Skip to main content

Algebraic Multigrid Methods and the Schur Complement

  • Chapter
Robust Multi-Grid Methods

Part of the book series: Notes on Numerical Fluid Mechanics ((NNFM,volume 23))

Abstract

In this paper we propose and discuss a general purely algebraic framework for multilevel iterative schemes for solving linear Systems where the role of the ‘coarse grid’ Operators is played by Schur complements.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 44.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 59.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. O. Axelsson, A survey of vectorizable preconditioning methods for large scale finite element matrix problems, Report CNA-190, Center for Numerical Analysis, Univ. of Texas at Austin, 1984.

    Google Scholar 

  2. O. Axelsson, A general incomplete block-matrix factorization method, Linear Algebra and its Applications 74 (1986), 179–190.

    Article  MathSciNet  MATH  Google Scholar 

  3. O. Axelsson, I. Gustafsson, Preconditioning and two-level multi-grid methods of arbitrary denree of approximation, Math. Comp., 40 (1983), 219–242.

    Article  MathSciNet  MATH  Google Scholar 

  4. O. Axelsson, B. Polman, On approximate factorization methods for block matrices suitable for vector and parallel processors, Linear Algebra and its Applications 77 (1986), 3–26.

    Article  MathSciNet  MATH  Google Scholar 

  5. A. Brand, S.F. McCormick, J. Ruge, Algebraic Multinrid for automatic multigrid solution with application to geodetic computation. Submitted (1983) to SIAM J. Sci. Stat. Comp.

    Google Scholar 

  6. W. Hackbusch, U. Trottenberg, Multinrid Methods, Lecture Notes in Mathematics Vol. 960, Springer Verlag

    Google Scholar 

  7. O.G. Johnson, C.A. Micchelli, G. Paul, Polynomial preconditioned for conjugate qradient calculations, SIAM J. Numer. Anal. 20 (1983), 362–376.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  8. S.F. McCormick, An Algebraic Interpretation of Multinrid Methods, SIAM J. Numer. Anal. 19, (1982), 548–560.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  9. D.V. Ouellette, Schur Complements and Statistics, Linear Alnebra Appl. 36, (1981), 187–295.

    Article  MathSciNet  MATH  Google Scholar 

  10. P. Rosza, On the inverse of Band Matrices, Integral Equations and Operator Theory 10 (1987), 82–95.

    MathSciNet  Google Scholar 

  11. J. Ruge, K. Stliben, Algebraic Multinrid (AMG) Arbeitspapiere der GMD 210 (1986) a chapter in the book Multigrid Methods (McCormick, ed.) Frontiers in Applied Mathematics, Vol. 5, SIAM, Philadelphia

    Google Scholar 

  12. K. Stüben, Algebraic Multigrid (AMG), Experiences and Comparisons: Arbeitspapiere der GMD 23 (1983)

    Google Scholar 

  13. R.S. Varga, Matrix Iterative Analysis, Prentice Hall, Ennlewood Cliffs, N.J., 1962.

    Google Scholar 

  14. P.S. Vassilevski, Nearly optimal iterative methods for solving finite element elliptic equations based on the multilevel splitting of the matrix, Research Report, Institute of Mathematics with Computing Center, Bulgarian Academy of Sciences, 1987.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Wolfgang Hackbusch

Rights and permissions

Reprints and permissions

Copyright information

© 1989 Friedr. Vieweg & Sohn Verlagsgesellschaft mbH, Braunschweig

About this chapter

Cite this chapter

Dahmen, W., Elsner, L. (1989). Algebraic Multigrid Methods and the Schur Complement. In: Hackbusch, W. (eds) Robust Multi-Grid Methods. Notes on Numerical Fluid Mechanics, vol 23. Vieweg+Teubner Verlag, Wiesbaden. https://doi.org/10.1007/978-3-322-86200-6_5

Download citation

  • DOI: https://doi.org/10.1007/978-3-322-86200-6_5

  • Publisher Name: Vieweg+Teubner Verlag, Wiesbaden

  • Print ISBN: 978-3-528-08097-6

  • Online ISBN: 978-3-322-86200-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics