A Flexible 2-Level Neumann-Neumann Method for Structural Analysis Problems

  • Petter E. Bjørstad
  • Piotr Krzyżanowski
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2328)


We discuss a new approach for the construction of the second-level Neumann-Neumann coarse space. Our method is based on an inexpensive and parallel analysis of the lower part spectrum of each subdomain stiffness matrix. We show that the method is flexible enough to converge fast on nonstandard decompositions and various types of finite elements used in structural analysis packages.


Domain Decomposition Domain Decomposition Method Coarse Space Rigid Body Mode Domain Decomposition Algorithm 
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  1. 1.
    P. E. Bjørstad, J. Koster, AND P. Krżyzanowski, Domain decomposition solvers for large scale industrial finite element problems, in Applied Parallel Computing. New Paradigms for HPC in Industry and Academia, T. Sorevik, F. Manne, R. Moe, and A. Gebremedhin, eds., vol. 1947 of Lecture Notes in Computer Science, Springer-Verlag, 2001, pp. 374–384. Proceedings of the 5th International Workshop, PARA2000 Bergen, Norway, June 18-20, 2000.Google Scholar
  2. 2.
    S. C. Brenner AND L.-y. Sung, Balancing domain decomposition for noncon-forming plate elements, Numer. Math., 83 (1999), pp. 25–52.MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    M. Brezina, C. Heberton, J. Mandel, AND P. Vanek, An iterative method with convergence rate chosen a priori, Tech. Report 140, University of Colorado in Denver, USA, April 1999. An earlier version has also been presented at the 1998 Copper Mountain Conference on Iterative Methods.Google Scholar
  4. 4.
    Y.-H. De ROECK AND P. Le TALLEC, Analysis and test of a local domain decomposition preconditioner, in Fourth International Symposium on Domain Decomposition Methods for Partial Differential Equations, R. Glowinski, Y. Kuznetsov, G. Meurant, J. Périaux, and O. Widlund, eds., SIAM, Philadelphia, PA, 1991, pp. 112–128.Google Scholar
  5. 5.
    M. Dryja AND O. B. Widlund, Additive Schwarz methods for elliptic finite element problems in three dimensions, in Fifth International Symposium on Domain Decomposition Methods for Partial Differential Equations (Norfolk, VA, 1991), SIAM, Philadelphia, PA, 1992, pp. 3–18.Google Scholar
  6. 6.
    -, Schwarz methods of Neumann-Neumann type for three-dimensional elliptic finite element problems, Comm. Pure Appl. Math., 48 (1995), pp. 121–155.MathSciNetzbMATHCrossRefGoogle Scholar
  7. 7.
    G. Karypis AND V. Kumar, METIS-Serial Graph Partitioning Algorithm. Available electronically via
  8. 8.
    P. Le TALLEC, J. Mandel, AND M. Vidrascu, Balancing domain decomposition for plates, in Domain decomposition methods in scientific and engineering computing (University Park, PA, 1993), Amer. Math. Soc., Providence, RI, 1994, pp. 515–524.CrossRefGoogle Scholar
  9. 9.
    -, A Neumann-Neumann domain decomposition algorithm for solving plate and shell problems, SIAM J. Numer. Anal., 35 (1998), pp. 836–867.MathSciNetzbMATHCrossRefGoogle Scholar
  10. 10.
    J. Mandel, Balancing domain decomposition, Comm. Numer. Methods Engrg., 9 (1993), pp. 233–241.MathSciNetzbMATHCrossRefGoogle Scholar
  11. 11.
    J. Mandel AND M. Brezina, Balancing domain decomposition for problems with large jumps in coefficients, Math. Comp., 65 (1996), pp. 1387–1401.MathSciNetzbMATHCrossRefGoogle Scholar
  12. 12.
    J. Mandel AND P. Krzyżanowski, Robust Balancing Domain Decomposition, August 1999. Presentation at The Fifth US National Congress on Computational Mechanics, University of Colorado at Boulder, CO.Google Scholar
  13. 13.
    B. F. Smith, P. E. Bjørstad, AND W. D. Gropp, Domain decomposition, Cambridge University Press, Cambridge, 1996. Parallel multilevel methods for elliptic partial differential equations.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Petter E. Bjørstad
    • 1
  • Piotr Krzyżanowski
    • 2
  1. 1.Institute of InformaticsUniversity of BergenBergenNorway
  2. 2.Institute of Applied MathematicsWarsaw UniversityWarszawaPoland

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