A general approach for the development of unsplit-field time-domain implementations of perfectly matched layers for FDTD grid truncation

Zhao, Lanhao; Cangellaris, A.C.

doi:10.1109/75.491508

Cited by 70 publications

(52 citation statements)

References 7 publications

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“…This type of mathematical questions has already been widely investigated by several authors [6,27,29,30,38] in the case of MaxwellÕs equations. For elastodynamics equations, it is easy to show that the PML model is well-posed (cf.…”

Section: Introductionmentioning

confidence: 99%

Stability of perfectly matched layers, group velocities and anisotropic waves

Bécache

Fauqueux

Joly

2003

Journal of Computational Physics

306

355

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Perfectly matched layers (PML) are a recent technique for simulating the absorption of waves in open domains. They have been introduced for electromagnetic waves and extended, since then, to other models of wave propagation, including waves in elastic anisotropic media. In this last case, some numerical experiments have shown that the PMLs are not always stable. In this paper, we investigate this question from a theoretical point of view. In the first part, we derive a necessary condition for the stability of the PML model for a general hyperbolic system. This condition can be interpreted in terms of geometrical properties of the slowness diagrams and used for explaining instabilities observed with elastic waves but also with other propagation models (anisotropic MaxwellÕs equations, linearized Euler equations). In the second part, we specialize our analysis to orthotropic elastic waves and obtain separately a necessary stability condition and a sufficient stability condition that can be expressed in terms of inequalities on the elasticity coefficients of the model.

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Section: Introductionmentioning

confidence: 99%

Stability of perfectly matched layers, group velocities and anisotropic waves

Bécache

Fauqueux

Joly

2003

Journal of Computational Physics

306

355

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“…More precisely, we show the decay in time of some quadratic energy in the electromagnetic field. For this we exploit the formulation proposed in [15]. This is probably the more original contribution of this paper.…”

Section: Definitionmentioning

confidence: 99%

“…The idea of Zhao and Cangellaris [15] is to restore the usual operator by introducing a new unknown. Let us present how to go from the formulation of Bérenger to the one of Zhao and Cangellaris.…”

Section: Zhao-cangellaris's Formulation In a Layer Parallel To The Y mentioning

confidence: 99%

See 1 more Smart Citation

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

Bécache¹,

Joly²

2002

ESAIM: M2AN

100

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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.Résumé. Dans ce travail, nous considérons le modèle de couches parfaitement adaptées, dit PML (Perfectly Matched Layers), introduit par Bérenger [3] pour la modélisation de frontières absorbantes enélectromagnétisme. Nous menons une analyse mathématique de ce modèle, d'une part par une analyse modale par transformation de Fourier, d'autre part par des techniquesénergétiques. Nous obtenons ainsi des résultats de stabilité uniforme en temps (qui précisent des résultats déjà connus dans la littérature) etétablissons des résultats de décroissance d'énergie qui illustrent les propriétés d'absorption du modèle. Cette dernière technique permet aussi de démontrer la stabilité du schéma de Yee pour discrétiser les couches absorbantes. Mathematics Subject Classification.

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“…Moreover, Sack et al imposed a physical model with perfectly matched medium on an anisotropic parameters without splitting the fields [6]. These two formulations are also mathematically identical, and the fact was proved by Zhao and Cangellaris, provided that the electric and magnetic fields presented in the Chew-Weedon stretched-coordinate formulation are properly defined [9]. Bramble and Pasciak have shown the existence and uniqueness of solutions to the truncated time harmonic PML problem provided that the truncated domain is sufficiently large [10].…”

Section: Introductionmentioning

confidence: 88%

Stability Analysis of Yee Schemes to PML and UPML for Maxwell Equations

Ying¹

2009

JCM

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We utilize Fourier methods to analyze the stability of the Yee difference schemes for Bérenger PML (perfectly matched layer) as well as the UPML (uniaxial perfectly matched layer) systems of two-dimensional Maxwell equations. Using a practical spectrum stability concept, we find that the two schemes are spectrum stable under the same conditions for mesh sizes. Besides, we prove that the UPML schemes with the same damping in both directions are stable. Numerical examples are given to confirm the stability analysis for the PML method.Mathematics subject classification: 65M12.

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A general approach for the development of unsplit-field time-domain implementations of perfectly matched layers for FDTD grid truncation

Cited by 70 publications

References 7 publications

Stability of perfectly matched layers, group velocities and anisotropic waves

Stability of perfectly matched layers, group velocities and anisotropic waves

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

Stability Analysis of Yee Schemes to PML and UPML for Maxwell Equations

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