Comparison of implicit and explicit parallel programming models for a finite element simulation algorithm

  • Joanna Płażek
  • Krzysztof Banaś
  • Jacek Kitowski
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1541)


In this paper we compare efficiency of two versions of a parallel algorithm for finite element compressible fluid flow simulations on unstructued grids. The first version is based on the explicit model of parallel programming (with message-passing paradigm), while the second incorporates the implicit model (in which data-parallel programming is used). Time discretization of the compressible Euler equations is organized with a linear, implicit version of the Taylor-Galerkin time scheme, while finite elements are employed for space discretization of one step problems. The resulting nonsymmetric system of linear equations is solved iteratively with the preconditioned GMRES method.

The algorithm has been tested on HP Exemplar SPP1600 computer using a benchmark problem of 2D inviscid flow simulations—the ramp problem.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Carey, G.F., Bose, A., Davis, B., Harle, C. and McLay, M., Parallel computation of viscous flows, in Proceedings of the 1997 Simulation Multiconference. High Performance Computing ’97, 6–10 April 1997, Atlanta, USA.Google Scholar
  2. 2.
    Finite Element Method in Large-Scale Computational Fluid Dynamics, International Journal for Numerical Methods in Fluids, 21, (1995).Google Scholar
  3. 3.
    Donea, J., A Taylor-Galerkin method for convective transport problems, International Journal for Numerical Methods in Engineering, 20, 101–119, (1984).MATHCrossRefGoogle Scholar
  4. 4.
    Banaś, K., and Płażek, J., Dynamic load balancing for the preconditioned GMRES solver in a parallel, adaptive finite element Euler code, in: Desideri, J.-A., et al. (eds.) Proc. of the Third ECCOMAS Computational Fluid Dynamics Conference, Sept.9–13, 1996, paris, J. Wiley & Sons Ltd., 1996, pp. 1025–1031.Google Scholar
  5. 5.
    Saad, Y., and Schultz, M., GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems, SIAM Journal of Scientific and Statistical Computing, 7, 856–869, (1986).MATHMathSciNetCrossRefGoogle Scholar
  6. 6.
    Saad, Y., Iterative Methods for Sparse Linear Systems, PWS Publ. Company, Boston, 1996.MATHGoogle Scholar
  7. 7.
    de Sturler, E., and Van der Vorst, H.A., Communication cost reduction for Krylov methods on paralle computers, Proc. of High Performance Computing and Networking Conference, April 18–20, 1994, Munich, vol. II, 190–195, Springer Verlag.Google Scholar
  8. 8.
    CONVEX Exemplar Programming Guide, First Edition, October 1994, CONVEX Press, Richardson, Texas, USA.Google Scholar
  9. 9.
    Woodward, P., and Colella, P., The numerical simulation of two dimensional fluid flow with strong shocks, Journal of Computational Physics, 54 (1984) 115–173.MATHMathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Joanna Płażek
    • 1
  • Krzysztof Banaś
    • 1
  • Jacek Kitowski
    • 2
    • 3
  1. 1.Section of Applied Mathematics UCKCracow University of TechnologyCracowPoland
  2. 2.Institute of Computer ScienceAGHCracowPoland
  3. 3.ACC CYFRONETCracowPoland

Personalised recommendations