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(N t N s 2 ) operations, where N s denotes the number of basis functions that model the spatial field distribution over the surface of the scatterer and N t 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(N t N s 1.5 log N s ). 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.

A time-space decomposition method for calculating the nearfield pressure generated by a pulsed circular piston

“…The simulation packages Field II [12] and DREAM [13], which evaluate sampled versions of the impulse response, also compute transient pressures within Matlab. All simulations are evaluated in a medium with sound speed c = 1.5 mm/μs using the broadband pulse defined in (15).…”

“…The result is a sum of products of polynomial, exponential, sine, and cosine terms that define f n (τ) and g n (t) with N = 8 for (15). In the following simulations, the center frequency is f 0 = 2.5 MHz, the temporal duration of the pulse is W = 1.2 μs, and the damping factor is β = 9.3750 μs −1 .…”

“…Therefore, the memory requirement scales as N N Gauss (N Gauss + 1)/2, or 4N Gauss (N Gauss + 1) for the broadband pulse defined by (15). To achieve a maximum error of 1%, N Gauss = 9, so 360 memory locations are required.…”

“…The time-space decomposition method also is applicable in conjunction with first-order scattering models or other solvers that use fast integral methods [15] or k-space methods [16]. This combination of fast and accurate tools for finding incident and scattered fields can aid in the design and evaluation of transducer array geometries.…”

A Transient Boundary Element Method for Acoustic Scattering from Mixed Regular and Thin Rigid Bodies

“…Acceleration algorithms 5,6,7 have been published to address this issue but, as these are derived from the time-marching solvers for which instability issues remain, the focus herein remains on modelling smaller problems in a non-accelerated fashion. In addition some interesting work has been done on alternative solvers 8,9,10,11 that may be less sensitive to divergent poles than the current time-marching generation.…”