Three-dimensional approximate local DtN boundary conditions for prolate spheroid boundariesReport as inadecuate




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* Corresponding author 1 LMAP - Laboratoire de Mathématiques appliquées de Pau 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.

Keywords : Absorbing boundary conditions prolate spheroidal coordinates Dirichlet-to-Neumann operator scattering problems





Author: Hélène Barucq - Rabia Djellouli - Anne-Gaëlle Saint-Guirons -

Source: https://hal.archives-ouvertes.fr/



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