Solution of a nonlinear system of equations by a damped Newton-method. More...

#include <nleq_err.hh>

Detailed Description

template<class Grid, class Equation, class VariableSet, class Spaces>
class Kaskade::NleqSolver< Grid, Equation, VariableSet, Spaces >

Solution of a nonlinear system of equations by a damped Newton-method.

Template Parameters

Grid	The underlying Grid, eg. UGGrid, AlbertaGrid or some type of ALUGrid.
Equation	The name of the equation class, which defines the subclass DomainCache with d1, d2 and BoundaryCache with d1, d2.
VariableSet	The VariableSet of which representation-type is the Newton-iteration vector.
Spaces	The spaces used in the problem formulation.

Definition at line 289 of file nleq_err.hh.

Classes
struct	NleqInfo

Public Types
enum	PrintLevel { none =0 , minimum =1 , verbose =2 , debug =3 }

enum	NonlinProblemType { mildlyNonlinear =2 , highlyNonlinear =3 , extremelyNonlinear =4 }

Public Member Functions
	NleqSolver ()

void	setTolerance (double tol_)
	Sets the error tolerance which the final approximate solution \(x_k\) must fit. The default value is 1.0e-5. More...

void	setNonlinProblemType (NonlinProblemType nonlinType_)
	Set the classification of the nonlinear problem. The default value is highlyNonlinear. More...

void	setMaximumNoIterations (int maximumIter_)
	Sets the maximum allowed number of Newton-iterations. The default value is 50. More...

void	setPreconFillLevel (int preconFillLevel_)
	Sets the fillin-level of the preconditioner PrecondType::ILUK. The default fillin-level is 0. More...

void	setRestricted (bool restricted_)
	Sets the restricted monotonicity-test flag. The default value depends on the selected NonlinProblemType. More...

void	setErrorStream (std::ostream &errorStream_)
	Sets the error-output stream. The default error-output stream is std::cerr. More...

void	setMonitorStream (std::ostream &monitorStream_)
	Sets the monitor-output stream. The default monitor-output stream is std::cout. More...

void	setErrorLevel (PrintLevel errorLevel_)
	Sets the error-output level. The default error-output level is verbose. More...

void	setMonitorLevel (PrintLevel monitorLevel_)
	Sets the monitor-output level. The default monitor-output level is none. More...

void	setDataLevel (PrintLevel dataLevel_)
	Sets the plot-data-output level. The default plot-data-output level is none. More...

void	setStatistics (bool statistics_)
	Sets the Timings statistics flag. The default Timings statistics flag level is off. More...

void	setOutFilePrefix (const std::string &outFilePrefix_)
	Sets the prefix of the output-files named <prefix>nnn.vtu, where n denotes a decimal digit. The default-prefix is iter_ . More...

void	setScalingVector (std::vector< double > *scale_)
	Sets a user-defined scaling-threshold vector. More...

struct NleqInfo	getInfo ()
	After calling nleqErr, getInfo returns the info structure contents. More...

void	nleqErr (GridManager< Grid > &gridManager, Equation &eq, VariableSet const &variableSet, typename VariableSet::VariableSet *x, Spaces const &spaces, Timings &timer=Timings::instance())
	Calls the nleqErr damped Newton-iteration solver. More...

Member Enumeration Documentation

◆ NonlinProblemType

template<class Grid , class Equation , class VariableSet , class Spaces >

enum Kaskade::NleqSolver::NonlinProblemType

The nonlinearity-level of the problem to be solved.

Enumerator
mildlyNonlinear	problem is mildly nonlinear
highlyNonlinear	problem is highly nonlinear
extremelyNonlinear	problem is extremely nonlinear

Definition at line 303 of file nleq_err.hh.

◆ PrintLevel

template<class Grid , class Equation , class VariableSet , class Spaces >

enum Kaskade::NleqSolver::PrintLevel

The level of error-, monitor- and data-output.

Enumerator
none	no output
minimum	summary output
verbose	detailed output - info about each iterate
debug	additional debug output - reserved for future use

Definition at line 292 of file nleq_err.hh.

Constructor & Destructor Documentation

◆ NleqSolver()

template<class Grid , class Equation , class VariableSet , class Spaces >

Kaskade::NleqSolver< Grid, Equation, VariableSet, Spaces >::NleqSolver ( )

inline

Definition at line 359 of file nleq_err.hh.

