Fast analysis of transient acoustic wave scattering from rigid bodies using the multilevel plane wave time domain algorithm

The analysis of transient wave scattering from rigid bodies using integral equation-based techniques is computationally intensive: if carried out using classical schemes, the evaluation of the velocity potential on the surface of a three-dimensional scatterer, represented in terms of Ns spatial basis functions for Nt time steps, requires O(NtNs2) operations. The recently developed plane wave time domain (PWTD) algorithm permits the rapid evaluation of transient fields that are generated by bandlimited source distributions. It has been shown that incorporation of the PWTD algorithm into integral equation-based solvers in a two-level setting reduces the computational complexity of a transient analysis to O(NtNs1.5 logNs). In this paper, it is shown that casting the PWTD scheme into a multilevel framework permits the analysis of transient acoustic surface scattering phenomena in O(NtNslog2Ns) operations using O(NtNs) memory. Numerical examples that demonstrate the efficacy of the multilevel implementation are also presented.