An overview of multilevel methods with aggressive coarsening and massive polynomial smoothing. (English) Zbl 1327.65058

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

ETNA, Electron. Trans. Numer. Anal. 44, 401-442 (2015).

Summary: 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.

MSC:

65F10	Iterative numerical methods for linear systems
65M55	Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs

Keywords:

multigrid; aggressive coarsening; optimal convergence result