Proceedings chapter
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Optimized Schwarz methods for advection diffusion equations in bounded domains

Published inNumerical mathematics and advanced applications, Editors Radu, Florin Adrian ; Kumar, Kundan ; Berre, Inga ; Nordbotten, Jan Martin & Pop, Iuliu sorin, p. 921-929
Presented at ENUMATH 2017, Bergen, September 25 to 29, 2017
PublisherCham : Springer
  • Lecture Notes in Computational Science and Engineering; 126
Publication date2019-01-05
First online date2019-01-05

Optimized Schwarz methods use better transmission conditions than the classical Dirichlet conditions that were used by Schwarz. These transmission conditions are optimized for the physical problem that needs to be solved to lead to fast convergence. The opimization is typically performed in the geometrically simplified setting of two unbounded subdomains using Fourier transforms. Recent studies for both homogeneous and heterogeneous domain decomposition methods indicate that the geometry of the physical domain has actually an influence on this opimization process. We study here this influence for an advection diffusion equation in a bounded domain using separation of variables. We provide theoretical results for the min-max problems characterizing the optimized transmission conditions. Our numerical experiments show significant improvements of the new transmission conditions which take the geometry into account, especially for strong tangential advection.

Citation (ISO format)
GANDER, Martin Jakob, VANZAN, Tommaso. Optimized Schwarz methods for advection diffusion equations in bounded domains. In: Numerical mathematics and advanced applications. Bergen. Cham : Springer, 2019. p. 921–929. (Lecture Notes in Computational Science and Engineering) doi: 10.1007/978-3-319-96415-7_87
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