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Journal Articles SIAM Journal on Scientific Computing Year : 2018

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.

Dates and versions

hal-01964336 , version 1 (21-12-2018)

Identifiers

Cite

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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