Stable perfectly matched layers for a class of anisotropic dispersive models. Part I: Necessary and sufficient conditions of stability

Eliane Bécache (1) , Maryna Kachanovska (1)

1 POEMS - Propagation des Ondes : Étude Mathématique et Simulation

In this work we consider a problem of modelling of 2D anisotropic dispersive wave propagation in unbounded domains with the help of perfectly matched layers (PML). 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.

Mots clés: passive metamaterials; stability; Maxwell equations; Laplace transform; perfectly matched layers

Domaines: Analyse numérique [math.NA]

Eliane Bécache, Maryna Kachanovska. 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, 2017, 51 (6), pp.2399-2434. ⟨10.1051/m2an/2017019⟩. ⟨hal-01356811v2⟩