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On the analysis of perfectly matched layers for a class of dispersive media and application to negative index metamaterials


Authors: Éliane Bécache, Patrick Joly and Valentin Vinoles
Journal: Math. Comp. 87 (2018), 2775-2810
MSC (2010): Primary 35B35, 35L05, 35L40, 35Q61, 65M12
DOI: https://doi.org/10.1090/mcom/3307
Published electronically: March 29, 2018
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Abstract: This work deals with Perfectly Matched Layers (PMLs) in the context of dispersive media, and in particular for Negative Index Metamaterials (NIMs). We first present some properties of dispersive isotropic Maxwell equations that include NIMs. We propose and analyse the stability of very general PMLs for a large class of dispersive systems using a new change of variable. We give necessary criteria for the stability of such models that show in particular that the classical PMLs applied to NIMs are unstable and we confirm this numerically. For dispersive isotropic Maxwell equations, this analysis is completed by giving necessary and sufficient conditions of stability. Finally, we propose new PMLs that satisfy these criteria and demonstrate numerically their efficiency.


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Additional Information

Éliane Bécache
Affiliation: Laboratoire Poems, UMR 7231 CNRS/Inria/ENSTA ParisTech, ENSTA ParisTech, 828, Boulevard des Maréchaux, 91762 Palaiseau, France
Email: eliane.becache@inria.fr

Patrick Joly
Affiliation: Laboratoire Poems, UMR 7231 CNRS/Inria/ENSTA ParisTech, ENSTA ParisTech, 828, Boulevard des Maréchaux, 91762 Palaiseau, France
Email: patrick.joly@inria.fr

Valentin Vinoles
Affiliation: École Polytechnique Fédérale de Lausanne, SB MATHAA CAMA, Station 8, CH-1015 Lausanne, Switzerland
Email: valentin.vinoles@gmail.com

DOI: https://doi.org/10.1090/mcom/3307
Keywords: Perfectly matched layer (PML), dispersive system, negative index metamaterial (NIM), stability, Maxwell equations
Received by editor(s): June 6, 2016
Received by editor(s) in revised form: February 14, 2017, and June 15, 2017
Published electronically: March 29, 2018
Additional Notes: The third author was partially supported by the ANR project METAMATH (ANR-11-MONU-0016)
Article copyright: © Copyright 2018 American Mathematical Society

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