On the numerical approximation of high-frequency acoustic multiple scattering problems by circular cylinders

Xavier Antoine (1) , Chokri Chniti (1) , Karim Ramdani (1)

1 CORIDA - Robust control of infinite dimensional systems and applications

The aim of this paper is to propose a numerical strategy for computing the solution of two-dimensional time-harmonic scattering problems at high-frequency. The scatterers are assumed to be circular leading therefore to semi-analytical representation formulae of the scattered field through the solution of a large linear system of equations. An adapted numerical solution is proposed, taking care of the special block Toeplitz structure of the matrix involved in the formulation. This yields large memory savings. Moreover, a specific preconditioned iterative and fast algorithm is given and analyzed for computing the field scattered by general configurations. Several numerical experiments are presented to show the efficiency of the numerical method.

Mots clés: Multiple scattering; High frequency; Acoustic; Iterative solver; Fast algorithm

Domaines: Equations aux dérivées partielles [math.AP]

Xavier Antoine, Chokri Chniti, Karim Ramdani. On the numerical approximation of high-frequency acoustic multiple scattering problems by circular cylinders. Journal of Computational Physics, 2008, 227 (3), pp.1754-1771. ⟨10.1016/j.jcp.2007.09.030⟩. ⟨hal-00260393⟩