Explicit error bound of the fast multipole method for scattering problems in 2-D

This paper is concerned with the error estimation of fast multipole method (FMM) for scattering problems in 2-D. The FMM caused by truncating Graf’s addition theorem each step algorithm, including two expansions and three translations. We first give a novel bound on truncation limiting forms Bessel Neumann functions, then estimate FMM. Explicit its convergence order are derived. proposed this can also be used to other problems, such as potential elastostatic Stokes flow so on.