  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.
