CMSC828G – Final Project

where G is the gravitational constant, rnk = xk − xn, and rnk = |rkn|. Since this expression is evaluated for each body separately, and the expression contains a sum over every other body, a direct computation of the forces would require O (N). For large problems, such as those containing more than a few thousand bodies, this can be prohibitive. Therefore, a faster algorithm is needed. The Barnes-Hut algorithm is one such algorithm [X]. The multi-level Barnes-Hut algorithm is an O (N log (N)) algorithm. However, to keep things simple, I implemented a single-level version, which runs in O ( N ) .