Conservative explicit local time-stepping schemes for the shallow water equations

Hoang, Thi-Thao-Phuong; Leng, Wei; Ju, Lili; Wang, Zhu; Pieper, Konstantin

doi:10.1016/j.jcp.2019.01.006

Cited by 26 publications

(58 citation statements)

References 40 publications

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“…The idea of allowing different subsystems to advance with different timesteps has been extensively examined for Runge-Kutta methods [17,29]. Extending these methods to conservation laws has seen considerable work [11,12,18,22,28,30]. Additionally, other fields have arrived at related time integration schemes.…”

Section: Previous Workmentioning

confidence: 99%

Speculative Parallel Execution for Local Timestepping

Bremer

Bachan

Chan

et al. 2021

Proceedings of the 2021 ACM SIGSIM Conference on Principles of Advanced Discrete Simulation

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Currently, synchronous timestepping for fluid and plasma simulations requires selection of a global time step that conservatively satisfies stability conditions everywhere. However, this approach causes substantial unnecessary work in the presence of large variations of element sizes or local wavespeeds. Local timestepping can significantly reduce work by allowing subdomains to take steps according to local rather than global stability constraints. However, parallelizing this algorithm presents considerable difficulty. Since the stability condition depends on the state of the submesh and its neighbors, dependencies become irregular and may dynamically change as neighbors take smaller or larger timesteps. Furthermore, coarsening and refining timesteps introduces dynamic load imbalance. In order to correctly resolve these dependencies in a distributed setting, we parallelize the local timestepping algorithm using an optimistic (Timewarp-based) parallel discrete event simulation. We introduce waiting heuristics to eliminate misspeculation when dependencies can be identified early, and present a semi-static load balancing strategy to improve scalability. We present detailed performance characterizations of event overheads, misspeculation, and scalability of our approach. Our numerical experiments demonstrate up to a 2.8x speedup versus a baseline unoptimized approach; a 4x improvement in per-node throughput compared to an MPI parallelization of synchronous timestepping; and scalability up to 3,072 cores on NERSC Cori's Haswell partition. CCS CONCEPTS• Mathematics of computing → Partial differential equations;• Computing methodologies → Discrete-event simulation; Massively parallel and high-performance simulations; • Applied computing → Earth and atmospheric sciences.

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Section: Previous Workmentioning

confidence: 99%

Speculative Parallel Execution for Local Timestepping

Bremer

Bachan

Chan

et al. 2021

Proceedings of the 2021 ACM SIGSIM Conference on Principles of Advanced Discrete Simulation

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“…There are available two common approaches to accomplish this goal. One approach are explicit local time-stepping (LTS) schemes [7,8,9,10]. Because CFL conditions vary greatly over the whole ocean domain, LTS methods apply spatially-dependent time-step sizes on different subdomains to achieve better efficiency compared to that obtained using globally uniform time-stepping methods.…”

Section: Introductionmentioning

confidence: 99%

High-Order Multirate Explicit Time-Stepping Schemes for the Baroclinic-Barotropic Split Dynamics in Primitive Equations

Lan,

Ju,

Wang

et al. 2021

Preprint

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In order to treat the multiple time scales of ocean dynamics in an efficient manner, the baroclinicbarotropic splitting technique has been widely used for solving the primitive equations for ocean modeling. In this paper, we propose second and third-order multirate explicit time-stepping schemes for such split systems based on the strong stability-preserving Runge-Kutta (SSPRK) framework. Our method allows for a large time step to be used for advancing the three-dimensional (slow) baroclinic mode and a small time step for the two-dimensional (fast) barotropic mode, so that each of the two mode solves only need satisfy their respective CFL condition to maintain numerical stability. It is well known that the SSPRK method achieves high-order temporal accuracy by utilizing a convex combination of forward-Euler steps. At each time step of our method, the baroclinic velocity is first computed by using the SSPRK scheme to advance the baroclinic-barotropic system with the large time step, then the barotropic velocity is specially corrected by using the same SSPRK scheme with the small time step to advance the barotropic subsystem with a barotropic forcing interpolated based on values from the preceding baroclinic solves. Finally, the fluid thickness and the sea surface height perturbation is updated by coupling the predicted baroclinic and barotropic velocities. Temporal truncation error analyses are also carried out for the proposed schemes. Two benchmark tests drawn from the "MPAS-Ocean" platform are used to numerically demonstrate the accuracy and parallel performance of the proposed schemes.

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“…For an example of work that tackles specifically coastal applications we refer to [21]. The LTS work that is most relevant to the MPAS-Ocean framework is perhaps [22], where the authors developed second and third order schemes based on the strong stability preserving Runge-Kutta (SSPRK) methods for the shallow water equations discretized with TRiSK on SCVT grids. The effort of the authors of [22] was to deliberately design LTS schemes to be then implemented in unstructured-mesh models such as MPAS-Ocean.…”

Section: Introductionmentioning

confidence: 99%

Local time stepping for the shallow water equations in MPAS

Capodaglio,

Petersen

2021

Preprint

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We assess the performance of a set of local time-stepping schemes for the shallow water equations implemented in the global ocean model MPAS-Ocean. The availability of local time-stepping tools is of major relevance for ocean codes such as MPAS-Ocean, which rely on a multi-resolution approach to perform regional grid refinement, for instance in proximity of the coast. In presence of variable resolution, the size of the time-step of explicit numerical integrators is bounded above by the size of the smallest cell on the grid, according to the Courant-Friedrichs-Lewy (CFL) condition. This constraint means that the time-step size used in low resolution regions must be the same as the one used in high resolution regions, resulting in an unnecessary computational effort. Local time-stepping, on the other hand, allows one to select different time-step sizes according to local, rather than global, CFL conditions, resulting in a more tailored integration process and reduced computational times. The present work is a preliminary but necessary effort aimed at paving the way for a more comprehensive work on local time-stepping for the primitive equation set with realistic geography.

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Conservative explicit local time-stepping schemes for the shallow water equations

Cited by 26 publications

References 40 publications

Speculative Parallel Execution for Local Timestepping

Speculative Parallel Execution for Local Timestepping

High-Order Multirate Explicit Time-Stepping Schemes for the Baroclinic-Barotropic Split Dynamics in Primitive Equations

Local time stepping for the shallow water equations in MPAS

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