A Fast Algorithm for Particle Simulations

We restrict our attention in this paper to the case where the potential (or force) at a point is a sum of pairwise An algorithm is presented for the rapid evaluation of the potential and force fields in systems involving large numbers of particles interactions. More specifically, we consider potentials of whose interactions are Coulombic or gravitational in nature. For a the form system of N particles, an amount of work of the order O(N 2) has traditionally been required to evaluate all pairwise interactions, unF 5 Ffar 1 (Fnear 1 Fexternal), less some approximation or truncation method is used. The algorithm of the present paper requires an amount of work proportional to N to evaluate all interactions to within roundoff error, making it where Fnear (when present) is a rapidly decaying potential considerably more practical for large-scale problems encountered in (e.g., Van der Waals), Fexternal (when present) is indepenplasma physics, fluid dynamics, molecular dynamics, and celestial dent of the number of particles, and Ffar , the far-field mechanics. Q 1987 Academic Press potential, is Coulombic or gravitational. Such models describe classical celestial mechanics and many problems in plasma physics and molecular dynamics. In the vortex