Modal analysis of a domain decomposition method for Maxwell's equations in a waveguide

[2502.15548] Modal analysis of a domain decomposition method for Maxwell's equations in a waveguide Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Numerical Analysis arXiv:2502.15548 (math) [Submitted on 21 Feb 2025 ( v1 ), last revised 14 Apr 2026 (this version, v3)] Title: Modal analysis of a domain decomposition method for Maxwell's equations in a waveguide Authors: Victorita Dolean , Antoine Tonnoir , Pierre-Henri Tournier View a PDF of the paper titled Modal analysis of a domain decomposition method for Maxwell's equations in a waveguide, by Victorita Dolean and Antoine Tonnoir and Pierre-Henri Tournier View PDF HTML (experimental) Abstract: Time-harmonic wave propagation problems, especially those governed by Maxwell's equations, pose significant computational challenges due to the non-self-adjoint nature of the operators and the large, non-Hermitian linear systems resulting from discretization. Domain decomposition methods, particularly one-level Schwarz methods, offer a promising framework to tackle these challenges, with recent advancements showing the potential for weak scalability under certain conditions. In this paper, we analyze the weak scalability of one-level Schwarz methods for Maxwell's equations in strip-wise domain decompositions, focusing on waveguides with general cross sections and different types of transmission conditions such as impedance or perfectly matched layers (PMLs). By combining techniques from the limiting spectrum analysis of Toeplitz matrices and the modal decomposition of Maxwell's solutions, we provide a novel theoretical framework that extends previous work to more complex geometries and transmission conditions. Numerical experiments confirm that the limiting spectrum effectively predicts practical behavior even with a modest number of subdomains. Furthermore, we demonstrate that the one-level Schwarz method can achieve robustness with respect to the wave number under specific domain decomposition parameters, offering new insights into its applicability for large-scale electromagnetic wave problems. Subjects: Numerical Analysis (math.NA) ; Computational Physics (physics.comp-ph) Cite as: arXiv:2502.15548 [math.NA] (or arXiv:2502.15548v3 [math.NA] for this version) https://doi.org/10.48550/arXiv.2502.15548 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Victorita Dolean [ view email ] [v1] Fri, 21 Feb 2025 15:56:07 UTC (934 KB) [v2] Thu, 23 Oct 2025 03:24:07 UTC (618 KB) [v3] Tue, 14 Apr 2026 05:15:49 UTC (2,891 KB) Full-text links: Access Paper: View a PDF of the paper titled Modal analysis of a domain decomposition method for Maxwell's equations in a waveguide, by Victorita Dolean and Antoine Tonnoir and Pierre-Henri Tournier View PDF HTML (experimental) TeX Source view license Current browse context: math.NA < prev | next > new | recent | 2025-02 Change to browse by: cs cs.NA math physics physics.comp-ph References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... 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