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 usi ng classical schemes, the evaluation of the velocity potential on the surfa ce of a three-dimensional scatterer, represented in terms of N-s spatial ba sis functions for N-t time steps, requires O(NtNs2) operations. The recentl y developed plane wave time domain (PWTD) algorithm permits the rapid evalu ation of transient fields that are generated by bandlimited source distribu tions. It has been shown that incorporation of the PWTD algorithm into inte gral equation-based solvers in a two-level setting reduces the computationa l complexity of a transient analysis to O(NtNs1.5 log N-s). In this paper, it is shown that casting the PWTD scheme into a multilevel framework permit s the analysis of transient acoustic surface scattering phenomena in O(NtNs log(2) N-s) operations using O(NtNs) memory. Numerical examples that demon strate the efficacy of the multilevel implementation are also presented. (C ) 2000 Acoustical Society of America. [S0001-4966(00)04802-5].