Detailed Description

Newton step strategy that applies a fixed base damping factor and relaxes it linearly toward 1.0 as iterations proceed.

The effective damping at iteration \( k \) is

\[ \alpha_k = \alpha + (1 - \alpha)\,\mathrm{clamp}(k / r,\, 0,\, 1), \]

where \( \alpha \) is the base damping factor and \( r \) is the reduction parameter. The accepted step is \( x_{\rm new} = x - \alpha_k \cdot \Delta x \).

Definition at line 21 of file DampingReductionStrategy.h.

#include <DampingReductionStrategy.h>

Inheritance diagram for NumLib::DampingReductionStrategy:

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Collaboration diagram for NumLib::DampingReductionStrategy:

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Public Member Functions
	DampingReductionStrategy (double damping, double damping_reduction)
StepResult	applyStep (GlobalVector const &x, GlobalVector const &minus_delta_x, GlobalVector const &res, GlobalMatrix const &J, GlobalVector &x_new, NewtonStepContext &ctx, int iteration) override
Public Member Functions inherited from NumLib::NewtonStepStrategy
virtual void	initialize (GlobalVector const &)
void	setDampingPolicy (DampingPolicy const *policy)
virtual	~NewtonStepStrategy ()=default

Private Attributes
double	_damping
double	_damping_reduction

Additional Inherited Members
Protected Attributes inherited from NumLib::NewtonStepStrategy
DampingPolicy const *	_damping_policy = nullptr

Constructor & Destructor Documentation

◆ DampingReductionStrategy()

NumLib::DampingReductionStrategy::DampingReductionStrategy	(	double	damping,
		double	damping_reduction )

Definition at line 13 of file DampingReductionStrategy.cpp.

    : _damping(damping), _damping_reduction(damping_reduction)
{
}

References _damping, and _damping_reduction.

Member Function Documentation

◆ applyStep()

StepResult NumLib::DampingReductionStrategy::applyStep	(	GlobalVector const &	x,
		GlobalVector const &	minus_delta_x,
		GlobalVector const &	res,
		GlobalMatrix const &	J,
		GlobalVector &	x_new,
		NewtonStepContext &	ctx,
		int	iteration )

overridevirtual

Given the current solution x, the Newton direction minus_delta_x, the residual res, and the Jacobian J, compute and apply a step to x_new. The strategy is free to re-evaluate F(x) internally.

Parameters

[in]	x	current solution
[in]	minus_delta_x	full Newton step (J^{-1} r)
[in]	res	residual at x
[in]	J	Jacobian at x (may be used for curvature)
[out]	x_new	accepted new solution
[in]	ctx	equation system context for re-evaluation
[in]	iteration	current outer iteration number

Implements NumLib::NewtonStepStrategy.

Definition at line 19 of file DampingReductionStrategy.cpp.

{
    double damping = _damping;
 
    if (_damping_policy)
    {
        damping = _damping_policy->apply(minus_delta_x, x, _damping);
    }
 
    damping +=
        (1.0 - damping) * std::clamp(iteration / _damping_reduction, 0.0, 1.0);
 
    MathLib::LinAlg::axpy(x_new, -damping, minus_delta_x);
 
    return {.success = true, .step_length = damping, .x_new_is_set = true};
}

References _damping, NumLib::NewtonStepStrategy::_damping_policy, _damping_reduction, and MathLib::LinAlg::axpy().

Member Data Documentation

◆ _damping

double NumLib::DampingReductionStrategy::_damping

private

Definition at line 35 of file DampingReductionStrategy.h.

Referenced by DampingReductionStrategy(), and applyStep().

◆ _damping_reduction

double NumLib::DampingReductionStrategy::_damping_reduction

private

Definition at line 36 of file DampingReductionStrategy.h.

Referenced by DampingReductionStrategy(), and applyStep().

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