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

Hélène Barucq 1, 2 Rabia Djellouli 2 Anne-Gaëlle Saint-Guirons 2, 1, *
* Corresponding author
2 Magique 3D - Advanced 3D Numerical Modeling in Geophysics
LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau], Inria Bordeaux - Sud-Ouest
Abstract : We propose a new class of approximate local DtN boundary conditions to be applied on prolate spheroid-shaped exterior boundaries when solving acoustic scattering problems 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 ac- curacy 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.
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Hélène Barucq, Rabia Djellouli, Anne-Gaëlle Saint-Guirons. Three-dimensional approximate local DtN boundary conditions for prolate spheroid boundaries. Journal of Computational and Applied Mathematics, Elsevier, 2009, ⟨10.1016/j.cam.2009.08.032⟩. ⟨inria-00338506⟩

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