ABSTRACT
We present a fast algorithm, called the fast Fourier transform on multipoles (FFTM) method, for accelerating the boundary element method. The algorithm employs the multipole and local expansions to approximate far-field potentials and exploits the discrete convolution nature of the multipole to local translation operator to accelerate the potential evaluation process. The method is illustrated with a three-dimensional acoustics scattering problem governed by the Helmholtz equation. It is shown that the method has approximately linear computational complexity and it achieves accurate results with a relatively low order of expansion.