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Algebraic analysis of multigrid algorithms

✍ Scribed by Christoph Pflaum

Publisher: John Wiley and Sons
Year: 1999
Tongue: English
Weight: 158 KB
Volume: 6
Category: Article
ISSN: 1070-5325
DOI: 10.1002/(sici)1099-1506(199912)6:8<701::aid-nla181>3.0.co;2-l

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✦ Synopsis

We study the convergence rate of multilevel algorithms from an algebraic point of view. This requires a detailed analysis of the constant in the strengthened Cauchy-Schwarz inequality between the coarse-grid space and a so-called complementary space. This complementary space may be spanned by standard hierarchical basis functions, prewavelets or generalized prewavelets. Using generalized prewavelets, we are able to derive a constant in the strengthened Cauchy-Schwarz inequality which is less than 0.31 for the L 2 and H 1 bilinear form. This implies a convergence rate less than 0.15. So, we are able to prove fast multilevel convergence. Furthermore, we obtain robust estimations of the convergence rate for a large class of anisotropic ellipic equations, even for some that are not H 1 -elliptic.

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