On the analysis of Bérenger’s perfectly matched layers for Maxwell’s equations

Eliane Bécache; Patrick Joly

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2002)

  • Volume: 36, Issue: 1, page 87-119
  • ISSN: 0764-583X

Abstract

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In this work, we investigate the Perfectly Matched 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 modal analysis with standard Fourier techniques, then via energy techniques. We obtain uniform in time stability results (that make precise some results known in the literature) and state some energy decay results that illustrate the absorbing properties of the model. This last technique allows us to prove the stability of the Yee’s scheme for discretizing PML’s.

How to cite

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Bécache, Eliane, and Joly, Patrick. "On the analysis of Bérenger’s perfectly matched layers for Maxwell’s equations." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 36.1 (2002): 87-119. <http://eudml.org/doc/245233>.

@article{Bécache2002,
abstract = {In this work, we investigate the Perfectly Matched 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 modal analysis with standard Fourier techniques, then via energy techniques. We obtain uniform in time stability results (that make precise some results known in the literature) and state some energy decay results that illustrate the absorbing properties of the model. This last technique allows us to prove the stability of the Yee’s scheme for discretizing PML’s.},
author = {Bécache, Eliane, Joly, Patrick},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {absorbing layers; PML; Maxwell’s equations; stability; hyperbolic systems; Fourier analysis; energy techniques; Yee’s scheme; Maxwell's equations; Yee's scheme},
language = {eng},
number = {1},
pages = {87-119},
publisher = {EDP-Sciences},
title = {On the analysis of Bérenger’s perfectly matched layers for Maxwell’s equations},
url = {http://eudml.org/doc/245233},
volume = {36},
year = {2002},
}

TY - JOUR
AU - Bécache, Eliane
AU - Joly, Patrick
TI - On the analysis of Bérenger’s perfectly matched layers for Maxwell’s equations
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 2002
PB - EDP-Sciences
VL - 36
IS - 1
SP - 87
EP - 119
AB - In this work, we investigate the Perfectly Matched 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 modal analysis with standard Fourier techniques, then via energy techniques. We obtain uniform in time stability results (that make precise some results known in the literature) and state some energy decay results that illustrate the absorbing properties of the model. This last technique allows us to prove the stability of the Yee’s scheme for discretizing PML’s.
LA - eng
KW - absorbing layers; PML; Maxwell’s equations; stability; hyperbolic systems; Fourier analysis; energy techniques; Yee’s scheme; Maxwell's equations; Yee's scheme
UR - http://eudml.org/doc/245233
ER -

References

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  2. [2] S. Abarbanel and D. Gottlieb, On the construction and analysis of absorbing layers in CEM. Appl. Numer. Math. 27 (1998) 331–340. Zbl0924.35160
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  10. [10] 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. Zbl0928.35176
  11. [11] P.G. Petropoulos, L. Zhao and A.C. Cangellaris, 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. Zbl0915.65123
  12. [12] A.N. Rahmouni, Des modèles PML bien posés pour divers problèmes hyperboliques. Ph.D. thesis, Université Paris Nord-Paris XIII (2000). 
  13. [13] Allen Taflove, Computational electrodynamics: the finite-difference time-domain method. Artech House (1995). Zbl0840.65126MR1338377
  14. [14] E. Turkel and A. Yefet, Absorbing PML boundary layers for wave-like equations. Appl. Numer. Math. 27 (1998) 533–557. Zbl0933.35188
  15. [15] 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. 
  16. [16] R.W. Ziolkowski, Time-derivative lorentz material model-based absorbing boundary condition. IEEE Trans. Antennas Propagation 45 (1997) 1530–1535. 

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