Chapter 9 Methods for numerical conformal mapping. Dedicated to the memory of Dieter Gaier

Handbook of Complex Analysis

Volumn 2, Issue , 2005, Pages 351-477

  Wegmann, Rudolf ^a  

^a MAX PLANCK INSTITUT FÜR ASTROPHYSIK   (Germany)

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[No Author keywords available]

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EID: 66049164376     PISSN: 18745709     EISSN: None     Source Type: Book Series    
DOI: 10.1016/S1874-5709(05)80013-7     Document Type: Chapter

References (298)

1. Ahlfors L.V. Remarks on the Neumann-Poincaré integral equation. Pacific J. Math. 2 (1952) 271-280
2. Amano K. A charge simulation method for the numerical conformal mapping of interior exterior and doubly-connected domains. J. Comput. Appl. Math. 53 (1994) 353-370
3. Amano K. A charge simulation method for numerical conformal mapping onto circular and radial slit domains. SIAM J. Sci. Comput. 19 (1998) 1169-1187
4. Anderson C., Christiansen S.E., Møller O., and Tornehave H. conformal Mapping, Selected Numerical Methods. In: Gram C. (Ed) (1962), Regnecentralen, Kopenhagen
5. Anderson C., and Dillon Daleh M. Rapid computation of the discrete Fourier transform. SIAM J. Sci. Comput. 17 (1996) 913-919
6. Atkinson K.E. The numerical solution of boundary integral equations. In: Duff I.S., et al. (Ed). The State of the Art in Numerical Analysis (1997), Clarendon Press, Oxford 223-259
7. (in Russian, English summary). Banzuri P.D. On the Riemann-Hilbert-problem for doubly connected domains. Soobshch. Akad. Nauk Gruzin. SSR (1975) 549-552
8. Baty R.S., and Morris P.J. conformal grid generation for high aspect ratio simply and doubly connected regions. Internat. J. Numer. Methods Engrg. 38 (1995) 3817-3830
9. Bell S. Numerical computation of the Ahlfors map of a multiply connected planar domain. J. Math. Anal. Appl. 120 (1986) 211-217
10. Bell S.R. The Cauchy Transform, Potential Theory, and conformal Mapping (1992), CRC Press, Boca Raton, FL
11. Bell S. Complexity of the classical kernel functions of potential theory. Indiana Univ. Math. J. 44 (1995) 1337-1369
12. Bell S. Recipes for classical kernel functions associated to a multiply connected domain in the plane. Complex Var. 29 (1996) 367-378
13. Bergman (n) S. Über die Entwicklung der harmonischen Funktionen der Ebene und des Raumes nach Orthogonalfunktionen. Math. Ann. 86 (1922) 238-271
14. Bergman S. The Kernel Function and conformal Mapping. Math. Surveys 5 (1950), Amer. Math. Soc., New York
15. Bergman S., and Chalmers B. A procedure for conformal mapping of triply-connected domains. Math. Comp. 21 (1967) 527-542
16. 193-198. Bergström H. An approximation of the analytic function mapping a given domain inside or outside the unit circle (1958), Mém. Publ. Soc. Sci. Arts Lettr., Hainaut
17. Beirut J.-P. A Fredholm integral equation of the second kind for conformal mapping. J. Comput. Appl. Math. 14 (1986) 99-110
18. Beirut J.-P., and Trummer M.R. Equivalence of Nyström's method and Fourier mathods for the numerical solution of Fredholm integral equations. Math. Comp. 48 (1987) 617-623
19. Beylkin G. On the fast Fourier transform of functions with singularities. Appl. Comput. Harmon. Anal. 2 (1995) 363-381
20. Bieberbach L. Zur Theorie und Praxis der konformen Abbildung. Rend. Cire. Mat. Palermo 38 (1914) 98-112
21. Bisshopp F. Numerical conformal mapping and analytic continuation. Quarterly Appl. Math. 41 (1983) 125-142
22. Braβ H. Zur numerischen Berechnung konjugierter Funktionen. In: Collatz L., Meinardus G., and Werner H. (Eds). Numer. Meth. Approx. Theory Vol. 6 (1982), Birkhäuser, Basel 43-66
23. Burbea J., and procedure A. for conformal maps of simply connected domains by using the Bergman function. Math. Comp. 24 (1970) 821-829
24. Burbea J. A numerical determination of the modulus of doubly connected domains by using the Bergman curvature. Math. Comp. 25 (1971) 743-756
25. Carey G.F., and Muleshkov A. Some conformal map constructs for numerical grids. Comm. Numer. Meth-ods Engrg. 11 (1995) 127-135
26. Challis N.V., and Burley D.M. A numerical method for conformal mapping. IMA J. Numer. Anal. 2 (1982) 169-181
27. Chakravarty S., and Anderson D. Numerical conformal mapping. Math. Comp. 33 (1979) 953-969
28. Christiansen S. Condition number of matrices derived from two classes of integral equations. Math. Meth-ods Appl. Sci. 3 (1981) 364-392
29. Chung Y.-B. An expression of the Bergman kernel function in terms of the Szegö kernel. J. Math. Pures Appl. 75 (1996) 1-7
30. Cooley J.W., and Tukey J.W. An algorithm for the machine calculation of complex Fourier series. Math. Comp. 19 (1965) 297-301
31. Courant R., Manel B., and Shiftman M. A general theorem on conformal mapping of multiply connected domains. Proc. Natl. Acad. Sci. USA 26 (1940) 503-507
32. Courant R. Dirichlet's Principle, conformal Mapping, and Minimal Surfaces (1950), Interscience, New York
33. Curtiss J.H. Solution of the Dirichlet problem by interpolating harmonic polynomials. Bull. Amer. Math. Soc. 68 (1962) 333-337
34. DeLillo T.K. On some relations among numerical conformal mapping methods. J. Comput. Appl. Math. 19 (1987) 363-377
35. DeLillo T.K. A note on Rengel's inequality and the crowding phenomenon in conformal mapping. Appl. Math. Lett. 3 (1990) 25-27
36. DeLillo T.K. On the use of numerical conformal mapping methods in solving boundary value problems for the Laplace equation. Adv. Comp. Methods Partial Differential Equations 7 (1992) 190-194
37. DeLillo T.K. The accuracy of numerical conformal mapping methods: A survey of examples and results. SIAM J. Numer. Anal. 31 (1994) 788-812
38. DeLillo T.K., and Elcrat A.R. A comparison of some numerical conformal mapping methods for exterior regions. SIAM J. Sci. Stat. Comput. 12 (1991) 399-422
39. DeLillo T.K., and Elcrat A.R. A Fornberg-like conformal mapping method for slender regions. J. Comput. Appl. Math. 46 (1993) 49-64
40. DeLillo T.K., and Elcrat A.R. Numerical conformal mapping methods for exterior regions with corners. J. Comput. Phys. 108 (1993) 199-208
41. DeLillo T.K., Elcrat A.R., and Pfaltzgraff J.A. Numerical conformal mapping methods based on Faber series. J. Comput. Appl. Math. 83 (1997) 205-236
42. DeLillo T.K., A. Horn M., and Pfaltzgraff J.A. Numerical conformal mapping of multiply connected regions by Fornberg-like methods. Numer. Math. 83 (1999) 205-230
43. DeLillo T.K., and Pfaltzgraff J.A. Extremal distance and harmonic measure and numerical conformal map-ping. J. Comput. Appl. Math. 46 (1993) 103-113
44. DeLillo T.K., and Pfaltzgraff J.A. Numerical conformal mapping methods for simply and doubly connected regions. SIAM J. Sci. Comput. 19 (1998) 155-171
45. Dittmar B. Bemerkungen zu einem Funktional von M. Schiffer und N.S. Hawley in der Theorie konformer Abbildungen. Math. Nachr. 97 (1980) 21-37
46. Driscoll T.A. A nonoverlapping domain decomposition method for Symm 's equation for conformal map-ping. SIAM J. Numer. Anal. 36 (1999) 922-934
47. Driscoll T.A., and Trefethen L.N. Schwarz-Christojfel Mapping (2002), Cambridge University Press, Cambridge
48. Dundučenko L.E. On the Riemann-Hilbert problem for a multiply connected domain. Soviet Math. Dokl. 12 (1971) 34-37
49. Dutt A., and Rokhlin V. Fast Fourier transforms for nonequispaced data. SIAM J. Sci. Comput. 14 (1993) 1368-1393
50. Ellacott S.W. A technique for approximate conformal mapping. Multivariate Approximation (Sympos. Durham 1977) (1978), Academic Press, London 301-314
51. Ellacott S.W. On the approximate conformal mapping of multiply connected domains. Numer. Math. 33 (1979) 437-446
52. Elschner J., and Stephan E.P. A discrete collocation method for Symm's integral equation on curves with corners. J. Comput. Appl. Math. 75 (1996) 131-146
53. Elschner J., and Graham I.G. Quadrature methods for Symm's integral equation on polygons. IMA J. Numer. Anal. 17 (1997) 643-664
54. (in Russian). Erohin V. On the theory of conformal and quasiconformal mapping of multiply connected regions. Dokl. Akad. Nauk SSSR 127 (1959) 1155-1157
55. Falcão M.I., Papamichael N., and Stylianopoulos N.S. Curvilinear crosscuts of subdivision for a domain decomposition method in numerical conformal mapping. J. Comput. Appl. Math. 106 (1999) 177-196
56. Falcao M.I., Papamichael N., and Stylianopoulos N.S. Approximating the conformal maps of elongated quadrilaterals by domain decomposition. Constr. Approx. 17 (2001) 589-617
57. (in Russian). Fil'čakov P.F. Approximate Methods of conformal Mapping (1964), Naukova Dumka, Kiev
58. (in Russian). Fil'čakova V.P. conformal Mappings of Domains of Special Type (1972), Naukova Dumka, Kiev
59. Floryan J.M., and Zemach C. Schwarz-Christoffel mappings: A general approach. J. Comput. Phys. 72 (1987) 347-371
60. Floryan J.M., and Zemach C. On the generalized Schwarz-Christoffel mappings and their numerical im-plementation. Z. Angew. Math. Mech. 69 (1989) T75-T77
61. Floryan J.M., and Zemach C. Schwarz-Christoffel methods for conformal mapping of regions with aperi-odic boundary. J. Comput. Appl. Math. 46 1/2 (1993) 77-102
62. Fornberg B. A numerical method for conformal mappings. SIAM J. Sci. Stat. Comput. 1 (1980) 386-400
63. Fornberg B. A numerical method for conformal mapping of doubly connected regions. SIAM J. Sci. Stat. Comput. 5 (1984) 771-783
64. Friberg M.S. A new method for the effective determination of conformal maps. Thesis Univ. Minnesota (1951)
65. Gaier D. Konstruktive Methoden der konformen Abbildung (1964), Springer, Berlin
66. Gaier D. Ermittlung des konformen Moduls von Vierecken mit Differenzenmethoden. Numer. Math. 19 (1972) 179-194
67. Gaier D. Ableitungsfreie Abschätzungen bei trigonometrischer Interpolation und Konjugierten-Bestimmung. Computing 12 (1974) 145-148
68. Gaier D. Integralgleichung erster Art und konforme Abbildung. Math. Z. 147 (1976) 113-129
69. Gaier D. Konforme Abbildung mehrfach zusammenhängender Gebiete. Jahresber. Deutsch. Math.-Ver. 81 (1978) 25-44
70. Gaier D. Das logarithmische Potential und die konforme Abbildung mehrfach zusammenhängender Gebiete. In: Butzer P.L., Christoffel E.B., and Feher F. (Eds). The Influence of His Work on Mathematics and the Physical Sciences (1981), Birkhäuser, Basel 290-303
71. Gaier D. Numerical methods in conformal mapping. In: Werner H., et al. (Ed). Computational Aspects of Complex Analysis (1983), Reidel, Boston 51-78
72. Gaier D. On a polynomial lemma of Andrievskii. Arch. Math. 49 (1987) 119-123
73. Gaier D. On the convergence of the Bieberbach polynomials in regions with piecewise analytic boundary. Arch. Math. 58 (1992) 462-470
74. Gaier D. conformal mapping of analytic corners in a generalized sense. Analysis 12 (1992) 187-193
75. Gaier D. conformal modules and their computation. Computational Methods and Function Theory (1994), Penang, Malaysia 159-171
76. Gaier D. Polynomial approximation of conformal maps. Constr. Approx. 14 (1998) 27-30
77. Gaier D., and Hayman W.K. Modules of long quadrilaterals and thick ring domains. Rend. Mat. Appl. 10 (1990) 809-834
78. Gaier D., and Hayman W. On the computation of modules of long quadrilaterals. Constr. Approx. 7 (1991) 453-467
79. Gaier D., and Papamichael N. On the comparison of two numerical methods for conformal mapping. IMA J. Numer. Anal. 7 (1987) 261-282
80. Garabedian P. Schwarz's lemma and the Szegö kernel function. Trans. Amer. Math. Soc. 67 (1949) 1-35
81. Garrick I.E. Potential flow about arbitrary biplane wing sections. NACA Report 542 (1936)
82. Gautschi W. Attenuation factors in practical Fourier analysis. Numer. Math. 18 (1972) 373-400
83. Gillot G. Calcule numérique de la transformation conforme faisant correspondre l'intérieur d'un cercle a l'intérieur d'une courbe fermée. C. R. Acad. Sci. Paris 262 (1966) 1243-1246
84. Goluzin G.M. Geometrie Theory of Functions of a Complex Variable. 2nd edn (1969), Amer. Math. Soc., Providence, RI
85. Graham L.G., and Atkinson K.E. On the Sloan iteration applied to integral equations of the first kind. IMA J. Numer. Anal. 13 (1993) 29-41
86. Grassmann E. Numerical experiments with a method of successive approximation for conformal mapping. J. Appl. Math. Phys. (ZAMP) 30 (1979) 873-884
87. Grinshpan A.Z., and Saff E.B. Estimating the argument of approximate conformal mappings. Complex Var. 26 (1994) 191-202
88. Grötzsch H. Über das Parallelschlitztheorem der konformen Abbildung schlichter Bereiche. Ber. Verh. Sächs. Akad. Wiss. Leipzig Math.-Phys. Kl. 84 (1932) 15-36
89. Grunsky H. Lectures on Theory of Functions in Multiply Connected Domains (1978), Vandenhoeck & Ruprecht, Göttingen
90. Gutknecht M.H. Existence of a solution to the discrete Theodorsen equation for conformal mappings. Math. Comp. 31 (1977) 478-480
91. Gutknecht M.H. Fast algorithms for the conjugate periodic function. Computing 22 (1979) 79-91
92. Gutknecht M.H. Solving Theodorsen's integral equation for conformal maps with the fast Fourier trans-form and various nonlinear iterative methods. Numer. Math. 36 (1981) 405-429
93. Gutknecht M.H. On the computation of the conjugate trigonometric rational function and on a related splitting problem. SIAM J. Numer. Anal. 20 (1983) 1198-1205
94. Gutknecht M.H. Numerical experiments on solving Theodorsen's integral equation for conformal maps with the fast Fourier transform and various nonlinear iterative methods. SIAM J. Sci. Stat. Comput. 4 (1983) 1-30
95. Gutknecht M.H. Numerical conformal mapping methods based on function conjugation. J. Comput. Appl. Math. 14 (1986) 31-77
96. Halsey N.D. Potential flow analysis of multielement airfoils using conformal mapping. AIAA J. 17 (1979) 1281-1288
