An improved convergence analysis of smoothed aggregation algebraic multigrid |
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Authors: | Marian Brezina Petr Vaněk Panayot S Vassilevski |
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Institution: | 1. Department of Applied Mathematics, Campus Box 526, University of Colorado at Boulder, Boulder, CO 80309‐0526, U.S.A.;2. Department of Mathematics, University of West Bohemia, 30614 Plzeň, Czech Republic;3. Center for Applied Scientific Computing, Lawrence Livermore National Laboratory, P.O. Box 808, L‐560, Livermore, CA 94550, U.S.A. |
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Abstract: | We present an improved analysis of the smoothed aggregation algebraic multigrid method extending the original proof in Numer. Math. 2001; 88 :559–579] and its modification in Multilevel Block Factorization Preconditioners. Matrix‐based Analysis and Algorithms for Solving Finite Element Equations. Springer: New York, 2008]. The new result imposes fewer restrictions on the aggregates that makes it easier to verify in practice. Also, we extend a result in Appl. Math. 2011] that allows us to use aggressive coarsening at all levels. This is due to the properties of the special polynomial smoother that we use and analyze. In particular, we obtain bounds in the multilevel convergence estimates that are independent of the coarsening ratio. Numerical illustration is also provided. Copyright © 2011 John Wiley & Sons, Ltd. |
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Keywords: | smoothed aggregation algebraic multigrid convergence analysis polynomial smoother aggressive coarsening |
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