Skip to main content

Elliptic Solver Performance Evaluation on Modern Hardware Architectures

  • Conference paper
  • First Online:
Parallel Processing and Applied Mathematics (PPAM 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8384))

Abstract

The recent advent of novel multi- and many-core architectures forces application programmers to deal with hardware-specific implementation details and to be familiar with software optimisation techniques to benefit from new high-performance computing machines. An extra care must be taken for communication-intensive algorithms, which may be a bottleneck for forthcoming era of exascale computing. This paper aims to present performance evaluation of preliminary adaptation techniques to hybrid MPI+OpenMP parallelisation schemes we provided into the EULAG code. Various techniques are discussed, and the results will lead us toward efficient algorithms and methods to scale communication-intensive elliptic solver with preconditioner, including GPU architectures to be provided later in the future.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Kurzak, J., Bader, D., Dongarra, J.: Scientific Computing with Multicore and Accelerators. Computer and Information Science Series. Chapmann and Hall/CRC, Boca Raton (2010)

    Book  Google Scholar 

  2. Rojek, K., Szustak, L., Wyrzykowski, R.: Using Intel Xeon Phi coprocessor to accelerate computations in MPDATA algorithm. In: Wyrzykowski, R., Dongarra, J., Karczewski, K., Waśniewski, J. (eds.) PPAM 2013, Part I. LNCS, vol. 8384, pp. 582–592. Springer, Heidelberg (2014)

    Google Scholar 

  3. Rojek, K., Szustak, L., Wyrzykowski, R.: Performance analysis for stencil-based 3D MPDATA algorithm on GPU architecture. In: Wyrzykowski, R., Dongarra, J., Karczewski, K., Waśniewski, J. (eds.) PPAM 2013, Part I. LNCS, vol. 8384, pp. 145–154. Springer, Heidelberg (2014)

    Google Scholar 

  4. Georgescu, S., Okuda, H.: Conjugate gradients on multiple GPUs. Int J. Numer. Meth. Fluids 64, 1254–1273 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  5. Zhang, Y., Cohen, J.M., Owens, J.D.: Fast tridiagonal solvers on GPU. In: Newsletter ACM SIGPLAN Notices - PPoPP’10, vol. 45, No. 5 (2010)

    Google Scholar 

  6. Prusa, J.M., Smolarkiewicz, P.K., Wyszogrodzki, A.: EULAG, a computational model for multiscale flows. Comput. Fluids 37(9), 1193–1207 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  7. Smolarkiewicz, P.K., Margolin, L.G.: Variational elliptic solver for atmospheric applications. Appl. Math. Comp. Sci. 4, 527–551 (1994)

    MATH  MathSciNet  Google Scholar 

  8. Smolarkiewicz, P.K., Grubisic, V., Margolin, L.G.: On forward-in-time differencing for fluids: stopping criteria for iterative solutions of anelastic pressure equations. Mon. Wea. Rev. 125, 647–654 (1997)

    Article  Google Scholar 

  9. Skamarock, W.C., Smolarkiewicz, P.K., Klemp, J.B.: Preconditioned conjugate-residual solvers for helmholtz equations in nonhydrostatic models. Mon. Wea. Rev. 125, 587–599 (1997)

    Article  Google Scholar 

  10. Smolarkiewicz, P. K., Margolin, L.G.: Variational methods for elliptic problems in fluid models. In: Proceeding of ECMWF Workshop on Developments in numerical methods for very high resolution global models, ECMWF, pp. 137–159. Reading, UK, 5–7, June 2000

    Google Scholar 

  11. Thomas, S.J., Hacker, J.P., Smolarkiewicz, P.K., Stull, R.B.: Spectral pre conditioners for non hydrostatic atmospheric models. Mon. Wea. Rev. 131, 2464–2478 (2003)

    Article  Google Scholar 

  12. Wyszogrodzki, A.A., Piotrowski, Z.P., Grabowski, W.W.: Parallel implementation and scalability of cloud resolving EULAG model. In: Wyrzykowski, R., Dongarra, J., Karczewski, K., Waśniewski, J. (eds.) PPAM 2011, Part II. LNCS, vol. 7204, pp. 252–261. Springer, Heidelberg (2012)

    Google Scholar 

  13. Piotrowski, Z.P., Wyszogrodzki, A., Smolarkiewicz, P.K.: Towards petascale simulation of atmospheric circulations with soundproof equations. Acta Geophys. 59(6), 1294–1311 (2011)

    Article  Google Scholar 

  14. Shalf, J., Dosanjh, S., Morrison, J.: Exascale computing technology challenges. In: Palma, J., Daydé, M., Marques, O., Lopes, J. (eds.) VECPAR 2010. LNCS, vol. 6449, pp. 1–25. Springer, Heidelberg (2011)

    Google Scholar 

  15. Strikwerda, J.: Finite difference schemes and partial differential equations. 2nd Edn. SIAM: Society for Industrial and Applied Mathematics (2004). ISBN: 978-0-89871-567-5. doi:10.1137/1.9780898717938

  16. Kamata, S.I., Eason, R.O., Bandou, Y.: A new algorithm for n-dimensional hilbert scanning. IEEE Trans. Image Process. 8(7), 964–973 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  17. Smolarkiewicz, P.K., Margolin, L.G., Wyszogrodzki, A.A.: A class of nonhydrostatic global models. J. Atmos. Sci. 58(4), 349–364 (2001)

    Article  Google Scholar 

  18. Drikakis, D., Fureby, C., Grinstein, F.F., Youngs, D.: Simulation of transition and turbulence decay in the Taylor Green vortex. J. Turbul. 8(20), 1–12 (2007)

    Google Scholar 

Download references

Acknowledgements

We gratefully acknowledge the help and support provided by Jamie Wilcox from Intel EMEA Technical Marketing HPC Lab. This work is supported by the Polish National Center of Science under Grant No. UMO-2011/03/B/ST6/03500.

Author information

Authors and Affiliations

Authors

Corresponding authors

Correspondence to Milosz Ciznicki or Michal Kulczewski .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Ciznicki, M., Kopta, P., Kulczewski, M., Kurowski, K., Gepner, P. (2014). Elliptic Solver Performance Evaluation on Modern Hardware Architectures. In: Wyrzykowski, R., Dongarra, J., Karczewski, K., Waśniewski, J. (eds) Parallel Processing and Applied Mathematics. PPAM 2013. Lecture Notes in Computer Science(), vol 8384. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-55224-3_16

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-55224-3_16

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-55223-6

  • Online ISBN: 978-3-642-55224-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics