1. Convergence analysis of time-domain PMLs for 2D electromagnetic wave propagation in dispersive waveguides
- Author
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Bécache, Eliane, Kachanovska, Maryna, Wess, Markus, Kachanovska, Maryna, Propagation des Ondes : Étude Mathématique et Simulation (POEMS), Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Unité de Mathématiques Appliquées (UMA), École Nationale Supérieure de Techniques Avancées (ENSTA Paris)-École Nationale Supérieure de Techniques Avancées (ENSTA Paris)-Centre National de la Recherche Scientifique (CNRS), Fakultät für Mathematik und Geoinformation [Wien] (TU Wien), and Vienna University of Technology (TU Wien)
- Subjects
metamaterials ,Laplace transform ,time-dependent Maxwell equations ,perfectly matched layers ,dispersive media ,waveguides ,[MATH.MATH-NA] Mathematics [math]/Numerical Analysis [math.NA] ,[MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA] - Abstract
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.
- Published
- 2022