## N-body Simulation I: Fast Algorithms for Potential Field Evaluation and Trummer's Problem (1996)

Citations: | 7 - 5 self |

### BibTeX

@TECHREPORT{Reif96n-bodysimulation,

author = {John H. Reif and Stephen R. Tate},

title = {N-body Simulation I: Fast Algorithms for Potential Field Evaluation and Trummer's Problem},

institution = {},

year = {1996}

}

### OpenURL

### Abstract

In this paper, we describe a new approximation algorithm for the n-body problem. The algorithm is a non-trivial modification of the fast multipole method that works in both two and three dimensions. Due to the equivalence between the two-dimensional n-body problem and Trummer's problem, our algorithm also gives the fastest known approximation algorithm for Trummer's problem. Let A be the sum of the absolute values of the particle charges in the n-body problem under consideration (or the sum of the masses if the simulation is gravitational). To approximate the particle potentials with error bound ffl, we let p = dlog(A=ffl)e and give complexity bounds in terms of p. Note that, under reasonable assumptions on the particle charges, if we desire the output to be accurate to b bits, then p = \Theta(b). In two dimensions, our algorithm runs in time O(n log 2 p), which is a substantial improvement over the previous best algorithm which requires \Theta(np log p) time. We also apply our new ...