| Issue |
ESAIM: M2AN
Volume 57, Number 4, July-August 2023
|
|
|---|---|---|
| Page(s) | 2451 - 2491 | |
| DOI | https://doi.org/10.1051/m2an/2023060 | |
| Published online | 27 July 2023 | |
Convergence analysis of time-domain PMLS for 2D electromagnetic wave propagation in dispersive waveguides
1
POEMS, CNRS, Inria, ENSTA Paris, Institut Polytechnique de Paris, 828 Bd. des Maréchaux, 91120 Palaiseau, France
2
Institute of Analysis and Scientific Computing, TU Wien, Wiedner Hauptstraße 8-10, 1040 Wien, Austria
* Corresponding author: markus.wess@tuwien.ac.at
Received:
22
December
2022
Accepted:
11
July
2023
This work is dedicated to the analysis of generalized perfectly matched layers (PMLs) for 2D electromagnetic wave propagation in dispersive waveguides. Under quite general assumptions on frequency-dependent dielectric permittivity and magnetic permeability we prove convergence estimates in homogeneous waveguides and show that the PML error decreases exponentially with respect to the absorption parameter and the length of the absorbing layer. The optimality of this error estimate is studied both numerically and analytically. Finally, we demonstrate that in the case when the waveguide contains a heterogeneity supported away from the absorbing layer, instabilities may occur, even in the case of the non-dispersive media. Our findings are illustrated by numerical experiments.
Mathematics Subject Classification: 35L05 / 35Q61 / 65M12
Key words: Perfectly matched layers / Time-dependent Maxwell equations / Laplace transform / Waveguides / Dispersive media / Metamaterials
© The authors. Published by EDP Sciences, SMAI 2023
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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