Numerical conformal mapping methods based on Faber series

Journal of Computational and Applied Mathematics

Volumn 83, Issue 2, 1997, Pages 205-236

  DeLillo, Thomas K ^a   Elcrat, Alan R ^a   Pfaltzgraff, John A ^b  

^a WICHITA STATE UNIVERSITY   (United States)

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

Author keywords

Crowding; Faber series; Fornberg's methods; Numerical conformal mapping

Indexed keywords

APPROXIMATION THEORY; BOUNDARY CONDITIONS; COMPUTATIONAL METHODS; FAST FOURIER TRANSFORMS; ITERATIVE METHODS; MATHEMATICAL OPERATORS;

DISCRETIZATION;

CONFORMAL MAPPING;

EID: 0031558492     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0377-0427(97)00099-X     Document Type: Article

References (33)

1. R.H. Chan, T.K. DeLillo, M.A. Horn, The numerical solution of the biharmonic equation by conformal mapping, SIAM J. Sci. Comput., to appear.
2. J.H. Curtis, Faber polynomials and the Faber series, Amer. Math. Monthly 78 (1971) 577-596.
3. G. Dahlquist, Å. Björck, Numerical Methods, Prentice-Hall, Englewood Cliffs, NJ, 1974.
4. T.K. DeLillo, The accuracy of numerical conformal mapping methods: a survey of examples and results, SIAM J. Numer. Anal. 31 (1994) 788-812.
5. T.K. DeLillo, A.R. Elcrat, A comparison of some numerical conformal mapping methods for exterior regions, SIAM J. Sci. Statist. Comput. 12 (1991) 399-422.
6. T.K. DeLillo, A.R. Elcrat, A Fornberg-like conformal mapping method for slender regions, J. Comput. Appl. Math. 46 (1993) 49-64.
7. T.K. DeLillo, A.R. Elcrat, K.G. Miller, Constant vorticity Riabouchinsky flows from a variational principle, ZAMP 41 (1990) 755-765.
8. T.K. DeLillo, M.A. Horn, The numerical solution of the Laplace equation for slender regions, in preparation.
9. T.K. DeLillo, M.A. Horn, J.A. Pfaltzgraff, work in progress.
10. T.K. DeLillo, J.A. Pfaltzgraff, Extremal distance, harmonic measure and numerical conformal mapping, J. Comput. Appl. Math. 46 (1993) 103-113.
11. T.K. DeLillo, J.A. Pfaltzgraff, Numerical conformal mapping methods for simply and doubly connected regions, SIAM J. Sci. Comput., to appear.
12. T.A. Driscoll, S.A. Vavasis, Numerical conformal mapping using cross-ratios and Delauney triangulation, Cornell Theory Center Technical Report. CTC96TR233 (1996).
13. S.W. Ellacott, Computation of Faber series with application to numerical polynomial approximation in the complex plane, Math. Comput. 40 (1983) 575-587.
14. B. Fornberg, A numerical method for conformal mappings, SIAM J. Sci. Statist. Comput. 1 (1980) 386-400.
15. D. Gaier, Konstruktive Methoden der konformen Abbildung, Springer, Berlin, Göttingen, Heidelberg, 1964.
16. G.H. Golub, C.F. Van Loan, Matrix Computations, 2nd ed., Johns Hopkins, Baltimore, 1989.
17. G.M. Goluzin, Geometric Theory of Functions of a Complex Variable, AMS Trans. Math. Monographs, vol. 26, AMS, Providence, RI, 1969.
18. P. Henrici, Applied and Computational Complex Analysis, vol. III, Wiley, New York, 1986.
19. W.D. Hoskins, P.R. King, Periodic cubic spline interpolation using parametric splines, Algorithm 73, Comput. J. 15 (1972) 282-283.
20. L.H. Howell, L.N. Trefethen, A modified Schwarz-Christoffel transformation for elongated regions, SIAM J. Sci. Statist. Comput. 11 (1990) 928-949.
21. Z. Nehari, Conformal Mapping, McGraw-Hill, New York, 1952.
22. N. Papamichael, N. Stylianopoulos, On the theory and application of a domain decomposition method for computing conformal modules, J. Comput. Appl. Math. 50 (1994) 33-50.
23. G. Schober, Univalent Functions - Selected Topics, Lecture Notes in Math. vol. 478, Springer, Berlin, 1975.
24. R. Wegmann, Ein Iterationsverfahren zur konformen Abbildung, Numer. Math. 30 (1978) 453-466; translated as: An iterative method for conformal mapping, in: L.N. Trefethen (Ed.), Numerical Conformal Mapping, North-Holland, Amsterdam, 1986; also in J. Comput. Appl. Math. 14 (1986) 7-18.
25. R. Wegmann, Ein Iterationsverfahren zur konformen Abbildung, Numer. Math. 30 (1978) 453-466; translated as: An iterative method for conformal mapping, in: L.N. Trefethen (Ed.), Numerical Conformal Mapping, North-Holland, Amsterdam, 1986; also in J. Comput. Appl. Math. 14 (1986) 7-18.
26. R. Wegmann, Ein Iterationsverfahren zur konformen Abbildung, Numer. Math. 30 (1978) 453-466; translated as: An iterative method for conformal mapping, in: L.N. Trefethen (Ed.), Numerical Conformal Mapping, North-Holland, Amsterdam, 1986; also in J. Comput. Appl. Math. 14 (1986) 7-18.
27. R. Wegmann, Convergence proofs and error estimates for an iterative method for conformal mapping, Numer. Math. 44 (1984) 435-461.
28. R. Wegmann, On Fornberg's numerical method for conformal mapping, SIAM J. Numer. Anal. 23 (1986) 1199-1213.
29. R. Wegmann, Discrete Riemann-Hilbert problems, interpolation of simply closed curves, and numerical conformal mapping, J. Comput. Appl. Math. 23 (1988) 323-352.
30. R. Wegmann, Discretized versions of Newton type iterative methods for conformal mapping, J. Comput. Appl. Math. 29 (1990) 207-224.
31. R. Wegmann, Fast conformal mapping of an ellipse to a simply connected region, J. Comput. Appl. Math. 72 (1996) 101-126.
32. O. Widlund, On a numerical method for conformal mapping due to Fornberg, unpublished.
33. C. Zemach, A conformal map formula for difficult cases, in: L.N. Trefethen (Ed.), Numerical Conformal Mapping, North-Holland, Amsterdam, 1986, pp. 207-216.