Volume 44, pp. 401-442, 2015.

An overview of multilevel methods with aggressive coarsening and massive polynomial smoothing

Jan Brousek, Pavla Franková, Milan Hanuš, Hana Kopincová, Roman Kužel, Radek Tezaur, Petr Vaněk, and Zbyněk Vastl

Abstract

We review our two-level and multilevel methods with aggressive coarsening and polynomial smoothing. These methods can be seen as a less expensive and more flexible (in the multilevel case) alternative to domain decomposition methods. The polynomial smoothers employed by the reviewed methods consist of a sequence of Richardson iterations and can be performed using up to $n$ processors, where $n$ is the size of the considered matrix, thereby allowing for a higher level of parallelism than domain decomposition methods.

Full Text (PDF) [432 KB]

Key words

multigrid, aggressive coarsening, optimal convergence result

AMS subject classifications

65F10,65M55

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