High Performance Direct Gravitational N-body Simulations on Graphics Processing Units -- II: An implementation in CUDA

TL;DR

This paper demonstrates that modern GPUs, specifically the NVIDIA GeForce 8800GTX, can effectively perform direct gravitational N-body simulations, offering a cost-effective alternative to specialized hardware like GRAPE-6Af, with competitive accuracy and performance for large N.

Contribution

The authors implement and evaluate gravitational N-body simulations on a GPU using CUDA, showing significant performance gains and comparable accuracy to specialized hardware.

Findings

GPU outperforms GRAPE-6Af for N > 512 with softening

Energy conservation is within one part in 10^6 on GPU

GPU achieves about 100x speedup over CPU for N ≥ 10^5

Abstract

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 speed-up 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 $N \apgt 10^5$ the 8800GTX outperforms the host CPU by a factor of about 100 and runs at about the same speed as the GRAPE-6Af.