Optimized Schwarz methods (OSM) have shown to be an efficient iterative solver and preconditioner in solving partial differential equations. Different investigations have been devoted to study optimized Schwarz methods and many applications have shown their great performance compared to the classical Schwarz methods. By simply making slight modifications of transmission conditions between subdomains, and without changing the size of the matrix, we obtain a fast and a robust family of methods. In this paper we give an extension of optimized Schwarz methods to cover three-dimensional partial differential equations. We present the asymptotic behaviors of optimal and optimized Schwarz methods and compare it to the performance of the classical Schwarz methods. We confirm the obtained theoretical results with numerical experiments.
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Laayouni, L. (2008). Optimized Domain Decomposition Methods for Three-dimensional Partial Differential Equations. In: Langer, U., Discacciati, M., Keyes, D.E., Widlund, O.B., Zulehner, W. (eds) Domain Decomposition Methods in Science and Engineering XVII. Lecture Notes in Computational Science and Engineering, vol 60. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-75199-1_41
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DOI: https://doi.org/10.1007/978-3-540-75199-1_41
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