Classes and functions used in implementation of size control. More...

Classes
struct	ControlErrorArgs
	Packages some of the inputs to the State::control_error, so that State::control_error doesn't need a large number of arguments. More...

struct	CrossingTimeInfo
	Holds information about crossing times, as computed by ZeroCrossingPredictors. More...

struct	ErrorDiagnostics
	A simple struct to hold diagnostic information about computing the size control error. More...

struct	Info
	Holds information that is saved between calls of SizeControl. More...

struct	is_size

struct	is_size< Systems::Size< Label, DerivOrder > >

class	State
	Represents a 'state' of the size control system. More...

struct	StateHistory
	A struct for holding a history of control errors for each state in the `control_system::Systems::Size` control system. More...

struct	StateUpdateArgs
	Packages some of the inputs to the State::update, so that State::update doesn't need a large number of arguments. More...

Functions
double	control_error_delta_r (const double horizon_00, const double dt_horizon_00, const double lambda_00, const double dt_lambda_00, const double grid_frame_excision_sphere_radius)
	Function that computes the control error for `control_system::size::States::DeltaR`. More...

template<typename Frame >
ErrorDiagnostics	control_error (const gsl::not_null< Info * > info, const gsl::not_null< intrp::ZeroCrossingPredictor * > predictor_char_speed, const gsl::not_null< intrp::ZeroCrossingPredictor * > predictor_comoving_char_speed, const gsl::not_null< intrp::ZeroCrossingPredictor * > predictor_delta_radius, double time, double control_error_delta_r, std::optional< double > control_error_delta_r_outward, std::optional< double > max_allowed_radial_distance, double dt_lambda_00, const ylm::Strahlkorper< Frame > &apparent_horizon, const ylm::Strahlkorper< Frame > &excision_boundary, const Scalar< DataVector > &lapse_on_excision_boundary, const tnsr::I< DataVector, 3, Frame > &frame_components_of_grid_shift, const tnsr::ii< DataVector, 3, Frame > &spatial_metric_on_excision_boundary, const tnsr::II< DataVector, 3, Frame > &inverse_spatial_metric_on_excision_boundary)
	Computes the size control error, updating the stored info. More...

void	register_derived_with_charm ()

template<size_t DerivOrder, ::domain::ObjectLabel Horizon, typename Metavariables >
void	update_averager (const gsl::not_null< Averager< DerivOrder - 1 > * > averager, const gsl::not_null< ControlErrors::Size< DerivOrder, Horizon > * > control_error, const Parallel::GlobalCache< Metavariables > &cache, const double time, const DataVector &current_timescale, const std::string &function_of_time_name, const int current_measurement)
	Updates the Averager with information from the Size control error . More...

template<size_t DerivOrder, ::domain::ObjectLabel Horizon, typename Metavariables >
void	update_tuner (const gsl::not_null< TimescaleTuner< false > * > tuner, const gsl::not_null< ControlErrors::Size< DerivOrder, Horizon > * > control_error, const Parallel::GlobalCache< Metavariables > &cache, const double time, const std::string &function_of_time_name)
	Updates the TimescaleTuner with information from the Size control error . More...

Variables
template<typename T >
constexpr bool	is_size_v = is_size<T>::value
	Check whether a control system is the `control_system::Systems::Size` system or not.

Detailed Description

Classes and functions used in implementation of size control.

