ForwardDifferencesJacobianAssembler.cpp

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// SPDX-FileCopyrightText: Copyright (c) OpenGeoSys Community (opengeosys.org)
// SPDX-License-Identifier: BSD-3-Clause
 
#include "ForwardDifferencesJacobianAssembler.h"
 
#include "BaseLib/Error.h"
#include "LocalAssemblerInterface.h"
#include "MathLib/LinAlg/Eigen/EigenMapTools.h"
 
namespace ProcessLib
{
ForwardDifferencesJacobianAssembler::ForwardDifferencesJacobianAssembler(
    std::vector<double>&& absolute_epsilons)
    : NumericalJacobianAssembler(std::move(absolute_epsilons))
{
}
 
void ForwardDifferencesJacobianAssembler::assembleWithJacobian(
    std::size_t const /*mesh_item_id*/,
    LocalAssemblerInterface& local_assembler, const double t, double const dt,
    const std::vector<double>& local_x_data,
    const std::vector<double>& local_x_prev_data,
    std::vector<double>& local_b_data, std::vector<double>& local_Jac_data)
{
    std::vector<double> local_M_data(local_Jac_data.size());
    std::vector<double> local_K_data(local_Jac_data.size());
 
    auto const num_r_c =
        static_cast<Eigen::MatrixXd::Index>(local_x_data.size());
 
    auto const x = MathLib::toVector<Eigen::VectorXd>(local_x_data, num_r_c);
    auto const x_prev =
        MathLib::toVector<Eigen::VectorXd>(local_x_prev_data, num_r_c);
 
    Eigen::VectorXd const local_xdot = (x - x_prev) / dt;
 
    auto local_Jac =
        MathLib::createZeroedMatrix(local_Jac_data, num_r_c, num_r_c);
 
    assert(this->non_deformation_component_ids_.size() > 0);
 
    auto const num_dofs_per_component =
        local_x_data.size() / this->non_deformation_component_ids_.size();
 
    // Assemble with unperturbed local x to get M0, K0, and b0 used in the
    // finite differences below.
    local_assembler.assemble(t, dt, local_x_data, local_x_prev_data,
                             local_M_data, local_K_data, local_b_data);
 
    auto const nved = local_assembler.getNumberOfVectorElementsForDeformation();
 
    // Residual  res := M xdot + K x - b
    // Computing Jac := dres/dx
    //                = M dxdot/dx + dM/dx xdot + K dx/dx + dK/dx x - db/dx
    //                  with dxdot/dx = 1/dt and dx/dx = 1
    //                  (Note: dM/dx and dK/dx actually have the second and
    //                  third index transposed.)
    // The loop computes the dM/dx, dK/dx and db/dx terms, the rest is computed
    // afterwards. The loop skips the entries corresponding to the deformation
    // part of the solution vector if a vector segment size is given by nved.
    // This is to avoid recomputing the analytic block of the deformation
    // process.
    auto const num_purterbated_colums = num_r_c - nved;
    auto const perturbations = this->getVariableComponentEpsilonsView();
    for (Eigen::MatrixXd::Index i = 0; i < num_purterbated_colums; ++i)
    {
        // assume that local_x_data is ordered by component.
        auto const component = i / num_dofs_per_component;
        auto const eps = perturbations[component];
 
        // Assemble with perturbed local x.
        _local_x_perturbed_data = local_x_data;
        _local_x_perturbed_data[i] = local_x_data[i] + eps;
 
        local_assembler.assemble(t, dt, _local_x_perturbed_data,
                                 local_x_prev_data, _local_M_data,
                                 _local_K_data, _local_b_data);
 
        if (!local_M_data.empty() && !_local_M_data.empty())
        {
            auto const local_M_0 =
                MathLib::toMatrix(local_M_data, num_r_c, num_r_c);
            auto const local_M_p =
                MathLib::toMatrix(_local_M_data, num_r_c, num_r_c);
            local_Jac.col(i).noalias() +=
                // dM/dxi * x_dot
                (local_M_p - local_M_0) * local_xdot / eps;
            _local_M_data.clear();
        }
        if (!local_K_data.empty() && !_local_K_data.empty())
        {
            auto const local_K_0 =
                MathLib::toMatrix(local_K_data, num_r_c, num_r_c);
            auto const local_K_p =
                MathLib::toMatrix(_local_K_data, num_r_c, num_r_c);
 
            local_Jac.col(i).noalias() +=
                // dK/dxi * x
                (local_K_p - local_K_0) * x / eps;
            _local_K_data.clear();
        }
        if (!local_b_data.empty() && !_local_b_data.empty())
        {
            auto const local_b_0 =
                MathLib::toVector<Eigen::VectorXd>(local_b_data, num_r_c);
            auto const local_b_p =
                MathLib::toVector<Eigen::VectorXd>(_local_b_data, num_r_c);
            local_Jac.col(i).noalias() -= (local_b_p - local_b_0) / eps;
            _local_b_data.clear();
        }
    }
 
    // Assemble with unperturbed local x, i.e. compute M dxdot/dx + K dx/dx =
    // M/dt + K
    // Compute remaining terms of the Jacobian.
    if (!local_M_data.empty())
    {
        auto local_M = MathLib::toMatrix(local_M_data, num_r_c, num_r_c);
        local_Jac.noalias() += local_M / dt;
    }
    if (!local_K_data.empty())
    {
        auto local_K = MathLib::toMatrix(local_K_data, num_r_c, num_r_c);
        local_Jac.noalias() += local_K;
    }
 
    // Move the M and K contributions to the residuum for evaluation of nodal
    // forces, flow rates, and the like. Cleaning up the M's and K's storage so
    // it is not accounted for twice.
    auto b = [&]()
    {
        if (!local_b_data.empty())
        {
            return MathLib::toVector<Eigen::VectorXd>(local_b_data, num_r_c);
        }
        return MathLib::createZeroedVector<Eigen::VectorXd>(local_b_data,
                                                            num_r_c);
    }();
 
    if (!local_M_data.empty())
    {
        auto M = MathLib::toMatrix(local_M_data, num_r_c, num_r_c);
        b -= M * (x - x_prev) / dt;
        local_M_data.clear();
    }
    if (!local_K_data.empty())
    {
        auto K = MathLib::toMatrix(local_K_data, num_r_c, num_r_c);
 
        // Note: The deformation segment of \c b is already computed as
        // int{B^T sigma}dA, which is identical to K_uu * u. Therefore the
        // corresponding K block is set to zero.
        if (nved != 0)
        {
            auto const dm_start_index = num_purterbated_colums;
            auto const dm_size = nved;
            K.block(dm_start_index, dm_start_index, dm_size, dm_size).setZero();
        }
 
        b -= K * x;
        local_K_data.clear();
    }
}
 
std::unique_ptr<AbstractJacobianAssembler>
ForwardDifferencesJacobianAssembler::copy() const
{
    return std::make_unique<ForwardDifferencesJacobianAssembler>(*this);
}
 
}  // namespace ProcessLib