A Fast Multipole Method for the Yukawa Potential

Jingfang Huang
Courant Institute of Mathematical Sciences
251 Mercer Street
New York, NY 10012
Email : huangjf@cims.nyu.edu

Abstract
We present a fast multipole method for the Yukawa (sreened Coulomb) potential. The multipole expansions use spherical Bessel functions in the radial direction combined with spherical harmonics. We derive a diagonal form for the multipole to local translation operator. Compared with direct summation, the work of evaluating all interactions in a system with N particles is reduced from O(N^2) to O(N). Numerical experiments show a break even point of N=1000 for six digit accuracy.