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Stability of perfectly matched layers, group velocities and anisotropic waves.

Eliane Bécache 1 Sandrine Fauqueux 1 Patrick Joly 1 
1 POEMS - Propagation des Ondes : Étude Mathématique et Simulation
Inria Saclay - Ile de France, UMA - Unité de Mathématiques Appliquées, CNRS - Centre National de la Recherche Scientifique : UMR7231
Abstract : 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 Maxwell's 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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Submitted on : Friday, May 9, 2014 - 4:06:31 PM
Last modification on : Wednesday, May 11, 2022 - 12:06:04 PM

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Eliane Bécache, Sandrine Fauqueux, Patrick Joly. Stability of perfectly matched layers, group velocities and anisotropic waves.. Journal of Computational Physics, 2003, 188 (2), pp.399-433. ⟨10.1016/S0021-9991(03)00184-0⟩. ⟨hal-00989051⟩



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