Nonlinear

Nonlinear solvers: Newton method. More...

Description

Nonlinear solvers: Newton method.

Files
file	newtonsolver.hh
	Newton sover for coupled problems.
file	findscalarroot.hh
	Root finding algorithms for scalar functions.
file	newtonconvergencewriter.hh
	This class provides the infrastructure to write the convergence behaviour of the newton method into a VTK file.
file	newtonsolver.hh
	Reference implementation of the Newton solver.
file	staggerednewtonconvergencewriter.hh
	This class provides the infrastructure to write the convergence behaviour of the newton method for the staggered discretization scheme into a VTK file.

Classes
class	Dumux::MultiDomainNewtonSolver< Assembler, LinearSolver, CouplingManager, Reassembler, Comm >
	Newton sover for coupled problems. More...
class	Dumux::NewtonConvergenceWriter< GridGeometry, SolutionVector >
	Writes the intermediate solutions for every Newton iteration. More...
class	Dumux::NewtonSolver< Assembler, LinearSolver, Reassembler, Comm >
	An implementation of a Newton solver. More...
class	Dumux::StaggeredNewtonConvergenceWriter< GridGeometry, SolutionVector >
	Writes the intermediate solutions for every Newton iteration (for staggered grid scheme). More...

Functions
template<class Scalar, class ResFunc, class DerivFunc, typename std::enable_if_t< std::is_invocable_r_v< Scalar, ResFunc, Scalar > &&std::is_invocable_r_v< Scalar, DerivFunc, Scalar > > ...>
Scalar	Dumux::findScalarRootNewton (Scalar xOld, const ResFunc &residual, const DerivFunc &derivative, const Scalar tol=1e-13, const int maxIter=200)
	Newton's root finding algorithm for scalar functions (secant method).
template<class Scalar, class ResFunc, typename std::enable_if_t< std::is_invocable_r_v< Scalar, ResFunc, Scalar > > ...>
Scalar	Dumux::findScalarRootNewton (Scalar xOld, const ResFunc &residual, const Scalar tol=1e-13, const int maxIter=200)
	Newton's root finding algorithm for scalar functions (secant method).
template<class Scalar, class ResFunc, typename std::enable_if_t< std::is_invocable_r_v< Scalar, ResFunc, Scalar > > ...>
Scalar	Dumux::findScalarRootBrent (Scalar a, Scalar b, const ResFunc &residual, const Scalar tol=1e-13, const int maxIter=200)
	Brent's root finding algorithm for scalar functions.

Function Documentation

findScalarRootBrent()

template<class Scalar, class ResFunc, typename std::enable_if_t< std::is_invocable_r_v< Scalar, ResFunc, Scalar > > ...>

Scalar Dumux::findScalarRootBrent	(	Scalar	a,
		Scalar	b,
		const ResFunc &	residual,
		const Scalar	tol = 1e-13,
		const int	maxIter = 200 )

Brent's root finding algorithm for scalar functions.

Note

Modified from pseudo-code on wikipedia: https://en.wikipedia.org/wiki/Brent%27s_method

See also R.P. Brent "An algorithm with guaranteed convergence for finding a zero of a function", The Computer Journal (1971).

This is usually more robust than Newton's method

Parameters

a	Lower bound
b	Upper bound
residual	Residual function
tol	Relative shift tolerance
maxIter	Maximum number of iterations

findScalarRootNewton() [1/2]

template<class Scalar, class ResFunc, class DerivFunc, typename std::enable_if_t< std::is_invocable_r_v< Scalar, ResFunc, Scalar > &&std::is_invocable_r_v< Scalar, DerivFunc, Scalar > > ...>

Scalar Dumux::findScalarRootNewton	(	Scalar	xOld,
		const ResFunc &	residual,
		const DerivFunc &	derivative,
		const Scalar	tol = 1e-13,
		const int	maxIter = 200 )

Newton's root finding algorithm for scalar functions (secant method).

Parameters

xOld	initial guess
residual	Residual function
derivative	Derivative of the residual
tol	Relative shift tolerance
maxIter	Maximum number of iterations

findScalarRootNewton() [2/2]

template<class Scalar, class ResFunc, typename std::enable_if_t< std::is_invocable_r_v< Scalar, ResFunc, Scalar > > ...>

Scalar Dumux::findScalarRootNewton	(	Scalar	xOld,
		const ResFunc &	residual,
		const Scalar	tol = 1e-13,
		const int	maxIter = 200 )

Newton's root finding algorithm for scalar functions (secant method).

Note

The derivative is numerically computed. If the derivative is know use signature with derivative function.

Parameters

xOld	initial guess
residual	Residual function
tol	Relative shift tolerance
maxIter	Maximum number of iterations