Base class for representing a system of differential-algebraic equations and solving for its steady-state response. More...

#include <SteadyStateSystem.h>

Inheritance diagram for SteadyStateSystem:

[legend]

Detailed Description

Base class for representing a system of differential-algebraic equations and solving for its steady-state response.

Since: New in Cantera 3.2.

Definition at line 23 of file SteadyStateSystem.h.

Public Member Functions
	SteadyStateSystem (const SteadyStateSystem &)=delete

SteadyStateSystem &	operator= (const SteadyStateSystem &)=delete

virtual void	eval (double x, double r, double rdt=-1.0, int count=1)=0
	Evaluate the residual function.

virtual void	evalJacobian (double *x0)=0
	Evaluates the Jacobian at x0 using finite differences.

virtual double	weightedNorm (const double *step) const =0
	Compute the weighted norm of `step`.

int	solve (double x0, double x1, int loglevel)
	Solve \( F(x) = 0 \), where \( F(x) \) is the residual function.

void	setInitialGuess (const double *x)
	Set the initial guess. Should be called before solve().

void	solve (int loglevel=0)
	Solve the steady-state problem, taking internal timesteps as necessary until the Newton solver can converge for the steady problem.

void	getState (double *x) const
	Get the converged steady-state solution after calling solve().

double	ssnorm (double x, double r)
	Steady-state max norm (infinity norm) of the residual evaluated using solution x.

size_t	size () const
	Total solution vector length;.

virtual void	resize ()
	Call to set the size of internal data structures after first defining the system or if the problem size changes, for example after grid refinement.

size_t	bandwidth () const
	Jacobian bandwidth.

virtual string	componentName (size_t i) const
	Get the name of the i-th component of the state vector.

virtual pair< string, string >	componentTableHeader () const
	Get header lines describing the column names included in a component label.

virtual string	componentTableLabel (size_t i) const
	Get elements of the component name, aligned with the column headings given by componentTableHeader().

virtual double	upperBound (size_t i) const =0
	Get the upper bound for global component i in the state vector.

virtual double	lowerBound (size_t i) const =0
	Get the lower bound for global component i in the state vector.

MultiNewton &	newton ()
	Return a reference to the Newton iterator.

void	setLinearSolver (shared_ptr< SystemJacobian > solver)
	Set the linear solver used to hold the Jacobian matrix and solve linear systems as part of each Newton iteration.

shared_ptr< SystemJacobian >	linearSolver () const
	Get the the linear solver being used to hold the Jacobian matrix and solve linear systems as part of each Newton iteration.

double	rdt () const
	Reciprocal of the time step.

bool	transient () const
	True if transient mode.

bool	steady () const
	True if steady mode.

virtual void	initTimeInteg (double dt, double *x)
	Prepare for time stepping beginning with solution x and timestep dt.

virtual void	setSteadyMode ()
	Prepare to solve the steady-state problem.

vector< int > &	transientMask ()
	Access the vector indicating which equations contain a transient term.

double	timeStep (int nsteps, double dt, double x, double r, int loglevel)
	Take time steps using Backward Euler.

virtual void	resetBadValues (double *x)
	Reset values such as negative species concentrations.

void	setJacAge (int ss_age, int ts_age=-1)
	Set the maximum number of steps that can be taken using the same Jacobian before it must be re-evaluated.

void	setInterrupt (Func1 *interrupt)
	Set a function that will be called every time eval is called.

void	setTimeStepCallback (Func1 *callback)
	Set a function that will be called after each successful timestep.

void	setJacobianPerturbation (double relative, double absolute, double threshold)
	Configure perturbations used to evaluate finite difference Jacobian.

virtual void	writeDebugInfo (const string &header_suffix, const string &message, int loglevel, int attempt_counter)
	Write solver debugging based on the specified log level.

virtual void	clearDebugFile ()
	Delete debug output file that may be created by writeDebugInfo() when solving with high `loglevel`.

Options
void	setTimeStep (double stepsize, size_t n, const int *tsteps)
	Set the number of time steps to try when the steady Newton solver is unsuccessful.

void	setMinTimeStep (double tmin)
	Set the minimum time step allowed during time stepping.

void	setMaxTimeStep (double tmax)
	Set the maximum time step allowed during time stepping.

void	setTimeStepFactor (double tfactor)
	Sets a factor by which the time step is reduced if the time stepping fails.

void	setMaxTimeStepCount (int nmax)
	Set the maximum number of timeteps allowed before successful steady-state solve.

int	maxTimeStepCount () const
	Get the maximum number of timeteps allowed before successful steady-state solve.

