skip to main content
article
Free Access

Solving the biharmonic equation in a square: a direct versus a semidirect method

Published:01 November 1973Publication History
Skip Abstract Section

Abstract

Two methods for solving the biharmonic equation are compared. One method is direct, using eigenvalue-eigenvector decomposition. The other method is iterative, solving a Poisson equation directly at each iteration.

References

  1. 1 Smith, J. The coupled equation approach to the numerical solution of the biharmonic equation by finite differences, I. SIAM J. Num. Anal 5 (1970), 104-111.Google ScholarGoogle ScholarCross RefCross Ref
  2. 2 Ehrlich, L.W. Solving the biharmonic equation as coupled finite difference equations. SIAM J. Num. Anal. 8 (1971), 278-287.Google ScholarGoogle ScholarCross RefCross Ref
  3. 3 Ehrlich, L.W. Coupled harmonic equations, SOR, and Chebyshev acceleration. M.O.C. 26 (1970), 335-343.Google ScholarGoogle Scholar
  4. 4 Ehrlich, L.W. Point and block SOR applied to a coupled set of difference equations. APL/JHU TG-1166, 1971.Google ScholarGoogle Scholar
  5. 5 Golub, G.H. An algorithm for the discrete biharmonic equation. Personal communication.Google ScholarGoogle Scholar
  6. 6 Hockney, R.W. A fast direct solution of Poisson's equation using Fourier analysis. J. ACM 12, 1 (Jan. 1965), 95-113. Google ScholarGoogle ScholarDigital LibraryDigital Library
  7. 7 Hockney, R.W. The potential calculation and some applications. Methods in Computat. Physics 9 (1970), 135-211.Google ScholarGoogle Scholar
  8. 8 Buzbee, B.L., Golub, G.H., and Nielson, C.W. On direct methods for solving Poisson's equation. SlAM J. Num. Anal. 7 (1970), 627-656.Google ScholarGoogle ScholarCross RefCross Ref
  9. 9 Colony, R., and Reynolds, R.R. An application of Hockney's method for solving Poisson's equation. Proc. AFIPS 1970 SJCC, Vol. 36, AFIPS Press, Montvale, N.J., pp. 409-416.Google ScholarGoogle Scholar
  10. 10 Householder, A.S. The Theory of Matrices in Numerical Analysis. Blaisdell Pub. Co., New York, 1964.Google ScholarGoogle Scholar
  11. 11 Young, D. lterative Solution of Large Linear Systems. Academic Press, New York, 1971.Google ScholarGoogle Scholar
  12. 12 McLaurin, Johnnie William. A general coupled equation approach for solving the biharmonic boundary value problem. Dept. of Math., UCLA, Los Angeles, Calif., 1971.Google ScholarGoogle Scholar
  13. 13 Gupta Murli Manohar. Convergence and stability of finite difference schemes for some elliptic equations. Ph.D. Diss., Dept. of Math., U. of Saskatchewan, Saskatoon, Saskatchewan, Canada, Aug. 1971. (See also On numerical solution of biharmonic equation by splitting. M.M. Gupta and R. Manohar in Proc. Manitoba Conf. on Num. Math., U. of Manitoba, Winnipeg, Manitoba, Canada, Oct. 7-9, 1971.)Google ScholarGoogle Scholar

Recommendations

Comments

Login options

Check if you have access through your login credentials or your institution to get full access on this article.

Sign in

Full Access

  • Published in

    cover image Communications of the ACM
    Communications of the ACM  Volume 16, Issue 11
    Nov. 1973
    135 pages
    ISSN:0001-0782
    EISSN:1557-7317
    DOI:10.1145/355611
    Issue’s Table of Contents

    Copyright © 1973 ACM

    Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

    Publisher

    Association for Computing Machinery

    New York, NY, United States

    Publication History

    • Published: 1 November 1973

    Permissions

    Request permissions about this article.

    Request Permissions

    Check for updates

    Qualifiers

    • article

PDF Format

View or Download as a PDF file.

PDF

eReader

View online with eReader.

eReader