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Title

Convergence behavior of a two-level optimized schwarz preconditioner

Authors
Dubois, Olivier
Published in Bercovier, M., Gander, Martin J., Kornhuber, R., Widlund, O. 18th International Conference on Domain Decomposition Methods. Jerusalem (Israel) - 12-17 January 2008 - Heidelberg: Springer. 2009
Collection Lecture Notes in Computational Science and Engineering; 70
Abstract Optimized Schwarz methods form a class of domain decomposition al- gorithms in which the transmission conditions are optimized in order to achieve fast convergence. They are usually derived for a model problem with two subdomains, and give efficient transmission conditions for the local coupling between neighboring subdomains. However, when using a large number of subdomains, a coarse space correction is required to achieve parallel scalability. In this paper we demonstrate with a simple model problem that a two-level optimized Schwarz preconditioner is much more effective than a corresponding two-level Restricted Additive Schwarz preconditioner. The weak dependence on the mesh size is retained from the one-level method, while gaining independence on the number of subdomains. Moreover, the best Robin transmission condition is well approximated by using the analysis from the two subdomain case, under Krylov acceleration.
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ISBN: 978-3-642-02677-5
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DUBOIS, Olivier, GANDER, Martin Jakob. Convergence behavior of a two-level optimized schwarz preconditioner. In: Bercovier, M., Gander, Martin J., Kornhuber, R., Widlund, O. (Ed.). 18th International Conference on Domain Decomposition Methods. Jerusalem (Israel). Heidelberg : Springer, 2009. (Lecture Notes in Computational Science and Engineering; 70) https://archive-ouverte.unige.ch/unige:6853

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Deposited on : 2010-06-11

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