Protected Member Functions
void	evalSSJacobian (double x, double rsd)
	Evaluate the steady-state Jacobian, accessible via linearSolver()

Protected Attributes
vector< int >	m_steps = { 10 }
	Array of number of steps to take after each unsuccessful steady-state solve before re-attempting the steady-state solution.

double	m_tstep = 1.0e-5
	Initial timestep.

double	m_tmin = 1e-16
	Minimum timestep size.

double	m_tmax = 1e+08
	Maximum timestep size.

double	m_tfactor = 0.5
	Factor time step is multiplied by if time stepping fails ( < 1 )

shared_ptr< vector< double > >	m_state
	Solution vector.

vector< double >	m_xnew
	Work array used to hold the residual or the new solution.

vector< double >	m_xlast_ts
	State vector after the last successful set of time steps.

unique_ptr< MultiNewton >	m_newt
	Newton iterator.

double	m_rdt = 0.0
	Reciprocal of time step.

shared_ptr< SystemJacobian >	m_jac
	Jacobian evaluator.

bool	m_jac_ok = false
	If `true`, Jacobian is current.

size_t	m_bw = 0
	Jacobian bandwidth.

size_t	m_size = 0
	Solution vector size

vector< double >	m_work1
	Work arrays used during Jacobian evaluation.

vector< double >	m_work2

vector< int >	m_mask
	Transient mask.

int	m_ss_jac_age = 20
	Maximum age of the Jacobian in steady-state mode.

int	m_ts_jac_age = 20
	Maximum age of the Jacobian in time-stepping mode.

int	m_attempt_counter = 0
	Counter used to manage the number of states stored in the debug log file generated by writeDebugInfo()

int	m_max_history = 10
	Constant that determines the maximum number of states stored in the debug log file generated by writeDebugInfo()

Func1 *	m_interrupt = nullptr
	Function called at the start of every call to eval.

Func1 *	m_time_step_callback = nullptr
	User-supplied function called after each successful timestep.

int	m_nsteps = 0
	Number of time steps taken in the current call to solve()

int	m_nsteps_max = 500
	Maximum number of timesteps allowed per call to solve()

double	m_jacobianThreshold = 0.0
	Threshold for ignoring small elements in Jacobian.

double	m_jacobianRelPerturb = 1e-5
	Relative perturbation of each component in finite difference Jacobian.

double	m_jacobianAbsPerturb = 1e-10
	Absolute perturbation of each component in finite difference Jacobian.

Constructor & Destructor Documentation

◆ SteadyStateSystem()

SteadyStateSystem ( )

Definition at line 15 of file SteadyStateSystem.cpp.

◆ ~SteadyStateSystem()

~SteadyStateSystem ( )

virtual

Definition at line 21 of file SteadyStateSystem.cpp.

Member Function Documentation

◆ eval()

virtual void eval	(	double *	x,
		double *	r,
		double	rdt = `-1.0`,
		int	count = `1`
	)

pure virtual

Evaluate the residual function.

Parameters

[in]	x	State vector
[out]	r	On return, contains the residual vector
	rdt	Reciprocal of the time step. if omitted, then the internally stored value (accessible using the rdt() method) is used.
	count	Set to zero to omit this call from the statistics

Implemented in OneDim, Sim1D, and SteadyReactorSolver.

◆ evalJacobian()

virtual void evalJacobian ( double * x0 )

pure virtual

Evaluates the Jacobian at x0 using finite differences.

The Jacobian is computed by perturbing each component of x0, evaluating the residual function, and then estimating the partial derivatives numerically using finite differences to determine the corresponding column of the Jacobian.

Parameters

x0	State vector at which to evaluate the Jacobian

Implemented in OneDim, and SteadyReactorSolver.

◆ weightedNorm()

virtual double weightedNorm ( const double * step ) const

pure virtual

Compute the weighted norm of step.

The purpose is to measure the "size" of the step vector \( \Delta x \) in a way that takes into account the relative importance or scale of different solution components. Each component of the step vector is normalized by a weight that depends on both the current magnitude of the solution vector and specified tolerances. This makes the norm dimensionless and scaled appropriately, avoiding issues where some components dominate due to differences in their scales. See OneDim::weightedNorm() for a representative implementation.

