Scientific article
English

Asymptotic analysis of optimized Schwarz methods for Maxwell’s equations with discontinuous coefficients

Published inModélisation mathématique et analyse numérique, vol. 52, no. 6, p. 2457-2477
Publication date2019-02-08
First online date2019-02-08
Abstract

Discretized time harmonic Maxwell’s equations are hard to solve by iterative methods, and the best currently available methods are based on domain decomposition and optimized transmission conditions. Optimized Schwarz methods were the first ones to use such transmission conditions, and this approach turned out to be so fundamentally important that it has been rediscovered over the last years under the name sweeping preconditioners, source transfer, single layer potential method and the method of polarized traces. We show here how one can optimize transmission conditions to take benefit from the jumps in the coefficients of the problem, when they are aligned with the subdomain interface, and obtain methods which converge for two subdomains in certain situations independently of the mesh size, which would not be possible without jumps in the coefficients.

Citation (ISO format)
DOLEAN MAINI, Victorita, GANDER, Martin Jakob, VENEROS ALFARO, Erwin German. Asymptotic analysis of optimized Schwarz methods for Maxwell’s equations with discontinuous coefficients. In: Modélisation mathématique et analyse numérique, 2019, vol. 52, n° 6, p. 2457–2477. doi: 10.1051/m2an/2018041
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Additional URL for this publicationhttps://www.esaim-m2an.org/10.1051/m2an/2018041
Journal ISSN0764-583X
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