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

Victorita Dolean, Martin J. Gander, Erwin Veneros

Research output: Contribution to journalArticle

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.

LanguageEnglish
Pages2457-2477
Number of pages21
JournalESAIM: Mathematical Modelling and Numerical Analysis
Volume52
Issue number6
DOIs
Publication statusPublished - 30 Nov 2018

Fingerprint

Schwarz Methods
Discontinuous Coefficients
Asymptotic analysis
Maxwell equations
Maxwell's equations
Asymptotic Analysis
Transmission Conditions
Jump
Iterative methods
Single Layer Potential
Sweeping
Coefficient
Domain Decomposition
Preconditioner
Decomposition
Harmonic
Trace
Optimise
Mesh
Converge

Keywords

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

Cite this

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Asymptotic analysis of optimized Schwarz methods for Maxwell's equations with discontinuous coefficients. / Dolean, Victorita; Gander, Martin J.; Veneros, Erwin.

In: ESAIM: Mathematical Modelling and Numerical Analysis, Vol. 52, No. 6, 30.11.2018, p. 2457-2477.

Research output: Contribution to journalArticle

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