 
Summary: On the numerical approximation of highfrequency acoustic
multiple scattering problems by circular cylinders
Xavier Antoine
, Chokri Chniti
, Karim Ramdani
Abstract. The aim of this paper is to propose a numerical strategy for computing the solution
of twodimensional timeharmonic acoustic multiple scattering problems at highfrequency. The
scatterers are assumed to be circular, leading therefore to semianalytical representation formulae
of the scattered field through the solution of a large linear system of equations. Taking advantage
of the special block Toeplitz structure of the matrix of the linear system, a fast iterative and
preconditioned numerical method yielding large memory savings is proposed. Several numerical
experiments for general configurations are presented to show the efficiency of the numerical method.
1 Introduction
Multiple scattering problems find their origins in many applications related to different areas of
applied sciences: acoustics, electromagnetism, elasticity and water waves. For such problems,
the scattered field appears as the superposition of elementary scattered fields resulting from the
interaction between the incident wave and the scatterers on one hand, and between the scatterers
on the other hand. A better understanding of such problems requires a precise knowledge of the
influence of the different physical and geometrical parameters of the problem on these interactions.
Due to the complexity of this problem, computing a numerical solution requires a special care,
