Performance assessment of a new class of local absorbing boundary conditions for elliptical- and prolate spheroidal-shaped boundaries

Authors:
H. Barucq;R. Djellouli;A. Saint-Guirons
Affiliations:
INRIA, Bordeaux Sud-Ouest Research Center, Team-Project Magique 3D, France and Laboratoire de Mathématiques Appliquées, CNRS UMR 5142, Université de Pau et des Pays de l'Adour, IPRA ...;INRIA, Bordeaux Sud-Ouest Research Center, Team-Project Magique 3D, France and Department of Mathematics, California State University Northridge, CA 91330-8313, USA;INRIA, Bordeaux Sud-Ouest Research Center, Team-Project Magique 3D, France and Laboratoire de Mathématiques Appliquées, CNRS UMR 5142, Université de Pau et des Pays de l'Adour, IPRA ...
Venue:
Applied Numerical Mathematics
Year:
2009

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Abstract

New approximate local DtN boundary conditions are proposed to be applied on elliptical- or prolate-spheroid exterior boundaries when solving respectively two- or three-dimensional acoustic scattering problems by elongated obstacles. These new absorbing conditions are designed to be exact for the first modes. They can be easily incorporated in any finite element parallel code while preserving the local structure of the algebraic system. Unlike the standard approximate local DtN boundary conditions that are restricted to circular- or spherical-shaped boundaries, the proposed conditions are applicable to exterior elliptical-shaped boundaries that are more suitable for surrounding elongated scatterers because they yield to smaller computational domains. The mathematical and numerical analysis of the effect of the frequency and the eccentricity values of the boundary on the accuracy of these conditions, when applied for solving radiating and scattering problems, reveals - in particular - that the new second-order DtN boundary condition retains a good level of accuracy, in the low frequency regime, regardless of the slenderness of the boundary.