Skip to main content
SpringerLink
Log in

Conformal mapping of doubly-connected domains

  • Published:
Numerische Mathematik Aims and scope Submit manuscript

Abstract

This paper describes an integral equation method for computing the conformal mapping of a finite doubly-connected domain ontoR <|w|<1, whereR is uniquely determined. The method is illustrated by numerical examples.

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. Gaier, D.: Konstruktive Methoden der konformen Abbildung. Springer Tracts in Natural Philosophy, Vol. 3. Berlin-Göttingen-Heidelberg-New York: Springer 1964.

    Google Scholar 

  2. Garrick, I. E.: Potential flow about arbitrary biplane wing sections. NACA Report 542, 1936.

  3. Jaswon, M. A.: Integral equation methods in potential theory. I. Proc. Roy. Soc. A275, 23–32 (1963).

    Google Scholar 

  4. Kantorovich, L. V., Krylov, V. I.: Approximate methods of higher analysis. Groningen: Noordhoff 1964.

    Google Scholar 

  5. Laura, P. A.: Conformal mapping of a class of doubly connected regions. NASA Tech. Rep. No. 8, The Catholic University of America, Washington, 1965

    Google Scholar 

  6. Lewis, G. K.: Flow and load parameters of hydrostatic oil bearings for several port shapes. J. Mech. Eng. Sci.8, 173–184 (1966).

    Google Scholar 

  7. Mikhlin, S. G.: Integral equations. London: Pergamon 1957.

    Google Scholar 

  8. Muskhelishvili, N. I.: Some basic problems of the mathematical theory of elasticity. Groningen: Noordhoff 1953.

    Google Scholar 

  9. Opfer, G.: Untere, beliebig verbesserbare Schranken für den Modul eines zweifach zusammenhängenden Gebietes mit Hilfe von Differenzenverfahren. Dissertation, Hamburg, 1967.

  10. Royden, H. L.: A modification of the Neumann-Poincaré method for multiply connected regions. Pacific J. Maths.2, 385–394 (1952).

    Google Scholar 

  11. Savin, G. N.: Stress concentration around holes. London: Pergamon 1961.

    Google Scholar 

  12. Sugiyama, H., Joh, K.: A numerical procedure of conformal mapping in case of simply, doubly and multiply connected domains from the viewpoint of Monte Carlo approach (I). Tech. Rep. Osaka Univ.12, No. 488 (1962).

  13. Symm, G. T.: An integral equation method in conformal mapping. Num. Math.9, 250–258 (1966).

    Google Scholar 

  14. —— Numerical mapping of exterior domains. Num. Math.10, 437–445 (1967)

    Google Scholar 

  15. Ugodčikov, A. G.: Electromodelling of the conformal mapping of a circular cylinder onto a given doubly connected region. Ukrain. Mat. Ž.7, 305–312 (1955)

    Google Scholar 

  16. Wilson, H. B.: A method of conformal mapping and the determination of stresses in solid propellant rocket grains. Report No. S-38, Rohm and Haas Co., Alabama, 1963

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Division of Numerical and Applied Mathematics, National Physical Laboratory, Teddington, Middlesex, G. B.

    George T. Symm

Authors
  1. George T. Symm
    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

Symm, G.T. Conformal mapping of doubly-connected domains. Numer. Math. 13, 448–457 (1969). https://doi.org/10.1007/BF02163272

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02163272

Keywords

Search

Navigation