Newton solver for solving non-linear problems. More...

#include <dune/pdelab/solver/newton.hh>

Public Types
using	GridOperator = GridOperator_
	Type of the grid operator.

using	LinearSolver = LinearSolver_
	Type of the linear solver.

using	Domain = typename GridOperator::Traits::Domain
	Type of the domain (solution)

using	Range = typename GridOperator::Traits::Range
	Type of the range (residual)

using	Jacobian = typename GridOperator::Traits::Jacobian
	Type of the Jacobian matrix.

using	Real = typename Dune::FieldTraits< typename Domain::ElementType >::real_type
	Number type.

using	Result = PDESolverResult< Real >
	Type of results.

using	LineSearch = LineSearchInterface< Domain >
	Type of line search interface.

Public Member Functions
const Result &	result () const
	Return results.

virtual void	prepareStep (Domain &solution)

virtual void	linearSolve ()

virtual void	apply (Domain &solution)
	Solve the nonlinear problem using solution as initial guess and for storing the result.

virtual void	updateDefect (Domain &solution)
	Update _residual and defect in _result.

void	setVerbosityLevel (unsigned int verbosity)
	Set how much output you get.

unsigned int	getVerbosityLevel () const
	Get verbosity level.

void	setReduction (Real reduction)
	Set reduction Newton needs to achieve.

Real	getReduction () const
	Get reduction.

void	setAbsoluteLimit (Real absoluteLimit)
	Set absolute convergence limit.

Real	getAbsoluteLimit () const

void	setKeepMatrix (bool b)
	Set whether the jacobian matrix should be kept across calls to apply().

void	setUseMaxNorm (bool b)
	Set whether to use the maximum norm for stopping criteria.

void	setHangingNodeModifications (bool b)
	Does the problem have hanging nodes.

bool	keepMatrix () const
	Return whether the jacobian matrix is kept across calls to apply().

void	discardMatrix ()
	Discard the stored Jacobian matrix.

void	setMinLinearReduction (Real minLinearReduction)
	Set the minimal reduction in the linear solver.

void	setFixedLinearReduction (bool fixedLinearReduction)
	Set wether to use a fixed reduction in the linear solver.

void	setReassembleThreshold (Real reassembleThreshold)
	Set a threshold, when the linear operator is reassembled.

void	setParameters (const ParameterTree &parameterTree)
	Interpret a parameter tree as a set of options for the newton solver.

void	setTerminate (std::shared_ptr< TerminateInterface > terminate)
	Set the termination criterion.

std::shared_ptr< TerminateInterface >	getTerminate () const
	Return a pointer to the stored termination criterion.

void	setLineSearch (std::shared_ptr< LineSearch > lineSearch)
	Set the line search.

std::shared_ptr< LineSearch >	getLineSearch () const
	Return a pointer to the stored line search.

void	printParameters (const std::string &_name="NewtonMethod") const
	Output NewtonMethod parameters.

	NewtonMethod (const GridOperator &gridOperator, LinearSolver &linearSolver)
	Construct Newton using default parameters with default parameters.

	NewtonMethod (const GridOperator &gridOperator, LinearSolver &linearSolver, const ParameterTree &parameterTree)
	Construct Newton passing a parameter tree.

virtual	~NewtonMethod ()

Detailed Description

template<typename GridOperator_, typename LinearSolver_>
class Dune::PDELab::NewtonMethod< GridOperator_, LinearSolver_ >

Newton solver for solving non-linear problems.

The line search and the termination criterion can be changed at runtime by the setTerminate() and the setLineSearch() methods.
If Newton is created using the default parameters it is an inexact Newton since the default reduction for the linear systems is quite low. You can change this through setMinLinearReduction()

Template Parameters

GridOperator_	Grid operator for evaluation of residual and Jacobian
LinearSolver_	Solver backend for solving linear system of equations

Examples: recipe-operator-splitting.cc.

