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Spectral and Condition Number Estimates of the Acoustic Single-Layer Operator for Low-Frequency Multiple Scattering.
 

Summary: Spectral and Condition Number Estimates of the Acoustic
Single-Layer Operator for Low-Frequency Multiple Scattering.
Part II: Dense Media
Xavier Antoine
Bertrand Thierry
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 the analysis
initiated in [6] to dense media. 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.
Contents
1 Introduction 2
2 The single-layer operator for multiple scattering 2
2.1 Single-layer potential for multiple scattering . . . . . . . . . . . . . . . . . . . . . . . 2
2.2 Expression of the single-layer potential for M circular cylinders . . . . . . . . . . . . 3
3 Low frequency condition number estimates of the single-layer potential for close
obstacles: the case of circular cylinders 4
3.1 The limit matrix approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
3.2 Estimates of the eigenvalue with smallest modulus . . . . . . . . . . . . . . . . . . . 11

  

Source: Antoine, Xavier - Institut de Mathématiques Élie Cartan, Université Henri Poincaré - Nancy 1

 

Collections: Mathematics