97. Halsey N.D. Comparison of the convergence characteristics of two conformal mapping methods. AIAA J. 20 (1982) 724-726
98. Hammerschick J. Über die discrete Form der Integralgleichungen von Garrick zur konformen Abbildung von Ringgebieten. Mitt. Math. Sem. Giessen 70 (1966)
99. Harrington A.N. conformal mappings onto domains with arbitrarily specified boundary shapes. J. Anal. Math. 41 (1982) 39-53
100. Hartmann M., and Opfer G. Uniform approximation as a numerical tool for constructing conformal maps. J. Comput. Appl. Math. 14 (1986) 193-206
101. Hayes J.K., Kahaner D.K., and Kellner R.G. An improved method for numerical conformal mapping. Math. Comp. 26 (1972) 327-334
102. Hayes J.K., Kahaner D.K., and Kellner R.G. A numerical comparison of integral equations of the first and second kind for conformal mapping. Math. Comp. 29 (1975) 512-521
103. Henrici P. Einige Anwendungen der schnellen Fouriertransformation. Int. Ser. Numer. Math. 32 (1976) 111-124
104. Henrici P. Fast Fourier methods in computational complex analysis. SIAM Rev. 21 (1979) 481-527
105. Henrici P. Pointwise error estimates for trigonometric interpolation and conjugation. J. Comput. Appl. Math. 8 (1982) 131-132
106. Henrici P. A general theory of osculation algorithms for conformal mapping. Linear Algebra Appl. 52/53 (1983) 361-382
107. Henrici P. Applied and Computational Complex Analysis Vol. 3 (1986), Wiley, New York
108. Hof mann R. Zur punktweisen konformen Abbildung unter Verwendung des harmonischen Maβes. Beiträge Numer. Math. 1 (1974) 57-60
109. Hoidn H.P. Osculation methods for the conformal mapping of doubly connected regions. J. Appl. Math. Phys. (ZAMP) 33 (1982) 640-651
110. Hoidn H.P. A reparametrisation method to determine conformal maps. J. Comput. Appl. Math. 14 (1986) 155-161
111. Homentcovschi D. conformal mapping of the domain exterior to a thin region. SIAM J. Math. Anal. 10 (1979) 1246-1257
112. Homentcovschi D. conformal mapping of multiply connected domains exterior to thin regions. Z. Angew. Math. Phys. 33 (1982) 503-511
113. Hough D.M. User's Guide of CONFPACK. IPS Research Report 90-11 (1990), ETH, Zürich
114. Hough D.M., Levesley J., and Chandler-Wilde S.N. Numerical conformal mapping via Chebyshev weighted solutions of Symm's integral equation. J. Comput. Appl. Math. 46 (1993) 29-48
115. Hough D.M., and Papamichael N. The use of splines and singular functions in an integral equation method for conformal mapping. Numer. Math. 37 (1981) 133-147
116. Hough D.M., and Papamichael N. An integral equation method for the numerical conformal mapping of interior,exterior and doubly-connected domains. Numer. Math. 41 (1983) 287-307
117. Hübner O. Funktionentheoretische Iterationsverfahren zur konformen Abbildung ein-und mehrfach zusammenhängender Gebiete. Mitt. Math. Sem. Giessen 63 (1964)
118. Hübner O. Die Faktorisierung konformer Abbildungen und Anwendungen. Math. Z. 92 (1966) 95-109
119. Hübner O. Zur Numerik der Theodorsenschen Integralgleichung in der konformen Abbildung. Mitt. Math. Sem. Giessen 140 (1979) 1-32
120. Hübner O. Über die Anzahl der Lösungen der diskreten Theodorsen-Gleichung. Numer. Math. 39 (1982) 195-204
121. Hübner O. Über die Existenz einer Lösung der diskreten Theodorsen-Gleichung in der Nähe der Restrik-tion der Ränderzuordnungsfunktion. Mitt. Math. Sem. Giessen 175 (1986) 27-42
122. Hübner O. On the fast solution of a linear system arising in numerical conformal mapping. J. Comput. Appl. Math. 16 (1986) 381-386
123. Hübner O. The Newton method for solving the Theodorsen integral equation. J. Comput. Appl. Math. 14 (1986) 19-30
124. Inoue T. Algorithm for computing an inverse function of a conformal mapping by fundamental solution method. Trans. Inform. Process. Soc. Japan 38 (1997) 377-379
125. Inoue T. New charge simulation method for numerical conformal mapping of ring domains. Japan J. Industr. Appl. Math. 14 (1997) 295-301
126. Inoue T. Theoretical consideration of charge simulation method for numerical conformal mappings in a ring domain. Int. J. Math. Math. Sci. 21 (1998) 289-298
127. Inoue T. Numerical conformal mappings of the domain whose outer boundary is a unit circle. Japan J. Industr. Appl. Math. 19 (2002) 249-256
128. with 1 IBM-PC floppy disk. Ivanov V.l., and Trubetskov M.K. Handbook of conformal Mapping with Computer-Aided Visualization (1995), CRC Press, Boca Raton, FL
129. Ives D.C. A modern look at conformal mapping including multiply connected regions. AIAA J. 14 (1976) 1006-1011
