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

Robert G. Belleman, Jeroen Bedorf, Simon F. Portegies Zwart
Section Computational Science, University of Amsterdam, Amsterdam, The Netherlands
New Astronomy, Vol. 13, No. 2. (16 February 2008), pp. 103-112.

@article{belleman2008high,

   title={High performance direct gravitational N-body simulations on graphics processing units II: An implementation in CUDA},

   author={Belleman, R.G. and B{‘e}dorf, J. and Portegies Zwart, S.F.},

   journal={New Astronomy},

   volume={13},

   number={2},

   pages={103–112},

   issn={1384-1076},

   year={2008},

   publisher={Elsevier}

}

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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    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.
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