Detailed Description

This class gives an adaptive algorithm whose time step control is evolutionary PID controller. With an definition of relative solution change \(e_n=\frac{\|u^{n+1}-u^n\|}{\|u^{n+1}\|}\), the algorithm gives a time step size estimation as

\[ h_{n+1} = \left(\frac{e_{n-1}}{e_n}\right)^{k_P} \left(\frac{TOL}{e_n}\right)^{k_I} \left(\frac{e^2_{n-1}}{e_n e_{n-2}}\right)^{k_D} \]

where \(k_P=0.075\), \(k_I=0.175\), \(k_D=0.01\) are empirical PID parameters.

In the computation, \( e_n\) is calculated firstly. If \(e_n>TOL\), the current time step is rejected and repeated with a new time step size of \(h=\frac{TOL}{e_n} h_n\).

Limits of the time step size are given as

\[ h_{\mbox{min}} \leq h_{n+1} \leq h_{\mbox{max}}, l \leq \frac{h_{n+1}}{h_n} \leq L \]

Similar algorithm can be found in [1] .

Definition at line 51 of file EvolutionaryPIDcontroller.h.

#include <EvolutionaryPIDcontroller.h>

Inheritance diagram for NumLib::EvolutionaryPIDcontroller:

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Collaboration diagram for NumLib::EvolutionaryPIDcontroller:

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Public Member Functions
	EvolutionaryPIDcontroller (const double t0, const double t_end, const double h0, const double h_min, const double h_max, const double rel_h_min, const double rel_h_max, const double tol)

std::tuple< bool, double >	next (double solution_error, int number_iterations) override

bool	accepted () const override
	return if current time step is accepted or not More...

void	setAcceptedOrNot (const bool accepted) override

bool	isSolutionErrorComputationNeeded () const override

virtual bool	canReduceTimestepSize () const override
	Query the timestepper if further time step size reduction is possible. More...

Public Member Functions inherited from NumLib::TimeStepAlgorithm
	TimeStepAlgorithm (const double t0, const double t_end)

	TimeStepAlgorithm (const double t0, const double t_end, const double dt)

	TimeStepAlgorithm (const double t0, const double t_end, const std::vector< double > &all_step_sizes)

virtual	~TimeStepAlgorithm ()=default

double	begin () const
	return the beginning of time steps More...

double	end () const
	return the end of time steps More...

const TimeStep	getTimeStep () const
	return current time step More...

void	resetCurrentTimeStep (const double dt)
	reset the current step size from the previous time More...

const std::vector< double > &	getTimeStepSizeHistory () const
	return a history of time step sizes More...

Private Member Functions
double	limitStepSize (const double h_new, const bool previous_step_accepted) const

Private Attributes
const double	_kP = 0.075
	Parameter. More...

const double	_kI = 0.175
	Parameter. More...

const double	_kD = 0.01
	Parameter. More...

const double	_h0
	initial time step size. More...

const double	_h_min
	minimum step size. More...

const double	_h_max
	maximum step size. More...

const double	_rel_h_min
	\(l\) in \( h_{\mbox{min}} \leq h_{n+1} \leq h_{\mbox{max}},\) More...

const double	_rel_h_max
	\(L\) in \( h_{\mbox{min}} \leq h_{n+1} \leq h_{\mbox{max}},\) More...

const double	_tol

double	_e_n_minus1
	\(e_{n-1}\). More...

double	_e_n_minus2
	\(e_{n-2}\). More...

bool	_is_accepted

Additional Inherited Members
Protected Attributes inherited from NumLib::TimeStepAlgorithm
const double	_t_initial
	initial time More...

const double	_t_end
	end time More...

TimeStep	_ts_prev
	previous time step information More...

TimeStep	_ts_current
	current time step information More...

std::vector< double >	_dt_vector
	a vector of time step sizes More...

Constructor & Destructor Documentation

◆ EvolutionaryPIDcontroller()

NumLib::EvolutionaryPIDcontroller::EvolutionaryPIDcontroller	(	const double	t0,
		const double	t_end,
		const double	h0,
		const double	h_min,
		const double	h_max,
		const double	rel_h_min,
		const double	rel_h_max,
		const double	tol
	)

inline

Definition at line 54 of file EvolutionaryPIDcontroller.h.

         : TimeStepAlgorithm(t0, t_end),
           _h0(h0),
           _h_min(h_min),
           _h_max(h_max),
           _rel_h_min(rel_h_min),
           _rel_h_max(rel_h_max),
           _tol(tol),
           _e_n_minus1(0.),
           _e_n_minus2(0.),
           _is_accepted(true)
     {
     }

Member Function Documentation

◆ accepted()

bool NumLib::EvolutionaryPIDcontroller::accepted ( ) const

inlineoverridevirtual

return if current time step is accepted or not

Implements NumLib::TimeStepAlgorithm.

Definition at line 74 of file EvolutionaryPIDcontroller.h.

74 { return _is_accepted; }

References _is_accepted.

Referenced by setAcceptedOrNot().

◆ canReduceTimestepSize()

bool NumLib::EvolutionaryPIDcontroller::canReduceTimestepSize ( ) const

overridevirtual

Query the timestepper if further time step size reduction is possible.

Reimplemented from NumLib::TimeStepAlgorithm.

Definition at line 139 of file EvolutionaryPIDcontroller.cpp.

 {
     // If current and previous dt are both at minimum dt, then cannot reduce
     // further.
     return !(_ts_current.dt() == _h_min && _ts_prev.dt() == _h_min);
 }

References _h_min, NumLib::TimeStepAlgorithm::_ts_current, NumLib::TimeStepAlgorithm::_ts_prev, and NumLib::TimeStep::dt().

◆ isSolutionErrorComputationNeeded()

bool NumLib::EvolutionaryPIDcontroller::isSolutionErrorComputationNeeded ( ) const

inlineoverridevirtual

Get a flag to indicate whether this algorithm needs to compute solution error. The default return value is false.

Reimplemented from NumLib::TimeStepAlgorithm.

Definition at line 81 of file EvolutionaryPIDcontroller.h.

81 { return true; }

◆ limitStepSize()

double NumLib::EvolutionaryPIDcontroller::limitStepSize	(	const double	h_new,
		const bool	previous_step_accepted
	)		const

private

Forced the computed time step size in the given range (see the formulas in the documentation of the class) or use the half of the previous time step size under some other constrains.

Parameters

h_new	The computed time step size.
previous_step_accepted	An indicator for whether the previous time step is rejected.

Returns: The new time step after apply the constrains.

Definition at line 103 of file EvolutionaryPIDcontroller.cpp.

 {
     const double h_n = _ts_current.dt();
     // Forced the computed time step size in the given range
     // (see the formulas in the documentation of the class)
     const double h_in_range = std::max(_h_min, std::min(h_new, _h_max));
     // Limit the step size change ratio.
     double limited_h =
         std::max(_rel_h_min * h_n, std::min(h_in_range, _rel_h_max * h_n));
  
     if (!previous_step_accepted)
     {
         // If the last time step was rejected and the new predicted time step
         // size is identical to that of the previous rejected step, the new
         // step size is then reduced by half.
         if (std::abs(limited_h - _ts_current.dt()) <
             std::numeric_limits<double>::min())
         {
             limited_h = std::max(_h_min, 0.5 * limited_h);
         }
  
         // If the last time step was rejected and the new predicted time step
         // size is larger than the step size of the rejected step, the new step
         // size takes the half of the size of the rejected step. This could
         // happen when a time step is rejected due to a diverged non-linear
         // solver. In such case, this algorithm may give a large time step size
         // by using the diverged solution.
         if (limited_h > _ts_current.dt())
         {
             limited_h = std::max(_h_min, 0.5 * _ts_current.dt());
         }
     }
     return limited_h;
 }

References _h_max, _h_min, _rel_h_max, _rel_h_min, NumLib::TimeStepAlgorithm::_ts_current, and NumLib::TimeStep::dt().

Referenced by next().

◆ next()

std::tuple< bool, double > NumLib::EvolutionaryPIDcontroller::next	(	double	solution_error,
		int	number_iterations
	)

overridevirtual

Move to the next time step

Parameters

solution_error	Solution error \(e_n\) between two successive time steps.
number_iterations	Number of non-linear iterations used.

Returns: A step acceptance flag and the computed step size.

Implements NumLib::TimeStepAlgorithm.

Definition at line 23 of file EvolutionaryPIDcontroller.cpp.

 {
     const bool is_previous_step_accepted = _is_accepted;
  
     const double e_n = solution_error;
     const double zero_threshlod = std::numeric_limits<double>::epsilon();
     // step rejected.
     if (e_n > _tol)
     {
         _is_accepted = false;
  
         double h_new = (e_n > zero_threshlod) ? _ts_current.dt() * _tol / e_n
                                               : 0.5 * _ts_current.dt();
  
         h_new = limitStepSize(h_new, is_previous_step_accepted);
  
         WARN(
             "This step is rejected due to the relative change from the"
             " solution of the previous\n"
             "\t time step to the current solution exceeds the given tolerance"
             " of {:g}.\n"
             "\t This time step will be repeated with a new time step size of"
             " {:g}\n"
             "\t or the simulation will be halted.",
             _tol, h_new);
  
         return std::make_tuple(false, h_new);
     }
  
     // step accepted.
     _is_accepted = true;
  
     if (_ts_current.steps() == 0)
     {
         _e_n_minus1 = e_n;
  
         return std::make_tuple(true, _h0);
     }
     else
     {
         const double h_n = _ts_current.dt();
         double h_new = h_n;
  
         if (e_n > zero_threshlod)
         {
             if (_e_n_minus1 > zero_threshlod)
             {
                 if (_e_n_minus2 > zero_threshlod)
                 {
                     h_new = std::pow(_e_n_minus1 / e_n, _kP) *
                             std::pow(_tol / e_n, _kI) *
                             std::pow(
                                 _e_n_minus1 * _e_n_minus1 / (e_n * _e_n_minus2),
                                 _kD) *
                             h_n;
                 }
                 else
                 {
                     h_new = std::pow(_e_n_minus1 / e_n, _kP) *
                             std::pow(_tol / e_n, _kI) * h_n;
                 }
             }
             else
             {
                 h_new = std::pow(_tol / e_n, _kI) * h_n;
             }
         }
  
         h_new = limitStepSize(h_new, is_previous_step_accepted);
  
         _e_n_minus2 = _e_n_minus1;
         _e_n_minus1 = e_n;
  
         return std::make_tuple(true, h_new);
     }
  
     return {};
 }

References _e_n_minus1, _e_n_minus2, _h0, _is_accepted, _kD, _kI, _kP, _tol, NumLib::TimeStepAlgorithm::_ts_current, NumLib::TimeStep::dt(), limitStepSize(), NumLib::TimeStep::steps(), and WARN().

◆ setAcceptedOrNot()

void NumLib::EvolutionaryPIDcontroller::setAcceptedOrNot ( const bool accepted )

inlineoverridevirtual

Set the status of the step.

Parameters

accepted A boolean parameter is needed to indicated whether the step is accepted or not.

Reimplemented from NumLib::TimeStepAlgorithm.

Definition at line 76 of file EvolutionaryPIDcontroller.h.

     {
         _is_accepted = accepted;
     }

References _is_accepted, and accepted().

Member Data Documentation

◆ _e_n_minus1

double NumLib::EvolutionaryPIDcontroller::_e_n_minus1

private

\(e_{n-1}\).

Definition at line 101 of file EvolutionaryPIDcontroller.h.

Referenced by next().

◆ _e_n_minus2

double NumLib::EvolutionaryPIDcontroller::_e_n_minus2

private

\(e_{n-2}\).

Definition at line 102 of file EvolutionaryPIDcontroller.h.

Referenced by next().

◆ _h0

const double NumLib::EvolutionaryPIDcontroller::_h0

private

initial time step size.

Definition at line 90 of file EvolutionaryPIDcontroller.h.

Referenced by next().

◆ _h_max

const double NumLib::EvolutionaryPIDcontroller::_h_max

private

maximum step size.

Definition at line 92 of file EvolutionaryPIDcontroller.h.

Referenced by limitStepSize().

◆ _h_min

const double NumLib::EvolutionaryPIDcontroller::_h_min

private

minimum step size.

Definition at line 91 of file EvolutionaryPIDcontroller.h.

Referenced by canReduceTimestepSize(), and limitStepSize().

◆ _is_accepted

bool NumLib::EvolutionaryPIDcontroller::_is_accepted

private

Definition at line 104 of file EvolutionaryPIDcontroller.h.

Referenced by accepted(), next(), and setAcceptedOrNot().

◆ _kD

const double NumLib::EvolutionaryPIDcontroller::_kD = 0.01

private

Parameter.

See also: EvolutionaryPIDcontroller

Definition at line 88 of file EvolutionaryPIDcontroller.h.

Referenced by next().

◆ _kI

const double NumLib::EvolutionaryPIDcontroller::_kI = 0.175

private

Parameter.

See also: EvolutionaryPIDcontroller

Definition at line 87 of file EvolutionaryPIDcontroller.h.

Referenced by next().

◆ _kP

const double NumLib::EvolutionaryPIDcontroller::_kP = 0.075

private

Parameter.

See also: EvolutionaryPIDcontroller

Definition at line 86 of file EvolutionaryPIDcontroller.h.

Referenced by next().

◆ _rel_h_max

const double NumLib::EvolutionaryPIDcontroller::_rel_h_max

private

\(L\) in \( h_{\mbox{min}} \leq h_{n+1} \leq h_{\mbox{max}},\)

Definition at line 97 of file EvolutionaryPIDcontroller.h.

Referenced by limitStepSize().

◆ _rel_h_min

const double NumLib::EvolutionaryPIDcontroller::_rel_h_min

private

\(l\) in \( h_{\mbox{min}} \leq h_{n+1} \leq h_{\mbox{max}},\)

Definition at line 95 of file EvolutionaryPIDcontroller.h.

Referenced by limitStepSize().

◆ _tol

const double NumLib::EvolutionaryPIDcontroller::_tol

private

Definition at line 99 of file EvolutionaryPIDcontroller.h.

Referenced by next().

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

NumLib/TimeStepping/Algorithms/EvolutionaryPIDcontroller.h
NumLib/TimeStepping/Algorithms/EvolutionaryPIDcontroller.cpp

Detailed Description

Public Member Functions

Private Member Functions

Private Attributes

Additional Inherited Members

Constructor & Destructor Documentation

◆ EvolutionaryPIDcontroller()

Member Function Documentation

◆ accepted()

◆ canReduceTimestepSize()

◆ isSolutionErrorComputationNeeded()

◆ limitStepSize()

◆ next()

◆ setAcceptedOrNot()

Member Data Documentation

◆ _e_n_minus1

◆ _e_n_minus2

◆ _h0

◆ _h_max

◆ _h_min

◆ _is_accepted

◆ _kD

◆ _kI

◆ _kP

◆ _rel_h_max

◆ _rel_h_min

◆ _tol