Applicability of Load Balancing Strategies to Data-Parallel Embedded Runge-Kutta Integrators

  • Matthias Korch
  • Thomas Rauber
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4128)


Embedded Runge-Kutta methods are among the most popular methods for the solution of non-stiff initial value problems of ordinary differential equations (ODEs). We investigate the use of load balancing strategies in a data-parallel implementation of embedded Runge-Kutta integrators. Since the parallelism contained in the function evaluation of the ODE system is typically very fine-grained, our aim is to find out whether the employment of load balancing strategies can be profitable in spite of the additional overhead they involve.


Load Balance Work Unit Cache Line Good Speedup Atomic Operation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Ehrig, R., Nowak, U., Deuflhard, P.: Massively parallel linearly-implicit extrapolation algorithms as a powerful tool in process simulation. In: D’Hollander, E.H., et al. (eds.) Parallel Computing: Fundamentals, Applications and New Directions, pp. 517–524. Elsevier, Amsterdam (1998)CrossRefGoogle Scholar
  2. 2.
    Burrage, K.: Parallel and Sequential Methods for Ordinary Differential Equations. Oxford Science Publications, Oxford (1995)zbMATHGoogle Scholar
  3. 3.
    van der Houwen, P.J., Sommeijer, B.P.: Parallel iteration of high-order Runge-Kutta methods with stepsize control. J. Comput. Appl. Math. 29, 111–127 (1990)zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Prince, P.J., Dormand, J.R.: High order embedded Runge-Kutta formulae. J. Comput. Appl. Math. 7(1), 67–75 (1981)zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Korch, M., Rauber, T.: Scalable parallel RK solvers for ODEs derived by the method of lines. In: Kosch, H., Böszörményi, L., Hellwagner, H. (eds.) Euro-Par 2003. LNCS, vol. 2790, pp. 830–839. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  6. 6.
    Korch, M., Rauber, T.: Optimizing locality and scalability of embedded Runge-Kutta solvers using block-based pipelining. J. Par. Distr. Comp. 6(3), 444–468 (2006)CrossRefGoogle Scholar
  7. 7.
    Jackson, K.R., Nørsett, S.P.: The potential for parallelism in Runge-Kutta methods. Part 1: RK formulas in standard form. SIAM J. Numer. Anal. 32(1), 49–82 (1995)zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Hoffmann, R., Korch, M., Rauber, T.: Performance evaluation of task pools based on hardware synchronization. In: SC 2004: Proceedings of the 2004 ACM/IEEE conference on Supercomputing, Washington, DC, USA, p. 44. IEEE Computer Society, Los Alamitos (2004)Google Scholar
  9. 9.
    Korch, M., Rauber, T.: A comparison of task pools for dynamic load balancing of irregular algorithms. Concurrency and Computation: Practice and Experience 16, 1–47 (2004)CrossRefGoogle Scholar
  10. 10.
    Lioen, W.M., de Swart, J.J.B.: Test Set for Initial Value Problem Solvers, Release 2.1. CWI, Amsterdam, The Netherlands (1999)Google Scholar
  11. 11.
    Hussels, H.G.: Schrittweitensteuerung bei der Integration gewöhnlicher Differentialgleichungen mit Extrapolationsverfahren. Diploma thesis, University of Cologne, Cologne, Germany (1973)Google Scholar
  12. 12.
    Lecar, M.: Comparison of eleven numerical integrations of the same gravitational 25-body problem. Bulletin Astronomique 3, 91 (1968)Google Scholar
  13. 13.
    Hairer, E., Nørsett, S.P., Wanner, G.: Solving Ordinary Differential Equations I: Nonstiff Problems, 2nd rev. edn. Springer, Berlin (2000)Google Scholar
  14. 14.
    Banicescu, I., Carino, R., Pabico, J., Balasubramaniam, M.: Design and implementation of a novel dynamic load balancing library for cluster computing. Parallel Computing 31(7), 736–756 (2005)CrossRefGoogle Scholar
  15. 15.
    Tabirca, S., Tabirca, T., Yang, L.T., Freeman, L.: Evaluation of the feedback guided dynamic loop scheduling (FGDLS) algorithms. IEICE Trans. Inf. & Syst. E87-D(7), 1829–1833 (2004)Google Scholar
  16. 16.
    Nieh, J., Levoy, M.: Volume rendering on scalable shared-memory MIMD architectures. In: Proceedings of the Boston Workshop on Volume Visualization, pp. 17–24. ACM Press, New York (1992)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Matthias Korch
    • 1
  • Thomas Rauber
    • 1
  1. 1.Department of Computer ScienceUniversity of Bayreuth 

Personalised recommendations