Sets a goal based on time-stepper truncation error. More...
#include <ErrorControl.hpp>
Classes | |
| struct | AbsoluteTolerance |
| struct | MaxFactor |
| struct | MinFactor |
| struct | RelativeTolerance |
| struct | SafetyFactor |
Public Types | |
| using | options = tmpl::list< AbsoluteTolerance, RelativeTolerance, MaxFactor, MinFactor, SafetyFactor > |
| using | argument_tags = tmpl::list<::Tags::StepperErrors< EvolvedVariableTag > > |
Public Member Functions | |
| ErrorControl (const double absolute_tolerance, const double relative_tolerance, const double max_factor, const double min_factor, const double safety_factor) | |
| TimeStepRequest | operator() (const typename ::Tags::StepperErrors< EvolvedVariableTag >::type &errors, const double) const |
| bool | uses_local_data () const override |
| Whether the result can differ on different elements, so requiring communication to synchronize the result across the domain. This is ignored for LTS step changing. More... | |
| bool | can_be_delayed () const override |
| Whether the result can be applied with a delay. More... | |
| std::unordered_map< std::type_index, StepperErrorTolerances > | tolerances () const override |
| A map from the type of a variables tag to the tolerances for that variable. More... | |
| void | pup (PUP::er &p) override |
 Public Member Functions inherited from StepChooser< StepChooserUse > | |
| WRAPPED_PUPable_abstract (StepChooser) | |
| virtual bool | uses_local_data () const =0 |
| Whether the result can differ on different elements, so requiring communication to synchronize the result across the domain. This is ignored for LTS step changing. More... | |
| virtual bool | can_be_delayed () const =0 |
| Whether the result can be applied with a delay. More... | |
| template<typename StepChoosersToUse = AllStepChoosers, typename DbTags > | |
| TimeStepRequest | desired_step (const double last_step, const db::DataBox< DbTags > &box) const |
The last_step parameter describes the step size to be adjusted. It may be the step size or the slab size, or may be infinite if the appropriate size cannot be determined. More... | |
| virtual std::unordered_map< std::type_index, StepperErrorTolerances > | tolerances () const =0 |
| A map from the type of a variables tag to the tolerances for that variable. More... | |
Static Public Member Functions | |
| static std::string | name () |
Static Public Attributes | |
| static constexpr Options::String | help |
Detailed Description
class StepChoosers::ErrorControl< StepChooserUse, EvolvedVariableTag, ErrorControlSelector >
Sets a goal based on time-stepper truncation error.
Details
The suggested step is calculated via a simple specialization of the scheme suggested in [91]. We first compute the aggregated error measure from the stepper error:
\[ E = \max_i(|E_i| / sc_i), \]
where \(E_i\) is the ODE error reported for each individual grid point, reported by the time stepper, and \(sc_i\) is the step control measure determined by the tolerances:
\[ sc_i = Atol_i + \max(|y_i|,|y_i + E_i|) Rtol_i, \]
and \(y_i\) is the value of the function at the previous step at grid point \(i\). (The estimate is more commonly done comparing with the current step, but using the previous step avoids a memory allocation in the TimeStepper and should not have a major effect on the result.)
When choosing a step size for LTS or when no record of previous error is available, the step has size:
\[ h_{\text{new}} = h \cdot \min\left(F_{\text{max}}, \max\left(F_{\text{min}}, \frac{F_{\text{safety}}}{E^{1/(q + 1)}}\right)\right), \]
where \(h_{\text{new}}\) is the new suggested step size \(h\) is the previous step size, \(F_{\text{max}}\) is the maximum factor by which we allow the step to increase, \(F_{\text{min}}\) is the minimum factor by which we allow the step to decrease. \(F_{\text{safety}}\) is the safety factor on the computed error – this forces the step size slightly lower than we would naively compute so that the result of the step will likely be within the target error. \(q\) is the order of the stepper error calculation. Intuitively, we should change the step less drastically for a higher order stepper.
When controlling slab size, after the first error calculation, the error \(E\) is recorded in the DataBox, and subsequent error calculations use a simple PI scheme suggested in [172] section 17.2.1:
\[ h_{\text{new}} = h \cdot \min\left(F_{\text{max}}, \max\left(F_{\text{min}}, F_{\text{safety}} E^{-0.7 / (q + 1)} E_{\text{prev}}^{0.4 / (q + 1)}\right)\right), \]
where \(E_{\text{prev}}\) is the error computed in the previous step. This method is never used for choosing an LTS step because the restriction of step size changes to factors of two was found to interfere with the more gradual increase chosen by the PI controller.
- Note
- The template parameter
ErrorControlSelectoris used to disambiguate in the input-file options betweenErrorControlstep choosers that are based on different variables. This is needed if multiple systems are evolved in the same executable. The name used for the input file includesErrorControlSelector::name()if it is provided.
Member Function Documentation
◆ can_be_delayed()
|
inlineoverridevirtual |
Whether the result can be applied with a delay.
StepChoosers setting the .end or .end_hard_limit fields of TimeStepRequest must return false here.
Implements StepChooser< StepChooserUse >.
◆ tolerances()
|
inlineoverridevirtual |
A map from the type of a variables tag to the tolerances for that variable.
Implements RequestsStepperErrorTolerances.
◆ uses_local_data()
|
inlineoverridevirtual |
Whether the result can differ on different elements, so requiring communication to synchronize the result across the domain. This is ignored for LTS step changing.
- Note
- As this is only used for slab-size changing, the
last_steppassed to the call operator is not considered local data.
Implements StepChooser< StepChooserUse >.
Member Data Documentation
◆ help
|
staticconstexpr |
The documentation for this class was generated from the following file:
- src/Time/StepChoosers/ErrorControl.hpp