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Optimization of cosmological N-body simulation with FMM-PM on SIMT accelerators

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Abstract

Cosmological N-body simulation is associated with hyper-scale and high-resolution computing, and time will increase exponentially as the scale increases, which is always the most important issue that needs to be considered in N-body problems. With the increasing computing scale demand, high-performance computing systems and effective parallel algorithms have been applied to solve the N-body problem. PHotoNs-2, a parallel N-body simulation code designed for Lambda cold dark matter modelled simulation, was developed using the hybrid fast multipole method and particle-mesh method. In this study, PHotoNs-2 is migrated on a parallel heterogeneous CPU+Accelerator platform, which is referred to as PhotoNs-MA, and challenges are imposed on its performance by the massive data transmission, memory access, and complex mathematical functions. In this paper, the main optimizations for the kernel functions of short-range force calculations on the SIMT architecture are listed as follows: transmission of large amounts of data using page-locked memory and the structure of array to improve the efficiency of memory access, the transmission of index lists instead of particle interaction lists to reduce the transfer overhead, and using the interpolation method to replace the modified formula for interaction forces. Finally, compared with PHotoNs-2 run on 4 CPU cores, the optimized PHotoNs-MA on 4 accelerators accelerates the P2P operator 1000x times. We compared the results with Gadget-2 run on 64 CPU cores, and the overall performance is improved by 6 times for 4 accelerators. As for large-scale simulations, near-linear scalability is observed in P2P, and the parallel efficiency ultimately reaching 89.28%.

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Acknowledgements

This paper was supported by the National Key R&D Program for Developing Basic Sciences (Grant Nos.2020YFB0204802), the Strategic Priority Research Program of the Chinese Academy of Sciences (Grant No.XDC01000000) and GHFUND A No.20210701. The numerical calculation in the paper was carried out on CAS Xiandao-1 computing environment.

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Authors and Affiliations

  1. Computer Network Information Center, Chinese Academy of Sciences, Beijing, 100190, China

    Wen-Long Zhao & Wu Wang

  2. University of Chinese Academy of Sciences, Beijing, 100049, China

    Wen-Long Zhao & Qiao Wang

  3. Key Laboratory for Computational Astrophysics, National Astronomical Observatories, Chinese Academy of Sciense, Beijing, 100101, China

    Qiao Wang

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  1. Wen-Long Zhao
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Correspondence to Wu Wang.

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Zhao, WL., Wang, W. & Wang, Q. Optimization of cosmological N-body simulation with FMM-PM on SIMT accelerators. J Supercomput 78, 7186–7205 (2022). https://doi.org/10.1007/s11227-021-04153-0

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