An improved convergence analysis of smoothed aggregation algebraic multigrid

Journal Article · Wed Mar 02 00:00:00 EST 2011 · Numerical Linear Algebra with Applications

DOI:https://doi.org/10.1002/nla.775· OSTI ID:1227005

Brezina, Marian ^[1]; Vaněk, Petr ^[2]; Vassilevski, Panayot S. ^[3]

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1. Univ. of Colorado, Boulder, CO (United States). Dept. of Applied Mathematics
2. University of West Bohemia (Czech Republic). Dept. of Mathematics
3. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States). Center for Applied Scientific Computing

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.

• Research Organization: Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
• Sponsoring Organization: USDOE
• DOE Contract Number: AC52-07NA27344
• OSTI ID: 1227005
• Report Number(s): LLNL-JRNL-448115
• Journal Information: Numerical Linear Algebra with Applications, Vol. 19, Issue 3; ISSN 1070-5325
• Publisher: Wiley
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICS AND COMPUTING
smoothed aggregation
algebraic multigrid
convergence analysis
polynomial smoother
aggressive coarsening