Abstract
We present direct astrophysical N-body simulations with up to six million bodies using our parallel MPI-CUDA code on large GPU clusters in Beijing, Berkeley, and Heidelberg, with different kinds of GPU hardware. The clusters are linked in the cooperation of ICCS (International Center for Computational Science). We reach about one third of the peak performance for this code, in a real application scenario with hierarchically block time-steps and a core-halo density structure of the stellar system. The code and hardware is used to simulate dense star clusters with many binaries and galactic nuclei with supermassive black holes, in which correlations between distant particles cannot be neglected.
Similar content being viewed by others
References
Aarseth SJ (2003) Gravitational N-body simulations. Cambridge University Press, Cambridge, p 430. ISBN: 0521432723
Aarseth SJ (1999a) From NBODY to NBODY6: the growth of an industry. Publ Astron Soc Pac 111:1333
Aarseth SJ (1999b) Star cluster simulations: the state of the art. Celest Mech Dyn Astron 73:127
Ahmad A, Cohen L (1973) A numerical integration scheme for the N-body gravitational problem. J Comput Phys 12:389–402
Akeley K, Nguyen H, Nvidia X (2007) GPU gems 3, programming techniques for high-performance graphics and general-purpose computation. Addison-Wesley, Reading
Barnes J, Hut P (1986) A hierarchical O(Nlog N) force-calculation algorithm. Nature 324:446
Barsdell BR, Barnes DG, Fluke CJ (2009) Advanced architectures for astrophysical supercomputing. In: The proceedings of ADASS XIX, Sapporo, Japan, Oct 4–8 2009. ASP Conf. Series. arXiv:1001.2048
Belleman RG, Bedorf J, Portegies Zwart SF (2008) High performance direct gravitational N-body simulations on graphics processing units II. An implementation in CUDA. New Astron 13:103
Berczik P, Hamada T, Nitadori K, Spurzem R (2011, in preparation) The parallel GPU N-body code ϕGPU
Berczik P, Merritt D, Spurzem R, Bischof H-P (2006) Efficient merger of binary supermassive black holes in nonaxisymmetric galaxies. Astrophys J 642:L21
Berczik P, Merritt D, Spurzem R (2005) Long-term evolution of massive black hole binaries. II. Binary evolution in low-density galaxies. Astrophys J 633:680
Berczik P, Nakasato N, Berentzen I, Spurzem R, Marcus G, Lienhart G, Kugel A, Männer R, Burkert A, Wetzstein M, Naab T, Vasquez H, Vinogradov SB (2007). Special, hardware accelerated, parallel SPH code for galaxy evolution. In: SPHERIC—smoothed particle hydrodynamics European research interest community. p. 5
Berentzen I, Preto M, Berczik P, Merritt D, Spurzem R (2009) Astrophys J 695:455
Chen Y, Cui X, Mei H (2010) Large-scale FFT on GPU clusters. In: Proceedings of the 24th ACM International Conference on Supercomputing, Tsukuba, Ibaraki, Japan, ICS ’10. ACM, New York, pp 315–324
Couchman HMP, Thomas PA, Pearce FR (1995) Hydra: an adaptive-mesh implementation of P 3M-SPH. Astrophys J 452:797
Cui D, Liao N, Wu W, Tan B, Lin Y (2010) Fast ARFTIS reconstruction algorithms using CUDA. In: Zhang W, Chen Z, Douglas C, Tong W (eds) High Performance Computing and Applications. Lecture Notes in Computer Science, vol 5938. Springer, Heidelberg, pp 119–126
Dehnen W (2002) A hierarchical O(N) force calculation algorithm. J Comput Phys 179:27
Dehnen W (2000) A very fast momentum-conserving tree code. Astrophys J 536:L39
Egri G et al. (2007) Comput Phys Commun 177:631
Fellhauer M, Kroupa P, Baumgardt H, Bien R, Boily CM, Spurzem R, Wassmer N (2000) SUPERBOX—an efficient code for collisionless galactic dynamics. New Astron 5:305
Fukushige T, Makino J, Kawai A (2005) GRAPE-6A: a single-card GRAPE-6 for parallel PC-GRAPE cluster systems. Publ Astron Soc Jpn 57:1009
Greengard L, Rokhlin V (1987) A fast algorithm for particle simulations. J Comput Phys 73:325
Greengard L, Rokhlin V (1997) A fast algorithm for particle simulations. J Comput Phys 135:280
Gualandris A, Merritt D (2008) Ejection of supermassive black holes from Galaxy cores. Astrophys J 678:780–797. doi:10.1086/586877
Hamada T, Iitaka T The chamomile scheme: an optimized algorithm for N-body simulations on programmable graphics processing units (2007). arXiv:astro-ph/0703100
Harfst S, Gualandris A, Merritt D, Spurzem R, Portegies Zwart S, Berczik P (2007) Performance analysis of direct N-body algorithms on special-purpose supercomputers. New Astron 12:357
