On the Solution Method for the Non-uniqueness Problem in Using the Time-domain Acoustic Boundary Element Method

The time-domain solution from the Kirchhoff integral equation for an exterior problem is not unique at certain eigen-frequencies associated with the fictitious internal modes as happening in frequency-domain analysis. One of the solution methods is the CHIEF (Combined Helmholtz Integral Equation Formulation) approach, which is based on employing additional zero-pressure constraints at some interior points inside the body. Although this method has been widely used in frequency-domain boundary element method due to its simplicity, it was not used in time-domain analysis. In this work, the CHIEF approach is formulated appropriately for time-domain acoustic boundary element method by constraining the unknown surface pressure distribution at the current time, which was obtained by setting the pressure at the interior point to be zero considering the shortest retarded time between boundary nodes and interior point. Sound radiation of a pulsating sphere was used as a test example. By applying the CHIEF method, the low-order fictitious modes could be damped down satisfactorily, thus solving the non-uniqueness problem. However, it was observed that the instability due to high-order fictitious modes, which were beyond the effective frequency, was increased.