Nonlinear solver based on Anderson Acceleration. More...

#include <NOX_Solver_AndersonAcceleration.H>

Inheritance diagram for NOX::Solver::AndersonAcceleration:

Collaboration diagram for NOX::Solver::AndersonAcceleration:

Public Member Functions
	AndersonAcceleration (const Teuchos::RCP< NOX::Abstract::Group > &grp, const Teuchos::RCP< NOX::StatusTest::Generic > &tests, const Teuchos::RCP< Teuchos::ParameterList > &params)
	Constructor. More...

virtual	~AndersonAcceleration ()
	Destructor.

virtual void	reset ()
	Resets the solver for another solve. This resets the counters and status only. Uses the final solution from the last solve as the initial guess for the next solve. More...

virtual void	reset (const NOX::Abstract::Vector &initialGuess)
	Resets the solver and sets a new initial guess.

virtual void	reset (const NOX::Abstract::Vector &initialGuess, const Teuchos::RCP< NOX::StatusTest::Generic > &tests)
	Resets the solver, sets a new status test, and sets a new initial guess.

virtual NOX::StatusTest::StatusType	step ()
	Do one nonlinear step in the iteration sequence and return status.

virtual NOX::StatusTest::StatusType	solve ()
	Solve the nonlinear problem and return final status. More...

virtual const NOX::Abstract::Group &	getSolutionGroup () const
	Return a reference to the current solution group.

virtual const NOX::Abstract::Group &	getPreviousSolutionGroup () const
	Return a reference to the previous solution group.

virtual NOX::StatusTest::StatusType	getStatus () const
	Returns the current status of the solver.

virtual int	getNumIterations () const
	Get number of iterations.

virtual const Teuchos::ParameterList &	getList () const
	Return a reference to the solver parameters.

virtual double	getStepSize () const

virtual Teuchos::RCP< const NOX::Abstract::Group >	getSolutionGroupPtr () const
	Return a RCP to the solution group.

virtual Teuchos::RCP< const NOX::Abstract::Group >	getPreviousSolutionGroupPtr () const
	Return a RCP to the previous solution group.

virtual Teuchos::RCP< const Teuchos::ParameterList >	getListPtr () const
	Return a RCP to the solver parameters.

virtual Teuchos::RCP< const NOX::SolverStats >	getSolverStatistics () const
	Return a RCP to the solver statistics.

Public Member Functions inherited from NOX::Solver::Generic
	Generic ()
	Constructor (does nothing)

virtual	~Generic ()
	Destructor (does nothing)

Protected Member Functions
virtual void	init ()
	Print out initialization information and calcuate the RHS.

virtual void	printUpdate ()
	Prints the current iteration information.

void	qrAdd (NOX::Abstract::Vector &newCol)
	Updates QR factors by addition of a column.

void	qrDelete ()
	Updates QR factors by deletion of a column.

void	reorthogonalize ()
	Reorthogonalized columns of Q and updates factorization.

Protected Attributes
Teuchos::RCP< NOX::GlobalData >	globalDataPtr
	Pointer to the global data object.

Teuchos::RCP< NOX::Utils >	utilsPtr
	Utils.

Teuchos::RCP < NOX::Abstract::Group >	solnPtr
	Current solution.

Teuchos::RCP < NOX::Abstract::Group >	oldSolnPtr
	Previous solution pointer.

Teuchos::RCP < NOX::StatusTest::Generic >	testPtr
	Stopping test.

Teuchos::RCP < Teuchos::ParameterList >	paramsPtr
	Input parameters.

Teuchos::RCP < NOX::LineSearch::Generic >	lineSearchPtr
	Linesearch.

bool	precond
	Flag for preconditioning.

bool	recomputeJacobian
	Flag to recompute Jacobian each iterate. Needed if Jacobian required to apply preconditioner.

Teuchos::RCP < NOX::Abstract::Vector >	workVec
	Vector for temporary storage.

Teuchos::RCP < NOX::Abstract::Vector >	precF
	Current preconditioned function value.

Teuchos::RCP < NOX::Abstract::Vector >	oldPrecF
	Previous preconditioned function value.

int	storeParam
	Maximum storage depth.

int	nStore
	Current storage depth.

double	mixParam
	Mixing parameter.

double	stepSize
	Current step.

std::vector< Teuchos::RCP < NOX::Abstract::Vector > >	xMat
	"Matrix" of successive iterate differences

std::vector< Teuchos::RCP < NOX::Abstract::Vector > >	qMat
	Q factor the for least-squares problem.

Teuchos::SerialDenseMatrix < int, double >	rMat
	R factor for the least-squares problem.

int	nIter
	Number of nonlinear iterations.

int	orthoFrequency
	Frequency for reorthogonalization of QR factors. If nonpositive, we never reorthogonalize.

