| Issue |
ESAIM: M2AN
Volume 51, Number 6, November-December 2017
|
|
|---|---|---|
| Page(s) | 2399 - 2434 | |
| DOI | https://doi.org/10.1051/m2an/2017019 | |
| Published online | 18 December 2017 | |
Stable perfectly matched layers for a class of anisotropic dispersive models. Part I: necessary and sufficient conditions of stability∗
Laboratoire Poems (UMR 7231 CNRS/Inria/ENSTA ParisTech, Université Paris Saclay), ENSTA ParisTech, 828 Boulevard des Maréchaux, 91120 Palaiseau, France.
eliane.becache@inria.fr; maryna.kachanovska@ensta.fr
Received: 18 August 2016
Revised: 28 February 2017
Accepted: 10 April 2017
In this work we consider the problem of modelling of 2D anisotropic dispersive wave propagation in unbounded domains with the help of perfectly matched layers (PMLs). We study the Maxwell equations in passive media with a frequency-dependent diagonal tensor of dielectric permittivity and magnetic permeability. An application of the traditional PMLs to this kind of problems often results in instabilities. We provide a recipe for the construction of new, stable PMLs. For a particular case of non-dissipative materials, we show that a known necessary stability condition of the perfectly matched layers is also sufficient. We illustrate our statements with theoretical and numerical arguments.
Mathematics Subject Classification: 65M12 / 35Q60
Key words: Perfectly matched layers / stability / Maxwell equations / passive metamaterials / Laplace transform
© EDP Sciences, SMAI 2017
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