New features of parallel implementation of N-body problems on GPU (1803.01190v1)
Abstract: This paper focuses on the parallel implementation of a direct $N$-body method~(particle-particle algorithm) and the application of multiple GPUs for galactic dynamics simulations. Application of a hybrid OpenMP-CUDA technology is considered for models with a number of particles $N \sim 105 \div 107$. By means of $N$-body simulations of gravitationally unstable stellar galactic we have investigated the algorithms parallelization efficiency for various Nvidia Tesla graphics processors~(K20, K40, K80). Particular attention was paid to the parallel performance of simulations and accuracy of the numerical solution by comparing single and double floating-point precisions~(SP and DP). We showed that the double-precision simulations are slower by a factor of~$1.7$ than the single-precision runs performed on Nvidia Tesla K-Series processors. We also claim that application of the single-precision operations leads to incorrect result in the evolution of the non-axisymmetric gravitating $N$-body systems. In particular, it leads to significant quantitative and even qualitative distortions in the galactic disk evolution. For instance, after $104$ integration time steps for the single-precision numbers the total energy, momentum, and angular momentum of a system with $N = 2{20}$ conserve with accuracy of $10{-3}$, $10{-2}$ and $10{-3}$ respectively, in comparison to the double-precision simulations these values are $10{-5}$, $10{-15}$ and $10{-13}$, respectively. Our estimations evidence in favour of usage of the second-order accuracy schemes with double-precision numbers since it is more efficient than in the fourth-order schemes with single-precision numbers.