Member Typedef Documentation

◆ Domain

template<typename GridOperator_ , typename LinearSolver_ >

using Dune::PDELab::NewtonMethod< GridOperator_, LinearSolver_ >::Domain = typename GridOperator::Traits::Domain

Type of the domain (solution)

◆ GridOperator

template<typename GridOperator_ , typename LinearSolver_ >

using Dune::PDELab::NewtonMethod< GridOperator_, LinearSolver_ >::GridOperator = GridOperator_

Type of the grid operator.

◆ Jacobian

template<typename GridOperator_ , typename LinearSolver_ >

using Dune::PDELab::NewtonMethod< GridOperator_, LinearSolver_ >::Jacobian = typename GridOperator::Traits::Jacobian

Type of the Jacobian matrix.

◆ LinearSolver

template<typename GridOperator_ , typename LinearSolver_ >

using Dune::PDELab::NewtonMethod< GridOperator_, LinearSolver_ >::LinearSolver = LinearSolver_

Type of the linear solver.

◆ LineSearch

template<typename GridOperator_ , typename LinearSolver_ >

using Dune::PDELab::NewtonMethod< GridOperator_, LinearSolver_ >::LineSearch = LineSearchInterface<Domain>

Type of line search interface.

◆ Range

template<typename GridOperator_ , typename LinearSolver_ >

using Dune::PDELab::NewtonMethod< GridOperator_, LinearSolver_ >::Range = typename GridOperator::Traits::Range

Type of the range (residual)

◆ Real

template<typename GridOperator_ , typename LinearSolver_ >

using Dune::PDELab::NewtonMethod< GridOperator_, LinearSolver_ >::Real = typename Dune::FieldTraits<typename Domain::ElementType>::real_type

Number type.

◆ Result

template<typename GridOperator_ , typename LinearSolver_ >

using Dune::PDELab::NewtonMethod< GridOperator_, LinearSolver_ >::Result = PDESolverResult<Real>

Type of results.

Constructor & Destructor Documentation

◆ NewtonMethod() [1/2]

template<typename GridOperator_ , typename LinearSolver_ >

Dune::PDELab::NewtonMethod< GridOperator_, LinearSolver_ >::NewtonMethod	(	const GridOperator &	gridOperator,
		LinearSolver &	linearSolver
	)

inline

Construct Newton using default parameters with default parameters.

in p

◆ NewtonMethod() [2/2]

template<typename GridOperator_ , typename LinearSolver_ >

Dune::PDELab::NewtonMethod< GridOperator_, LinearSolver_ >::NewtonMethod	(	const GridOperator &	gridOperator,
		LinearSolver &	linearSolver,
		const ParameterTree &	parameterTree
	)

inline

Construct Newton passing a parameter tree.

◆ ~NewtonMethod()

template<typename GridOperator_ , typename LinearSolver_ >

virtual Dune::PDELab::NewtonMethod< GridOperator_, LinearSolver_ >::~NewtonMethod ( )

inlinevirtual

Member Function Documentation

◆ apply()

template<typename GridOperator_ , typename LinearSolver_ >

virtual void Dune::PDELab::NewtonMethod< GridOperator_, LinearSolver_ >::apply ( Domain & solution )

inlinevirtual

Solve the nonlinear problem using solution as initial guess and for storing the result.

◆ discardMatrix()

template<typename GridOperator_ , typename LinearSolver_ >

void Dune::PDELab::NewtonMethod< GridOperator_, LinearSolver_ >::discardMatrix ( )

inline

Discard the stored Jacobian matrix.

◆ getAbsoluteLimit()

template<typename GridOperator_ , typename LinearSolver_ >

Real Dune::PDELab::NewtonMethod< GridOperator_, LinearSolver_ >::getAbsoluteLimit ( ) const

inline

◆ getLineSearch()

template<typename GridOperator_ , typename LinearSolver_ >

std::shared_ptr< LineSearch > Dune::PDELab::NewtonMethod< GridOperator_, LinearSolver_ >::getLineSearch ( ) const

inline

Return a pointer to the stored line search.

◆ getReduction()

template<typename GridOperator_ , typename LinearSolver_ >

Real Dune::PDELab::NewtonMethod< GridOperator_, LinearSolver_ >::getReduction ( ) const

inline

Get reduction.

◆ getTerminate()

template<typename GridOperator_ , typename LinearSolver_ >

std::shared_ptr< TerminateInterface > Dune::PDELab::NewtonMethod< GridOperator_, LinearSolver_ >::getTerminate ( ) const

inline

Return a pointer to the stored termination criterion.

◆ getVerbosityLevel()

template<typename GridOperator_ , typename LinearSolver_ >

unsigned int Dune::PDELab::NewtonMethod< GridOperator_, LinearSolver_ >::getVerbosityLevel ( ) const

inline

Get verbosity level.

◆ keepMatrix()

template<typename GridOperator_ , typename LinearSolver_ >

bool Dune::PDELab::NewtonMethod< GridOperator_, LinearSolver_ >::keepMatrix ( ) const

inline

Return whether the jacobian matrix is kept across calls to apply().

◆ linearSolve()

template<typename GridOperator_ , typename LinearSolver_ >

virtual void Dune::PDELab::NewtonMethod< GridOperator_, LinearSolver_ >::linearSolve ( )

inlinevirtual

◆ prepareStep()

template<typename GridOperator_ , typename LinearSolver_ >

virtual void Dune::PDELab::NewtonMethod< GridOperator_, LinearSolver_ >::prepareStep ( Domain & solution )

inlinevirtual

◆ printParameters()

template<typename GridOperator_ , typename LinearSolver_ >

void Dune::PDELab::NewtonMethod< GridOperator_, LinearSolver_ >::printParameters ( const std::string & _name = "NewtonMethod< GridOperator_, LinearSolver_ >" ) const

inline

Output NewtonMethod parameters.

Setting parameters using ParameterTree is quite error prone. Checking parameters without setting up the debugger can be useful.

◆ result()

template<typename GridOperator_ , typename LinearSolver_ >

const Result & Dune::PDELab::NewtonMethod< GridOperator_, LinearSolver_ >::result ( ) const

inline

Return results.

◆ setAbsoluteLimit()

template<typename GridOperator_ , typename LinearSolver_ >

void Dune::PDELab::NewtonMethod< GridOperator_, LinearSolver_ >::setAbsoluteLimit ( Real absoluteLimit )

inline

Set absolute convergence limit.

◆ setFixedLinearReduction()

template<typename GridOperator_ , typename LinearSolver_ >

void Dune::PDELab::NewtonMethod< GridOperator_, LinearSolver_ >::setFixedLinearReduction ( bool fixedLinearReduction )

inline

Set wether to use a fixed reduction in the linear solver.

Note: If fixedLinearReduction is true, the linear reduction rate will always be fixed to minLinearReduction.

◆ setHangingNodeModifications()

template<typename GridOperator_ , typename LinearSolver_ >

void Dune::PDELab::NewtonMethod< GridOperator_, LinearSolver_ >::setHangingNodeModifications ( bool b )

inline

Does the problem have hanging nodes.

◆ setKeepMatrix()

template<typename GridOperator_ , typename LinearSolver_ >

void Dune::PDELab::NewtonMethod< GridOperator_, LinearSolver_ >::setKeepMatrix ( bool b )

inline

Set whether the jacobian matrix should be kept across calls to apply().

◆ setLineSearch()

template<typename GridOperator_ , typename LinearSolver_ >

void Dune::PDELab::NewtonMethod< GridOperator_, LinearSolver_ >::setLineSearch ( std::shared_ptr< LineSearch > lineSearch )

inline

Set the line search.

See getLineSearch() for already implemented line searches

◆ setMinLinearReduction()

template<typename GridOperator_ , typename LinearSolver_ >

void Dune::PDELab::NewtonMethod< GridOperator_, LinearSolver_ >::setMinLinearReduction ( Real minLinearReduction )

inline

Set the minimal reduction in the linear solver.

