On Absorbing Boundary Conditions for Linearized Euler Equations by a Perfectly Matched Layer

Hu, Fang Q.

doi:10.1006/jcph.1996.0244

Cited by 324 publications

(244 citation statements)

References 14 publications

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“…In particular, the instabilities observed for the linearized Euler equations or for the elasticity equations (see [5][6][7]) are related to an exponential behavior in time, and this is the object of a forthcoming paper.…”

Section: Definitionmentioning

confidence: 99%

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

Bécache¹,

Joly²

2002

ESAIM: M2AN

101

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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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Section: Definitionmentioning

confidence: 99%

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

Bécache¹,

Joly²

2002

ESAIM: M2AN

101

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“…[11,12,28,37,39]). The method has been extended to various propagation models (the paraxial wave equations [15], the linearized Euler equations [22,24,32], etc. ), including in particular elastic wave propagation in isotropic [21] and anisotropic media [17].…”

Section: Introductionmentioning

confidence: 99%

Stability of perfectly matched layers, group velocities and anisotropic waves

Bécache

Fauqueux

Joly

2003

Journal of Computational Physics

308

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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“…The third type of condition is the perfectly matched layer (PML) boundary condition. The method was proposed by Hu [86,87] where spacial PML equations are solved in a buffer zone to minimize the reflections at outflow.…”

Section: Acoustic Farfield Conditionsmentioning

confidence: 99%

“…The PML method proposed by Hu [86,87] was originally formulated for electromagnetic problems [91]. The idea of PML approach is to divide the computational domain into two parts, the interior part and a PML (buffer layer) area around the computational edges.…”

Section: Absorbing Boundary Conditions Using Pmlmentioning

confidence: 99%