Fast transient analysis of acoustic wave scattering from rigid bodies using a two-level plane wave time domain algorithm

Abstract

It is well known that the computational cost associated with the application of classical time domain integral equation methods to the analysis of scattering from acoustical targets scales unfavorably with problem size. Indeed, performing a three-dimensional scattering analysis using these methods requires O(NtNs2) operations, where Ns denotes the number of basis functions that model the spatial field distribution over the surface of the scatterer and Nt is the number of time steps in the analysis. Recently, novel plane wave time domain algorithms that augment these classical methods and thereby reduce their high computational cost have been introduced. This paper describes such a plane wave time domain algorithm within the context of the analysis of acoustic scattering from rigid bodies and outlines its incorporation into a time domain integral equation solver in a two-level setting. It is shown that the resulting scheme has a computational complexity of O(NtNs1.5 log Ns). Examples comparing the accuracy and computational efficiency of the conventional and accelerated methods are presented. The proposed two-level scheme renders feasible the broadband analysis of scattering from large and complex bodies.