NOX::StatusTest::StatusType	status
	Status of nonlinear solver.

NOX::StatusTest::CheckType	checkType
	Type of check to use for status tests. See NOX::StatusTest for more details.

Teuchos::RCP< NOX::Observer >	observer
	Pointer to a user defined NOX::Observer object.

std::vector< double >	WORK
	Scratch space for condition number estimation using LAPACK.

std::vector< int >	IWORK
	Scratch space for condition number estimation using LAPACK.

bool	adjustForConditionNumber
	If true, the QR matrix will be resized if the condiiton number is greater than the dropTolerance.

double	dropTolerance
	Value of the condition number above which the QR matrix is resized.

int	accelerationStartIteration
	The nonlinear iteration where Anderson Acceleration will start.

bool	disableChecksForUnitTesting
	Disables the storage depth size check - used for unit testing corner cases only.

Detailed Description

Nonlinear solver based on Anderson Acceleration.

Solves $F(x)=0$ using Anderson Acceleration.

This method requires a mixing parameter $\beta$ and a preconditioner $M(x)$ . If preconditioning is not supported, it is taken to be the identity.

For the first iteration, the solver computes $x_1 = x_0 + \beta M(x_0)F(x_0)$ .

Each iteration afterward, the solver does the following.

Set $m_k = \min\{m,k\}$ , where is a parameter that determines the maximum number of iterates for which we store iterate and function values in addition to the current iterate. represents the number of previous iterates stored currently.
Solve the least-squares problem: $\min_{\gamma}\|\sum_{i=0}^{m_k} \alpha_iM(x_{k-i})F(x_{k-i}) \|$ , such that $\sum_{i=1}^{m_k} \alpha_i = 1$ . In this implementation, we solve an equivalent unconstrained problem for which the QR factors are stored and updated.
Calculate the new iterate: $x_{k+1} = {i=0}^{m_k} [x_{k-i} + M(x_{k-i})F(x_{k-i})]$.

The iterations progress until the status tests (see NOX::StatusTest) determine either failure or convergence.

Input Parameters

The following parameter list entries are valid for this solver:

"Anderson Parameters" - Sublist of parameters specific to AA
"Line Search" - Sublist of the line search parameters, passed to the NOX::LineSearch::Manager constructor. Defaults to an empty list.
"Solver Options" - Sublist of general solver options.
- "User Defined Pre/Post Operator" is supported. See NOX::Parameter::PrePostOperator for more details.

Output Parameters

Every time solve() is called, a sublist for output parameters called "Output" will be created and contain the following parameters.

"Output":

"Nonlinear Iterations" - Number of nonlinear iterations
"2-Norm of Residual" - Two-norm of final residual

Author: Alex Toth and Roger Pawlowski

Constructor & Destructor Documentation

NOX::Solver::AndersonAcceleration::AndersonAcceleration	(	const Teuchos::RCP< NOX::Abstract::Group > &	grp,
		const Teuchos::RCP< NOX::StatusTest::Generic > &	tests,
		const Teuchos::RCP< Teuchos::ParameterList > &	params
	)

Constructor.

See reset(NOX::Abstract::Group&, NOX::StatusTest::Generic&, Teuchos::ParameterList&) for description

References NOX::DeepCopy, globalDataPtr, init(), observer, NOX::Solver::parseObserver(), Teuchos::rcp(), NOX::ShapeCopy, Teuchos::ParameterList::sublist(), utilsPtr, and NOX::Solver::validateSolverOptionsSublist().

Member Function Documentation

void NOX::Solver::AndersonAcceleration::reset ( )

virtual

Resets the solver for another solve. This resets the counters and status only. Uses the final solution from the last solve as the initial guess for the next solve.

NOTE: All NOX solvers will call reset() automatically at teh beginning of the solve() method. We add the reset() method to the solver interface for the application to call in case the application needs to reset counters and status manually before the next call to solve() is made.

Implements NOX::Solver::Generic.

References NOX::StatusTest::Unconverged.

NOX::StatusTest::StatusType NOX::Solver::AndersonAcceleration::solve ( )

virtual

Solve the nonlinear problem and return final status.

By "solve", we call iterate() until the NOX::StatusTest value is either NOX::StatusTest::Converged or NOX::StatusTest::Failed.

Implements NOX::Solver::Generic.

References Teuchos::ParameterList::set(), Teuchos::ParameterList::sublist(), and NOX::StatusTest::Unconverged.

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

NOX_Solver_AndersonAcceleration.H
NOX_Solver_AndersonAcceleration.C

Public Member Functions

Protected Member Functions

Protected Attributes

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation