Abstract
This paper is a continuation of Melenk et al., “Stability analysis for electromagnetic waveguides. Part 1: acoustic and homogeneous electromagnetic waveguides” (2023) [5], extending the stability results for homogeneous electromagnetic (EM) waveguides to the non-homogeneous case. The analysis is done using perturbation techniques for self-adjoint operators eigenproblems. We show that the non-homogeneous EM waveguide problem is well-posed with the stability constant scaling linearly with waveguide length L. The results provide a basis for proving convergence of a Discontinuous Petrov-Galerkin (DPG) discretization based on a full envelope ansatz, and the ultraweak variational formulation for the resulting modified system of Maxwell equations, see Part 1.
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Acknowledgements
J.M. Melenk was supported by the JTO fellowship and the Austrian Science Fund (FWF) under grant F65 “Taming complexity in partial differential systems.” L. Demkowicz, J. Badger, and S. Henneking were supported by AFOSR grants FA9550-19-1-0237, FA9550-23-1-0103, and NSF award 2103524.
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Communicated by: Paul Houston
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Demkowicz, L., Melenk, J.M., Badger, J. et al. Stability analysis for electromagnetic waveguides. Part 2: non-homogeneous waveguides. Adv Comput Math 50, 35 (2024). https://doi.org/10.1007/s10444-024-10130-x
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DOI: https://doi.org/10.1007/s10444-024-10130-x