A domain decomposition method for approximating the conformal modules of long quadrilaterals

Summary

This paper is concerned with the study of a domain decomposition method for approximating the conformal modules of long quadrilaterals. The method has been studied already by us and also by D. Gaier and W.K. Hayman, but only in connection with a special class of quadrilaterals, viz. quadrilaterals where: (a) the defining domain is bounded by two parallel straight lines and two Jordan arcs, and (b) the four specified boundary points are the four corners where the arcs meet the straight lines.

Our main purpose here is to explain how the method may be extended to a wider class of quadrilaterals than that indicated above.

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References

  1. 1.

    Bowman, F. (1953): Introduction to Elliptic Functions. English University Press, London

    Google Scholar 

  2. 2.

    Gaier, D., Hayman, W.K. (1991): On the computation of modules of long quadrilaterals. Constr. Approx.7, 453–467

    Google Scholar 

  3. 3.

    Gaier, D., Hayman, W.K. (1990): Modules of long quadrilaterals and thick ring domains. Rendiconti di Matematica Roma10, 809–834

    Google Scholar 

  4. 4.

    Gaier, D., Papamichael, N. (1987): On the comparison of two numerical methods for conformal mapping. IMA J. Numer. Anal.7, 261–282

    Google Scholar 

  5. 5.

    Hayman, W.K. (1948): Remarks on Ahlfors' distortion theorem. Quart. Appl. Math. Oxford Ser.19, 33–53

    Google Scholar 

  6. 6.

    Henrici P. (1986): Applied and Computational Complex Analysis, Vol. III. Wiley, New York

    Google Scholar 

  7. 7.

    Howell, I.H., Trefethen, L.N. (1990): A modified Schwarz-Christoffel transformation for elongated regions. SIAM J. Sci. Statist. Comput.11, 928–949

    Google Scholar 

  8. 8.

    Papamichael, N. (1989): Numerical conformal mapping onto a rectangle with applications to the solution of Laplacian problems. J. Comput. Appl. Math.28, 63–83

    Google Scholar 

  9. 9.

    Papamichael, N., Stylianopoulos, N.S. (1991): A domain decomposition method for conformal mapping onto a rectangle. Constr. Approx.7, 349–379

    Google Scholar 

  10. 10.

    Papamichael, N., Stylianopoulos, N.S. (1990): On the numerical performance of a domain decomposition method for conformal mapping, pp. 155–169. In: S. Ruscheweyh, E.B. Saff, L.C. Salinas, R.S. Varga, eds., Computational Methods and Function Theory. Lecture Notes in Maths.1435. Springer, Berlin Heidelberg New York

    Google Scholar 

  11. 11.

    trefethen, L.N. (1989): SCPACK User's Guide. Numerical Analysis Report 89-2, Dept. of Math., Massachusetts Institute of Technology, Cambridge, MA

    Google Scholar 

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Correspondence to N. Papamichael.

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Papamichael, N., Stylianopoulos, N.S. A domain decomposition method for approximating the conformal modules of long quadrilaterals. Numer. Math. 62, 213–234 (1992). https://doi.org/10.1007/BF01396227

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Mathematics Subject Classification (1991)

  • 30C30
  • 65E05