An improved convergence analysis of smoothed aggregation algebraic multigrid

Authors

  • Marian Brezina,

    1. Department of Applied Mathematics, Campus Box 526, University of Colorado at Boulder, Boulder, CO 80309-0526, U.S.A.
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  • Petr Vaněk,

    1. Department of Mathematics, University of West Bohemia, 30614 Plzeň, Czech Republic
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  • Panayot S. Vassilevski

    Corresponding author
    1. Center for Applied Scientific Computing, Lawrence Livermore National Laboratory, P.O. Box 808, L-560, Livermore, CA 94550, U.S.A.
    • Center for Applied Scientific Computing, Lawrence Livermore National Laboratory, 7000 East avenue, Mail-Stop L-560, Livermore, CA 94551, U.S.A.
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SUMMARY

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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