Note: with minLinearReduction > 0, the linear reduction will be determined as mininum of the minLinearReduction and the linear reduction needed to achieve second order Newton convergence. (As long as you are not using a fixed linear reduction)

◆ setParameters()

template<typename GridOperator_ , typename LinearSolver_ >

void Dune::PDELab::NewtonMethod< GridOperator_, LinearSolver_ >::setParameters ( const ParameterTree & parameterTree )

inline

Interpret a parameter tree as a set of options for the newton solver.

Possible parameters:

example configuration:

[newton_parameters]
ReassembleThreshold = 0.1
AbsoluteLimit = 1e-6
Reduction = 1e-4
MinLinearReduction = 1e-3
MaxIterations = 15
LineSearchDampingFactor = 0.7

and invocation in the code:

newton.setParameters(param.sub("NewtonParameters"));

This can also be used to set single parameters like this

Dune::ParameterTree ptree;
ptree["verbosity"] = "4";
newton.setParameters(ptree);

◆ setReassembleThreshold()

template<typename GridOperator_ , typename LinearSolver_ >

void Dune::PDELab::NewtonMethod< GridOperator_, LinearSolver_ >::setReassembleThreshold ( Real reassembleThreshold )

inline

Set a threshold, when the linear operator is reassembled.

We allow to keep the linear operator over several newton iterations. If the reduction in the newton drops below a given threshold the linear operator is reassembled to ensure convergence.

◆ setReduction()

template<typename GridOperator_ , typename LinearSolver_ >

void Dune::PDELab::NewtonMethod< GridOperator_, LinearSolver_ >::setReduction ( Real reduction )

inline

Set reduction Newton needs to achieve.

◆ setTerminate()

template<typename GridOperator_ , typename LinearSolver_ >

void Dune::PDELab::NewtonMethod< GridOperator_, LinearSolver_ >::setTerminate ( std::shared_ptr< TerminateInterface > terminate )

inline

Set the termination criterion.

◆ setUseMaxNorm()

template<typename GridOperator_ , typename LinearSolver_ >

void Dune::PDELab::NewtonMethod< GridOperator_, LinearSolver_ >::setUseMaxNorm ( bool b )

inline

Set whether to use the maximum norm for stopping criteria.

◆ setVerbosityLevel()

template<typename GridOperator_ , typename LinearSolver_ >

void Dune::PDELab::NewtonMethod< GridOperator_, LinearSolver_ >::setVerbosityLevel ( unsigned int verbosity )

inline

Set how much output you get.

◆ updateDefect()

template<typename GridOperator_ , typename LinearSolver_ >

virtual void Dune::PDELab::NewtonMethod< GridOperator_, LinearSolver_ >::updateDefect ( Domain & solution )

inlinevirtual

Update _residual and defect in _result.

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

solver/newton.hh

Public Types

Public Member Functions

Detailed Description

Member Typedef Documentation

◆ Domain

◆ GridOperator

◆ Jacobian

◆ LinearSolver

◆ LineSearch

◆ Range

◆ Real

◆ Result

Constructor & Destructor Documentation

◆ NewtonMethod() [1/2]

◆ NewtonMethod() [2/2]

◆ ~NewtonMethod()

Member Function Documentation

◆ apply()

◆ discardMatrix()

◆ getAbsoluteLimit()

◆ getLineSearch()

◆ getReduction()

◆ getTerminate()

◆ getVerbosityLevel()

◆ keepMatrix()

◆ linearSolve()

◆ prepareStep()

◆ printParameters()

◆ result()

◆ setAbsoluteLimit()

◆ setFixedLinearReduction()

◆ setHangingNodeModifications()

◆ setKeepMatrix()

◆ setLineSearch()

◆ setMinLinearReduction()

◆ setParameters()

◆ setReassembleThreshold()

◆ setReduction()

◆ setTerminate()

◆ setUseMaxNorm()

◆ setVerbosityLevel()

◆ updateDefect()