A perturbative approach to acoustic scattering from a vibrating bounded obstacle

In this paper we study a mathematical model to describe a three dimensional acoustic scattering problem associated to a "vibrating" obstacle that is a bounded simply connected domain contained in the three dimensional real Euclidean space whose shape changes in time. In particular we propose a numerical method based on a perturbation series and the operator expansion method to solve the mathematical model considered. This method makes possible to obtain highly parallelizable algorithms able to compute the solution of the problem considered order by order in perturbation theory, and able to obtain the required solution of the scattering problem summing up the perturbation series. Really impressive speed up factors are observed and reported when the algorithm is executed on the Chiba Cluster, a parallel machine of the Argonne National Laboratory, USA. We validate the mathematical model and the numerical method proposed solving some test problems. The quantitative character of the numerical results obtained is established. The results obtained on the test problems are discussed both from the numerical and the physical point of view. In particular we show that the Doppler spectrum associated to the far field patterns of the scattered acoustic fields depends mainly from the incoming wave and from the excited vibrational modes (Figs. 9–13). The website: http://www.econ.unian.it/recchioni/w7 shows some Applets relative to the numerical examples.