How to avoid computing the neareld in the Fast Multipole Method

Abstract. This paper introduces a fast method for the application of sur-face integral operators which typically arise in potential theory, elasticity, and scattering. The principal idea is to decompose the Green's function into a smooth and a local part. The local part is expanded in a series in the mol-li cation parameter; evaluating the truncated series amounts to multiplying with a diagonal matrix. A modication of Fast Multipole Method is used to compute the potential of smooth kernels. The outline of the algorithms and some preliminary numerical results are presented