Implemented in OneDim, and SteadyReactorSolver.

◆ solve() [1/2]

int solve	(	double *	x0,
		double *	x1,
		int	loglevel
	)

Solve \( F(x) = 0 \), where \( F(x) \) is the residual function.

Parameters

[in]	x0	Starting estimate of solution.
[out]	x1	Final solution satisfying \( F(x1) = 0 \).
	loglevel	Controls amount of diagnostic output.

Returns

1 for success
-2 failure (maximum number of damping steps was reached)
-3 failure (solution was up against the bounds

Deprecated:: To be removed after Cantera 3.2. Use setInitialGuess(), solve(int), and getState() instead.

Definition at line 37 of file SteadyStateSystem.cpp.

◆ setInitialGuess()

void setInitialGuess ( const double * x )

Set the initial guess. Should be called before solve().

Definition at line 25 of file SteadyStateSystem.cpp.

◆ solve() [2/2]

void solve ( int loglevel = 0 )

Solve the steady-state problem, taking internal timesteps as necessary until the Newton solver can converge for the steady problem.

Parameters

loglevel Controls amount of diagnostic output.

Definition at line 48 of file SteadyStateSystem.cpp.

◆ getState()

void getState ( double * x ) const

Get the converged steady-state solution after calling solve().

Definition at line 32 of file SteadyStateSystem.cpp.

◆ ssnorm()

double ssnorm	(	double *	x,
		double *	r
	)

Steady-state max norm (infinity norm) of the residual evaluated using solution x.

On return, array r contains the steady-state residual values.

Definition at line 216 of file SteadyStateSystem.cpp.

◆ size()

size_t size ( ) const

inline

Total solution vector length;.

Definition at line 91 of file SteadyStateSystem.h.

◆ resize()

void resize ( )

virtual

Call to set the size of internal data structures after first defining the system or if the problem size changes, for example after grid refinement.

The m_size variable should be updated before calling this method

Reimplemented in OneDim, and Sim1D.

Definition at line 235 of file SteadyStateSystem.cpp.

◆ bandwidth()

size_t bandwidth ( ) const

inline

Jacobian bandwidth.

Definition at line 102 of file SteadyStateSystem.h.

◆ componentName()

virtual string componentName ( size_t i ) const

inlinevirtual

Get the name of the i-th component of the state vector.

Reimplemented in OneDim, and SteadyReactorSolver.

Definition at line 107 of file SteadyStateSystem.h.

◆ componentTableHeader()

virtual pair< string, string > componentTableHeader ( ) const

inlinevirtual

Get header lines describing the column names included in a component label.

Headings should be aligned with items formatted in the output of componentTableLabel(). Two lines are allowed. If only one is needed, the first line should be blank.

Reimplemented in OneDim.

Definition at line 113 of file SteadyStateSystem.h.

◆ componentTableLabel()

virtual string componentTableLabel ( size_t i ) const

inlinevirtual

Get elements of the component name, aligned with the column headings given by componentTableHeader().

Reimplemented in OneDim.

Definition at line 119 of file SteadyStateSystem.h.

◆ upperBound()

virtual double upperBound ( size_t i ) const

pure virtual

Get the upper bound for global component i in the state vector.

Implemented in OneDim, and SteadyReactorSolver.

◆ lowerBound()

virtual double lowerBound ( size_t i ) const

pure virtual

Get the lower bound for global component i in the state vector.

Implemented in OneDim, and SteadyReactorSolver.

◆ newton()

MultiNewton & newton ( )

Return a reference to the Newton iterator.

Definition at line 300 of file SteadyStateSystem.cpp.

◆ setLinearSolver()

void setLinearSolver ( shared_ptr< SystemJacobian > solver )

Set the linear solver used to hold the Jacobian matrix and solve linear systems as part of each Newton iteration.

Definition at line 251 of file SteadyStateSystem.cpp.

◆ linearSolver()

shared_ptr< SystemJacobian > linearSolver ( ) const

inline

Get the the linear solver being used to hold the Jacobian matrix and solve linear systems as part of each Newton iteration.

Definition at line 136 of file SteadyStateSystem.h.