130. James R.M. A new look at two-dimensional incompressible airfoil theory. Report MDC-J0918/01 (1971), Douglas Aircraft Company
131. Kaiser A. L8-Konvergenz verschiedener Verfahren der sukzessiven Konjugation zur Berechnung konformer Abbildungen. Dissertation, ETH (1986), Zürich
132. Kantorowitsch L.W., and Krylow W.I. Approximation Methods in Higher Analysis (1958), Interscience, New York
133. Kerzman N., and Stein E.M. The Cauchy kernel the Szegö kernel and the Riemann mapping function. Math. Ann. 236 (1978) 85-93
134. Kerzman N., and Trummer M.R. Numerical conformal mapping via the Szegö kernel. J. Comput. Appl. Math. 14 (1986) 111-123
135. Kleiner W. Sur l'approximation de la représentation conforme par la méthode des points extrémaux de M. Leja. Ann. Polon. Math. 14 (1964) 131-140
136. Klonowska M.E., and Prosnak W.J. On an effective method for conformal mapping of multiply connected domains. Acta Mech. 119 (1996) 35-52
137. Kober H. Dictionary of conformal Representations (1952), Pover Publication, New York
138. Koebe P. Über die konforme Abbildung mehrfach zusammenhängender ebener Bereiche insbesondere solcher Bereiche, deren Begrenzung von Kreisen gebildet wird. Jahresber. Deutsch. Math.-Verein. 15 (1906) 142-153
139. Koebe P. Über die konforme Abbildung mehrfach zusammenhängender Bereiche. Jahresber. Deutsch. Math.-Verein. 19 (1910) 339-348
140. Koebe P. Über eine neue Methode der konformen Abbildung und Uniformisierung. Nachr. Kgl. Ges. Wiss. Göttingen Math.-Phys. Kl. (1912) 844-848
141. Koebe P. Abhandlung zur Theorie der konformen Abbildung: V Abbildung mehrfach zusammenhängender schlichter Bereiche auf Schlitzbereiche. Math. Z. 2 (1919) 198-236
142. Kokkinos C.A. A unified orthonormalization method for the approximate conformal mapping of simply and multiply-connected domains. In: Papamichael N., et al. (Ed). Proc. CMFT Conference Nicosia. 1997 (1999) 327-344
143. Kokkinos C.A., Papamichael N., and Sideridis A.B. An orthonormalization method for the approximate conformal mapping of multiply-connected domains. IMA J. Numer. Anal. 9 (1990) 343-359
144. 1949. Komatu Y. Ein alternierendes Approximationsverfahren fuer konforme Abbildung von einem Ringgebiete auf einen Kreisring. Proc. Japan Acad. 21 (1945) 146-155
145. von Koppenfels W., and Stallmann F. Praxis der konformen Abbildung (1959), Springer-Verlag, Berlin-Göttingen-Heidelberg
146. Kosma Z. On an algorithm for conformal mapping of plane multiply-connected domains. Bull. Pol. Acad. Sci. 35 (1987) 41-52
147. Krabs W., and Opfer G. Eine Methode zur Lösung des komplexen Approximationsproblems mit einer Anwendung auf konforme Abbildungen. Z. Angew. Math. Mech. 55 (1975) T208-T211
148. Kreβ R. Uber die numerische Berechnung konjugierter Funktionen. Computing 10 (1972) 177-187
149. Krutitskii P.A. Equivalence of the problem of the directional derivative and the Riemann-Hilbert problem. Differ. Equ. 28 (1992) 698-707
150. Kühnau R. Numerische Realisierung konformer Abbildungen durch Interpolation. Z. Angew. Math. Mech. 63 (1983) 631-637
151. Kulisch U. Ein Iterationsverfahren zur konformen Abbildung des Einheitskreises auf einen Stern. Z. Angew. Math. Mech. 43 (1963) 403-410
152. Kythe P.K. Computational conformal Mapping (1998), Birkhäuser, Boston
153. Lamb H. Hydrodynamics. 6th edn (1993), Cambridge University Press, Cambridge
154. Landweber L., and Miloh T. Elimination of corners in the mapping of a closed curve. J. Engrg. Math. 6 (1972) 369-375
155. Lanza de Cristoforis M. A note on conformal representation in Sobolev spaces. Complex Var. 20 (1992) 121-133
156. Laugesen R. conformal mapping of long quadrilaterals and thick doubly connected domains. Constr. Approx. 10 (1994) 523-554
157. (in Russian). Lavrik V.l., and Savenkov V.N. A Handbook on conformal Mappings (1970), Naukova Dumka, Kiev
158. Lawrentjew M.A., and Schabat B.W. Methoden der komplexen Funktionentheorie (1967), VEB Deutscher Verlag der Wissenschaften, Berlin
159. Lee B., and Trummer M.R. Multigrid conformal mapping via the Szegö kernel. Electron. Trans. Numer. Anal. 2 (1994) 22-43
160. Lehman R.S. Development of the mapping function at an analytic corner. Pacific J. Math. 7 (1957) 1437-1449
161. Leja F. Sur certaines suites liées aux ensembles plans et leur application à la représentation conforme. Ann. Polon. Math. 4 (1957) 8-13
162. Lesley F.D. Hölder continuity of conformal mappings at the boundary via the strip method. Indiana Univ. Math. J. 31 (1982) 341-354
