A Parallel Robust Multigrid Algorithm Based on Semi-coarsening

  • M. Prieto
  • R. Santiago
  • I. M. Llorente
  • F. Tirado
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1697)


This paper compares two common approaches to achieve robustness in the parallel multigrid resolution of anisotropic operators on structured grids: alternating plane smoothers with full coarsening and plane smoothers combined with semicoarsening. Both, numerical and architectural properties are compared. A parallel implementation based on MPI is studied in a realistic way by considering the exploitation of the cache memory and the negative effect that the parallelization has on the convergence properties of the methods.


Coarse Grid Domain Decomposition Multigrid Method Memory Hierarchy Convergence Factor 
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.
    A. Brandt, Multigrid techniques: 1984 guide with applications to fluid dynamics, Tech. Rep. GMD-Studien 85, May 1984.Google Scholar
  2. 2.
    J. E. Deny, S. F. McCormick, J. Ruge, T. Russell, and S. Schaffer, Multigrid-methods for three-dimensional petroleum reservoir simulation, in Tenth SPE Symposium on Reservoir Simulation, february 1989.Google Scholar
  3. 3.
    D. Espadas, M. Prieto, I. M. Llorente, and F. Tirado, Parallel resolution of alternating-line processes by means of pipelined techniques, in Proceedings of the 7th. Euromicro Workshop on Parallel and Distributed Systems, IEEE Computer Society Press, Febraury 1999, pp. 289–296.Google Scholar
  4. 4.
    Krechel, Plum, and StÜben, Parallelization and vectorization aspects of the solution of tridiagonal linear systems, Parallel Comput., 14 (1990), pp. 31–49.zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    I. M. Llorente and N. D. Melson, Robust multigrid smoothers for three dimensional elliptic equations with strong anisotropies, Tech. Rep. 98-37, ICASE, 1998.Google Scholar
  6. 6.
    I. M. Llorente and F. Tirado, Relationships between efficiency and execution time of full multigrid methods on parallel computers, IEEE Trans. on Parallel and Distributed Systems, 8 (1997), pp. 562–573.CrossRefGoogle Scholar
  7. 7.
    M. Prieto, I. Llorente, and F. Tirado, Partitioning regular domains on modern parallel computers, in Proceedings of the 3th International Meeting on Vector and Parallel Processing, J.M. L.M. Palma, J. Dongarra, and V. Hernández, eds., 1999, pp. 411–424.Google Scholar
  8. 8.
    P. Wesseling, An Introduction to Multigrid Methods, John Wiley & Sons, New York, 1992.zbMATHGoogle Scholar
  9. 9.
    D. Xie and L. R. Scott, The parallel u-cycle multigrid method, in Proceedings of the 8th Copper Mountain Conference on Multigrid Methods, 1996.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • M. Prieto
    • 1
  • R. Santiago
    • 1
  • I. M. Llorente
    • 1
  • F. Tirado
    • 1
  1. 1.Departamento de Arquitectura de Computadores y Automatica Facultad de Ciencias FisicasUniversidad ComplutenseMadridSpain

Personalised recommendations