Hockney RW, Eastwood JW (1988) Computer simulation using particles. Hilger, Bristol
Hwu W-MW (2011) GPU computing gems. Kaufmann, Los Altos
Ishiyama T, Fukushige T, Makino J (2009) GreeM: Massively parallel TreePM code for large cosmological N-body simulations. Publ Astron Soc Jpn 61:1319
Just A, Khan FM, Berczik P, Ernst A, Spurzem R (2010) Dynamical friction of massive objects in galactic centres. Mon Not R Astron Soc Lett 411:653
Makino J, Hut P (1988) Performance analysis of direct N-body calculations. Astrophys J Suppl Ser 68:833
Makino J, Aarseth SJ (1992) On a Hermite integrator with Ahmad-Cohen scheme for gravitational many-body problems. Publ Astron Soc Jpn 44:141
Makino J, Fukushige T, Koga M, Namura K (2003) Publ Astron Soc Jpn 55:1163
Makino J (2004) A fast parallel treecode with GRAPE. Publ Astron Soc Jpn 56:521
Nitadori K, Makino J (2008) Sixth- and eighth-order Hermite integrator for N-body simulations. New Astron 13:498
Pearce FR, Couchman HMP (1997) Hydra: a parallel adaptive grid code. New Astron 2:411
Portegies Zwart SF, Belleman RG, Geldof PM (2007) High-performance direct gravitational N-body simulations on graphics processing units. New Astron 12:641
Schive H-Y, Tsai Y-C, Chiueh T (2010) GAMER: a graphic processing unit accelerated adaptive-mesh-refinement code for astrophysics. Astrophys J Suppl Ser 186:457
Springel V (2005) The cosmological simulation code GADGET-2. Mon Not R Astron Soc Lett 364:1105
Spurzem R (1999) Direct N-body simulations. J Comput Appl Math 109:407
Spurzem R, Berczik P, Hensler G, Theis C, Amaro-Seoane P, Freitag M, Just A (2004) Physical processes in star-gas systems. Publ Astron Soc Aust 21:188
Spurzem R, Berczik P, Berentzen I, Merritt D, Nakasato N, Adorf HM, Brüsemeister T, Schwekendiek P, Steinacker J, WambsganßJ, Martinez GM, Lienhart G, Kugel A, Männer R, Burkert A, Naab T, Vasquez H, Wetzstein M (2007) From Newton to Einstein—N-body dynamics in galactic nuclei and SPH using new special hardware and astrogrid-D. J Phys Conf Ser 78:012071
Spurzem R, Berentzen I, Berczik P, Merritt D, Amaro-Seoane P, Harfst S, Gualandris A (2008) Parallelization special hardware and post-Newtonian dynamics in direct N-body simulations. Lecture notes in physics, vol 760. Springer, Berlin, p 377
Spurzem R, Berczik P, Marcus G, Kugel A, Lienhart G, Berentzen I, Männer R, Klessen R, Banerjee R (2009) Accelerating astrophysical particle simulations with programmable hardware (FPGA and GPU). Comput Sci Res Dev 23:231–239
Spurzem R, Berczik P, Berentzen I, Ge W, Wang X, Schive H-Y, Nitadori K, Hamada T (2011, in press) Physics and astrophysics—multiscale simulations: accelerated many-core GPU computing on three continents. In: Dubitzky W, Kurowski K, Schott B (eds) Special volume on “Large scale computing techniques for complex systems and simulations”. Wiley, New York
Thompson AC, Fluke CJ, Barnes DG, Barsdell BR (2010) Teraflop per second gravitational lensing ray-shooting using graphics processing units. New Astron 15:16
Wang P, Abel T, Kaehler R (2010) Adaptive mesh fluid simulations on GPU. New Astron 15:581
Wong H-C, Wong U-H, Feng X, Tang Z (2009) Efficient magnetohydrodynamic simulations on graphics processing units with CUDA. arXiv:0908.4362
Xu G (1995) A new parallel N-body gravity solver: TPM. Astrophys J Suppl Ser 98:355
Yasuda Koji (2007) J Comput Chem 29:334
Yang J, Wang Y, Chen Y (2007) GPU accelerated simulation. J Comput Phys 221:799
Yokota R, Barba L (2010) Treecode and fast multipole method for N-body simulation with CUDA. arXiv:1010.1482
Yokota R, Bardhan JP, Knepley MG, Barba LA, Hamada T (2010) Biomolecular electrostatics simulation with a parallel FMM-based BEM, using up to 512 GPU’s. arXiv:1007.4591
Yoshikawa K, Fukushige T (2005) PPPM and TreePM methods on GRAPE systems for cosmological N-body simulations. Publ Astron Soc Jpn 57:849
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Spurzem, R., Berczik, P., Berentzen, I. et al. Astrophysical particle simulations with large custom GPU clusters on three continents. Comput Sci Res Dev 26, 145–151 (2011). https://doi.org/10.1007/s00450-011-0173-1
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00450-011-0173-1