◆ rdt()

double rdt ( ) const

inline

Reciprocal of the time step.

Definition at line 139 of file SteadyStateSystem.h.

◆ transient()

bool transient ( ) const

inline

True if transient mode.

Definition at line 144 of file SteadyStateSystem.h.

◆ steady()

bool steady ( ) const

inline

True if steady mode.

Definition at line 149 of file SteadyStateSystem.h.

◆ initTimeInteg()

void initTimeInteg	(	double	dt,
		double *	x
	)

virtual

Prepare for time stepping beginning with solution x and timestep dt.

Reimplemented in OneDim, and SteadyReactorSolver.

Definition at line 269 of file SteadyStateSystem.cpp.

◆ setSteadyMode()

void setSteadyMode ( )

virtual

Prepare to solve the steady-state problem.

After invoking this method, subsequent calls to solve() will solve the steady-state problem. Sets the reciprocal of the time step to zero, and, if it was previously non-zero, signals that a new Jacobian will be needed.

Reimplemented in OneDim.

Definition at line 280 of file SteadyStateSystem.cpp.

◆ transientMask()

vector< int > & transientMask ( )

inline

Access the vector indicating which equations contain a transient term.

Elements are 1 for equations with a transient terms and 0 otherwise.

Definition at line 164 of file SteadyStateSystem.h.

◆ timeStep()

double timeStep	(	int	nsteps,
		double	dt,
		double *	x,
		double *	r,
		int	loglevel
	)

Take time steps using Backward Euler.

Parameters

nsteps	number of steps
dt	initial step size
x	current solution vector
r	solution vector after time stepping
loglevel	controls amount of printed diagnostics

Returns: size of last timestep taken

Definition at line 122 of file SteadyStateSystem.cpp.

◆ resetBadValues()

virtual void resetBadValues ( double * x )

inlinevirtual

Reset values such as negative species concentrations.

Reimplemented in OneDim, and SteadyReactorSolver.

Definition at line 179 of file SteadyStateSystem.h.

◆ setTimeStep()

void setTimeStep	(	double	stepsize,
		size_t	n,
		const int *	tsteps
	)

Set the number of time steps to try when the steady Newton solver is unsuccessful.

Parameters

stepsize	Initial time step size [s]
n	Length of `tsteps` array
tsteps	A sequence of time step counts to take after subsequent failures of the steady-state solver. The last value in `tsteps` will be used again after further unsuccessful solution attempts.

Definition at line 226 of file SteadyStateSystem.cpp.

◆ setMinTimeStep()

void setMinTimeStep ( double tmin )

inline

Set the minimum time step allowed during time stepping.

Definition at line 194 of file SteadyStateSystem.h.

◆ setMaxTimeStep()

void setMaxTimeStep ( double tmax )

inline

Set the maximum time step allowed during time stepping.

Definition at line 199 of file SteadyStateSystem.h.

◆ setTimeStepFactor()

void setTimeStepFactor ( double tfactor )

inline

Sets a factor by which the time step is reduced if the time stepping fails.

The default value is 0.5.

Parameters

tfactor factor time step is multiplied by if time stepping fails

Definition at line 207 of file SteadyStateSystem.h.

◆ setMaxTimeStepCount()

void setMaxTimeStepCount ( int nmax )

inline

Set the maximum number of timeteps allowed before successful steady-state solve.

Definition at line 212 of file SteadyStateSystem.h.

◆ maxTimeStepCount()

int maxTimeStepCount ( ) const

inline

Get the maximum number of timeteps allowed before successful steady-state solve.

Definition at line 217 of file SteadyStateSystem.h.

◆ setJacAge()

void setJacAge	(	int	ss_age,
		int	ts_age = `-1`
	)

Set the maximum number of steps that can be taken using the same Jacobian before it must be re-evaluated.

Parameters

ss_age	Age limit during steady-state mode
ts_age	Age limit during time stepping mode. If not specified, the steady-state age is also used during time stepping.

Definition at line 290 of file SteadyStateSystem.cpp.

◆ setInterrupt()

void setInterrupt ( Func1 * interrupt )

inline

Set a function that will be called every time eval is called.

Can be used to provide keyboard interrupt support in the high-level language interfaces.

Definition at line 232 of file SteadyStateSystem.h.

◆ setTimeStepCallback()

void setTimeStepCallback ( Func1 * callback )

inline

Set a function that will be called after each successful timestep.

