Stability of perfectly matched layers, group velocities and anisotropic waves

  • Authors:

  • E. Bécache;S. Fauqueux;P. Joly

  • Affiliations:

  • INRIA, Domaine de Voluceau-Rocquencourt, BP 105, F-78153 Le Chesnay Cédex, France;INRIA, Domaine de Voluceau-Rocquencourt, BP 105, F-78153 Le Chesnay Cédex, France and IFP, 1 avenue Bois Préau, 92500 Reuil Malmaison, France;INRIA, Domaine de Voluceau-Rocquencourt, BP 105, F-78153 Le Chesnay Cédex, France

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2003

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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.