On the Long-Time Behavior of Unsplit Perfectly Matched Layers

Bécache, Éliane; Petropoulos, Peter G.; Gedney, Stephen D.

doi:10.1109/tap.2004.827253

Cited by 132 publications

(86 citation statements)

References 16 publications

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“…A more pertinent concept is the one of stability, which imposes an estimate of the type CðtÞ 6 Ct k . In particular, this concept of stability does not exclude a linear growth as the one studied in [2,4] for MaxwellÕs equations. Furthermore, note that the notion of stability described here is linked to the continuous model and is distinct from the numerical stability related to a particular numerical scheme.…”

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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“…Instabilities of PML in long time simulations have been studied in electromagnetics (Abarbanel et al, 2002;Bécache et al, 2004). For elastodynamics, remedies have been proposed by Meza-Fajardo & Papageorgiou (2008) for an isotropic medium with standard PML.…”

Section: Absorbing Boundary Conditionmentioning

confidence: 99%

Seismic Waves - Research and Analysis

Kanao¹

2012

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“…Eq. (2.1) is supplemented with a Dirichlet boundary condition on the interior-domain boundary 2) and the Sommerfeld radiation condition at infinity…”

Section: Problem Statementmentioning

confidence: 99%

“…Refs. [1,18]), causality [6,28], long-time behavior [1,2], termination of the PML [9,26] and finite-element dispersion and convergence analysis in the frequency domain [5,17]. A recommendable review of the PML in the context of Maxwell's equations is presented in Ref.…”

Section: Introductionmentioning

confidence: 99%

Improving the Performance of Perfectly Matched Layers by Means of hp-Adaptivity

Michler¹,

Demkowicz²,

Kurtz³

et al. 2006

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We improve the performance of the Perfectly Matched Layer by using an automatic hp-adaptive discretization. By means of hp-adaptivity, we obtain a sequence of discrete solutions that converges exponentially to the continuum solution. Asymptotically, we thus recover the property of the PML of having a zero reflection coefficient for all angles of incidence and all frequencies on the continuum level. This allows us to minimize the reflections from the discrete PML to an arbitrary level of accuracy while retaining optimal computational efficiency. Since our hp-adaptive scheme is automatic, no interaction with the user is required. This renders tedious parameter tuning of the PML obsolete. We demonstrate the improvement of the PML performance by hp-adaptivity through numerical results for acoustic, elastodynamic and electromagnetic wave-propagation problems in the frequency domain and in different systems of coordinates.

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On the Long-Time Behavior of Unsplit Perfectly Matched Layers

Cited by 132 publications

References 16 publications

Stability of perfectly matched layers, group velocities and anisotropic waves

Stability of perfectly matched layers, group velocities and anisotropic waves

Seismic Waves - Research and Analysis

Improving the Performance of Perfectly Matched Layers by Means of hp-Adaptivity

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