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A performance model with a fixed point for a molecular dynamics kernel

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Computer Science - Research and Development

Abstract

Analysis of a timing formula for a molecular dynamics kernel reveals an equivalence class of parallel machines with a fixed point that is independent of the particular machine in the class. Three different machines, CRAY, IBM and SGI, are self-similar in that they follow the same path along a performance surface as the processor count and problem size change. The path is attracted to a fixed point that limits performance, the same fixed point for all three machines. An analytic formula, with two parameters determined from measured data, reproduces the path along the surface.

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References

  1. Barenblatt GI (1987) Dimensional Analysis. Gordon and Breach Science Publishers, New York, London

  2. Barenblatt GI (1996) Scaling, Self-Similarity, and Intermediate Asymptotics. Cambridge University Press, Cambridge, UK

  3. Barenblatt GI (2003) Scaling. Cambridge University Press, Cambridge, UK

  4. Bhatelé A, Kumar S, Mei C, Phillips JC, Zheng G, Kalé LV (2008) Overcoming scaling challenges in biomolecular simulations across multiple platforms. IEEE International Symposium on Parallel and Distributed Processing. IPDPS 2008, pp 1–12

  5. Birkhoff G (1960) Hydrodynamics: A Study in Logic, Fact and Similitude, 2nd edn. Princeton University Press, Princeton, NJ

  6. Bowers KJ, Chow E, Xu H, Dror RO, Eastwood MP, Gregersen BA, Klepeis JL, Kolossvary I, Moraes MA, Sacerdoti FD, Salmon JK, Shan Y, Shaw DE (2006) Scalable Algorithms for Molecular Dynamics Simulations on Commodity Clusters. Proceedings of Supercomputing ’06, Tampa, FL

  7. Bridgman PW (1931) Dimensional Analysis, 2nd edn. Yale University Press, New Haven

    Google Scholar 

  8. Germain RS, Fitch B, Rayshubskiy A, Eleftheriou M, Pitman MC, Suits F, Giampapa M, Ward TJC (2005) Blue matter on Blue Gene/L: Massively parallel computation for biomolecular simulation. CODES + ISSS ’05: Proceedings of the 3rd IEEE/ACM/IFIP international conference on Hardware/software codesign and system synthesis, pp 207–212. New York, NY, ACM

  9. Mantevo http://software.sandia.gov/mantevo. Accessed 29 Apr 2009

  10. Numrich RW (2007) A note on scaling the Linpack benchmark. J Parall Distrib Comput 67(4):491–498

    Article  MATH  Google Scholar 

  11. Numrich RW (2007) Computational force: A unifying concept for scalability analysis. In: Bischof C, Bücker M, Gibbon P, Joubert G, Lippert T, Mohr B, Peters F (eds), Parallel Computing: Architectures, Algorithms and Applications, Proceedings of the International Conference ParCo 2007, pp 107–112. John von Neumann Institute for Computing (NIC) and Jülich Supercomputing Centre

  12. Numrich RW (2008) Computational forces in the Linpack benchmark. J Parall Distrib Comput 68(9):1283–1290

    Article  Google Scholar 

  13. Numrich RW (2008) Dimensional analysis applied to a parallel QR algorithm. In: Parallel Processing and Applied Mathematics: Proceedings of the Seventh International Conference on Parallel Processing and Applied Mathematics (PPAM07), pp 148–157. 9–12 September 2007, Gdansk, Poland, Springer Lecture Notes in Computer Science, LNCS 4967

  14. Numrich RW (2009) Computational forces in the SAGE benchmark. J Parall Distrib Comput 69:315–325

    Article  Google Scholar 

  15. Numrich RW (2007) A New Scaling Formula for the Linpack Benchmark. SIAM Conference on Computational Science and Engineering, Costa Mesa, CA, 19–23 February 2007

  16. Numrich RW, Heroux MA (2008) Self-similarity of parallel machines. Under review

  17. Plimpton S (1995) Fast parallel algorithms for short-range molecular dynamics. J Computat Phys 117:1–19

    Article  MATH  Google Scholar 

  18. Plimpton S, Pollock R, Stevens M (1997) Particle-mesh ewald and rrespa for parallel molecular dynamics. In Proceedings of the Eighth SIAM Conference on Parallel Processing for Scientific Computing

  19. Streitz FH, Glosli JN, Patel MV, Chan B, Yates RK, and de Supinski BR (2005) 100+ TFlop Solidification Simulation on BlueGene/L. Proceedings of Supercomputing ’05, Seattle, WA

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Authors and Affiliations

  1. Minnesota Supercomputing Institute, University of Minnesota, Minneapolis, MN, USA

    Robert W. Numrich

  2. Sandia National Laboratories, Albuquerque, NM and St. John’s University, Collegeville, MN, USA

    Michael A. Heroux

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  1. Robert W. Numrich
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  2. Michael A. Heroux
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Correspondence to Robert W. Numrich.

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Numrich, R.W., Heroux, M.A. A performance model with a fixed point for a molecular dynamics kernel . Comp. Sci. Res. Dev. 23, 195–201 (2009). https://doi.org/10.1007/s00450-009-0086-4

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  • DOI: https://doi.org/10.1007/s00450-009-0086-4

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