A new formalism for time-dependent wave scattering from a bounded obstacle

Abstract

A time-dependent three-dimensional acoustic scattering problem is considered. An incoming wave packet is scattered by a bounded, simply connected obstacle with locally Lipschitz boundary. The obstacle is assumed to have a constant boundary acoustic impedance. The limit cases of acoustically soft and acoustically hard obstacles are considered. The scattered acoustic field is the solution of an exterior problem for the wave equation. A new numerical method to compute the scattered acoustic field is proposed. This numerical method obtains the time-dependent scattered field as a superposition of time-harmonic acoustic waves and computes the time-harmonic acoustic waves by a new "operator expansion method." That is, the time-harmonic acoustic waves are solutions of an exterior boundary value problem for the Helmholtz equation. The method used to compute the time-harmonic waves improves on the method proposed by Misici, Pacelli, and Zirilli [J. Acoust. Soc. Am. 103, 106-113 (1998)] and is based on a "perturbative series" of the type of the one proposed in the operator expansion method by Milder [J. Acoust. Soc. Am. 89, 529-541 (1991)]. Computationally, the method is highly parallelizable with respect to time and space variables. Some numerical experiments on test problems obtained with a parallel implementation of the numerical method proposed are shown and discussed from the numerical and the physical point of view. The website: http://www.econ.unian.it/recchioni/w1 shows four animations relative to the numerical experiments.