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

Xavier Antoine (1, 2) , Bertrand Thierry (3)

1 CORIDA - Robust control of infinite dimensional systems and applications
2 IECL - Institut Élie Cartan de Lorraine
3 ACE - Applied and Computational Electromagnetics [Liège]

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 \cite{AntoineThierryPart1}. 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.

Mots clés: Helmholtz Equation; Spectral Analysis; Integral Equation; Acoustics

Domaines: Analyse numérique [math.NA]; Mathématiques générales [math.GM]

Xavier Antoine, Bertrand Thierry. 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, 2013, 239, pp.380-395. ⟨10.1016/j.cam.2012.09.005⟩. ⟨hal-00755676⟩