One way domain decomposition method with second order transmission conditions for solving electromagnetic wave problems

Authors:
Zhen Peng;Vineet Rawat;Jin-Fa Lee
Affiliations:
ElectroScience Laboratory, The Ohio State University, 1320 Kinnear Road, Columbus, OH 43212, USA;ElectroScience Laboratory, The Ohio State University, 1320 Kinnear Road, Columbus, OH 43212, USA;ElectroScience Laboratory, The Ohio State University, 1320 Kinnear Road, Columbus, OH 43212, USA
Venue:
Journal of Computational Physics
Year:
2010

Citing 8
Cited 2

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Domain decomposition: parallel multilevel methods for elliptic partial differential equations
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Nonoverlapping Domain Decomposition with Second Order Transmission Condition for the Time-Harmonic Maxwell's Equations

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Abstract

Non-overlapping domain decomposition (DD) methods with complex first order Robin-type transmission conditions (TCs) provide an efficient iterative solution for Maxwell's equation. Unfortunately, the first order TCs do not effectively account for some eigenmodes of the system matrix, which limits the scalability of the methods. In this work, we examine two TCs with a second order transverse derivative to improve the method's performance. A detailed convergence analysis of the two TCs is presented. We then investigate the use of the two second order TCs in non-conformal and non-overlapping one way DD methods. Numerical results illustrate the effectiveness of the proposed methods on some model problems and on several problems of practical interest.