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Nearly optimal convergence result for multigrid with aggressive coarsening and polynomial smoothing

Petr Vaněk; Marian Brezina — 2013

Applications of Mathematics

We analyze a general multigrid method with aggressive coarsening and polynomial smoothing. We use a special polynomial smoother that originates in the context of the smoothed aggregation method. Assuming the degree of the smoothing polynomial is, on each level $k$ , at least $C h_{k + 1} / h_{k}$ , we prove a convergence result independent of $h_{k + 1} / h_{k}$ . The suggested smoother is cheaper than the overlapping Schwarz method that allows to prove the same result. Moreover, unlike in the case of the overlapping Schwarz method, analysis...

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