163. Levesley J., Hough D.M., and Chandler-Wilde S.N. A Chebyshev collocation method for solving Symm's integral equation for conformal mapping: A partial error analysis. IMA J. Numer. Anal. 14 (1993) 57-79
164. Levin D., Papamichael N., and Sideridis A. The Bergman kernel method for the numerical conformal mapping of simply connected domains. J. Inst. Math. App. 22 (1978) 171-187
165. Li B.C., and Syngellakis S. Numerical conformal mapping based on the generalised conjugation operator. Math. Comp. 67 (1998) 619-639
166. Lind I. Some problems related to iterative methods in conformal mapping. Ark. Mat. 7 (1967) 101-143
167. (in Russian). Lotfullin M.V. A numerical method of conformal mapping of simply connected domains. Trudy Sem. Kraev. Zadacham 22 (1985) 148-151
168. Luchini P., and Manzo F. Flow around simply and multiply connected bodies: A new iterative scheme for conformal mapping. AIAA J. 27 (1989) 345-351
169. Luchini P., and Manzo F. A fast conformal mapping algorithm with no FFT. J. Comput. Phys. 101 (1992) 368-374
170. Preprint. Marshall D.E., and Rohde S. The Loewner differential equation and slit mappings (2003)
171. 2-approximation of power and logarithmic func-tions with applications to numerical conformal mapping. Numer. Math. 91 (1902) 503-542
172. Mayo A. The fast solution of Poisson's and the biharmonic equations on irregular regions. SIAM J. Numer. Anal. 21 (1984) 285-299
173. Mayo A. Rapid methods for the conformal mapping of multiply connected regions. J. Comput. Appl. Math. 14 (1986) 143-153
174. McLean W. A spectral Galerkin method for a boundary integral equation. Math. Comp. 47 (1986) 597-607
175. Meiron D.I., Orszag S.A., and Israeli M. Applications of numerical conformal mapping. J. Comput. Phys. 40 (1981) 345-360
176. Menikoff R., and Zemach C. Methods for numerical conformal mapping. J. Comput. Phys. 36 (1980) 366-410
177. Menke K. Extremalpunkte und konforme Abbildung. Math. Ann. 195 (1972) 292-308
178. Menke K. Bestimmung von Näherungen für die konforme Abbildung mit Hilfe von stationären Punktsys-temen. Numer. Math. 22 (1974) 111-117
179. Menke K. Point systems with extremal properties and conformal mapping. Numer. Math. 54 (1988) 125-143
180. Menke K. conformal mapping of doubly connected regions. Complex Var. 14 (1990) 251-260
181. Mikhlin S.G. Integral Equations and Their Applications (1957), Pergamon Press, New York
182. Mizumoto H., and Hara H. Determination of the moduli of ring domains by finite element methods. Int. J. Differential Equations Appl. 3 (2001) 325-337
183. Monegato G., and Scuderi L. Global polynomial approximation for Symm's equation on polygons. Numer. Math. 86 (2000) 655-683
184. Moretti G. Orthogonal grids around difficult bodies. AIAA J. 30 (1992) 933-938
185. Murid A.H.M., Nashed M.Z., and Razali M.R.M. Numerical conformal mapping for exterior regions via the Kerzman-Stein kernel. J. Integral Equations Appl. 10 (1998) 517-532
186. Murid A.H.M., Nashed M.Z., and Razali M.R.M. Some integral equations related to the Riemann map. In: Papamichael N., et al. (Ed). Proc. CMFT Conference. Nicosia, 1997 (1999) 405-419
187. Muskhelishvili N.I. Singular Integral Equations (1953), Noordhoff, Groningen
188. Nasyrov S.R., and Fokin D.A. Proof of the convergence of an approximate method of conformal map-ping of the exterior of an airfoil onto the exterior of a disk. Comput. Methods. Math. Phys. 33 (1993) 1447-1457
189. Nehari Z. conformal Mapping (1952), McGraw-Hill, New York
190. von Neumann J. Functional Operators, Vol II. The Geometry of Orthogonal Spaces. Ann. of Math. Stud. Vol. 22 (1950), Princeton Univ. Press
191. Niethammer W. Iterationsverfahren bei der konformen Abbildung. Computing 1 (1966) 146-153
192. Nieto J.L., Hureau J., and Mudry M. A general method for practical conformal mapping of aerodynamic shapes. Eur. J. Mech. B Fluids 10 (1991) 147-160
193. Nitsche J.A. Finite-element methods for conformal mapping. SIAM J. Numer. Anal. 26 (1989) 1525-1533
194. O'Donnell S.T., and Rokhlin V. A fast algorithm for the numerical evaluation of conformal mappings. SIAM J. Sci. Stat. Comput. 10 (1989) 475-487
195. Ogata H., Okano D., and Amano K. Numerical conformal mapping of periodic structure domains. Japan J. Industr. Appl. Math. 19 (2002) 257-275
196. Okano D., Ogata H., and Amano K. A method of numerical conformal mapping of curved slit domains by the charge simulation method. J. Comput. Appl. Math. 152 (2003) 441-450
197. Opfer G. Die Bestimmung des Moduls zweifach zusammenhängender Gebiete mit Hilfe von Differenzen-verfahren. Arch. Ration. Mech. Anal. 32 (1969) 281-297