The function will be called with the size of the timestep as the argument. Intended to be used for observing solver progress for debugging purposes.

Definition at line 240 of file SteadyStateSystem.h.

◆ setJacobianPerturbation()

void setJacobianPerturbation	(	double	relative,
		double	absolute,
		double	threshold
	)

inline

Configure perturbations used to evaluate finite difference Jacobian.

Parameters

relative	Relative perturbation (multiplied by the absolute value of each component). Default `1.0e-5`.
absolute	Absolute perturbation (independent of component value). Default `1.0e-10`.
threshold	Threshold below which to exclude elements from the Jacobian Default `0.0`.

Definition at line 251 of file SteadyStateSystem.h.

◆ writeDebugInfo()

virtual void writeDebugInfo	(	const string &	header_suffix,
		const string &	message,
		int	loglevel,
		int	attempt_counter
	)

inlinevirtual

Write solver debugging based on the specified log level.

See also: Sim1D::writeDebugInfo for a specific implementation of this capability.

Reimplemented in Sim1D, and SteadyReactorSolver.

Definition at line 260 of file SteadyStateSystem.h.

◆ clearDebugFile()

virtual void clearDebugFile ( )

inlinevirtual

Delete debug output file that may be created by writeDebugInfo() when solving with high loglevel.

Reimplemented in Sim1D.

Definition at line 265 of file SteadyStateSystem.h.

◆ evalSSJacobian()

void evalSSJacobian	(	double *	x,
		double *	rsd
	)

protected

Evaluate the steady-state Jacobian, accessible via linearSolver()

Parameters

[in]	x	Current state vector, length size()
[out]	rsd	Storage for the residual, length size()

Definition at line 260 of file SteadyStateSystem.cpp.

Member Data Documentation

◆ m_steps

vector<int> m_steps = { 10 }

protected

Array of number of steps to take after each unsuccessful steady-state solve before re-attempting the steady-state solution.

For subsequent time stepping calls, the final value is reused. See setTimeStep().

Definition at line 276 of file SteadyStateSystem.h.

◆ m_tstep

double m_tstep = 1.0e-5

protected

Initial timestep.

Definition at line 278 of file SteadyStateSystem.h.

◆ m_tmin

double m_tmin = 1e-16

protected

Minimum timestep size.

Definition at line 279 of file SteadyStateSystem.h.

◆ m_tmax

double m_tmax = 1e+08

protected

Maximum timestep size.

Definition at line 280 of file SteadyStateSystem.h.

◆ m_tfactor

double m_tfactor = 0.5

protected

Factor time step is multiplied by if time stepping fails ( < 1 )

Definition at line 283 of file SteadyStateSystem.h.

◆ m_state

shared_ptr<vector<double> > m_state

protected

Solution vector.

Definition at line 285 of file SteadyStateSystem.h.

◆ m_xnew

vector<double> m_xnew

protected

Work array used to hold the residual or the new solution.

Definition at line 288 of file SteadyStateSystem.h.

◆ m_xlast_ts

vector<double> m_xlast_ts

protected

State vector after the last successful set of time steps.

Definition at line 291 of file SteadyStateSystem.h.

◆ m_newt

unique_ptr<MultiNewton> m_newt

protected

Newton iterator.

Definition at line 293 of file SteadyStateSystem.h.

◆ m_rdt

double m_rdt = 0.0

protected

Reciprocal of time step.

Definition at line 294 of file SteadyStateSystem.h.

◆ m_jac

shared_ptr<SystemJacobian> m_jac

protected

Jacobian evaluator.

Definition at line 296 of file SteadyStateSystem.h.

◆ m_jac_ok

bool m_jac_ok = false

protected

If true, Jacobian is current.

Definition at line 297 of file SteadyStateSystem.h.

◆ m_bw

size_t m_bw = 0

protected

Jacobian bandwidth.

Definition at line 299 of file SteadyStateSystem.h.

◆ m_size

size_t m_size = 0

protected

Solution vector size

Definition at line 300 of file SteadyStateSystem.h.

◆ m_work1

vector<double> m_work1

protected

Work arrays used during Jacobian evaluation.

Definition at line 303 of file SteadyStateSystem.h.

◆ m_work2

vector<double> m_work2

protected

Definition at line 303 of file SteadyStateSystem.h.

◆ m_mask

vector<int> m_mask

protected

Transient mask.

See transientMask()

Definition at line 305 of file SteadyStateSystem.h.

◆ m_ss_jac_age

int m_ss_jac_age = 20

protected

Maximum age of the Jacobian in steady-state mode.

Definition at line 306 of file SteadyStateSystem.h.

◆ m_ts_jac_age

int m_ts_jac_age = 20

protected

Maximum age of the Jacobian in time-stepping mode.

Definition at line 307 of file SteadyStateSystem.h.

◆ m_attempt_counter

int m_attempt_counter = 0

protected

Counter used to manage the number of states stored in the debug log file generated by writeDebugInfo()

Definition at line 311 of file SteadyStateSystem.h.

◆ m_max_history

int m_max_history = 10

protected

Constant that determines the maximum number of states stored in the debug log file generated by writeDebugInfo()

Definition at line 315 of file SteadyStateSystem.h.

◆ m_interrupt

Func1* m_interrupt = nullptr

protected

Function called at the start of every call to eval.

Definition at line 318 of file SteadyStateSystem.h.

◆ m_time_step_callback

Func1* m_time_step_callback = nullptr

protected

User-supplied function called after each successful timestep.

Definition at line 321 of file SteadyStateSystem.h.

◆ m_nsteps

int m_nsteps = 0

protected

Number of time steps taken in the current call to solve()

Definition at line 323 of file SteadyStateSystem.h.

◆ m_nsteps_max

int m_nsteps_max = 500

protected

Maximum number of timesteps allowed per call to solve()

Definition at line 324 of file SteadyStateSystem.h.

◆ m_jacobianThreshold

double m_jacobianThreshold = 0.0

protected

Threshold for ignoring small elements in Jacobian.

Definition at line 327 of file SteadyStateSystem.h.

◆ m_jacobianRelPerturb

double m_jacobianRelPerturb = 1e-5

protected

Relative perturbation of each component in finite difference Jacobian.

Definition at line 329 of file SteadyStateSystem.h.

◆ m_jacobianAbsPerturb

double m_jacobianAbsPerturb = 1e-10

protected

Absolute perturbation of each component in finite difference Jacobian.

Definition at line 331 of file SteadyStateSystem.h.

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

Detailed Description

Public Member Functions

Protected Member Functions

Protected Attributes

Constructor & Destructor Documentation

◆ SteadyStateSystem()

◆ ~SteadyStateSystem()

Member Function Documentation

◆ eval()

◆ evalJacobian()

◆ weightedNorm()

◆ solve() [1/2]

◆ setInitialGuess()

◆ solve() [2/2]

◆ getState()

◆ ssnorm()

◆ size()

◆ resize()

◆ bandwidth()

◆ componentName()

◆ componentTableHeader()

◆ componentTableLabel()

◆ upperBound()

◆ lowerBound()

◆ newton()

◆ setLinearSolver()

◆ linearSolver()

◆ rdt()

◆ transient()

◆ steady()

◆ initTimeInteg()

◆ setSteadyMode()

◆ transientMask()

◆ timeStep()

◆ resetBadValues()

◆ setTimeStep()

◆ setMinTimeStep()

◆ setMaxTimeStep()

◆ setTimeStepFactor()

◆ setMaxTimeStepCount()

◆ maxTimeStepCount()

◆ setJacAge()

◆ setInterrupt()

◆ setTimeStepCallback()

◆ setJacobianPerturbation()

◆ writeDebugInfo()

◆ clearDebugFile()

◆ evalSSJacobian()

Member Data Documentation

◆ m_steps

◆ m_tstep

◆ m_tmin

◆ m_tmax

◆ m_tfactor

◆ m_state

◆ m_xnew

◆ m_xlast_ts

◆ m_newt

◆ m_rdt

◆ m_jac

◆ m_jac_ok

◆ m_bw

◆ m_size

◆ m_work1

◆ m_work2

◆ m_mask

◆ m_ss_jac_age

◆ m_ts_jac_age

◆ m_attempt_counter

◆ m_max_history

◆ m_interrupt

◆ m_time_step_callback

◆ m_nsteps

◆ m_nsteps_max

◆ m_jacobianThreshold

◆ m_jacobianRelPerturb

◆ m_jacobianAbsPerturb