Parallelization of a treecode

I describe here the performance of a parallel treecode with individual particle timesteps. The code is based on the Barnes-Hut algorithm and runs cosmological N-body simulations on parallel machines with a distributed memory architecture using the MPI message-passing library. For a configuration with a constant number of particles per processor the scalability of the code was tested up to P=128 processors on an IBM SP4 machine. In the large $P$ limit the average CPU time per processor necessary for solving the gravitational interactions is $\sim 10$ higher than that expected from the ideal scaling relation. The processor domains are determined every large timestep according to a recursive orthogonal bisection, using a weighting scheme which takes into account the total particle computational load within the timestep. The results of the numerical tests show that the load balancing efficiency $L$ of the code is high ($>=90$) up to P=32, and decreases to $L\sim 80$ when P=128. In the latter case it is found that some aspects of the code performance are affected by machine hardware, while the proposed weighting scheme can achieve a load balance as high as $L\sim 90$ even in the large $P$ limit.