ETNA - Electronic Transactions on Numerical Analysis
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Verlag der Österreichischen Akademie der Wissenschaften Austrian Academy of Sciences Press
A-1011 Wien, Dr. Ignaz Seipel-Platz 2
Tel. +43-1-515 81/DW 3420, Fax +43-1-515 81/DW 3400 https://verlag.oeaw.ac.at, e-mail: verlag@oeaw.ac.at |
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DATUM, UNTERSCHRIFT / DATE, SIGNATURE
BANK AUSTRIA CREDITANSTALT, WIEN (IBAN AT04 1100 0006 2280 0100, BIC BKAUATWW), DEUTSCHE BANK MÜNCHEN (IBAN DE16 7007 0024 0238 8270 00, BIC DEUTDEDBMUC)
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ETNA - Electronic Transactions on Numerical Analysis ISBN 978-3-7001-8258-0 Online Edition Research Article
Radek Tezaur,
Petr Vaněk
S. 264 - 285 doi:10.1553/etna_vol48s264 Verlag der Österreichischen Akademie der Wissenschaften doi:10.1553/etna_vol48s264
Abstract: An improved convergence bound for the polynomially accelerated two-level method of Brousek et al. [Electron. Trans. Numer. Anal., 44 (2015), pp. 401–442, Section 5] is proven. This method is a reinterpretation of the smoothed aggregation method with an aggressive coarsening and massive polynomial smoothing of Vaněk, Brezina, and Tezaur [SIAM J. Sci. Comput., 21 (1999), pp. 900–923], and its convergence rate estimate is improved here quantitatively. Next, since the symmetrization of the method requires two solutions of the coarse problem, a modification of the method is proposed that does not have this disadvantage, and a qualitatively better convergence result for the modification is established. In particular, it is shown that a bound of the convergence rate of the method with a multiply (k-times) smoothed prolongator is asymptotically inversely proportional to d^{2k}, where d is the degree of the smoothing polynomial. In earlier works, this acceleration effect is only quadratic. Finally, for another modified multiply smoothed method, it is proved that this convergence improvement is not limited only to an asymptotic regime but holds true everywhere. Keywords: two-level method with aggressive coarsening, coarse-space size independent convergence, smoothed aggregation, polynomial smoothing Published Online: 2018/07/02 12:35:39 Object Identifier: 0xc1aa5576 0x00390d55 Rights: . Electronic Transactions on Numerical Analysis (ETNA) is an electronic journal for the publication of significant new developments in numerical analysis and scientific computing. Papers of the highest quality that deal with the analysis of algorithms for the solution of continuous models and numerical linear algebra are appropriate for ETNA, as are papers of similar quality that discuss implementation and performance of such algorithms. New algorithms for current or new computer architectures are appropriate provided that they are numerically sound. However, the focus of the publication should be on the algorithm rather than on the architecture. The journal is published by the Kent State University Library in conjunction with the Institute of Computational Mathematics at Kent State University, and in cooperation with the Johann Radon Institute for Computational and Applied Mathematics of the Austrian Academy of Sciences (RICAM). Reviews of all ETNA papers appear in Mathematical Reviews and Zentralblatt für Mathematik. Reference information for ETNA papers also appears in the expanded Science Citation Index. ETNA is registered with the Library of Congress and has ISSN 1068-9613. …
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Verlag der Österreichischen Akademie der Wissenschaften Austrian Academy of Sciences Press
A-1011 Wien, Dr. Ignaz Seipel-Platz 2
Tel. +43-1-515 81/DW 3420, Fax +43-1-515 81/DW 3400 https://verlag.oeaw.ac.at, e-mail: verlag@oeaw.ac.at |