Distance-two interpolation for parallel algebraic multigrid

Algebraic multigrid (AMG) is one of the most efficient and scalable parallel algorithms for solving sparse linear systems on unstructured grids. However, for large 3D problems, the coarse grids that are normally used in AMG often lead to growing complexity in terms of memory use and execution time p...

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Veröffentlicht in:Numerical linear algebra with applications Jg. 15; H. 2-3; S. 115 - 139
Hauptverfasser: De Sterck, Hans, Falgout, Robert D., Nolting, Joshua W., Yang, Ulrike Meier
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Chichester, UK John Wiley & Sons, Ltd 01.03.2008
Schlagworte:
algebraic multigrid
long-range interpolation
parallel implementation
reduced complexity
truncation
ISSN:1070-5325, 1099-1506
Online-Zugang:Volltext
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Zusammenfassung:Algebraic multigrid (AMG) is one of the most efficient and scalable parallel algorithms for solving sparse linear systems on unstructured grids. However, for large 3D problems, the coarse grids that are normally used in AMG often lead to growing complexity in terms of memory use and execution time per AMG V‐cycle. Sparser coarse grids, such as those obtained by the parallel modified independent set (PMIS) coarsening algorithm, remedy this complexity growth but lead to nonscalable AMG convergence factors when traditional distance‐one interpolation methods are used. In this paper, we study the scalability of AMG methods that combine PMIS coarse grids with long‐distance interpolation methods. AMG performance and scalability are compared for previously introduced interpolation methods as well as new variants of them for a variety of relevant test problems on parallel computers. It is shown that the increased interpolation accuracy largely restores the scalability of AMG convergence factors for PMIS‐coarsened grids, and in combination with complexity reducing methods, such as interpolation truncation, one obtains a class of parallel AMG methods that enjoy excellent scalability properties on large parallel computers. Copyright © 2007 John Wiley & Sons, Ltd.
Bibliographie:istex:1093E18BB146F41415CBBA46C48F3DE198060146
ArticleID:NLA559
ark:/67375/WNG-WF0BW1ZT-Z
U.S. Department of Energy - No. W-7405-Eng-48
ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:1070-5325
1099-1506
DOI:10.1002/nla.559