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
José C. Garay,
Frédéric Magoulès,
Daniel B. Szyld
Synchronous and asynchronous optimized Schwarz methods for Poisson's equation in rectangular domains ()
S. 744 - 791doi:10.1553/etna_vol55s744 Verlag der Österreichischen Akademie der Wissenschaften doi:10.1553/etna_vol55s744
Abstract: Convergence results for optimized Schwarz methods (OSM) applied as solvers for Poisson's equation in a bounded rectangular domain with Dirichlet (physical) boundary conditions and zeroth-order (Robin) artificial transmission conditions between subdomains are presented. The analysis presented applies to a continuous formulation on an arbitrary number of subdomains with cross points. Both synchronous and asynchronous versions of OSM are discussed. Convergence theorems are presented, and it is shown numerically that the hypotheses of these theorems are satisfied for certain configurations of the subdomains. Additional numerical experiments illustrate the practical behavior of the methods discussed. Keywords: asynchronous iterations, optimized Schwarz methods, infinite-dimensional operator Published Online: 2022/09/16 12:17:24 Object Identifier: 0xc1aa5576 0x003db041 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 |