Geodesic
Stable perfectly matched layers for a class of anisotropic dispersive models. Part I: necessary and sufficient conditions of stability
Bécache, Eliane1  ; Kachanovska, Maryna1 
1 Laboratoire Poems (UMR 7231 CNRS/Inria/ENSTA ParisTech, Université Paris Saclay), ENSTA ParisTech, 828 Boulevard des Maréchaux, 91120 Palaiseau, France.
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 51 (2017) no. 6, pp. 2399-2434

Voir la notice de l'article provenant de la source Numdam

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.

Reçu le :
Accepté le :
DOI : 10.1051/m2an/2017019
Classification : 65M12, 35Q60
Keywords: Perfectly matched layers, stability, Maxwell equations, passive metamaterials, Laplace transform

Bécache, Eliane 1 ; Kachanovska, Maryna 1

1 Laboratoire Poems (UMR 7231 CNRS/Inria/ENSTA ParisTech, Université Paris Saclay), ENSTA ParisTech, 828 Boulevard des Maréchaux, 91120 Palaiseau, France. 
@article{M2AN_2017__51_6_2399_0,
     author = {B\'ecache, Eliane and Kachanovska, Maryna},
     title = {Stable perfectly matched layers for a class of anisotropic dispersive models. {Part} {I:} necessary and sufficient conditions of stability},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {2399--2434},
     publisher = {EDP-Sciences},
     volume = {51},
     number = {6},
     year = {2017},
     doi = {10.1051/m2an/2017019},
     mrnumber = {3745176},
     zbl = {1454.78010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an/2017019/}
}
TY  - JOUR
AU  - Bécache, Eliane
AU  - Kachanovska, Maryna
TI  - Stable perfectly matched layers for a class of anisotropic dispersive models. Part I: necessary and sufficient conditions of stability
JO  - ESAIM: Mathematical Modelling and Numerical Analysis 
PY  - 2017
SP  - 2399
EP  - 2434
VL  - 51
IS  - 6
PB  - EDP-Sciences
UR  - http://geodesic.mathdoc.fr/articles/10.1051/m2an/2017019/
DO  - 10.1051/m2an/2017019
LA  - en
ID  - M2AN_2017__51_6_2399_0
ER  - 
%0 Journal Article
%A Bécache, Eliane
%A Kachanovska, Maryna
%T Stable perfectly matched layers for a class of anisotropic dispersive models. Part I: necessary and sufficient conditions of stability
%J ESAIM: Mathematical Modelling and Numerical Analysis 
%D 2017
%P 2399-2434
%V 51
%N 6
%I EDP-Sciences
%U http://geodesic.mathdoc.fr/articles/10.1051/m2an/2017019/
%R 10.1051/m2an/2017019
%G en
%F M2AN_2017__51_6_2399_0
Bécache, Eliane; Kachanovska, Maryna. Stable perfectly matched layers for a class of anisotropic dispersive models. Part I: necessary and sufficient conditions of stability. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 51 (2017) no. 6, pp. 2399-2434. doi: 10.1051/m2an/2017019

Cité par Sources :