198. Opfer G. Uber einige Approximationsprobleme im Zusammenhang mit konformen Abbildungen. In: Collatz L., and Meinardus G. (Eds). Numer. Meth. der Approximationstheorie 1 (1972) 93-116
199. Opfer G. Konforme Abbildung und ihre numerische Behandlung. Überbl. Math. 7 (1974) 33-113
200. Opfer G. Ueber die Approximation der Identität im Komplexen. Numer. Meth. der Approximationstheorie 2 (1975) 93-100
201. Opfer G. New extremal properties for constructing conformal mappings. Numer. Math. 32 (1979) 423-429
202. Opfer G. conformal mappings onto prescribed regions via optimization techniques. Numer. Math. 35 (1980) 189-200
203. Opitz G. Zur Konvergenz bei genäherter konformer Abbildung. Z. Angew. Math. Mech. 30 (1950) 337-346
204. Ortega J.M., and Rheinboldt W.C. Iterative Solution of Nonlinear Equations in Several Variables (1970), Academic Press, New York
205. Ostrowski A.M. Math. Miszellen XV: Zur konformen Abbildung einfach zusammenhängender Gebiete. Jahresber. Deutsch. Math.-Verein. 38 (1929) 168-182
206. Ostrowski A.M. On the convergence of Theodorsen's and Garrick's method of conformal mapping. Nat. Bur. Standards Appl. Mat. Ser. 18 (1952) 149-163
207. Papamichael N. Numerical conformal mapping onto a rectangle with applications to the solution of Lapla-cian problems. J. Comput. Appl. Math. 28 (1989) 63-83
208. Papamichael N., and Kokkinos C.A. Two numerical methods for the conformal mapping of simply-connected domains. Comput. Methods Appl. Mech. Engrg. 28 (1981) 285-307
209. Papamichael N., and A. Kokkinos C. Numerical conformal mapping of exterior domains. Comput. Methods Appl. Mech. Engrg. 31 (1982) 189-203
210. Papamichael N., and Kokkinos C.A. The use of singular functions for the approximate conformal mapping of doubly-connected domains. SIAM J. Sci. Stat. Comput. 5 (1984) 684-700
211. Papamichael N., Kokkinos C.A., and Warby M.K. Numerical techniques for conformal mapping onto a rectangle. J. Comput. Appl. Math. 20 (1987) 349-358
212. Papamichael N., Pritsker I.E., Saff E.B., and Stylianopoulos N.S. Approximation of conformal mappings of annular regions. Numer. Math. 76 (1997) 489-513
213. Papamichael N., and Saff E.B. Local behaviour of the error in the Bergman kernel method for numerical conformal mapping. J. Comput. Appl. Math. 46 (1993) 65-75
214. Papamichael N., and Stylianopoulos N.S. A domain decomposition method for conformal mapping onto a rectangle. Constr. Approx. 7 (1991) 349-379
215. Papamichael N., and Stylianopoulos N.S. A domain decomposition method for approximating the conformal modules of long quadrilaterals. Numer. Math. 62 (1992) 213-234
216. Papamichael N., and Stylianopoulos N.S. On the theory and application of a domain decomposition method for computing conformal modules. J. Comput. Appl. Math. 50 (1994) 33-50
217. Papamichael N., and Warby M.K. Pole-type singularities and the numerical conformal mapping of doubly-connected domains. J. Comput. Appl. Math. 10 (1984) 93-106
218. Papamichael N., and Warby M.K. Stability and convergence properties of Bergman kernel methods for numerical conformal mapping. Numer. Math. 48 (1986) 639-669
219. Papamichael N., Warby M.K., and Hough D.M. The determination of the poles of the mapping function and their use in numerical conformal mapping. J. Comput. Appl. Math. 9 (1983) 155-166
220. Papamichael N., Warby M.K., and Hough D.M. The treatment of corner and pole-type singularities in numerical conformal mapping techniques. J. Comput. Appl. Math. 14 (1986) 163-191
221. Pommerenke C. Polynome und konforme Abbildung. Monatsh. Math. 69 (1965) 58-61
222. Pommerenke C. Über die Verteilung der Fekete-Punkte. Math. Ann. 168 (1967) 111-127
223. Pommerenke C. Über die Verteilung der Fekete-Punkte II. Math. Ann. 179 (1969) 212-218
224. Pommerenke C. Boundary Behaviour of conformal Maps (1992), Springer, Berlin
225. Porter R.M. An interpolating polynomial method for numerical conformal mapping. SIAM J. Sci. Com-put. 23 (2001) 1027-1041
226. Priwalow I.I. Randeigenschaften analytischer Funktionen. 2. Auflage (1956), VEB Deutscher Verlag der Wissenschaften, Berlin
227. Prosnak W.J. conformal representation of arbitrary multiconnected airfoil sections. Bull. Acad. Pol. Sci. 25 (1977) 25-36
228. Rabinovich B.I., and Tyurin Yu.V. A recursive numerical method in the conformal mapping of doubly connected regions onto a circular annulus. Soviet Math. Dokl. 28 (1983) 447-450
229. Rabinovich B.I., and Tyurin Yu.V. On a recursive numerical method in conformal mapping. Soviet Math. Dokl. 28 (1983) 415-418
