Numerical conformal mapping of multiply connected regions by Fornberg-like methods

Numerische Mathematik

Volumn 83, Issue 2, 1999, Pages 205-230

  DeLillo, Thomas K ^a   Horn, Mark A ^b   Pfaltzgraff, John A ^c  

^a WICHITA STATE UNIVERSITY   (United States)

^b ARINC Inc   (United States)

^c The University of North Carolina at Chapel Hill   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033443379     PISSN: 0029599X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002110050447     Document Type: Article

References (32)

1. Amano, K. (1995a): Numerical conformal mapping onto the circular slit domains. Trans. Inform. Process. Soc. Japan 36, 219-225 (in Japanese)
2. Amano, K. (1995b): Numerical conformal mapping onto the radial slit domains by the charge simulation method. Trans. Japan SIAM 5, 267-280 (in Japanese)
3. Amano, K. (c. 1996): A charge simulation method for numerical conformal mapping onto circular and radial slit domains. SIAM J. Sci. Comput. 19 (1998), 1169-1187
4. [De] DeLillo, T. K. (1994): The accuracy of numerical conformal mapping methods: a survey of examples and results. SIAM J. Numer. Anal., 31, 788-812
5. [DE] DeLillo, T. K., Elcrat, A. R. (1993): A Fornberg-like conformal mapping method for slender regions. J. Comput. Appl. Math. 46, 49-64
6. [DEP] DeLillo, T. K., Elcrat, A. R., Pfaltzgraff, J. A. (1997): Numerical conformal mapping methods based on Faber series. J. Comput. Appl. Math. 83, 205-236
7. [DP] DeLillo, T. K., Pfaltzgraff, J. A. (1998): Numerical conformal mapping methods for simply and doubly connected regions. SIAM J. Sci. Comput. 19, 155-171
8. Ellacott, S. W. (1979): On the approximate conformal mapping of multiply connected domains. Numer. Math. 33, 437-446
9. [Fo] Fornberg, B. (1980): A numerical method for conformal mappings. SIAM J. Sci. Statist. Comput. 1, 386-400
10. Gaier, D. (1964): Konstruktive Methoden der konformen Abbildung. Springer-Verlag, Berlin, Gottingen, Heidelberg
11. Gaier, D. (1978): Konformen Abbildung mehrfach zusammenhängender Gebiete. Jahresber. Dt. Math.-Ver. 81, 25-44
12. [Go] Goluzin, G. M. (1969): Geometric Theory of Functions of a Complex Variable. Amer. Math. Soc., Rhode Island
13. [Gr] Greenberg, M. D. (1998): Advanced Engineering Mathematics. Prentice-Hall, New Jersey
14. [Ha] Halsey, N. D. (1979): Potential flow analysis of multielement airfoils using conformal mapping. AIAA J. 17, 1281-1287
15. Harrington, A. N. (1982a): Conformal mappings onto domains with arbitrarily specified boundary shapes. J. D'Anal. Math. 41, 39-53
16. Harrington, A. N. (1982b): Conformal mappings onto multiply connected regions with specified boundary shapes. In: Numerical Grid Generation (J. F. Thompson, Ed.), Elsevier, p. 601
17. [He] Henrici, P. (1986): Applied and Computational Complex Analysis, Vol. III. John Wiley, New York
18. [Ho] Horn, M. A. (1997): Iterative Methods Applied to Some Problems in Conformal Mapping and Potential Theory. PhD thesis, Wichita State Univ. Math. Dept., Wichita, KS
19. [HK] Hoskins, W. D., King, P. R. (1972): Periodic cubic spline interpolation using parametric splines. The Computer Journal 15, 282-283
20. [KPS] Kokkinos, C. A., Papamichael, N., Sideridis, A. B. (1990): An orthogonalization method for the approximate conformal mapping of multiply-connected domains. IMA J. Numer. Anal. 9, 343-359
21. [LM] Luchini, P., Manzo, F. (1989): Flow around simply and multiply connected bodies: a new iterative scheme for conformal mapping. AIAA J. 27, 345-351
22. [Ma] Mayo, A. (1986): Rapid methods for the conformal mapping of multiply connected regions. In: Numerical Conformal Mapping (L. N. Trefethen, Ed.). Amsterdam: North-Holland, 125-142
23. [Ne] Nehari, Z. (1952): Conformal Mapping. Dover, New York
24. [Pros] Prosnak, W. (1977): Conformal representation of arbitrary multiconnected airfoil sections. Bull. Acad. Polon. Sci., Ser. Sci. Techn. 25, 25-36 (591-602)
25. [Re] Reichel, L. (1986): A fast method for solving certain integral equations of the first kind with application to conformal mapping. In: Numerical Conformal Mapping (L. N. Trefethen, Ed.). Amsterdam: North-Holland, 125-142
26. Volkov, E. A. (1994): Block Method for Solving the Laplace Equation and for Constructing Conformal Mappings. CRC Press, Boca Raton
27. Wegmann, R. (1984): Convergence proofs and error estimates for an iterative method for conformal mapping. Numer. Math. 44 (1984), 435-461
28. Wegmann, R. (1986a): On Fornberg's numerical method for conformal mapping. SIAM J. Numer. Anal. 23, 1199-1213
29. Wegmann, R. (1986b): An iterative method for the conformal mapping of doubly connected regions. J. Comput. Appl. Math. 14, 79-98
30. Wegmann, R. (1988): Discrete Riemann-Hilbert problems, interpolation of simply closed curves, and numerical conformal mapping. J. Comput. Appl. Math. 23, 323-352
31. Wegmann, R. (1996): Fast conformal mapping of an ellipse to a simply connected region. 72, 101-126
32. [Wid] Widlund, O. (c. 1981): On a numerical method for conformal mapping due to Fornberg. unpublished