Multigrid method for nearly singular and slightly indefinite problems

  • A. Brandt
  • S. Ta'asan
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 1228)


This paper deals with nearly singular, possibly indefinite problems for which the usual multigrid solvers converge very slowly or even diverge. The main difficulty is related to some badly approximated smooth functions which correspond to eigenfunctions with nearly zero eigenvalues. A modification to the usual coarse-grid equations is derived, both in Correction Scheme and in Full Approximation Scheme. With this modification, the algorithm exhibits the usual multigrid efficiency.


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  1. [1]
    A. Brandt, Multigrid Techniques: 1984 Guide With Applications to Fluid Dynamics. Monograph available as GMD-Studie No. 85, from GMD-FlT, Postfach 1240, D-5205, St. Augustin 1, W. Germany.Google Scholar
  2. [2]
    A. Brandt, Algebraic multigrid theory: the symmetric case. Preliminary Proceedings of International Multigrid Conference, Copper Mountain, Colorado, April 1983. Applied Math. Comp., to appear.Google Scholar
  3. [3]
    S. Ta'asan, Multigrid Methods for Highly Oscillatory Problems. Ph.D. Thesis, The Weizmann Institute of Science, Rehovot, Israel 1984.Google Scholar
  4. [4]
    K. Tanabe, Projection methods for solving a singular system of linear equations and its applications, Numer. Math., 17 (1971), pp. 203–214.MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag 1986

Authors and Affiliations

  • A. Brandt
    • 1
  • S. Ta'asan
    • 2
  1. 1.Weizmann Institute of ScienceRehovotIsrael
  2. 2.Institute for Computer Applications in Science and EngineeringIsrael

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