A time-domain boundary element method using a kernel-function library for 3D acoustic problems

Abstract

Time-domain boundary element method (TDBEM) can be applied in studying transient acoustic wave problems, especially in solving exterior problems. However, in order to avoid calculations of coefficients at different time steps, TDBEM usually requires storing or recomputing the coefficients at each time step. This can lead to significant amount of memory usage or long computing time. In this paper, an acoustic TDBEM based on a kernel-function library (KFL-BEM) is proposed, in order to reduce the memory consumption of the time-domain conventional BEM (CBEM) and speedup the computation. In this approach, the storage requirement is reduced from O(N2Ntmin) to O(N2), where N represents the number of degrees of freedom of the model, and Ntmin is the minimum number of time steps for which coefficients need to be computed and stored. To demonstrate the effectiveness of the KFL-BEM, two verification examples are presented using the problems of a pulsating sphere and sound propagating in a channel. Compared with the CBEM, the KFL-BEM can save significantly the memory storage as it does not require storing coefficients for any previous time steps. This method can also be applied to solve vibro-acoustic problems in the time domain. As an example, the acoustic radiation responses of a tuning fork under different striking loads are studied using the finite element method and the proposed KFL-BEM, which clearly shows the potentials of the KFL-BEM in solving time-domain acoustic problems.