Skip to main content
SpringerLink
Log in

Numerical experiments with a multiple grid and a preconditioned Lanczos type method

  • Conference paper
  • First Online:
Approximation Methods for Navier-Stokes Problems

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 771))

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

Access this chapter

Log in via an institution
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 59.00
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: Solution of linear systems of equations: iterative methods. In: V.A. Barker (ed.): Sparse matrix techniques. Lecture Notes in Mathematics 572, 1977, Berlin etc., Springer-Verlag.

    Google Scholar 

  2. O. Axelsson, I. Gustafsson: A modified upwind scheme for convective transport equations and the use of a conjugate gradient method for the solution of non-symmetric systems of equations. J. Inst. Math. Appl. 23, 321–338, 1979.

    Article  MATH  Google Scholar 

  3. N.S. Bakhvalov: On the convergence of a relaxation method with natural constraints on the elliptic operator. USSR Comp. Math. Math. Phys. 6 no. 5, 101–135, 1966.

    Article  MathSciNet  MATH  Google Scholar 

  4. K.E. Barrett: The numerical solution of singular-perturbation boundary-value problems. J. Mech. Appl. Math. 27, 57–68, 1974.

    Article  MathSciNet  MATH  Google Scholar 

  5. A. Brandt: Multi-level adaptive technique (MLAT) for fast numerical solution to boundary-value problems. Proc. 3rd Internat. Conf. on Numerical Methods in Fluid Mechanics, Paris, 1972. Lecture Notes in Physics 180, 82–89, Springer-Verlag 1973.

    Google Scholar 

  6. A. Brandt: Multi-level adaptive solutions to boundary value problems. Math. Comp. 31, 333–390, 1977.

    Article  MathSciNet  MATH  Google Scholar 

  7. J.C. Chien: A general finite difference formulation with application to the Navier-Stokes equations. Comp. Fl. 5, 15–31, 1977.

    Article  MATH  Google Scholar 

  8. R.P. Fedorenko: A relaxation method for solving elliptic difference equations. USSR Comp. Math. Math. Phys. 1, 1092–1096, 1962.

    Article  MATH  Google Scholar 

  9. R.P. Fedorenko: The speed of convergence of one iterative process USSR Comp. Math. Math. Phys. 4, no. 3, 227–235, 1964.

    Article  MATH  Google Scholar 

  10. P.O. Frederickson: Fast approximate inversion of large sparse linear systems. Mathematics Report 7-75, 1975, Lakehead University.

    Google Scholar 

  11. I. Gustafsson: A class of first order factorization methods. BIT 18, 142–156, 1978.

    Article  MathSciNet  MATH  Google Scholar 

  12. W. Hackbusch: On the multi-grid method applied to difference equations. Computing 20, 291–306, 1978.

    Article  MathSciNet  MATH  Google Scholar 

  13. W. Hackbusch: On the fast solutions of nonlinear elliptic equations. Num. Math. 32, 83–95, 1979.

    Article  MathSciNet  MATH  Google Scholar 

  14. R.W. Hockney: A fast direct solution of Poisson's equation using Fourier analysis. J. Ass. Comput. Mach. 12, 95–113, 1965.

    Article  MathSciNet  MATH  Google Scholar 

  15. R.W. Hockney: The potential calculation and some applications. Methods in Comp. Phys. 9, 135, 1970.

    Google Scholar 

  16. A.M. Il'in: Differencing scheme for a differential equation with a small parameter affecting the highest derivative. Math. Notes Acad. Sc. USSR 6, 596–602, 1969.

    Article  MATH  Google Scholar 

  17. D.S. Kershaw: The incomplete Cholesky-conjugate gradient method for the iterative solution of systems of linear equations. J. Comp. Phys. 26, 43–65, 1978.

    Article  MathSciNet  MATH  Google Scholar 

  18. J.A. Meijerink and H.A. van der Vorst: An iterative solution method for linear systems of which the coefficient matrix is a symmetric M-matrix. Math. Comp. 31, 148–162, 1977.

    MathSciNet  MATH  Google Scholar 

  19. R.A. Nicolaides: On multiple grid and related techniques for solving discrete elliptic systems. J. Comp. Phys. 19, 418–431, 1975.

    Article  MathSciNet  MATH  Google Scholar 

  20. D.W. Peaceman and H.H. Rachford Jr.: The numerical solution of parabolic and elliptic differential equations. JSIAM 3, 28–41, 1955.

    MathSciNet  MATH  Google Scholar 

  21. P.J. Roache: Computational fluid dynamics. Hermosa Publishers, Albuquerque, 1972.

    MATH  Google Scholar 

  22. P.J. Roache: The LAD, NOS and Split NOS methods for the steady-state Navier-Stokes equations. Computers and Fluids 3, 179–196, 1975.

    Article  MathSciNet  MATH  Google Scholar 

  23. P. Sonneveld: The method of induced dimension reduction, an iterative solver for non-symmetric linear systems. Publication in preparation.

    Google Scholar 

  24. R.V. Southwell: Stress calculation in frameworks by the method of systematic relaxation of constraints. Proc. Roy. Soc. London A 151, 56–95, 1935.

    Article  MATH  Google Scholar 

  25. E.L. Wachspress: Iterative solution of elliptic systems. Prentice-Hall, Inc., Englewood Cliffs, N.J., 1966.

    MATH  Google Scholar 

  26. P. Wesseling: The rate of convergence of a multiple grid method. To appear in the Proceedings of the Biennial Conference on Numerical Analysis, Dundee, 1979, Lecture Notes in Mathematics, Springer-Verlag.

    Google Scholar 

  27. D.M. Young: Iterative methods for solving partial difference methods of elliptic type. Trans. Amer. Math. Soc. 76, 92–111, 1954.

    Article  MathSciNet  MATH  Google Scholar 

  28. P.J. Roache and M.A. Ellis: The BID method for the steady-state Navier-Stokes equations. Computers and Fluids 3, 305–321, 1975.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dept. of Mathematics, Delft University of Technology, Julianalaan 132, 2600 AJ, Delft, The Netherlands

    P. Wesseling & P. Sonneveld

Authors
  1. P. Wesseling
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. P. Sonneveld
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Reimund Rautmann

Rights and permissions

Reprints and permissions

Copyright information

© 1980 Springer-Verlag

About this paper

Cite this paper

Wesseling, P., Sonneveld, P. (1980). Numerical experiments with a multiple grid and a preconditioned Lanczos type method. In: Rautmann, R. (eds) Approximation Methods for Navier-Stokes Problems. Lecture Notes in Mathematics, vol 771. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0086930

Download citation

  • DOI: https://doi.org/10.1007/BFb0086930

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-09734-1

  • Online ISBN: 978-3-540-38550-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation