ProcessLib::ForwardDifferencesJacobianAssembler Class Reference

Detailed Description

Assembles the Jacobian matrix using forward differences.

Definition at line 17 of file ForwardDifferencesJacobianAssembler.h.

#include <ForwardDifferencesJacobianAssembler.h>

Inheritance diagram for ProcessLib::ForwardDifferencesJacobianAssembler:

Collaboration diagram for ProcessLib::ForwardDifferencesJacobianAssembler:

Public Member Functions
	ForwardDifferencesJacobianAssembler (std::vector< double > &&absolute_epsilons)
void	assembleWithJacobian (LocalAssemblerInterface &local_assembler, double const t, double const dt, std::vector< double > const &local_x_data, std::vector< double > const &local_x_prev_data, std::vector< double > &local_b_data, std::vector< double > &local_Jac_data) override
std::unique_ptr< AbstractJacobianAssembler >	copy () const override
Public Member Functions inherited from ProcessLib::AbstractJacobianAssembler
virtual void	assembleWithJacobianForStaggeredScheme (LocalAssemblerInterface &, double const, double const, Eigen::VectorXd const &, Eigen::VectorXd const &, int const, std::vector< double > &, std::vector< double > &)
virtual	~AbstractJacobianAssembler ()=default

Private Attributes
std::vector< double > const	_absolute_epsilons
std::vector< double >	_local_M_data
std::vector< double >	_local_K_data
std::vector< double >	_local_b_data
std::vector< double >	_local_x_perturbed_data

Constructor & Destructor Documentation

ForwardDifferencesJacobianAssembler()

ProcessLib::ForwardDifferencesJacobianAssembler::ForwardDifferencesJacobianAssembler ( std::vector< double > && absolute_epsilons )

explicit

Constructs a new instance.

Parameters

absolute_epsilons

perturbations of the components of the local solution vector used for evaluating the finite differences.

Note

The size of absolute_epsilons defines the "number of components" of the local solution vector (This is not the number of elements of the vector!). Therefore the size of the local solution vector must be divisible by the size of absolute_epsilons. This is the only consistency check performed. It is not checked whether said "number of components" is sensible. E.g., one could pass one epsilon per node, which would be valid but would not make sense at all.

Definition at line 18 of file ForwardDifferencesJacobianAssembler.cpp.

    : _absolute_epsilons(std::move(absolute_epsilons))
{
    if (_absolute_epsilons.empty())
    {
        OGS_FATAL("No values for the absolute epsilons have been given.");
    }
}

References _absolute_epsilons, and OGS_FATAL.

Member Function Documentation

assembleWithJacobian()

void ProcessLib::ForwardDifferencesJacobianAssembler::assembleWithJacobian ( LocalAssemblerInterface & local_assembler, double const t, double const dt, std::vector< double > const & local_x_data, std::vector< double > const & local_x_prev_data, std::vector< double > & local_b_data, std::vector< double > & local_Jac_data )

overridevirtual

Assembles the Jacobian, the matrices \(M\) and \(K\), and the vector \(b\). For the assembly the assemble() method of the given local_assembler is called several times and the Jacobian is built from finite differences. The number of calls of the assemble() method is \(2N+1\) if \(N\) is the size of local_x.

Attention

It is assumed that the local vectors and matrices are ordered by component.

Implements ProcessLib::AbstractJacobianAssembler.

Definition at line 28 of file ForwardDifferencesJacobianAssembler.cpp.

{
    std::vector<double> local_M_data(local_Jac_data.size());
    std::vector<double> local_K_data(local_Jac_data.size());
 
    // TODO do not check in every call.
    if (local_x_data.size() % _absolute_epsilons.size() != 0)
    {
        OGS_FATAL(
            "The number of specified epsilons ({:d}) and the number of local "
            "d.o.f.s ({:d}) do not match, i.e., the latter is not divisible by "
            "the former.",
            _absolute_epsilons.size(), local_x_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);
 
    auto local_Jac =
        MathLib::createZeroedMatrix(local_Jac_data, num_r_c, num_r_c);
 
    auto const num_dofs_per_component =
        local_x_data.size() / _absolute_epsilons.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);
 
    // Residual  res := M xdot + K x - b
    // Computing Jac := dres/dx
    //                = d(M xdot)/dx + d(K x)/dx - db/dx
    for (Eigen::MatrixXd::Index i = 0; i < num_r_c; ++i)
    {
        // assume that local_x_data is ordered by component.
        auto const component = i / num_dofs_per_component;
        auto const eps = _absolute_epsilons[component];
 
        // Assemble with perturbed local x.
        _local_x_perturbed_data = local_x_data;
        _local_x_perturbed_data[i] = local_x_data[i] + eps;
        auto const x_p = MathLib::toVector<Eigen::VectorXd>(
            _local_x_perturbed_data, num_r_c);
 
        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() +=
                (local_M_p * (x_p - x_prev) - local_M_0 * (x - x_prev)) /
                (dt * 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() +=
                (local_K_p * x_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();
        }
    }
 
    local_M_data.clear();
    local_K_data.clear();
    local_b_data.clear();
    // Assemble with unperturbed local x to keep the internal assembler state
    // for next iteration or time step.
    local_assembler.assemble(t, dt, local_x_data, local_x_prev_data,
                             local_M_data, local_K_data, local_b_data);
 
    // 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);
        b -= K * x;
        local_K_data.clear();
    }
}

References _absolute_epsilons, _local_b_data, _local_K_data, _local_M_data, _local_x_perturbed_data, ProcessLib::LocalAssemblerInterface::assemble(), MathLib::createZeroedMatrix(), MathLib::createZeroedVector(), OGS_FATAL, MathLib::toMatrix(), and MathLib::toVector().

copy()

std::unique_ptr< AbstractJacobianAssembler > ProcessLib::ForwardDifferencesJacobianAssembler::copy ( ) const

overridevirtual

Implements ProcessLib::AbstractJacobianAssembler.

Definition at line 152 of file ForwardDifferencesJacobianAssembler.cpp.

{
    return std::make_unique<ForwardDifferencesJacobianAssembler>(*this);
}

Member Data Documentation

_absolute_epsilons

std::vector<double> const ProcessLib::ForwardDifferencesJacobianAssembler::_absolute_epsilons

private

Definition at line 56 of file ForwardDifferencesJacobianAssembler.h.

Referenced by ForwardDifferencesJacobianAssembler(), and assembleWithJacobian().

_local_b_data

std::vector<double> ProcessLib::ForwardDifferencesJacobianAssembler::_local_b_data

private

Definition at line 62 of file ForwardDifferencesJacobianAssembler.h.

Referenced by assembleWithJacobian().

_local_K_data

std::vector<double> ProcessLib::ForwardDifferencesJacobianAssembler::_local_K_data

private

Definition at line 61 of file ForwardDifferencesJacobianAssembler.h.

Referenced by assembleWithJacobian().

_local_M_data

std::vector<double> ProcessLib::ForwardDifferencesJacobianAssembler::_local_M_data

private

Definition at line 60 of file ForwardDifferencesJacobianAssembler.h.

Referenced by assembleWithJacobian().

_local_x_perturbed_data

std::vector<double> ProcessLib::ForwardDifferencesJacobianAssembler::_local_x_perturbed_data

private

Definition at line 63 of file ForwardDifferencesJacobianAssembler.h.

Referenced by assembleWithJacobian().

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The documentation for this class was generated from the following files:

• ProcessLib/ForwardDifferencesJacobianAssembler.h
• ProcessLib/ForwardDifferencesJacobianAssembler.cpp