Scalable Multigrid

  • Tobias Gradl
  • Christoph Freundl
  • Harald Köstler
  • Ulrich Rüde


This contribution presents three parallel multigrid solvers, two for finite element and one for finite difference simulations. They are focused on the different aspects of software design: efficiency, usability, and generality, but all have in common that they are highly scalable to large numbers of processors.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    M.F. Adams, H.H. Bayraktar, T.M. Keaveny, P. Papadopoulos, Ultrascalable implicit finite element analyses in solid mechanics with over a half a billion degrees of freedom, in ACM/IEEE Proceedings of SC2004: High Performance Networking and Computing, 2004 Google Scholar
  2. 2.
    B. Bergen, Hierarchical Hybrid Grids: Data structures and core algorithms for efficient finite element simulations on supercomputers, in Advances in Simulation, vol. 14, SCS Europe, July 2006 Google Scholar
  3. 3.
    B. Bergen, T. Gradl, F. Hülsemann, U. Rüde, A massively parallel multigrid method for finite elements. Comput. Sci. Eng. 8, 56–62 (2006) CrossRefGoogle Scholar
  4. 4.
    B. Bergen, F. Hülsemann, U. Rüde, Is 1.7×1010 unknowns the largest finite element system that can be solved today? in SC ’05: Proceedings of the 2005 ACM/IEEE Conference on Supercomputing (IEEE Computer Society, Washington, 2005), p. 5 Google Scholar
  5. 5.
    A. Bruhn, Variational optic flow computation: Accurate modeling and efficient numerics. PhD thesis, Department of Mathematics and Computer Science, Saarland University, Saarbrücken, Germany, 2006 Google Scholar
  6. 6.
    C. Freundl, B. Bergen, F. Hülsemann, U. Rüde, ParEXPDE: Expression templates and advanced PDE software design on the Hitachi SR8000, in High Performance Computing in Science and Engineering, ed. by A. Bode, F. Durst. Garching, 2004 (Springer, Berlin, 2005), pp. 167–179 Google Scholar
  7. 7.
    T. Gradl, C. Freundl, U. Rüde, Scalability on all levels for ultra-large scale finite element calculations. Technical report, Lehrstuhl für Informatik 10 (Systemsimulation), Friedrich-Alexander-Universität Erlangen-Nürnberg (2007); submitted to Parallel Comput. Google Scholar
  8. 8.
    G. Hager, B. Bergen, P. Lammers, G. Wellein, Taming the bandwidth behemoth. First experiences on a large SGI Altix system. inSiDE 3(2), 24 (2005) Google Scholar
  9. 9.
    B. Horn, B. Schunck, Determining optical flow. Artif. Intell. 17, 185–203 (1981) CrossRefGoogle Scholar
  10. 10.
    E.M. Kalmoun, H. Köstler, U. Rüde, 3D optical flow computation using a parallel variational multigrid scheme with application to cardiac C-arm CT motion. Image Vis. Comput. 25(9), 1482–1494 (2007) CrossRefGoogle Scholar
  11. 11.
    G. Karypis, V. Kumar, Multilevel k-way partitioning scheme for irregular graphs. J. Parallel Distrib. Comput. 48(1), 96–129 (1998) CrossRefMathSciNetGoogle Scholar
  12. 12.
    J. Modersitzki, Numerical Methods for Image Registration (Oxford University Press, Oxford, 2004) zbMATHGoogle Scholar
  13. 13.
    T.L. Veldhuizen, Expression templates. C++ Rep. 7(5), 26–31 (1995). Reprinted in C++ Gems, ed. by S. Lippman Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Tobias Gradl
    • 1
  • Christoph Freundl
    • 1
  • Harald Köstler
    • 1
  • Ulrich Rüde
    • 1
  1. 1.Chair for System SimulationUniversity Erlangen-NurembergErlangenGermany

Personalised recommendations