Parallel performance of algebraic multigrid domain decomposition

Algebraic multigrid (AMG) is a widely used scalable solver and preconditioner for large-scale linear systems resulting from the discretization of a wide class of elliptic PDEs. While AMG has optimal computational complexity, the cost of communication has become a significant bottleneck that limits i...

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Hauptverfasser: Mitchell, Wayne B. (VerfasserIn) , Strzodka, Robert (VerfasserIn) , Falgout, Robert D. (VerfasserIn)
Dokumenttyp: Article (Journal)
Sprache:Englisch
Veröffentlicht: 2021
In: Numerical linear algebra with applications
Year: 2021, Jahrgang: 28, Heft: 3, Pages: 1-24
ISSN:1099-1506
DOI:10.1002/nla.2342
Online-Zugang:Verlag, kostenfrei, Volltext: https://doi.org/10.1002/nla.2342
Verlag, kostenfrei, Volltext: https://onlinelibrary.wiley.com/doi/abs/10.1002/nla.2342
Volltext
Verfasserangaben:Wayne B. Mitchell, Robert Strzodka, Robert D. Falgout

MARC

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520 |a Algebraic multigrid (AMG) is a widely used scalable solver and preconditioner for large-scale linear systems resulting from the discretization of a wide class of elliptic PDEs. While AMG has optimal computational complexity, the cost of communication has become a significant bottleneck that limits its scalability as processor counts continue to grow on modern machines. This article examines the design, implementation, and parallel performance of a novel algorithm, algebraic multigrid domain decomposition (AMG-DD), designed specifically to limit communication. The goal of AMG-DD is to provide a low-communication alternative to standard AMG V-cycles by trading some additional computational overhead for a significant reduction in communication cost. Numerical results show that AMG-DD achieves superior accuracy per communication cost compared with AMG, and speedup over AMG is demonstrated on a large GPU cluster. 
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