Three-dimensional approximate local DtN boundary conditions for prolate spheroid boundaries

  • Authors:

  • H. Barucq;R. Djellouli;A. Saint-Guirons

  • Affiliations:

  • INRIA Bordeaux-Sud Ouest, Team-project Magique 3D, France and Laboratoire de Mathématiques Appliquées, CNRS UMR 5142, Université de Pau et des Pays de l'Adour, IPRA-Avenue de l'Univ ...;Department of Mathematics, California State University Northridge, CA 91330-8313, USA and INRIA Bordeaux-Sud Ouest, Team-project Magique 3D, France;Laboratoire de Mathématiques Appliquées, CNRS UMR 5142, Université de Pau et des Pays de l'Adour, IPRA-Avenue de l'Université, 64013 Pau, France and INRIA Bordeaux-Sud Ouest, T ...

  • Venue:
  • Journal of Computational and Applied Mathematics
  • Year:
  • 2010

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Abstract

We propose a new class of approximate local DtN boundary conditions to be applied on prolate spheroidal-shaped exterior boundaries when solving problems of acoustic scattering by elongated obstacles. These conditions are: (a) exact for the first modes, (b) easy to implement and to parallelize, (c) compatible with the local structure of the computational finite element scheme, and (d) applicable to exterior ellipsoidal-shaped boundaries that are more suitable in terms of cost-effectiveness for surrounding elongated scatterers. We investigate analytically and numerically the effect of the frequency regime and the slenderness of the boundary on the accuracy of these conditions. We also compare their performance to the second-order absorbing boundary condition (BGT2) designed by Bayliss, Gunzburger and Turkel when expressed in prolate spheroid coordinates. The analysis reveals that, in the low-frequency regime, the new second-order DtN condition (DtN2) retains a good level of accuracy regardless of the slenderness of the boundary. In addition, the DtN2 boundary condition outperforms the BGT2 condition. Such superiority is clearly noticeable for large eccentricity values.