See this comment and some associated discussion: Notebook on particle simulations - #3 by ChrisRackauckas
A curiosity: in a typical simulation with periodic boundary conditions, how big (system size) and how many particles (10^6?) are we talking about?
Can these calculations be performed with a cutoff (great enough such that the gravitational potential is small yet much smaller than the system size?). How many time-steps/second is a good benchmark? (I’m curious how would the trees compare with cell lists with a sufficiently large cutoff if that is possible).