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Optimized Schwarz methods with nonoverlapping circular domain decomposition


Authors: Martin J. Gander and Yingxiang Xu
Journal: Math. Comp. 86 (2017), 637-660
MSC (2010): Primary 65N55; Secondary 65F10
DOI: https://doi.org/10.1090/mcom/3127
Published electronically: May 17, 2016
MathSciNet review: 3584543
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Abstract: While the classical Schwarz method can only be used with overlap, optimized Schwarz methods can also be used without overlap, which can be an advantage when simulating heterogeneous problems, problems with jumping coefficients, or also for independent mesh generation per subdomain. The analysis of nonoverlapping optimized Schwarz methods has so far been restricted to the case of straight interfaces, even though the method has been successfully used with curved interfaces. We close this gap by presenting a rigorous analysis of optimized Schwarz methods for circular domain decompositions. We derive optimized zeroth and second order transmission conditions for a model elliptic operator in two dimensions, and show why the straight interface analysis results, when properly scaled to include the curvature, are also successful for curved interfaces. Our analysis thus complements earlier asymptotic results by Lui for curved interfaces, where the influence of the curvature remained unknown. We illustrate our results with numerical experiments.


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Additional Information

Martin J. Gander
Affiliation: Section de Mathématiques, Université de Genève, 2-4 rue du Lièvre, CP 64, CH-1211, Genève, Suisse
Email: Martin.Gander@unige.ch

Yingxiang Xu
Affiliation: School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, People’s Republic of China
Email: yxxu@nenu.edu.cn

DOI: https://doi.org/10.1090/mcom/3127
Keywords: Nonoverlapping optimized Schwarz method, circular domain decomposition, optimized transmission conditions, curved interfaces
Received by editor(s): September 23, 2014
Received by editor(s) in revised form: September 2, 2015
Published electronically: May 17, 2016
Additional Notes: The second author is the corresponding author, who was supported by NSFC-11201061, CPSF-2012M520657 and the Science and Technology Development Planning of Jilin Province 20140520058JH
Article copyright: © Copyright 2016 American Mathematical Society