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

Victorita Dolean, Martin J. Gander, Erwin Veneros

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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.

Original languageEnglish
Pages (from-to)2457-2477
Number of pages21
JournalESAIM: Mathematical Modelling and Numerical Analysis
Volume52
Issue number6
DOIs
Publication statusPublished - 30 Nov 2018

Keywords

  • discontinuous coefficients
  • domain decomposition
  • Maxwell's equations
  • optimized Schwarz methods

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