Abstract
We introduce a new domain decomposition strategy for time harmonic Maxwell’s equations that is valid in the case of automatically generated subdomain partitions with possible presence of cross-points. The convergence of the algorithm is guaranteed and we present a complete analysis of the matrix form of the method. The method involves transmission matrices responsible for imposing coupling between subdomains. We discuss the choice of such matrices, their construction and the impact of this choice on the convergence of the domain decomposition algorithm. Numerical results and algorithms are provided.
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Acknowledgements
The authors would like to thank the two anonymous reviewers for their numerous relevant remarks which clearly improved the quality of this paper.
Funding
Open access funding provided by Università degli Studi di Pavia within the CRUI-CARE Agreement. This work was supported by the project NonlocalDD funded by the French National Research Agency, grant ANR–15–CE23–0017–01.
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Claeys, X., Collino, F. & Parolin, E. Nonlocal optimized schwarz methods for time-harmonic electromagnetics. Adv Comput Math 48, 72 (2022). https://doi.org/10.1007/s10444-022-09987-7
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DOI: https://doi.org/10.1007/s10444-022-09987-7