Spectral and condition number estimates of the acoustic single-layer operator for low-frequency multiple scattering in dense media

Authors:
Bertrand Thierry;Xavier Antoine
Affiliations:
Institut Montéfiore, Université de Liège, ACE Team, Sart-Tilman Bldg. B28, B-4000 Liège, Belgique;Institut Elie Cartan Nancy, Université de Lorraine, CNRS UMR 7502, INRIA CORIDA Team, Boulevard des Aiguillettes B.P. 239, F-54506 Vandoeuvre-lès-Nancy, France
Venue:
Journal of Computational and Applied Mathematics
Year:
2013

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Spectral and condition number estimates of the acoustic single-layer operator for low-frequency multiple scattering in dense media

Journal of Computational and Applied Mathematics

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Abstract

The aim of this paper is to derive spectral and condition number estimates of the single-layer operator for low-frequency multiple scattering problems. This work extends to dense media the analysis initiated in Antoine and Thierry (in press) [19]. Estimates are obtained first in the case of circular cylinders by Fourier analysis and are next formally adapted to disks, ellipses and rectangles in the framework of boundary element methods. Numerical simulations validating the approach are also given.