Member Function Documentation

◆ getInfo()

template<class Grid , class Equation , class VariableSet , class Spaces >

struct NleqInfo Kaskade::NleqSolver< Grid, Equation, VariableSet, Spaces >::getInfo ( )

inline

After calling nleqErr, getInfo returns the info structure contents.

Definition at line 488 of file nleq_err.hh.

◆ nleqErr()

template<class Grid , class Equation , class VariableSet , class Spaces >

void Kaskade::NleqSolver< Grid, Equation, VariableSet, Spaces >::nleqErr	(	GridManager< Grid > &	gridManager,
		Equation &	eq,
		VariableSet const &	variableSet,
		typename VariableSet::VariableSet *	x,
		Spaces const &	spaces,
		Timings &	timer = `Timings::instance()`
	)

inline

Calls the nleqErr damped Newton-iteration solver.

Parameters

gridManager	The GridManager where the Grid is associated to.
eq	The weak formulation class instance with the problem- and Jacobian functions.
variableSet	The underlying VariableSet.
x	On input, the start-vector for the damped Newton-iteration. On output, the approximate solution vector \( x_k \), which fits the error condition \( \parallel x_k - x\star \parallel <= tol \) , where \( x\star \) denotes the exact solution, and \( \parallel \ldots \parallel \) is a scaled Euclidian norm.
spaces	The underlying problem spaces.

Definition at line 502 of file nleq_err.hh.

◆ setDataLevel()

template<class Grid , class Equation , class VariableSet , class Spaces >

void Kaskade::NleqSolver< Grid, Equation, VariableSet, Spaces >::setDataLevel ( PrintLevel dataLevel_ )

inline

Sets the plot-data-output level. The default plot-data-output level is none.

Parameters

dataLevel_ The desired plot-data-output level.

Definition at line 458 of file nleq_err.hh.

◆ setErrorLevel()

template<class Grid , class Equation , class VariableSet , class Spaces >

void Kaskade::NleqSolver< Grid, Equation, VariableSet, Spaces >::setErrorLevel ( PrintLevel errorLevel_ )

inline

Sets the error-output level. The default error-output level is verbose.

Parameters

errorLevel_ The desired error-output level.

Definition at line 444 of file nleq_err.hh.

◆ setErrorStream()

template<class Grid , class Equation , class VariableSet , class Spaces >

void Kaskade::NleqSolver< Grid, Equation, VariableSet, Spaces >::setErrorStream ( std::ostream & errorStream_ )

inline

Sets the error-output stream. The default error-output stream is std::cerr.

Parameters

errorStream_ The desired error-output stream.

Definition at line 430 of file nleq_err.hh.

◆ setMaximumNoIterations()

template<class Grid , class Equation , class VariableSet , class Spaces >

void Kaskade::NleqSolver< Grid, Equation, VariableSet, Spaces >::setMaximumNoIterations ( int maximumIter_ )

inline

Sets the maximum allowed number of Newton-iterations. The default value is 50.

Parameters

maximumIter_ The desired maximum number of Newton-iterations.

Definition at line 400 of file nleq_err.hh.

◆ setMonitorLevel()

template<class Grid , class Equation , class VariableSet , class Spaces >

void Kaskade::NleqSolver< Grid, Equation, VariableSet, Spaces >::setMonitorLevel ( PrintLevel monitorLevel_ )

inline

Sets the monitor-output level. The default monitor-output level is none.

Parameters

monitorLevel_ The desired monitor-output level.

Definition at line 451 of file nleq_err.hh.

◆ setMonitorStream()

template<class Grid , class Equation , class VariableSet , class Spaces >

void Kaskade::NleqSolver< Grid, Equation, VariableSet, Spaces >::setMonitorStream ( std::ostream & monitorStream_ )

inline

Sets the monitor-output stream. The default monitor-output stream is std::cout.

Parameters

monitorStream_ The desired monitor-output stream.

Definition at line 437 of file nleq_err.hh.

◆ setNonlinProblemType()

template<class Grid , class Equation , class VariableSet , class Spaces >

void Kaskade::NleqSolver< Grid, Equation, VariableSet, Spaces >::setNonlinProblemType ( NonlinProblemType nonlinType_ )

inline

Set the classification of the nonlinear problem. The default value is highlyNonlinear.

Parameters

nonlinType_ The following classifications may be used:
mildlyNonlinear: The problem is considered to be mildly nonlinear and NleqSolver starts up with dampingfactor=1.
highlyNonlinear: The problem is considered to be highly nonlinear and NleqSolver starts up with dampingfactor=1.0e-4.
extremelyNonlinear: The problem is considered to be extremely nonlinear and NleqSolver starts up with dampingfactor=1.0e-6. Moreover, restricted is set automatically to true.

Definition at line 394 of file nleq_err.hh.

◆ setOutFilePrefix()

template<class Grid , class Equation , class VariableSet , class Spaces >

void Kaskade::NleqSolver< Grid, Equation, VariableSet, Spaces >::setOutFilePrefix ( const std::string & outFilePrefix_ )

inline

Sets the prefix of the output-files named <prefix>nnn.vtu, where n denotes a decimal digit. The default-prefix is iter_ .

Parameters

outFilePrefix_ The desired filename-prefix.

Definition at line 473 of file nleq_err.hh.

◆ setPreconFillLevel()

template<class Grid , class Equation , class VariableSet , class Spaces >

void Kaskade::NleqSolver< Grid, Equation, VariableSet, Spaces >::setPreconFillLevel ( int preconFillLevel_ )

inline

Sets the fillin-level of the preconditioner PrecondType::ILUK. The default fillin-level is 0.

Parameters

preconFillLevel_ The desired PrecondType::ILUK fillin-level.

Definition at line 406 of file nleq_err.hh.

◆ setRestricted()

template<class Grid , class Equation , class VariableSet , class Spaces >

void Kaskade::NleqSolver< Grid, Equation, VariableSet, Spaces >::setRestricted ( bool restricted_ )

inline

Sets the restricted monotonicity-test flag. The default value depends on the selected NonlinProblemType.

Parameters

restricted_ true means the the restricted damping-strategy is applied.
This means, that the restricted monotonicity test will be applied for determination whether the next iterate (and the associate damping factor lambda) will be accepted. With \( \theta = \parallel \overline{\Delta x}_{k+1} \parallel / \parallel \Delta x_{k} \parallel \), (where \( \Delta x_{k} \) denotes the k-th Newton correction, and \( \overline{\Delta x}_{k+1} \) denotes the sucessive simplified Newton correction) the condition \( \theta <= 1 - \lambda / 4 \) must be fit.
If set to false, then the standard monotonicity test will be applied, i.e. the following condition must be fit: \( \theta < 1 \) .

Definition at line 423 of file nleq_err.hh.

◆ setScalingVector()

template<class Grid , class Equation , class VariableSet , class Spaces >

void Kaskade::NleqSolver< Grid, Equation, VariableSet, Spaces >::setScalingVector ( std::vector< double > * scale_ )

inline

Sets a user-defined scaling-threshold vector.

Parameters

*scale_ A pointer to the selected scaling-threshold vector.

Definition at line 479 of file nleq_err.hh.

◆ setStatistics()

template<class Grid , class Equation , class VariableSet , class Spaces >

void Kaskade::NleqSolver< Grid, Equation, VariableSet, Spaces >::setStatistics ( bool statistics_ )

inline

Sets the Timings statistics flag. The default Timings statistics flag level is off.

Parameters

statistics_ false=off, true=on.

Definition at line 465 of file nleq_err.hh.

◆ setTolerance()

template<class Grid , class Equation , class VariableSet , class Spaces >

void Kaskade::NleqSolver< Grid, Equation, VariableSet, Spaces >::setTolerance ( double tol_ )

inline

Sets the error tolerance which the final approximate solution \(x_k\) must fit. The default value is 1.0e-5.

Parameters

tol_	The desired error for the solution.

Definition at line 380 of file nleq_err.hh.

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

nleq_err.hh

Detailed Description

Classes

Public Types

Public Member Functions

Member Enumeration Documentation

◆ NonlinProblemType

◆ PrintLevel

Constructor & Destructor Documentation

◆ NleqSolver()

Member Function Documentation

◆ getInfo()

◆ nleqErr()

◆ setDataLevel()

◆ setErrorLevel()

◆ setErrorStream()

◆ setMaximumNoIterations()

◆ setMonitorLevel()

◆ setMonitorStream()

◆ setNonlinProblemType()

◆ setOutFilePrefix()

◆ setPreconFillLevel()

◆ setRestricted()

◆ setScalingVector()

◆ setStatistics()

◆ setTolerance()