Function Documentation

◆ control_error()

template<typename Frame >

ErrorDiagnostics control_system::size::control_error	(	const gsl::not_null< Info * >	info,
		const gsl::not_null< intrp::ZeroCrossingPredictor * >	predictor_char_speed,
		const gsl::not_null< intrp::ZeroCrossingPredictor * >	predictor_comoving_char_speed,
		const gsl::not_null< intrp::ZeroCrossingPredictor * >	predictor_delta_radius,
		double	time,
		double	control_error_delta_r,
		std::optional< double >	control_error_delta_r_outward,
		std::optional< double >	max_allowed_radial_distance,
		double	dt_lambda_00,
		const ylm::Strahlkorper< Frame > &	apparent_horizon,
		const ylm::Strahlkorper< Frame > &	excision_boundary,
		const Scalar< DataVector > &	lapse_on_excision_boundary,
		const tnsr::I< DataVector, 3, Frame > &	frame_components_of_grid_shift,
		const tnsr::ii< DataVector, 3, Frame > &	spatial_metric_on_excision_boundary,
		const tnsr::II< DataVector, 3, Frame > &	inverse_spatial_metric_on_excision_boundary
	)

Computes the size control error, updating the stored info.

Template Parameters

Frame should be Frame::Distorted if Frame::Distorted exists.

Parameters

info	struct containing parameters that will be used/filled. Some of the fields in info will guide the behavior of other control system components like the averager and (possibly) the time step.
predictor_char_speed	ZeroCrossingPredictor for the characteristic speed.
predictor_comoving_char_speed	ZeroCrossingPredictor for the comoving characteristic speed.
predictor_delta_radius	ZeroCrossingPredictor for the difference in radius between the horizon and the excision boundary.
time	the current time.
control_error_delta_r	the control error for the DeltaR state. This is used in other states as well.
control_error_delta_r_outward	the control error for the DeltaRDriftOutward state. If std::nullopt, then DeltaRDriftOutward will not be used.
max_allowed_radial_distance	the maximum average radial distance between the horizon and the excision boundary that is allowed without triggering the DeltaRDriftOutward state. If std::nullopt, then DeltaRDriftOutward will not be used.
dt_lambda_00	the time derivative of the map parameter lambda_00
apparent_horizon	the current horizon in frame Frame.
excision_boundary	a Strahlkorper representing the excision boundary in frame Frame. Note that the excision boundary is assumed to be a sphere in the grid frame.
lapse_on_excision_boundary	Lapse on the excision boundary.
frame_components_of_grid_shift	The quantity \(\beta^i \frac{\partial x^\hat{i}}{\partial x_i}\) (see below) evaluated on the excision boundary. This is a tensor in frame Frame.
spatial_metric_on_excision_boundary	metric in frame Frame.
inverse_spatial_metric_on_excision_boundary	metric in frame Frame.

Returns: Returns an ErrorDiagnostics object which, in addition to the actual control error, holds a lot of diagnostic information about how the control error was calculated. This information could be used to print to a file if desired.

The characteristic speed that is needed here is

\begin{align} v &= -\alpha -n_i\beta^i \\ v &= -\alpha -n_\hat{i}\hat{\beta}^\hat{i} - n_\hat{i}\frac{\partial x^\hat{i}}{\partial t} \\ v &= -\alpha -n_\bar{i}\bar{\beta}^\bar{i} - n_\bar{i}\frac{\partial x^\bar{i}}{\partial t} \\ v &= -\alpha - n_\hat{i} \frac{\partial x^\hat{i}}{\partial x^i} \beta^i, \end{align}

where we have written many equivalent forms in terms of quantities defined in different frames.

Here \(\alpha\) is the lapse, which is invariant under frame transformations, \(n_i\), \(n_\hat{i}\), and \(n_\bar{i}\) are the metric-normalized normal one-form to the Strahlkorper in the grid, distorted, and inertial frames, and \(\beta^i\), \(\hat{\beta}^\hat{i}\), and \(\bar{\beta}^\bar{i}\) are the shift in the grid, distorted, and inertial frames.

Note that we decorate the shift with hats and bars in addition to decorating its index, because the shift transforms in a non-obvious way under frame transformations so it is easy to make mistakes. To be clear, these different shifts are defined by

\begin{align} \beta^i &= \alpha^2 g^{0i},\\ \hat{\beta}^\hat{i} &= \alpha^2 g^{\hat{0}\hat{i}},\\ \bar{\beta}^\bar{i} &= \alpha^2 g^{\bar{0}\bar{i}}, \end{align}

where \(g^{ab}\) is the spacetime metric, and they transform like

\begin{align} \hat{\beta}^\hat{i} &= \beta^i \frac{\partial x^\hat{i}}{\partial x^i}- \frac{\partial x^\hat{i}}{\partial t}. \end{align}

The quantity we pass as frame_components_of_grid_shift is

\begin{align} \beta^i \frac{\partial x^\hat{i}}{\partial x^i} &= \hat{\beta}^\hat{i} + \frac{\partial x^\hat{i}}{\partial t} \\ &= \bar{\beta}^\bar{j}\frac{\partial x^\hat{i}}{\partial x^i} \frac{\partial x^i}{\partial x^\bar{j}} + \frac{\partial x^\hat{i}}{\partial x^\bar{j}} \frac{\partial x^\bar{j}}{\partial t}, \end{align}

where we have listed several equivalent formulas that involve quantities in different frames.

◆ control_error_delta_r()

double control_system::size::control_error_delta_r	(	const double	horizon_00,
		const double	dt_horizon_00,
		const double	lambda_00,
		const double	dt_lambda_00,
		const double	grid_frame_excision_sphere_radius
	)

Function that computes the control error for control_system::size::States::DeltaR.

This is helpful to have calculated separately because other control errors may make use of this quantity. The equation for the control error is given in Eq. 96 in [84].

Parameters

horizon_00	The \(l=0,m=0\) coefficient of the apparent horizon in the distorted frame.
dt_horizon_00	The \(l=0,m=0\) coefficient of the time derivative of the apparent horizon in the distorted frame, where the derivative is taken in the distorted frame as well.
lambda_00	The \(l=0,m=0\) component of the function of time for the time dependent map
dt_lambda_00	The \(l=0,m=0\) component of the time derivative of the function of time for the time dependent map
grid_frame_excision_sphere_radius	Radius of the excision sphere in the grid frame

◆ update_averager()

template<size_t DerivOrder, ::domain::ObjectLabel Horizon, typename Metavariables >

void control_system::size::update_averager	(	const gsl::not_null< Averager< DerivOrder - 1 > * >	averager,
		const gsl::not_null< ControlErrors::Size< DerivOrder, Horizon > * >	control_error,
		const Parallel::GlobalCache< Metavariables > &	cache,
		const double	time,
		const DataVector &	current_timescale,
		const std::string &	function_of_time_name,
		const int	current_measurement
	)

Updates the Averager with information from the Size control error .

Details

After we calculate the control error, we check if a discontinuous change has occurred (the internal control_system::size::State changed). If no discontinuous change has occurred, then we do nothing. If one did occur, we get a history of control errors from the Size control error and use that to repopulate the Averager history.

Note: See control_system::Tags::Averager for why the Averager is templated on DerivOrder - 1.

◆ update_tuner()

template<size_t DerivOrder, ::domain::ObjectLabel Horizon, typename Metavariables >

void control_system::size::update_tuner	(	const gsl::not_null< TimescaleTuner< false > * >	tuner,
		const gsl::not_null< ControlErrors::Size< DerivOrder, Horizon > * >	control_error,
		const Parallel::GlobalCache< Metavariables > &	cache,
		const double	time,
		const std::string &	function_of_time_name
	)

Updates the TimescaleTuner with information from the Size control error .

Details

We check for a suggested timescale from the Size control error . If one is suggested and it is smaller than the current damping timescale, we set the timescale in the TimescaleTuner to this suggested value. Otherwise, we let the TimescaleTuner adjust the timescale. Regardless of whether a timescale was suggested or not, we always reset the size control error.

Classes

Functions

Variables

Detailed Description

Function Documentation

◆ control_error()

◆ control_error_delta_r()

◆ update_averager()

Details

◆ update_tuner()

Details