Hostname: page-component-586b7cd67f-l7hp2 Total loading time: 0 Render date: 2024-11-24T11:13:35.194Z Has data issue: false hasContentIssue false
  • English
  • Français

On the analysis of Bérenger's Perfectly Matched Layers for Maxwell's equations

Published online by Cambridge University Press:  15 April 2002

Eliane Bécache  and
Patrick Joly
Eliane Bécache
Affiliation:
INRIA, Domaine de Voluceau-Rocquencourt, BP 105, 78153 Le Chesnay Cedex, France. eliane.becache@inria.fr.; patrick.joly@inria.fr.
Patrick Joly
Affiliation:
INRIA, Domaine de Voluceau-Rocquencourt, BP 105, 78153 Le Chesnay Cedex, France. eliane.becache@inria.fr.; patrick.joly@inria.fr.
Get access

Abstract

In this work, we investigate the PerfectlyMatched Layers (PML) introduced by Bérenger [3] for designing efficient numerical absorbing layers in electromagnetism.We make a mathematical analysis of this model, first via a modalanalysis with standard Fourier techniques, then via energytechniques. We obtain uniform in time stability results (that makeprecise some results known in the literature) and state some energydecay results that illustrate the absorbing properties of themodel. This last technique allows us to prove the stability of theYee's scheme for discretizing PML's.

Keywords

Absorbing layersPMLMaxwell's equationsstabilityhyperbolic systemsFourier analysisenergy techniquesYee's scheme.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 36 , Issue 1 , January 2002 , pp. 87 - 119
Copyright
© EDP Sciences, SMAI, 2002

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

S. Abarbanel and D. Gottlieb, A mathematical analysis of the PML method. J. Comput. Phys. 134 (1997) 357-363.
Abarbanel, S. and Gottlieb, D., On the construction and analysis of absorbing layers in CEM. Appl. Numer. Math. 27 (1998) 331-340. CrossRef
Bérenger, J.P., Perfectly Matched La, Ayer for the Absorption of Electromagnetic Waves. J. Comput. Phys. 114 (1994) 185-200. CrossRef
F. Collino and P. Monk, Conditions et couches absorbantes pour les équations de Maxwell, in G. Cohen and P. Joly, Aspects récents en méthodes numériques pour les équations de Maxwell, Eds. École des Ondes, Chapter 4, INRIA, Rocquencourt (1998).
J.W. Goodrich and T. Hagstrom, A comparison of two accurate boundary treatments for computational aeroacoustics. AIAA Paper-1585 (1997).
Hesthaven, J.S., On the Analysis and Construction of Perfectly Matched Layers for the Linearized Euler Equations. J. Comput. Phys. 142 (1998) 129-147. CrossRef
On, F.Q. Hu absorbing boundary conditions for linearized euler equations by a perfectly matched layer. J. Comput. Phys. 129 (1996) 201-219.
T. Kato, Perturbation Theory for Linear Operators. Springer (1995).
H.-O. Kreiss and J. Lorenz, Initial-Boundary Value Problems and the Navier-Stokes Equations, in Pure Appl. Math. 136, Academic Press, Boston, USA (1989).
J. Métral and O. Vacus, Caractère bien posé du problème de Cauchy pour le système de Bérenger. C.R. Acad. Sci. I Math. 10 (1999) 847-852.
Petropoulos, P.G., Zhao, L. and Cangellaris, A.C., A reflectionless sponge layer absorbing boundary condition for the solution of Maxwell's equations with high-order staggered finite difference schemes. J. Comput. Phys. 139 (1998) 184-208. CrossRef
A.N. Rahmouni, Des modèles PML bien posés pour divers problèmes hyperboliques. Ph.D. thesis, Université Paris Nord-Paris XIII (2000).
Allen Taflove, Computational electrodynamics: the finite-difference time-domain method. Artech House (1995).
Turkel, E. and Yefet, A., Absorbing PML boundary layers for wave-like equations. Appl. Numer. Math. 27 (1998) 533-557. CrossRef
L. Zhao and A.C. Cangellaris, A General Approach for the Development of Unsplit-Field Time-Domain Implementations of Perfectly Matched Layers for FDTD Grid Truncation. IEEE Microwave and Guided Letters 6 May 1996.
Ziolkowski, R.W., Time-derivative lorentz material model-based absorbing boundary condition. IEEE Trans. Antennas Propagation 45 (1997) 1530-1535. CrossRef