Advertisement

Some Computational Results for Dual-Primal FETI Methods for Elliptic Problems in 3D

  • Axel Klawonn
  • Oliver Rheinbach
  • Olof B. Widlund
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 40)

Summary

Iterative substructuring methods with Lagrange multipliers for elliptic problems are considered. The algorithms belong to the family of dual-primal FETI methods which were introduced for linear elasticity problems in the plane by Farhat et al. [2001] and were later extended to three dimensional elasticity problems by Farhat et al. [2000]. Recently, the family of algorithms for scalar diffusion problems was extended to three dimensions and successfully analyzed by Klawonn et al. [2002a,b]. It was shown that the condition number of these dual-primal FETI algorithms can be bounded polylogarithmically as a function of the dimension of the individual subregion problems and that the bounds are otherwise independent of the number of subdomains, the mesh size, and jumps in the diffusion coefficients. In this article, numerical results for some of these algorithms are presented and their relation to the theoretical bounds is studied. The algorithms have been implemented in PETSc, see Balay et al. [2001], and their parallel scalability is analyzed.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. S. Balay, K. Buschelman, W. D. Gropp, D. Kaushik, M. Knepley, L. C. McInnes, B. F. Smith, and H. Zhang. PETSc home page. URL http://www.mcs.anl.gov/petsc. 2001.Google Scholar
  2. C. Farhat, M. Lesoinne, P. LeTallec, K. Pierson, and D. Rixen. FETI-DP: A dual-primal unified FETI method-part i: A faster alternative to the two-level FETI method. Int. J. Numer. Meth. Engrg., 50:1523–1544, 2001.MathSciNetCrossRefGoogle Scholar
  3. C. Farhat, M. Lesoinne, and K. Pierson. A scalable dual-primal domain decomposition method. Numer. Lin. Alg. Appl., 7:687–714, 2000.MathSciNetCrossRefGoogle Scholar
  4. A. Klawonn, O. B. Widlund, and M. Dryja. Dual-Primal FETI methods for three-dimensional elliptic problems with heterogeneous coefficients. SIAM J.Numer.Anal., 40, 159–179 2002a.MathSciNetCrossRefGoogle Scholar
  5. A. Klawonn, O. B. Widlund, and M. Dryja. Dual-Primal FETI methods with face constraints. In L. F. Pavarino and A. Toselli, editors, Recent developments in domain decomposition methods, pages 27–40. Springer-Verlag, Lecture Notes in Computational Science and Engineering, Volume 23, 2002b.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Axel Klawonn
    • 1
  • Oliver Rheinbach
    • 1
  • Olof B. Widlund
    • 2
  1. 1.Fachbereich MathematikUniversität Duisburg-EssenEssen
  2. 2.Courant Institute of Mathematical SciencesNew York UniversityNew York

Personalised recommendations