk2);
            result.emplace_back("F", F);
        }
 
        void compute_stress_tensor(const OutputData &data,
                                   const ElasticityTensorType &type,
                                   Eigen::MatrixXd &stresses) const
        {
            assign_stress_tensor(data, size() * size(), type, stresses, [&](const Eigen::MatrixXd &stress) {
                Eigen::MatrixXd tmp = stress;
                auto a = Eigen::Map<Eigen::MatrixXd>(tmp.data(), 1, size() * size());
                return Eigen::MatrixXd(a);
            });
        }
 
        void compute_von_mises_stresses(const OutputData &data,
                                        Eigen::MatrixXd &stresses) const
        {
            assign_stress_tensor(data, 1, ElasticityTensorType::CAUCHY, stresses, [&](const Eigen::MatrixXd &stress) {
                Eigen::Matrix<double, 1, 1> res;
                res.setConstant(von_mises_stress_for_stress_tensor(stress));
                return res;
            });
        }
 
        bool is_solution_displacement() const override { return true; }
        bool is_tensor() const override { return true; }
        virtual bool allow_inversion() const = 0;
 
        virtual void assign_stress_tensor(const OutputData &data,
                                          const int all_size,
                                          const ElasticityTensorType &type,
                                          Eigen::MatrixXd &all,
                                          const std::function<Eigen::MatrixXd(const Eigen::MatrixXd &)> &fun) const = 0;
 
    protected:
        bool use_robust_jacobian = false;
    };
 
    class ElasticityNLAssembler : virtual public ElasticityAssembler, virtual public NLAssembler
    {
    };
 
} // namespace polyfem::assembler