High performance direct gravitational N-body simulations on graphics processing units II: An implementation in CUDA

We present the results of gravitational direct N-body simulations using the graphics processing unit (GPU) on a commercial NVIDIA GeForce 8800GTX designed for gaming computers. The force evaluation of the N-body problem is implemented in "Compute Unified Device Architecture" (CUDA) using the GPU to speedup the calculations. We tested the implementation on three different N-body codes: two direct N-body integration codes, using the 4th order predictor-corrector Hermite integrator with block time-steps, and one Barnes-Hut treecode, which uses a 2nd order leapfrog integration scheme. The integration of the equations of motions for all codes is performed on the host CPU.
We find that for N > 512 particles the GPU outperforms the GRAPE-6Af, if some softening in the force calculation is accepted. Without softening and for very small integration time-steps the GRAPE still outperforms the GPU. We conclude that modern GPUs offer an attractive alternative to GRAPE-6Af special purpose hardware. Using the same time-step criterion, the total energy of the N-body system was conserved better than to one in 10(6) on the GPU, only about an order of magnitude worse than obtained with GRAPE-6Af. For N greater than or similar to 10(5) the 8800GTX outperforms the host CPU by a factor of about 100 and runs at about the same speed as the GRAPE-6Af.