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On a Multigrid Eigensolver for Linear Elasticity Problems

  • Maxim Larin
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2542)

Abstract

In the early eighties the direct application of a multigrid technique for solving the partial eigenvalue problem of computing few of the smallest eigenvalues and their corresponding eigenvectors of a differential operator was proposed by Brandt, McCormick and Ruge [1]. In the present paper an experimental study of the method for model linear elasticity problems is carried out. Based on these results we give some practical advices for a good choice of multigrid-related parameters.

Keywords

Eigenvalue Problem Coarse Grid Multigrid Method Coarse Level Linear Elasticity Problem 
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References

  1. 1.
    Brandt, A., McCormick, S. and Ruge, J.: Multigrid Methods for Differential Eigenproblems. SIAM J. Sci. Stat. Comput., 4(2) (1983) 244–260.zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Hackbusch, W.: Multigrid Methods and Applications. Springer-Verlag, Berlin-Heidelberg-New York (1985)Google Scholar
  3. 3.
    Knyazev, A. V.: Preconditioned Eigensolvers-an Oxymoron? Electronic Transaction on Numerical Analysis, Vol. 7 (1998) 104–123.zbMATHMathSciNetGoogle Scholar
  4. 4.
    Lur'e, A. I.: Theory of Elasticity. Moscow, Nauka (1970)Google Scholar
  5. 5.
    Parlett, B.: The Symmetric Eigenvalue Problem. Prentice-Hall, Inc. (1980)Google Scholar
  6. 6.
    Trottenberg, U., Oosterlee, C. and Schüller, A.: Multigrid. Academic Press (2001)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Maxim Larin
    • 1
  1. 1.Rheinisch-Wesfälische Technische Hochschule AachenInstitut für Geometrie und Praktische MathematikAachenGermany

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