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Toward the design of a novel hybrid parallel N-body method in scope of modern cloud architectures

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Abstract

A hybrid parallel self mesh-adaptive N-body method based on approximate inverses and multiprojection techniques is proposed. This method is a three-dimensional hybrid parallel mesh-type N-body scheme based on the solution of the Poisson equation in the physical space with boundary conditions obtained from multipole expansion formulas. In order to improve the accuracy of the solution, especially in shallow regions, a self mesh-adaptive scheme is used to create a hierarchy of independent smaller N-body problems. The parallelization of the scheme is based on a uniform partitioning of the bodies with respect to available computer nodes, and communications are required only for the computation of the density and potential distributions. The proposed scheme is suitable for large-scale galaxy simulations with millions of bodies on high-resolution meshes, for distributed HPC systems with multicore computer nodes. Moreover, large-scale galaxy simulations are performed on modern Cloud environments in order to examine the applicability and performance. Implementation issues concerning the proposed scheme are also discussed. The parallel performance and speedup of the hybrid parallel N-body method on HPC systems as well as on Cloud environments are presented and discussed.

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References

  1. Aarseth SJ (2010) Gravitational N-body simulations: tools and algorithms. Cambridge University Press, Cambridge

    MATH  Google Scholar 

  2. Asanović K, Bodik R, Catanzaro BC, Gebis JJ, Husbands P, Keutzer K, Patterson DA, Plishker WL, Shalf J, Williams SW, Yelick KA (2006) The landscape of parallel computing research: a view from berkeley. Technical Report UCB/EECS-2006-183, EECS Department, University of California, Berkeley. http://www2.eecs.berkeley.edu/Pubs/TechRpts/2006/EECS-2006-183.html

  3. Barnes J, Hut P (1986) A hierarchical o(nlogn) force-calculation algorithm. Nature 324:446–449

    Article  Google Scholar 

  4. Binney J, Tremaine S (2008) Galactic dynamics, 2nd edn. Princeton University Press, Princeton

    MATH  Google Scholar 

  5. Briggs WL, Henson VE, McCormick SF (2000) A multigrid tutorial, 2nd edn. SIAM, Philadelphia, PA

    Book  MATH  Google Scholar 

  6. Bryan GL, Norman ML, O’Shea BW, Abel T, Wise JH, Turk MJ, Reynolds DR, Collins DC, Wang P, Skillman SW, Smith B, Harkness RP, Bordner J, Kim JH, Kuhlen M, Xu H, Goldbaum N, Hummels C, Kritsuk AG, Tasker E, Skory S, Simpson CM, Hahn O, Oishi JS, So GC, Zhao F, Cen R, Li Y, Collaboration TE (2014) Enzo: an adaptive mesh refinement code for astrophysics. Astrophys J Suppl Ser 211(2):19

    Article  Google Scholar 

  7. Cloudlightning (2017). http://cloudlightning.eu. Accessed 22 May 2017

  8. Douglas CC, Haase G, Langer U (2003) A tutorial on elliptic PDE solvers and their parallelization. SIAM, Philadelphia

    Book  MATH  Google Scholar 

  9. Greengard LF, Rokhlin V (1987) A fast algorithm for particle simulations. J Comput Phys 73(2):325–348

    Article  MathSciNet  MATH  Google Scholar 

  10. GRNET:  okeanos https://okeanos.grnet.gr (2017). [Online; accessed 22-May-2017]

  11. Gupta A, Milojicic D (2011) Evaluation of hpc applications on cloud. In: Proceedings of the 2011 Sixth Open Cirrus Summit, OCS ’11, pp 22–26. IEEE Computer Society, Washington, DC

  12. Haelterman R, Heule JVDV (2009) Non-stationary two-stage relaxation based on the principle of aggregation multigrid. In: Deconinck H, Dick E (eds) Computational Fluid Dynamics 2006, 4th International Conference on Computational Fluid Dynamics, pp 243–248. Springer, Berlin

  13. Harnois-Draps J, Pen UL, Iliev IT, Merz H, Emberson JD, Desjacques V (2013) High-performance p3m n-body code: cubep3m. Mon Not R Astron Soc 436(1):540

    Article  Google Scholar 

  14. Hassani R, Aiatullah M, Luksch P (2014) Improving HPC application performance in public cloud. IERI Procedia 10:169–176

  15. Hockney RW, Eastwood JW (1988) Computer simulation using particles. CRC Press, Taylor and Francis, Inc., Bristol, PA

    Book  MATH  Google Scholar 

  16. Intel Math Kernel Library (2009) Reference manual. Intel Corporation, Santa Clara, USA. ISBN:630813-054US

  17. Karypis G, Kumar V (1998) A fast and high quality multilevel scheme for partitioning irregular graphs. SIAM J Sci Comput 20(1):359–392

    Article  MathSciNet  MATH  Google Scholar 

  18. Kim JH, Abel T, Agertz O, Bryan GL, Ceverino D, Christensen C, Conroy C, Dekel A, Gnedin NY, Goldbaum NJ, Guedes J, Hahn O, Hobbs A, Hopkins PF, Hummels CB, Iannuzzi F, Keres D, Klypin A, Kravtsov AV, Krumholz MR, Kuhlen M, Leitner SN, Madau P, Mayer L, Moody CE, Nagamine K, Norman ML, Onorbe J, O’Shea BW, Pillepich A, Primack JR, Quinn T, Read JI, Robertson BE, Rocha M, Rudd DH, Shen S, Smith BD, Szalay AS, Teyssier R, Thompson R, Todoroki K, Turk MJ, Wadsley JW, Wise JH, Zolotov A (2014) For the AGORA Collaboration29: the agora high-resolution galaxy simulations comparison project. Astrophys J Suppl Ser 210(1):14

    Article  Google Scholar 

  19. Kravtsov AV, Klypin AA, Khokhlov AM (1997) Adaptive refinement tree—a new high-resolution N-body code for cosmological simulations. Astrophys J Suppl Ser 111:73–94

    Article  Google Scholar 

  20. Kyziropoulos PE (2017) A study of computational methods for parallel simulation of the gravitational n-body problem. Ph.D. thesis, Department of Electrical and Computer Engineering, Democritus University of Thrace (in preparation)

  21. Kyziropoulos PE, Efthymiopoulos C, Gravvanis GA, Patsis PP (2016) Structures induced by companions in galactic discs. MNRAS 463:2210–2228

    Article  Google Scholar 

  22. Kyziropoulos PE, Filelis-Papadopoulos CK, Gravvanis GA (2016) A class of symmetric factored approximate inverses and hybrid two-level solver. TR/ECE/ASC-AMA/2016/2 (submitted)

  23. Kyziropoulos PE, Filelis-Papadopoulos CK, Gravvanis GA, Efthymiopoulos C (2017) A parallel self mesh-adaptive n-body method based on approximate inverses. J Supercomput. doi:10.1007/s11227-017-2078-7

    Google Scholar 

  24. Moutafis BE, Filelis-Papadopoulos CK, Gravvanis GA (2017) Parallel multi-projection preconditioned methods based on semi-aggregation techniques . J Comp Sci 22:45–53. doi:10.1016/j.jocs.2017.08.020

  25. Moutafis BE, Filelis-Papadopoulos CK, Gravvanis GA (2017) Parallel multiprojection preconditioned methods based on subspace compression. Math Probl Eng 2017:2580820. doi:10.1155/2017/2580820

  26. Openstack (2017). https://www.openstack.org/. Accessed 22 May 2017

  27. O’Shea BW, Bryan G, Bordner J, Norman ML, Abel T, Harkness R, Kritsuk A (2005) Introducing enzo, an AMR cosmology application. Lect Notes Comput Sci Eng 41:341–349

    Article  MATH  Google Scholar 

  28. Rao J, Wang K, Zhou X, Xu CZ (2013) Optimizing virtual machine scheduling in numa multicore systems. In: 2013 IEEE 19th International Symposium on High Performance Computer Architecture (HPCA), pp 306–317

  29. Rodriguez MA, Buyya R (2017) Scheduling dynamic workloads in multi-tenant scientific workflow as a service platforms. Future Gener Comput Syst. doi:10.1016/j.future.2017.05.009

  30. Saad Y (2003) Iterative Methods for Sparse Linear Systems, 2nd edn. Society for Industrial and Applied Mathematics, Philadelphia, PA, USA

    Book  MATH  Google Scholar 

  31. Sellwood JA (2014) GALAXY package for N-body simulation. ArXiv e-prints

  32. Springel V (2005) The cosmological simulation code gadget-2. Monthly Notices of the Royal Astronomical Society 364:11051134

    Article  Google Scholar 

  33. Synnefo cloud platform (2017). http://www.synnefo.org. Accessed 22 May 2017

  34. Teuben PJ (1995) The stellar dynamics toolbox nemo. In: Astronomical Data Analysis Software and Systems IV, ASP Conference Series, vol 77, p 398

  35. Teyssier R (2002) Cosmological hydrodynamics with adaptive mesh refinement. A new high resolution code called RAMSES. Astron Astrophys 385:337–364

    Article  Google Scholar 

  36. Trottenberg U, Oosterlee CW, Schuller A (2000) Multigrid. Academic Press, Elsevier, New York

    MATH  Google Scholar 

  37. Verlet L (1967) Computer experiments on classical fluids. I. Thermodynamical properties of Lennard–Jones molecules. Phys Rev 159(1):98–103

    Article  Google Scholar 

  38. Villumsen J (1982) Simulations of galaxy mergers. Mon Not R Astron Soc 199:493–516

    Article  Google Scholar 

  39. Wesseling P (1982) Theoretical and practical aspects of a multigrid method. SIAM J Sci Stat Comput 3(4):387–407

    Article  MathSciNet  MATH  Google Scholar 

  40. Xi S, Li C, Lu C, Gill C, Xu M, Phan L, Lee I, Sokolsky O (2015) RT-open stack: CPU resource management for real-time cloud computing. In: 2015 IEEE 8th International Conference on Cloud Computing, pp 179–186. doi:10.1109/CLOUD.2015.33

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Acknowledgements

The authors acknowledge the Greek Research and Technology Network (GRNET) for the provision of the National HPC facility ARIS, under project PR002040-ScaleSciComp, and the õkeanos Cloud Environment. This work is partially funded by the General Secreteriat for Research and Technology (GSRT) through the CloudLightning project/Matching Funds.

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Correspondence to C. K. Filelis-Papadopoulos.

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Kyziropoulos, P.E., Filelis-Papadopoulos, C.K., Gravvanis, G.A. et al. Toward the design of a novel hybrid parallel N-body method in scope of modern cloud architectures. J Supercomput 74, 569–591 (2018). https://doi.org/10.1007/s11227-017-2140-5

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  • DOI: https://doi.org/10.1007/s11227-017-2140-5

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