Nonlinear

Nonlinear solvers: Newton method. More...

Description

Files
file	multidomain/newtonconvergencewriter.hh
	This class provides the infrastructure to write the convergence behaviour of the Newton method for multidomain simulations into a VTK file.
file	multidomain/newtonsolver.hh
file	findscalarroot.hh
	Root finding algorithms for scalar functions.
file	leastsquares.hh
	Levenberg-Marquardt algorithm for solving nonlinear least squares problems.
file	nonlinear/newtonconvergencewriter.hh
	This class provides the infrastructure to write the convergence behaviour of the newton method into a VTK file.
file	nonlinear/newtonsolver.hh
	Reference implementation of a Newton solver.
file	primaryvariableswitchadapter.hh
	An adapter for the Newton to manage models with primary variable switch.
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::MultiDomainNewtonConvergenceWriter< MDTraits >
	Writes the intermediate solutions for every Newton iteration. More...
class	Dumux::MultiDomainNewtonSolver< Assembler, LinearSolver, CouplingManager, Reassembler, Comm >
	Newton solver for coupled problems. More...
class	Dumux::Optimization::Detail::LevenbergMarquardt< Assembler, LinearSolver >
	A nonlinear least squares solver with \(n\) model parameters and \(m\) observations. More...
struct	Dumux::ConvergenceWriterInterface< SolutionVector, ResidualVector >
	A convergence writer interface Provide an interface that show the minimal requirements a convergence write passed to a newton method has to fulfill. More...
class	Dumux::NewtonConvergenceWriter< GridGeometry, SolutionVector, ResidualVector >
	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::PrimaryVariableSwitchAdapter< Variables, isValid >
	An adapter for the Newton to manage models with primary variable switch. More...
class	Dumux::PrimaryVariableSwitchAdapter< Variables, false >
	An empty adapter for the Newton for models without primary variable switch. More...
class	Dumux::StaggeredNewtonConvergenceWriter< GridGeometry, SolutionVector, ResidualVector >
	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) More...
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) More...
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. More...

Variables
template<class Variables >
constexpr bool	Dumux::hasPriVarsSwitch = Dune::Std::is_detected<Detail::DetectPVSwitch, Variables>()
	Helper boolean to check if the given variables involve primary variable switching. More...

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
	)

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
	)

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
	)

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

Variable Documentation

hasPriVarsSwitch

template<class Variables >

constexpr bool Dumux::hasPriVarsSwitch = Dune::Std::is_detected<Detail::DetectPVSwitch, Variables>()

inlineconstexpr