The dual boundary face method with FMM (CHFMM) is employed in this paper to deal with the drawback of the CFMM at the frequencies which are associated with the interior problem. Thus, we will further study the performance of the proposed adaptive expansion technique for the hyper-singular boundary face method with FMM (HFMM) and CHFMM here. The results are summarized in Tables 2 and 3. It can be seen from the two tables that the adaptive algorithm has achieved equivalent accuracy but higher efficiency then the standard algorithm using the HFMM and the CHFMM, respectively, although the adaptive the adaptive expansion technique is obtained by CFMM.