A new approach for controlling truncation error of the multipole expansion

The purpose of this paper is to clarify how to control the truncation error of the multipole expansion for FMM (fast multipole method) and MLFMA (multilevel fast multipole algorithm). The choice of truncation number still remains a complex issue. We perform the numerical experiment carefully and improve the control and prediction accuracy. The past selection rule is to use the excess bandwidth formula which becomes worse for small buffer sizes and high accuracy requirements. To improve this, a new approach is proposed.