Journal Article

FZJ-2024-00286

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png A Unified Analysis Framework for Iterative Parallel-in-Time Algorithms

Gander, M. J. ; Lunet, T. (Corresponding author) ; Ruprecht, D. ; Speck, R.FZJ*

2023
SIAM Philadelphia, Pa.

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Please use a persistent id in citations: doi:10.1137/22M1487163  doi:10.34734/FZJ-2024-00286

Abstract: Parallel-in-time integration has been the focus of intensive research efforts over the past two decades due to the advent of massively parallel computer architectures and the scaling limits of purely spatial parallelization. Various iterative parallel-in-time algorithms have been proposed, like Parareal, PFASST, MGRIT, and Space-Time Multi-Grid (STMG). These methods have been described using different notation, and the convergence estimates that are available are difficult to compare. We describe Parareal, PFASST, MGRIT, and STMG for the Dahlquist model problem using a common notation and give precise convergence estimates using generating functions. This allows us, for the first time, to directly compare their convergence. We prove that all four methods eventually converge superlinearly, and we also compare them numerically. The generating function framework provides further opportunities to explore and analyze existing and new methods.

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Contributing Institute(s):

1. Jülich Supercomputing Center (JSC)

Research Program(s):

1. 5112 - Cross-Domain Algorithms, Tools, Methods Labs (ATMLs) and Research Groups (POF4-511) (POF4-511)
2. TIME-X - TIME parallelisation: for eXascale computing and beyond (955701) (955701)
3. Verbundprojekt: TIME-X - Parallelisierung zeitabhängiger Simulationen für das zukünftige Supercomputing (16HPC047) (16HPC047)

Appears in the scientific report 2023

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Database coverage:
; ; ; Clarivate Analytics Master Journal List ; Current Contents - Physical, Chemical and Earth Sciences ; Ebsco Academic Search ; Essential Science Indicators ; IF < 5 ; JCR ; SCOPUS ; Science Citation Index Expanded ; Web of Science Core Collection

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