An Improved Series Expansion Method to Accelerate the Multi-Frequency Acoustic Radiation Prediction

Abstract

Multi-frequency calculation is usually very time-consuming due to the repeated numerical integration for numerous frequencies in acoustic scattering or radiation problems. A series expansion method has been proposed to speed up this process just by taking the frequency-dependent terms out of the integral sign. However, this method, constrained by the number of truncation terms, is only applicable to low and medium frequencies and/or small-size structures. This paper develops an improved series expansion method that can be employed in a wider frequency band and larger-scale problems but with less computing expense. In the present method, the frequency-dependent term kr in the integral kernel is firstly transformed into the range from −π to π due to the periodicity of sine and cosine functions. Afterwards, truncation error would be kept reasonably small while the number of expansion terms would not increase with kr. Test cases of acoustic radiation from a pulsating sphere and a cat's eye structure are conducted and numerical results show significant reduction of computational time but suffering little accuracy loss for multi-frequency problems with this approach.

The Boundary Element Method in Acoustics: A Survey

“…For example, for air-acoustics, the audible range for human being is up to 20 kHz and typically his could be resolved into components with a 10Hz resolution; multiplying the computational cost, considered in the previous Sub-subsection, by around 2000. The prospect of solving acoustic problems over the full frequency range has led to another set of techniques focus on reducing the computational burden by solving a range of frequencies together and these are usually termed multi-frequency methods [297,[348][349][350][351][352][353][354][355]. However, with the nature of an acoustic field, originating typically from structural vibration, is such that structural and acoustic resonances, and the driving profile, dominate the total acoustic response.…”

Krylov subspaces recycling based model order reduction for acoustic BEM systems and an error estimator

“…, 1150, 1200]. Subsequently, the collection of Krylov subspaces is or-thogonalized and truncated as in (22).…”

“…In detail, discrete form interpolation strategies have come to the fore and are related to the Green's function frequency and space interpolation [17,18,19]. Alongside, Taylor expansion of the Green's function has been exploited already since the early '80 [16,20,21], and has been further extended to account for the periodicity of the Green's function [22] and the indirect BEM formulation [23].…”

A greedy reduced basis scheme for multifrequency solution of structural acoustic systems

“…During the last decades, many researchers have made effort to accelerate the frequency sweep of acoustic as well as structural acoustic problems. Moreover, efficient procedures for the assembly of boundary element matrices in a frequency range have been developed . Approximating the acoustic response itself can also be efficient in cases where only a small partition of the solution is of interest .…”

“…Moreover, efficient procedures for the assembly of boundary element matrices in a frequency range have been developed. [19][20][21][22] Approximating the acoustic response itself can also be efficient in cases where only a small partition of the solution is of interest. 23,24 Furthermore, the high numerical complexity associated to fully populated boundary element matrices led to the development of several fast algorithms 25,26 that have also been combined with multifrequency strategies.…”