On the use of Perfectly Matched Layers at corners for scattering problems with sign-changing coefficients

JOURNAL OF COMPUTATIONAL PHYSICS

卷:322

Article

Bonnet-Ben Dhia, A. -S.¹  Carvalho, C.¹  Chesnel, L.²  Ciarlet, P., Jr.¹ 

[1] UMR 7231 CNRS INRIA ENSTA, POEMS, Palaiseau, France

[2] Univ Paris Saclay, Ecole Polytech, INRIA CMAP, Palaiseau, France

关键词: Scattering problem;    Sign-changing permittivity;    Corner singularities;    Black-hole waves;    Perfectly Matched Layers;    Finite element method;   

DOI  :  10.1016/j.jcp.2016.06.037

来源: Elsevier

【 摘 要 】

We investigate in a 2D setting the scattering of time-harmonic electromagnetic waves by a plasmonic device, represented as a non-dissipative bounded and penetrable obstacle with a negative permittivity. Using the T-coercivity approach, we first prove that the problem is well-posed in the classical framework H-loc(1) if the negative permittivity does not lie in some critical interval whose definition depends on the shape of the device. When the latter has corners, for values inside the critical interval, unusual strong singularities for the electromagnetic field can appear. In that case, well-posedness is obtained by imposing a radiation condition at the corners to select the outgoing black-hole plasmonic wave, that is the one which carries energy towards the corners. A simple and systematic criterion is given to define what is the outgoing solution. Finally, we propose an original numerical method based on the use of Perfectly Matched Layers at the corners. We emphasize that it is necessary to design an ad hoc technique because the field is too singular to be captured with standard finite element methods. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free