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A unified analysis framework for iterative parallel-in-time algorithms
Citation Link: https://doi.org/10.15480/882.4310
Publikationstyp
Journal Article
Date Issued
2023-10
Sprache
English
TORE-DOI
Volume
45
Issue
5
Start Page
A2275
End Page
A2303
Citation
SIAM Journal on Scientific Computing 45 (5): A2275-A2303 (2023-10)
Publisher DOI
Scopus ID
ArXiv ID
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 (PinT) algorithms have been proposed, like Parareal, PFASST, MGRIT, and Space-Time Multi-Grid (STMG). These methods have been described using different notations and the convergence estimates that are available for some of them 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 super-linearly and compare them directly numerically. Our framework also allows us to find new methods.
Subjects
Mathematics - Numerical Analysis
Mathematics - Numerical Analysis
Computer Science - Computational Engineering; Finance; and Science
Computer Science - Numerical Analysis
DDC Class
510: Mathematik
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