Skip to main content
SpringerLink
Log in

A preconditioned domain decomposition algorithm for the solution of the elliptic Neumann problem

  • Published:
Periodica Mathematica Hungarica Aims and scope Submit manuscript

Abstract

A new preconditioned conjugate gradient (PCG)-based domain decomposition method is given for the solution of linear equations arising in the finite element method applied to the elliptic Neumann problem. The novelty of the proposed method is in the recommended preconditioner which is constructed by using cyclic matrix. The resulting preconditioned algorithms are well suited to parallel computation.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. N. S.Bahvalov, N. P.Zhidkov and G. M.Kobelkov,Numerical Methods, (in Russian) Moscow, Nauka, 1987.

    Google Scholar 

  2. J. H.Bramble, J. E.Pasciak and A. H.Schatz, An iterative method for elliptic problems on region partitioned into substructures,Math. Comp. Vol.46 No. 174, 361–369, 1986.

    MathSciNet  Google Scholar 

  3. J. H.Bramble, J. E.Pasciak and A. H.Schatz, The construction of preconditioners for elliptic problems by substructuring I.Math. of Comp. 47 No. 175, (1986), 103–134.

    MathSciNet  Google Scholar 

  4. J. H.Bramble, J. E.Pasciak and A. H.Schatz. The construction of preconditioners for elliptic problems by substructuring II.,Math. of Comp. 49 No.184, (1986), 1–16.

    MathSciNet  Google Scholar 

  5. J. H.Bramble, J. E.Pasciak and A. H.Schatz, The construction of preconditioners for elliptic problems by substructuring III.,Math. of Comp. 51 No.184, (1988), 415–430.

    MathSciNet  Google Scholar 

  6. P. G. Ciarlet,The finite element method for elliptic problems, North-Holland, 1977.

  7. M.Dryja, A finite element capacitance method for elliptic problems on region partitioned into subregions,Numer. Math. 44 (1984), 153–168.

    Article  MATH  MathSciNet  Google Scholar 

  8. R. Glowinski,Numerical Methods for Nonlinear Variational Problems, Springer-Verlag, 1984.

  9. J. L.Lions and E.Magenes,Problèmes aux limites non homogènes et applications, Dunod, Paris, 1968.

    Google Scholar 

  10. J.Nečas,Les méthodes directes en théories des équations elliptiques, Academia, Prague, 1967.

    Google Scholar 

  11. P. A.Raviart and J. M.Thomas,Introduction à l'analyse numèrique des équations aux derivées partielles, Masson, Paris, 1983.

    Google Scholar 

  12. P.Rózsa,Linear algebra and their applications, (Lineáris algebra és alkalmazásai), Müszaki Kiadó, Budapest, 1974.

    Google Scholar 

  13. O. Widlund, An extension theorem for finite element spaces with three applications,Technical Report 233, Dept of Computer Science, Courant Inst. 1986.

  14. O. Widlund, Interative substructuring methods: Algorithm and theory for elliptic problems in the plane.Technical Report 287, Dept. of Computer Science, Cuorant Institute, 1987.

Download references

Author information

Authors and Affiliations

  1. Department of Numerical Analysis, Eötvös Lóránd University, Bogdánfy U. 10/B, 1117, Hungary

    B. Kiss & GY. Molnárka

Authors
  1. B. Kiss
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. GY. Molnárka
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kiss, B., Molnárka, G. A preconditioned domain decomposition algorithm for the solution of the elliptic Neumann problem. Period Math Hung 24, 151–165 (1992). https://doi.org/10.1007/BF02330875

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02330875

Mathematics subject classification numbers, 1980/85 Primary

Secondary

Key words and phrases

Search

Navigation