Performance Analysis of Direct N-Body Algorithms on Special-Purpose   Supercomputers
  Direct-summation N-body algorithms compute the gravitational interaction between stars in an exact way and have a computational complexity of O(N^2). Performance can be greatly enhanced via the use of special-purpose accelerator boards like the GRAPE-6A. However the memory of the GRAPE boards is limited. Here, we present a performance analysis of direct N-body codes on two parallel supercomputers that incorporate special-purpose boards, allowing as many as four million particles to be integrated. Both computers employ high-speed, Infiniband interconnects to minimize communication overhead, which can otherwise become significant due to the small number of "active" particles at each time step. We find that the computation time scales well with processor number; for 2*10^6 particles, efficiencies greater than 50% and speeds in excess of 2 TFlops are reached. 
Stefan Harfst, Alessia Gualandris, David Merritt, Rainer Spurzem,   Simon Portegies Zwart, Peter Berczik