TimeSteppers::adams_lts Namespace Reference

Shared LTS implementation for the two Adams-based methods. More...

Classes
struct	AdamsScheme
struct	LtsCoefficients
	Storage for LTS coefficients that should not allocate in typical cases. Each entry is a tuple of (local id, remote id, coefficient). The contents should be kept sorted, as some functions assume that. More...

Enumerations
enum class	SchemeType { Explicit , Implicit }
	Type of coefficients used for an AdamsScheme.

Functions
Time	exact_substep_time (const TimeStepId &id)
	Get the time of a substep as a Time, assuming substeps are at the end of the step.
LtsCoefficients &	operator+= (LtsCoefficients &a, const LtsCoefficients &b)
LtsCoefficients &	operator-= (LtsCoefficients &a, const LtsCoefficients &b)
LtsCoefficients	operator+ (LtsCoefficients &&a, LtsCoefficients &&b)
LtsCoefficients	operator+ (LtsCoefficients &&a, const LtsCoefficients &b)
LtsCoefficients	operator+ (const LtsCoefficients &a, LtsCoefficients &&b)
LtsCoefficients	operator+ (const LtsCoefficients &a, const LtsCoefficients &b)
LtsCoefficients	operator- (LtsCoefficients &&a, LtsCoefficients &&b)
LtsCoefficients	operator- (LtsCoefficients &&a, const LtsCoefficients &b)
LtsCoefficients	operator- (const LtsCoefficients &a, LtsCoefficients &&b)
LtsCoefficients	operator- (const LtsCoefficients &a, const LtsCoefficients &b)
template<typename T >
void	apply_coefficients (gsl::not_null< T * > result, const LtsCoefficients &coefficients, const BoundaryHistoryEvaluator< T > &coupling)
	Add the LTS boundary terms for to result for the given set of coefficients.
bool	operator== (const AdamsScheme &a, const AdamsScheme &b)
bool	operator!= (const AdamsScheme &a, const AdamsScheme &b)
template<typename TimeType >
LtsCoefficients	lts_coefficients (const ConstBoundaryHistoryTimes &local_times, const ConstBoundaryHistoryTimes &remote_times, const Time &start_time, const TimeType &end_time, const AdamsScheme &local_scheme, const AdamsScheme &remote_scheme, const AdamsScheme &small_step_scheme)

Variables
constexpr size_t	lts_coefficients_static_size

Detailed Description

Shared LTS implementation for the two Adams-based methods.

Function Documentation

lts_coefficients()

template<typename TimeType >

LtsCoefficients TimeSteppers::adams_lts::lts_coefficients	(	const ConstBoundaryHistoryTimes &	local_times,
		const ConstBoundaryHistoryTimes &	remote_times,
		const Time &	start_time,
		const TimeType &	end_time,
		const AdamsScheme &	local_scheme,
		const AdamsScheme &	remote_scheme,
		const AdamsScheme &	small_step_scheme
	)

Calculate the nonzero terms in an Adams LTS boundary contribution.

The coefficients are generated for a step from start_time to end_time, integrating using the small_step_scheme. Interpolation from the elements is performed using polynomials appropriate for the given local_scheme and remote_scheme.

This function returns the sum of the coefficients for the small steps, i.e., the steps between all the times either side updates between the time bounds. Each small step is calculated as

$$\begin{array}{}\text{(1)}& \mathrm{\Delta }{\tilde{y}}_n=\mathrm{\Delta }{\tilde{t}}_n\sum _{ij}D(y_{n,-i}^L,y_{n,-j}^R)\sum _q{\tilde{\alpha }}_{nq}{\ell }_i({\tilde{t}}_{n-q};t_{\cdots }^L,\dots ){\ell }_j({\tilde{t}}_{n-q};t_{\cdots }^R,\dots ),\end{array}$$

where $y_{n,0}^L$ and $y_{n,0}^R$ are the values of the local and remote variables at the start of the step containing small step $n$, $y_{n,1}^L$ and $y_{n,1}^R$ are the predictor values for those steps, and other index values count backwards in the history of that side. The range of $i$ and choice of the control times $t_{\cdots }^L$ are determined by local_scheme, $j$ and $t_{\cdots }^R$ are determined by remote_scheme, and the Adams coefficients ${\tilde{\alpha }}_{nq}$ correspond to small_step_scheme.

When called for dense output, the arguments must represent a single small step, i.e., the step cannot cross any of the control times. Any additional terms can be generated by a second call treating the remainder of the step as non-dense.

Template Parameters

TimeType

The type Time for a step aligned with the control times or ApproximateTime for dense output.

Variable Documentation

lts_coefficients_static_size

constexpr size_t TimeSteppers::adams_lts::lts_coefficients_static_size

constexpr

Initial value:

=
    adams_coefficients::maximum_order * (adams_coefficients::maximum_order + 1)