Geodesic
Asymptotic analysis of optimized Schwarz methods for maxwell’s equations with discontinuous coefficients
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 52 (2018) no. 6, pp. 2457-2477

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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.

DOI : 10.1051/m2an/2018041
Classification : 65N55, 65F10
Keywords: Domain decomposition, Maxwell’s equations, discontinuous coefficients, optimized Schwarz methods

Dolean, Victorita 1 ; Gander, Martin J. 1 ; Veneros, Erwin 1

1 
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     title = {Asymptotic analysis of optimized {Schwarz} methods for maxwell{\textquoteright}s equations with discontinuous coefficients},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {2457--2477},
     publisher = {EDP-Sciences},
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Dolean, Victorita; Gander, Martin J.; Veneros, Erwin. Asymptotic analysis of optimized Schwarz methods for maxwell’s equations with discontinuous coefficients. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 52 (2018) no. 6, pp. 2457-2477. doi: 10.1051/m2an/2018041

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