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In this paper, we consider the convergence rate of a smoothed aggregation algebraic multigrid method, which uses a simple polynomial (1 − t)ν or an optimal Chebyshev‐like polynomial to construct the smoother and prolongation operator. The result is purely algebraic, whereas a required main weak approximation property of the tentative interpolation operator is verified for a spectral element ... read moreagglomeration version of the method. More specifically, we prove that, for partial differential equations (PDEs), the two‐grid method converges uniformly without any regularity assumptions. Moreover, the convergence rate improves uniformly when the degree of the polynomials used for the smoother and the prolongation increases. Such a result, as is well‐known, would imply uniform convergence of the multilevel W‐cycle version of the algorithm. Numerical results, for both PDE and non‐PDE (graph Laplacian) problems are presented to illustrate the theoretical findings. Published 2016. This article is a U.S. Government work and is in the public domain in the USA.read less
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- Hu, X., Vassilevski, P. S., and Xu, J. ( 2016) A two‐grid SA‐AMG convergence bound that improves when increasing the polynomial degree. Numer. Linear Algebra Appl., 23: 746- 771. doi: 10.1002/nla.2053.
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