Parallel Simulation of Three–Dimensional Bursting with MPI and OpenMP

  • S. Tabik
  • L. F. Romero
  • E. M. Garzón
  • J. I. Ramos
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3992)


This work presents a mathematical model and its parallel implementation via two parallel paradigms for the simulation of three–dimensional bursting phenomena. The mathematical model consists of four nonlinearly coupled partial differential equations and includes fast and slow subsystems. The differential equations have been discretized by means of a linearly–implicit finite difference method in equally–spaced grids. The resulting system of equations at each time level has been solved by means of an optimized Preconditioned Conjugate Gradient (PCG) method. The proposed mathematical model has been implemented via: (1) a message passing paradigm based on the standard MPI and (2) a shared address space paradigm based on SPMD OpenMP. The two implementations have been evaluated on two current parallel architectures, i.e., a cluster of biprocessors Xeon and an SGI Altix 3700 Bx2 based on Itanium. It is shown that better performance and scalability are obtained on the second platform.


  1. 1.
    Rinzel, J., Lee, Y.S.: Dissection of a model for neuronal parabolic bursting. J. Math. Biol. 25, 653–675 (1987)MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    Rinzel, J.: Electrical excitability of cells, theory and experiment: review of the Hodgkin–Huxley foundation and an update. Bull. Math. Biol. 52, 5–23 (1990)CrossRefGoogle Scholar
  3. 3.
    Smolen, P., Keizer, J.: Slow voltage inactivation of Ca  + 2 currents and bursting mechanisms for the mouse pancreatic β–cell. J. Membr. Biol. 127, 9–19 (1992)Google Scholar
  4. 4.
    Bertram, R., Buttle, M.J., Kiemel, T., Sherman, A.: Topological and phenomenological classification of bursting oscillations. Bull. Math. Biol. 57, 413–439 (1995)zbMATHGoogle Scholar
  5. 5.
    Keener, J., Sneyd, J.: Mathematical Physiology. Springer, New York (1998)zbMATHGoogle Scholar
  6. 6.
    Ramos, J.I.: Linearization methods for reaction–diffusion equations: Multidimensional problems. Appl. Math. Comput. 88, 225–254 (1997)MathSciNetzbMATHCrossRefGoogle Scholar
  7. 7.
    Ortigosa, E.M., Romero, L.F., Ramos, J.I.: Parallel scheduling of the PCG method for banded matrices rising from FDM/FEM. J. Parall. Distr. Comput. 63, 1243–1256 (2003)zbMATHCrossRefGoogle Scholar
  8. 8.
    Protic, J., Tomasevi, M., Milutinovic, V.: Distributed Shared Memory: Concepts and Systems. Wiley, New York (1997)Google Scholar
  9. 9.
    Dunigan, T., Vetter, J., Worley, P.: Performance evaluation of the SGI Altix 3700. In: Proc. of the IEEE Int. Conf. Parallel Proc. ICPP, pp. 231–240 (2005)Google Scholar
  10. 10.
    Krawezik, G., Cappello, F.: Performance comparison of MPI and OpenMP on shared memory multiprocessors. Concurr. Comput.: Practice and Experience 18, 29–61 (2006)CrossRefGoogle Scholar
  11. 11.
  12. 12.
    Mellor–Crummey, J., Garvin, J.: Optimizing sparse matrix–vector product computations using unroll and jam. Int. J. High Perfor. Comput. Applic. 18, 225–236 (2004)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • S. Tabik
    • 1
  • L. F. Romero
    • 2
  • E. M. Garzón
    • 1
  • J. I. Ramos
    • 2
  1. 1.Depto de Arquitectura de Computadores y ElectrónicaUniversidad de AlmeríaSpain
  2. 2.Room I-320, E.T.S. Ingenieros IndustrialesUniversidad de Málaga29080Spain

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