Detailed Description

template<typename LinearSolver, typename JacobianMatrixUpdate, typename ResidualUpdate, typename SolutionUpdate>
class NumLib::NewtonRaphson< LinearSolver, JacobianMatrixUpdate, ResidualUpdate, SolutionUpdate >

Newton-Raphson solver for system of equations using an Eigen linear solvers library. The current implementation does not update the solution itself, but calls a function for the solution's update with the current increment.

Definition at line 26 of file NewtonRaphson.h.

#include <NewtonRaphson.h>

Classes
struct	FirstArgument
struct	FirstArgument< R(C::*)(Arg, Args...) const >

Public Member Functions
	NewtonRaphson (LinearSolver &linear_solver, JacobianMatrixUpdate jacobian_update, ResidualUpdate residual_update, SolutionUpdate solution_update, NewtonRaphsonSolverParameters const &solver_parameters)
std::optional< int >	solve (JacobianMatrix &jacobian) const

Private Types
template<typename F>
using	FirstArgumentType
using	JacobianMatrix = FirstArgumentType<JacobianMatrixUpdate>
using	ResidualVector = FirstArgumentType<ResidualUpdate>

Private Attributes
LinearSolver &	_linear_solver
JacobianMatrixUpdate	_jacobian_update
ResidualUpdate	_residual_update
SolutionUpdate	_solution_update
const int	_maximum_iterations
	Maximum number of iterations.
const double	_residuum_tolerance_squared
	Error tolerance for the residuum.
const double	_increment_tolerance_squared
	Error tolerance for the increment.

Member Typedef Documentation

◆ FirstArgumentType

template<typename LinearSolver, typename JacobianMatrixUpdate, typename ResidualUpdate, typename SolutionUpdate>

template<typename F>

using NumLib::NewtonRaphson< LinearSolver, JacobianMatrixUpdate, ResidualUpdate, SolutionUpdate >::FirstArgumentType

private

Initial value:

typename FirstArgument<

decltype(&std::remove_reference_t<F>::operator())>::type

NumLib::NewtonRaphson::FirstArgument

Definition NewtonRaphson.h:31

Definition at line 48 of file NewtonRaphson.h.

◆ JacobianMatrix

template<typename LinearSolver, typename JacobianMatrixUpdate, typename ResidualUpdate, typename SolutionUpdate>

using NumLib::NewtonRaphson< LinearSolver, JacobianMatrixUpdate, ResidualUpdate, SolutionUpdate >::JacobianMatrix = FirstArgumentType<JacobianMatrixUpdate>

private

Definition at line 51 of file NewtonRaphson.h.

◆ ResidualVector

template<typename LinearSolver, typename JacobianMatrixUpdate, typename ResidualUpdate, typename SolutionUpdate>

using NumLib::NewtonRaphson< LinearSolver, JacobianMatrixUpdate, ResidualUpdate, SolutionUpdate >::ResidualVector = FirstArgumentType<ResidualUpdate>

private

Definition at line 52 of file NewtonRaphson.h.

Constructor & Destructor Documentation

◆ NewtonRaphson()

template<typename LinearSolver, typename JacobianMatrixUpdate, typename ResidualUpdate, typename SolutionUpdate>

NumLib::NewtonRaphson< LinearSolver, JacobianMatrixUpdate, ResidualUpdate, SolutionUpdate >::NewtonRaphson	(	LinearSolver &	linear_solver,
		JacobianMatrixUpdate	jacobian_update,
		ResidualUpdate	residual_update,
		SolutionUpdate	solution_update,
		NewtonRaphsonSolverParameters const &	solver_parameters )

inline

Definition at line 55 of file NewtonRaphson.h.

        : _linear_solver(linear_solver),
          _jacobian_update(jacobian_update),
          _residual_update(residual_update),
          _solution_update(solution_update),
          _maximum_iterations(solver_parameters.maximum_iterations),
          _residuum_tolerance_squared(solver_parameters.residuum_tolerance *
                                      solver_parameters.residuum_tolerance),
          _increment_tolerance_squared(solver_parameters.increment_tolerance *
                                       solver_parameters.increment_tolerance)
    {
    }

References _increment_tolerance_squared, _jacobian_update, _linear_solver, _maximum_iterations, _residual_update, _residuum_tolerance_squared, and _solution_update.

Member Function Documentation

◆ solve()

template<typename LinearSolver, typename JacobianMatrixUpdate, typename ResidualUpdate, typename SolutionUpdate>

std::optional< int > NumLib::NewtonRaphson< LinearSolver, JacobianMatrixUpdate, ResidualUpdate, SolutionUpdate >::solve ( JacobianMatrix & jacobian ) const

inline

Returns true and the iteration number if succeeded, otherwise false and an undefined value for the number of iterations.

Definition at line 74 of file NewtonRaphson.h.

    {
        int iteration = 0;
        ResidualVector increment;
        ResidualVector residual;
        do
        {
            // The jacobian and the residual are updated simultaneously to keep
            // consistency. The jacobian is used after the non-linear solver
            // onward.
            _jacobian_update(jacobian);
            _residual_update(residual);
 
            if (residual.squaredNorm() < _residuum_tolerance_squared)
            {
                break;  // convergence criteria fulfilled.
            }
 
            increment.noalias() =
                _linear_solver.compute(jacobian).solve(-residual);
            // DBUG("Local linear solver accuracy |J dx - r| = {:g}",
            //      (jacobian * increment + residual).norm());
 
            _solution_update(increment);
 
            if (increment.squaredNorm() < _increment_tolerance_squared)
            {
                break;  // increment to small.
            }
 
            // DBUG("Local Newton: Iteration #{:d} |dx| = {:g}, |r| = {:g}",
            //      iteration, increment.norm(), residual.norm());
            // fmt::print("Local Newton: Increment {}\n",
            //      fmt::join(increment.data(),
            //                increment.data() + increment.size(), ", "));
            // fmt::print("Local Newton: Residuum {}\n",
            //      fmt::join(residual.data(),
            //                residual.data() + residual.size(), ", "));
        } while (iteration++ < _maximum_iterations);
 
        if (iteration > _maximum_iterations)
        {
            ERR("The local Newton method did not converge within the given "
                "number of iterations. Iteration: {:d}, increment {:g}, "
                "residual: "
                "{:g}",
                iteration - 1, increment.norm(), residual.norm());
            return std::nullopt;
        }
 
        return iteration;
    };

References _increment_tolerance_squared, _jacobian_update, _linear_solver, _maximum_iterations, _residual_update, _residuum_tolerance_squared, _solution_update, and ERR().

Referenced by ProcessLib::WellboreCompensateNeumannBoundaryConditionLocalAssembler< ShapeFunction, GlobalDim >::assemble(), and ProcessLib::WellboreSimulator::WellboreSimulatorFEM< ShapeFunction, GlobalDim >::assemble().

Member Data Documentation

◆ _increment_tolerance_squared

template<typename LinearSolver, typename JacobianMatrixUpdate, typename ResidualUpdate, typename SolutionUpdate>

const double NumLib::NewtonRaphson< LinearSolver, JacobianMatrixUpdate, ResidualUpdate, SolutionUpdate >::_increment_tolerance_squared

private

Error tolerance for the increment.

Definition at line 136 of file NewtonRaphson.h.

Referenced by NewtonRaphson(), and solve().

◆ _jacobian_update

template<typename LinearSolver, typename JacobianMatrixUpdate, typename ResidualUpdate, typename SolutionUpdate>

JacobianMatrixUpdate NumLib::NewtonRaphson< LinearSolver, JacobianMatrixUpdate, ResidualUpdate, SolutionUpdate >::_jacobian_update

private

Definition at line 129 of file NewtonRaphson.h.

Referenced by NewtonRaphson(), and solve().

◆ _linear_solver

template<typename LinearSolver, typename JacobianMatrixUpdate, typename ResidualUpdate, typename SolutionUpdate>

LinearSolver& NumLib::NewtonRaphson< LinearSolver, JacobianMatrixUpdate, ResidualUpdate, SolutionUpdate >::_linear_solver

private

Definition at line 128 of file NewtonRaphson.h.

Referenced by NewtonRaphson(), and solve().

◆ _maximum_iterations

template<typename LinearSolver, typename JacobianMatrixUpdate, typename ResidualUpdate, typename SolutionUpdate>

const int NumLib::NewtonRaphson< LinearSolver, JacobianMatrixUpdate, ResidualUpdate, SolutionUpdate >::_maximum_iterations

private

Maximum number of iterations.

Definition at line 132 of file NewtonRaphson.h.

Referenced by NewtonRaphson(), and solve().

◆ _residual_update

template<typename LinearSolver, typename JacobianMatrixUpdate, typename ResidualUpdate, typename SolutionUpdate>

ResidualUpdate NumLib::NewtonRaphson< LinearSolver, JacobianMatrixUpdate, ResidualUpdate, SolutionUpdate >::_residual_update

private

Definition at line 130 of file NewtonRaphson.h.

Referenced by NewtonRaphson(), and solve().

◆ _residuum_tolerance_squared

template<typename LinearSolver, typename JacobianMatrixUpdate, typename ResidualUpdate, typename SolutionUpdate>

const double NumLib::NewtonRaphson< LinearSolver, JacobianMatrixUpdate, ResidualUpdate, SolutionUpdate >::_residuum_tolerance_squared

private

Error tolerance for the residuum.

Definition at line 134 of file NewtonRaphson.h.

Referenced by NewtonRaphson(), and solve().

◆ _solution_update

template<typename LinearSolver, typename JacobianMatrixUpdate, typename ResidualUpdate, typename SolutionUpdate>

SolutionUpdate NumLib::NewtonRaphson< LinearSolver, JacobianMatrixUpdate, ResidualUpdate, SolutionUpdate >::_solution_update

private

Definition at line 131 of file NewtonRaphson.h.

Referenced by NewtonRaphson(), and solve().

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

NewtonRaphson.h

Detailed Description

Classes

Public Member Functions

Private Types

Private Attributes

Member Typedef Documentation

◆ FirstArgumentType

◆ JacobianMatrix

◆ ResidualVector

Constructor & Destructor Documentation

◆ NewtonRaphson()

Member Function Documentation

◆ solve()

Member Data Documentation

◆ _increment_tolerance_squared

◆ _jacobian_update

◆ _linear_solver

◆ _maximum_iterations

◆ _residual_update

◆ _residuum_tolerance_squared

◆ _solution_update