An improved convergence analysis of smoothed aggregation algebraic multigrid

We present an improved analysis of the smoothed aggregation (SA) alge- braic multigrid method (AMG) extending the original proof in [SA] and its modification in [Va08]. The new result imposes fewer restrictions on the aggregates that makes it eas- ier to verify in practice. Also, we extend a result...

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Bibliographic Details
Published in:Numerical linear algebra with applications 2011-03, Vol.19 (3)
Main Authors: Brezina, Marian, Vaněk, Petr, Vassilevski, Panayot S.
Format: Article
Language:English
Subjects:
aggressive coarsening
algebraic multigrid
convergence analysis
MATHEMATICS AND COMPUTING
polynomial smoother
smoothed aggregation
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Summary:We present an improved analysis of the smoothed aggregation (SA) alge- braic multigrid method (AMG) extending the original proof in [SA] and its modification in [Va08]. The new result imposes fewer restrictions on the aggregates that makes it eas- ier to verify in practice. Also, we extend a result in [Van] that allows us to use aggressive coarsening at all levels due to the special properties of the polynomial smoother, that we use and analyze, and thus provide a multilevel convergence estimate with bounds independent of the coarsening ratio.
ISSN:1070-5325
1099-1506