The multi-dimensional Newton method. More...

#include <newtonmethod.hh>

Inheritance diagram for Ewoms::NewtonMethod< TypeTag >:

Public Member Functions
	NewtonMethod (Simulator &simulator)

bool	converged () const
	Returns true if the error of the solution is below the tolerance. More...

Problem &	problem ()
	Returns a reference to the object describing the current physical problem. More...

const Problem &	problem () const
	Returns a reference to the object describing the current physical problem. More...

Model &	model ()
	Returns a reference to the numeric model. More...

const Model &	model () const
	Returns a reference to the numeric model. More...

int	numIterations () const
	Returns the number of iterations done since the Newton method was invoked. More...

Scalar	tolerance () const
	Return the current tolerance at which the Newton method considers itself to be converged. More...

void	setTolerance (Scalar value)
	Set the current tolerance at which the Newton method considers itself to be converged. More...

bool	apply ()
	Run the Newton method. More...

Scalar	linearizeTime () const
	Returns the wall time spend so far for linearizing the non-linear system for all iterations of the current time step. More...

Scalar	solveTime () const
	Returns the wall time spend so far for solving the linear systems for all iterations of the current time step. More...

Scalar	updateTime () const
	Returns the wall time spend so far for updating the iterative solutions of the non-linear system for all iterations of the current time step. More...

Scalar	suggestTimeStepSize (Scalar oldTimeStep) const
	Suggest a new time-step size based on the old time-step size. More...

std::ostringstream &	endIterMsg ()
	Message that should be printed for the user after the end of an iteration. More...

Static Public Member Functions
static void	registerParameters ()
	Register all run-time parameters for the Newton method. More...

Protected Member Functions
bool	verbose_ () const
	Returns true if the Newton method ought to be chatty. More...

void	begin_ (const SolutionVector &u)
	Called before the Newton method is applied to an non-linear system of equations. More...

void	beginIteration_ ()
	Indicates the beginning of a Newton iteration. More...

void	linearize_ ()
	Linearize the global non-linear system of equations. More...

bool	solveLinear_ (const JacobianMatrix &A, GlobalEqVector &x, GlobalEqVector &b)
	Solve the linear system of equations $\mathbf{A}x - b = 0$ . More...

void	updateError_ (const SolutionVector &nextSolution, const SolutionVector &currentSolution, const GlobalEqVector &currentResidual, const GlobalEqVector &solutionUpdate)
	Update the error of the solution given the previous iteration. More...

void	update_ (SolutionVector &nextSolution, const SolutionVector &currentSolution, const GlobalEqVector &solutionUpdate, const GlobalEqVector &currentResidual)
	Update the current solution with a delta vector. More...

void	updatePrimaryVariables_ (int globalDofIdx, PrimaryVariables &nextValue, const PrimaryVariables &currentValue, const EqVector &update, const EqVector &currentResidual)
	Update a single primary variables object. More...

void	writeConvergence_ (const SolutionVector &currentSolution, const GlobalEqVector &solutionUpdate)
	Write the convergence behaviour of the newton method to disk. More...

void	endIteration_ (const SolutionVector &nextSolution, const SolutionVector &currentSolution)
	Indicates that one Newton iteration was finished. More...

bool	proceed_ () const
	Returns true iff another Newton iteration should be done. More...

void	end_ ()
	Indicates that we're done solving the non-linear system of equations. More...

void	failed_ ()
	Called if the Newton method broke down. More...

void	succeeded_ ()
	Called if the Newton method was successful. More...

int	targetIterations_ () const

int	maxIterations_ () const

Protected Attributes
Simulator &	simulator_

Ewoms::Timer	linearizeTimer_

Ewoms::Timer	solveTimer_

Ewoms::Timer	updateTimer_

Scalar	linearizeTime_

Scalar	solveTime_

Scalar	updateTime_

std::ostringstream	endIterMsgStream_

Scalar	error_

Scalar	lastError_

Scalar	tolerance_

int	numIterations_

LinearSolverBackend	linearSolver_

CollectiveCommunication	comm_

ConvergenceWriter	convergenceWriter_

Detailed Description

template<class TypeTag>
class Ewoms::NewtonMethod< TypeTag >

The multi-dimensional Newton method.

This class uses static polymorphism to allow implementations to implement different update/convergence strategies.

Constructor & Destructor Documentation

template<class TypeTag >

Ewoms::NewtonMethod< TypeTag >::NewtonMethod ( Simulator & simulator )

inline

References Ewoms::NewtonMethod< TypeTag >::error_, EWOMS_GET_PARAM, Ewoms::NewtonMethod< TypeTag >::lastError_, Ewoms::NewtonMethod< TypeTag >::numIterations_, and Ewoms::NewtonMethod< TypeTag >::tolerance_.

Member Function Documentation

template<class TypeTag >

bool Ewoms::NewtonMethod< TypeTag >::apply ( )

inline

Run the Newton method.

The actual implementation can influence all the strategic decisions via callbacks using static polymorphism.

Referenced by Ewoms::FvBaseDiscretization< TypeTag >::update().

template<class TypeTag >

void Ewoms::NewtonMethod< TypeTag >::begin_ ( const SolutionVector & u )

inlineprotected

Called before the Newton method is applied to an non-linear system of equations.

Parameters

u	The initial solution

References Ewoms::NewtonMethod< TypeTag >::convergenceWriter_, EWOMS_GET_PARAM, and Ewoms::NewtonMethod< TypeTag >::numIterations_.

template<class TypeTag >

void Ewoms::NewtonMethod< TypeTag >::beginIteration_ ( )

inlineprotected

Indicates the beginning of a Newton iteration.

References Ewoms::NewtonMethod< TypeTag >::error_, Ewoms::NewtonMethod< TypeTag >::lastError_, and Ewoms::NewtonMethod< TypeTag >::problem().

Referenced by Ewoms::FvBaseNewtonMethod< TypeTag >::beginIteration_().

template<class TypeTag >

bool Ewoms::NewtonMethod< TypeTag >::converged ( ) const

inline

Returns true if the error of the solution is below the tolerance.

References Ewoms::NewtonMethod< TypeTag >::error_, and Ewoms::NewtonMethod< TypeTag >::tolerance().

Referenced by Ewoms::NewtonMethod< TypeTag >::apply(), and Ewoms::NewtonMethod< TypeTag >::proceed_().

template<class TypeTag >

void Ewoms::NewtonMethod< TypeTag >::end_ ( )

inlineprotected

Indicates that we're done solving the non-linear system of equations.

References Ewoms::NewtonMethod< TypeTag >::convergenceWriter_, and EWOMS_GET_PARAM.

template<class TypeTag >

void Ewoms::NewtonMethod< TypeTag >::endIteration_	(	const SolutionVector &	nextSolution,
		const SolutionVector &	currentSolution
	)

inlineprotected

Indicates that one Newton iteration was finished.

Parameters

nextSolution	The solution after the current Newton iteration
currentSolution	The solution at the beginning of the current Newton iteration

References Ewoms::NewtonMethod< TypeTag >::endIterMsg(), Ewoms::NewtonMethod< TypeTag >::endIterMsgStream_, Ewoms::NewtonMethod< TypeTag >::error_, Ewoms::NewtonMethod< TypeTag >::numIterations_, Ewoms::NewtonMethod< TypeTag >::problem(), and Ewoms::NewtonMethod< TypeTag >::verbose_().

template<class TypeTag >

std::ostringstream& Ewoms::NewtonMethod< TypeTag >::endIterMsg ( )

inline

Message that should be printed for the user after the end of an iteration.

References Ewoms::NewtonMethod< TypeTag >::endIterMsgStream_.

Referenced by Ewoms::NewtonMethod< TypeTag >::endIteration_().

template<class TypeTag >

void Ewoms::NewtonMethod< TypeTag >::failed_ ( )

inlineprotected

Called if the Newton method broke down.

This method is called after end_()

References Ewoms::NewtonMethod< TypeTag >::numIterations_, and Ewoms::NewtonMethod< TypeTag >::targetIterations_().

Referenced by Ewoms::FvBaseNewtonMethod< TypeTag >::failed_().

template<class TypeTag >

void Ewoms::NewtonMethod< TypeTag >::linearize_ ( )

inlineprotected

Linearize the global non-linear system of equations.

References Ewoms::NewtonMethod< TypeTag >::model().

template<class TypeTag >

Scalar Ewoms::NewtonMethod< TypeTag >::linearizeTime ( ) const

inline

Returns the wall time spend so far for linearizing the non-linear system for all iterations of the current time step.

References Ewoms::NewtonMethod< TypeTag >::linearizeTime_.

Referenced by Ewoms::FvBaseProblem< TypeTag >::timeIntegration().

template<class TypeTag >

int Ewoms::NewtonMethod< TypeTag >::maxIterations_ ( ) const

inlineprotected

References EWOMS_GET_PARAM.

Referenced by Ewoms::NewtonMethod< TypeTag >::proceed_().

template<class TypeTag >

Model& Ewoms::NewtonMethod< TypeTag >::model ( )

inline

Returns a reference to the numeric model.

References Ewoms::Simulator< TypeTag >::model(), and Ewoms::NewtonMethod< TypeTag >::simulator_.

Referenced by Ewoms::NewtonMethod< TypeTag >::apply(), Ewoms::NewtonMethod< TypeTag >::linearize_(), Ewoms::FvBaseNewtonMethod< TypeTag >::model_(), Ewoms::FvBaseNewtonMethod< TypeTag >::update_(), and Ewoms::NewtonMethod< TypeTag >::updateError_().

template<class TypeTag >

const Model& Ewoms::NewtonMethod< TypeTag >::model ( ) const

inline

Returns a reference to the numeric model.

References Ewoms::Simulator< TypeTag >::model(), and Ewoms::NewtonMethod< TypeTag >::simulator_.

template<class TypeTag >

int Ewoms::NewtonMethod< TypeTag >::numIterations ( ) const

inline

Returns the number of iterations done since the Newton method was invoked.

References Ewoms::NewtonMethod< TypeTag >::numIterations_.

Referenced by Ewoms::NewtonMethod< TypeTag >::proceed_().

template<class TypeTag >

Problem& Ewoms::NewtonMethod< TypeTag >::problem ( )

inline

Returns a reference to the object describing the current physical problem.

References Ewoms::Simulator< TypeTag >::problem(), and Ewoms::NewtonMethod< TypeTag >::simulator_.

Referenced by Ewoms::FvBaseNewtonConvergenceWriter< TypeTag >::beginIteration(), Ewoms::NewtonMethod< TypeTag >::beginIteration_(), Ewoms::NewtonMethod< TypeTag >::endIteration_(), and Ewoms::FvBaseNewtonConvergenceWriter< TypeTag >::writeFields().

template<class TypeTag >

const Problem& Ewoms::NewtonMethod< TypeTag >::problem ( ) const

inline

Returns a reference to the object describing the current physical problem.

References Ewoms::Simulator< TypeTag >::problem(), and Ewoms::NewtonMethod< TypeTag >::simulator_.

template<class TypeTag >

bool Ewoms::NewtonMethod< TypeTag >::proceed_ ( ) const

inlineprotected

Returns true iff another Newton iteration should be done.

References Ewoms::NewtonMethod< TypeTag >::converged(), Ewoms::NewtonMethod< TypeTag >::error_, Ewoms::NewtonMethod< TypeTag >::lastError_, Ewoms::NewtonMethod< TypeTag >::maxIterations_(), and Ewoms::NewtonMethod< TypeTag >::numIterations().

Referenced by Ewoms::NewtonMethod< TypeTag >::apply().

template<class TypeTag >

static void Ewoms::NewtonMethod< TypeTag >::registerParameters ( )

inlinestatic

Register all run-time parameters for the Newton method.

References EWOMS_REGISTER_PARAM.

Referenced by Ewoms::FvBaseDiscretization< TypeTag >::registerParameters().

template<class TypeTag >

void Ewoms::NewtonMethod< TypeTag >::setTolerance ( Scalar value )

inline

Set the current tolerance at which the Newton method considers itself to be converged.

References Ewoms::NewtonMethod< TypeTag >::tolerance_.

template<class TypeTag >

bool Ewoms::NewtonMethod< TypeTag >::solveLinear_	(	const JacobianMatrix &	A,
		GlobalEqVector &	x,
		GlobalEqVector &	b
	)

inlineprotected

Solve the linear system of equations $\mathbf{A}x - b = 0$ .

Throws Opm::NumericalProblem if the linear solver didn't converge.

Parameters

A	The matrix of the linear system of equations
x	The vector which solves the linear system
b	The right hand side of the linear system

References Ewoms::NewtonMethod< TypeTag >::linearSolver_.

template<class TypeTag >

Scalar Ewoms::NewtonMethod< TypeTag >::solveTime ( ) const

inline

Returns the wall time spend so far for solving the linear systems for all iterations of the current time step.

References Ewoms::NewtonMethod< TypeTag >::solveTime_.

Referenced by Ewoms::FvBaseProblem< TypeTag >::timeIntegration().

template<class TypeTag >

void Ewoms::NewtonMethod< TypeTag >::succeeded_ ( )

inlineprotected

Called if the Newton method was successful.

This method is called after end_()

Referenced by Ewoms::FvBaseNewtonMethod< TypeTag >::succeeded_().

template<class TypeTag >

Scalar Ewoms::NewtonMethod< TypeTag >::suggestTimeStepSize ( Scalar oldTimeStep ) const

inline

Suggest a new time-step size based on the old time-step size.

The default behavior is to suggest the old time-step size scaled by the ratio between the target iterations and the iterations required to actually solve the last time-step.

References Ewoms::NewtonMethod< TypeTag >::numIterations_, and Ewoms::NewtonMethod< TypeTag >::targetIterations_().

template<class TypeTag >

int Ewoms::NewtonMethod< TypeTag >::targetIterations_ ( ) const

inlineprotected

References EWOMS_GET_PARAM.

Referenced by Ewoms::NewtonMethod< TypeTag >::failed_(), and Ewoms::NewtonMethod< TypeTag >::suggestTimeStepSize().

template<class TypeTag >

Scalar Ewoms::NewtonMethod< TypeTag >::tolerance ( ) const

inline

Return the current tolerance at which the Newton method considers itself to be converged.

References Ewoms::NewtonMethod< TypeTag >::tolerance_.

Referenced by Ewoms::NewtonMethod< TypeTag >::converged().

template<class TypeTag >

void Ewoms::NewtonMethod< TypeTag >::update_	(	SolutionVector &	nextSolution,
		const SolutionVector &	currentSolution,
		const GlobalEqVector &	solutionUpdate,
		const GlobalEqVector &	currentResidual
	)

inlineprotected

Update the current solution with a delta vector.

Different update strategies, such as chopped updates can be implemented by overriding this method. The default behavior is use the standard Newton-Raphson update strategy, i.e.

$u^{k+1} = u^k - \Delta u^k$

Parameters

nextSolution	The solution vector after the current iteration
currentSolution	The solution vector after the last iteration
solutionUpdate	The delta vector as calculated by solving the linear system of equations
currentResidual	The residual vector of the current Newton-Raphson iteraton

template<class TypeTag >

void Ewoms::NewtonMethod< TypeTag >::updateError_	(	const SolutionVector &	nextSolution,
		const SolutionVector &	currentSolution,
		const GlobalEqVector &	currentResidual,
		const GlobalEqVector &	solutionUpdate
	)

inlineprotected

Update the error of the solution given the previous iteration.

For our purposes, the error of a solution is defined as the maximum of the weighted residual of a given solution.

Parameters

nextSolution	The solution after the current iteration
currentSolution	The solution at the beginning the current iteration
currentResidual	The residual (i.e., right-hand-side) of the current iteration's solution.
solutionUpdate	The difference between the current and the next solution

References Ewoms::NewtonMethod< TypeTag >::comm_, Ewoms::NewtonMethod< TypeTag >::error_, EWOMS_GET_PARAM, Ewoms::NewtonMethod< TypeTag >::lastError_, and Ewoms::NewtonMethod< TypeTag >::model().

template<class TypeTag >

void Ewoms::NewtonMethod< TypeTag >::updatePrimaryVariables_	(	int	globalDofIdx,
		PrimaryVariables &	nextValue,
		const PrimaryVariables &	currentValue,
		const EqVector &	update,
		const EqVector &	currentResidual
	)