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Asynchronous Parareal Time Discretization For Partial Differential Equations

Abstract : Asynchronous iterations have been investigated more and more for both scaling and fault-resilience purposes on high performance computing platforms. While so far, they have been exclusively applied within space domain decomposition frameworks, this paper advocates a novel application direction targeting time-decomposed time-parallel approaches. Specifically, an asynchronous iterative model is derived from the Parareal scheme, for which convergence and speedup analysis are then conducted. It turned out that Parareal and async-Parareal feature very close convergence conditions, asymptotically equivalent, including the finite-time termination property. Based on a computational cost model aware of unsteady communication delays, our speedup analysis shows the potential performance gain from asynchronous iterations, which is confirmed by some experimental cases of heat evolution on a homogeneous supercomputer. This primary work clearly suggests possible further benefits from asynchronous iterations.
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Contributor : Frédéric Magoulès Connect in order to contact the contributor
Submitted on : Friday, December 21, 2018 - 10:01:37 PM
Last modification on : Tuesday, October 18, 2022 - 8:34:05 AM

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Frédéric Magoulès, Guillaume Gbikpi-Benissan. Asynchronous Parareal Time Discretization For Partial Differential Equations. SIAM Journal on Scientific Computing, 2018, 40 (6), pp.C704-C725. ⟨10.1137/17m1149225⟩. ⟨hal-01964336⟩



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