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

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