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.
Accepté le :
DOI : 10.1051/m2an/2017019
Mots-clés : Perfectly matched layers, stability, Maxwell equations, passive metamaterials, Laplace transform
@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://archive.numdam.org/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://archive.numdam.org/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://archive.numdam.org/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. http://archive.numdam.org/articles/10.1051/m2an/2017019/
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