A novel acceleration method for the variational boundary element approach based on multipole expansion

The acoustic radiation of general structures with Neumannʹs boundary condition using Variational Boundary Element Method (VBEM) is considered. The classical numerical implementation of the VBEM su ers from the computation cost associated with double surface integration. To alleviate this limitation, a novel accel- eration method is proposed. The method is based on the expansion of the cross in uence matrices in terms of multipoles using the expansion of the Greenʹs function in terms of spherical Bessel functions. Since the resulting multipoles are not dependent on the elements locations, large computation time savings are achieved. Moreover, it is shown that by accounting for the monopole, dipole and quadrupole terms in the multipole expansion, the classical convergence criteria usually used in boundary element guarantee convergence of the proposed method. Several numerical examples are presented to demonstrate the e ciency and accuracy of the proposed method.