Skip to main content

The Frequency Decomposition Multi-Grid Method

  • Chapter
Multigrid Methods IV

Part of the book series: ISNM International Series of Numerical Mathematics ((ISNM,volume 116))

  • 214 Accesses

Abstract

The FD (frequency decomposition) multi-level algorithm is presented. It uses multiple coarse-grid corrections with particularly associated prolongations and restrictions. We discuss the construction of the algorithm and the proof of robustness by means of the techniques from domain decomposition methods.

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 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
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. Brand., A.: Stages in developing multigrid solutions. In: Numerical Methods for Engineers (eds.: E. Absi, R. Glowinski, H. Veysseyre), Paris, Dunod, 1980, pages 23–43.

    Google Scholar 

  2. Frederickson, P.O. and O.A. McBryan: Recent developments for the PSMG multiscale method. In Hackbusch — Trottenberg [10] 21–39.

    Google Scholar 

  3. Hackbusch, W.: Multi-grid methods and applications. Springer, Heidelberg, 1985.

    MATH  Google Scholar 

  4. Hackbusch, W.: A new approach to robust Multi-Grid methods. In: McKenna, J., Temam, R. (eds.) ICIAM’ 87: Proceedings of the First International Conference on Industrial and Applied Mathematics, SIAM, Philadelphia 1988.

    Google Scholar 

  5. Hackbusch, W.: (ed.): Robust Multi-Grid methods. Proceedings, 4th GAMM-Seminar Kiel, Jan. 1988. Notes on Numerical Fluid Mechanics, vol. 23, Vieweg, Braunschweig, 1989.

    Google Scholar 

  6. Hackbusch, W.: The frequence decomposition multi-grid method I. Application to anisotropic equations. Numer. Math. 56 (1989) 229–245.

    Article  MathSciNet  MATH  Google Scholar 

  7. Hackbusch, W.: The frequency decomposition multi-grid method II. Convergence analysis based on the additive Schwarz method. Numer. Math. 63 (1992) 433–453.

    Article  MathSciNet  MATH  Google Scholar 

  8. Hackbusch, W.: Iterative Lösung großer schwachbesetzter Gleichungs-systeme. Teubner, Stuttgart 1991. English translation: Iterative Solution of Large Sparse System of Equations. Springer-Verlag, New York 1993.

    Google Scholar 

  9. Hackbusch, W. and U. Trottenberg (eds.): Multi-Grid Methods, Proceedings, Lecture Notes in Mathematics 960. Springer Berlin-Heidelberg, 1982.

    Google Scholar 

  10. Hackbusch, W. and U. Trottenberg (eds.): Multi-Grid methods III. Proceedings, Bonn, Oktober 1990. ISNM 98, Brikhäuser, Basel, 1991.

    Google Scholar 

  11. Hemker, P.W.: The incomplete LU-decomposition as a relaxation method in Multi-Grid algorithms. In: Miller, J.J.H. (ed.): Boundary and interior layers — computational and asymptotic-methods, Boole Press, Dublin, 1980, pages 306–311.

    Google Scholar 

  12. Katzer, E.: A subspace decomposition two-grid method for hyperbolic equations. Contribution to this volume.

    Google Scholar 

  13. Kettler, R.: Analysis and comparison of relaxation schemes in robust multi-grid and preconditioned conjugate gradient methods. In: Hackbusch — Trottenberg R. Glowinski, H. Veysseyre), Paris, Dunod, 1980 [1] 502–534.

    Google Scholar 

  14. Mulder, W.: A new multigrid approach to convection problems. J. Comp. Phys. 83 (1989) 303–323.

    Article  MathSciNet  MATH  Google Scholar 

  15. Naik, N.H. and J. VAN ROSENDALE: The improved robustness of multigrid elliptic solvers based on multiple semicoarsened grids. SIAM Num. Anal. 30 (1993) 215–229.

    Article  MATH  Google Scholar 

  16. Oosterlee, C.W. and P. WESSELING: On the robustness of a multiple semi-coarsened grid method. To appear in ZAMM

    Google Scholar 

  17. Stüben, K. and U. TROTTENBERG: Multi-grid methods: fundamental algorithms, model problem analysis and applications. In Hackbusch — Trottenberg R. Glowinski, H. Veysseyre), Paris, Dunod, 1980 [1] 1–176.

    Google Scholar 

  18. Wesseling, P.: Theoretical and practical aspects of a multigrid method. SIAM J. Sci. Statist Comput. 3 (1982) 387–407.

    Article  MathSciNet  MATH  Google Scholar 

  19. Wesseling, P.: An introduction to multigrid methods. Wiley, Chichester 1991.

    Google Scholar 

  20. Widlund, O.: Optimal iterative refinement methods. In: Chan — Glowinski — Périaux — Widlund (eds.), Domain decomposition methods. Proceedings, SIAM Philadelphia 1989. Pages 114–125.

    Google Scholar 

  21. Wittum, G.: On the robustness of ILU-smoothing. In Hackbusch [3] 217–239.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1994 Springer Basel AG

About this chapter

Cite this chapter

Hackbusch, W. (1994). The Frequency Decomposition Multi-Grid Method. In: Hemker, P.W., Wesseling, P. (eds) Multigrid Methods IV. ISNM International Series of Numerical Mathematics, vol 116. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8524-9_4

Download citation

  • DOI: https://doi.org/10.1007/978-3-0348-8524-9_4

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9664-1

  • Online ISBN: 978-3-0348-8524-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics