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Optimized Schwarz methods for heterogeneous Helmholtz and Maxwell's equations

Dolean, Victorita and Gander, Martin J. and Veneros, Erwin and Zhang, Hui (2017) Optimized Schwarz methods for heterogeneous Helmholtz and Maxwell's equations. In: Domain Decomposition Methods in Science and Engineering XXIII. Lecture Notes in Computational Science and Engineering . Springer-Verlag, Berlin, pp. 145-152. ISBN 9783319523897

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Both the Helmholtz equation and the time-harmonic Maxwell’s equations are difficult to solve by iterative methods in the intermediate to high frequency regime, and domain decomposition methods are among the most promising techniques for this task. We focus here on the case of dissipative and conductive media with strongly heterogeneous coefficients, and develop optimized transmission conditions for this case. We establish a link for the use of such conditions between the case of Helmholtz and Maxwell’s equations, and show that in both cases jumps aligned with the interfaces of the subdomains can improve the convergence of the subdomain iteration.