Asynchronous Truncated Multigrid-Reduction-in-Time

Hahne, Jens; Southworth, Benjamin Scott; Friedhoff, Stephanie

doi:10.1137/21m1433149

Asynchronous Truncated Multigrid-Reduction-in-Time

Journal Article · Mon Nov 21 23:00:00 EST 2022 · SIAM Journal on Scientific Computing

DOI:https://doi.org/10.1137/21m1433149· OSTI ID:2441352

Hahne, Jens ^[1]; ^[2]; Friedhoff, Stephanie ^[1]

Univ. of Wuppertal (Germany)
Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

In this paper, we present the new “asynchronous truncated multigrid-reduction-in-time” (AT-MGRIT) algorithm for introducing time parallelism to the solution of discretized time-dependent problems. The new algorithm is based on the multigrid-reduction-in-time (MGRIT) approach, which, in certain settings, is equivalent to another common multilevel parallel-in-time method, Parareal. In contrast to Parareal and MGRIT that both consider a global temporal grid over the entire time interval on the coarsest level, the AT-MGRIT algorithm uses truncated local time grids on the coarsest level, each grid covering certain temporal subintervals. Further, these local grids can be solved completely in an independent way from each other, which reduces the sequential part of the algorithm and, thus, increases parallelism in the method. Here, we study the effect of using truncated local coarse grids on the convergence of the algorithm, both theoretically and numerically, and show, using challenging nonlinear problems, that the new algorithm consistently outperforms classical Parareal/MGRIT in terms of time to solution.

View Accepted Manuscript (DOE)

Research Organization:: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Organization:: USDOE

Grant/Contract Number:: 89233218CNA000001

OSTI ID:: 2441352

Report Number(s):: LA-UR--21-26105

Journal Information:: SIAM Journal on Scientific Computing, Journal Name: SIAM Journal on Scientific Computing Journal Issue: 3 Vol. 45; ISSN 1064-8275

Publisher:: Society for Industrial and Applied Mathematics (SIAM)Copyright Statement

Country of Publication:: United States

Language:: English

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97 MATHEMATICS AND COMPUTING
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truncated coarsest grids

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