230. Rabinovich B.L., Tyurin Yu.V., Livshits A.A., and Leviant A.S. Recursive numerical algorithm for confor mal mapping in two-dimensional hydrodynamics. AIAA J. 34 (1996) 2014-2020
231. Razali M.R.M. M.Z. Nashed and A.H.M. Murid. Numerical conformal mapping via the Bergman kernel J. Comput. Appl. Math. 82 (1997) 333-350
232. Razali M.R.M., Nashed M.Z., and Murid A.H.M. Numerical conformal mapping via the Bergman kernel using the generalized minimum residual method. Comput. Math. Appl. 40 (2000) 157-164
233. Reichel L. On polynomial approximation in the complex plane with application to conformal mapping. Math. Comp. 44 (1985) 425-433
234. Reichel L. A fast method for solving certain integral equations of the first kind with application to con-formal mapping. J. Comput. Appl. Math. 14 (1986) 125-142
235. Riemann B. Grundlagen für eine allgemeine Theorie der Functionen einer veränderlichen complexen Grösse Nachlaβ. In: Dedekind R., and Weber H. (Eds). Gesammelte mathematische Werke und wissenschaftlicher Nachlaβ (1876), Teubner, Leipzig
236. (in Russian). Sallinen E.V. Approximate determination of conformal mappings by means of methods of continuation and the Newton-Raphson method. Latv. Mat. Ezhegodnik 29 (1985) 236-242
237. Samli S.B. Uber die Konstruktion von Polynomen die ein gegebenes Gebiet näherungsweise auf einen Kreis abbilden. Z. Angew. Math. Mech. 43 (1963) T32-T35
238. Saranen J., and Vainikko G. Two-grid solution of Symm's integral equation. Math. Nachr. 177 (1996) 265-279
239. Schiffer M., and Hawley N.S. Connections and conformal mapping. Acta Math. 107 (1962) 175-274
240. Schinzinger R., and Laura P.A.A. conformal Mapping: Methods and Applications (1991), Elsevier, Amsterdam
241. Seidl A., and Klose H. Numerical conformal mapping of a towel-shaped region onto a rectangle. SI AM J. Sci. Stat. Comput. 6 (1985) 833-842
242. Semmes S. Nonlinear Fourier analysis. Bull. Amer. Math. Soc. 20 (1989) 1-18
243. Skwarczyński M. A general description of the Bergman projection. Ann. Polon. Math. 46 (1985) 311-315
244. Skwarczyński M. Alternating projections in complex analysis. Compl. Anal. Appl., Varna, 1983, Sofia (1985) 192-199
245. Song E.J. Methods for solving Theodorsen 's equation in numerical conformal mapping. Master thesis (1988), Nagoya Univ.
246. (in Japanese). Song E., and Sugiura H. Automatic numerical conformal mapping based on the Wegmann 's method. Trans. Inform. Proc. Soc. Japan 35 (1994) 309-312
247. (in Japanese). Song E., Sugiura H., and Sakurai T. Analysis of instability and stabilization on Wegmann's method for conformal mapping. Trans. Inform. Proc. Soc. Japan 32 (1991) 126-132
248. Sorokin A.S. The variational method of M.A. Lavrent'ev and the Hilbert problem for multiply connected circular domains. Dokl. Math. 54 (1996) 547-550
249. Steidl G. A note on fast Fourier transforms for nonequispaced grids. Adv. Comput. Math. 9 (1998) 337-352
250. Stenger F., and Schmidtlein R. conformal maps via Sinc methods. In: Papamichael N., et al. (Ed). Proc. CMFT Conf. Nicosia, 1997 (1999) 505-549
251. Sugiura H., and Torii T. Real fast Fourier transform on quasi-equidistant sample points. J. Inform. Process. 15 (1992) 460-465
252. Švecová H. On the Bauer's scaled condition number of matrices arising from approximate conformal mapping. Numer. Math. 14 (1970) 495-507
253. Symm G.T. An integral equation method in conformal mapping. Numer. Math. 9 (1966) 250-258
254. Symm G.T. Numerical mapping of exterior domains. Numer. Math. 10 (1967) 437-445
255. Symm G.T. conformal mapping of doubly-connected domains. Numer. Math. 13 (1969) 448-457
256. Szegö G. Über orthogonale Polynome die zu einer gegebenen Kurve der komplexen Ebene gehören. Math. Z. 9 (1921) 218-270
257. Szegö G. On conjugate trigonometric polynomials. Amer. J. Math. 65 (1943) 532-536
258. Theodorsen T. Theory of wing sections of arbitrary shape. NACA Report 411 (1931)
259. Theodorsen T., and Garrick L.E. General potential theory of arbitrary wing sections. NACA Report 452 (1933)
260. Thomas A.D. conformal mapping of nonsmooth domains via the Kerzman-Stein integral equation. J. Math. Anal. Appl. 200 (1996) 162-181
261. Thompson J.F., Warsi Z.U.A., and Mastin C.W. Boundary fitted coordinate systems for numerical solution of partial differential equations-A review. J. Comput. Phys. 47 (1982) 1-108
262. Thompson J.F., Warsi Z.U.A., and Mastin C.W. Numerical Grid Generation (1985), North-Holland, Amsterdam
263. Timman R. The direct and the inverse problem of airfoil theory: A method to obtain numerical solutions. Report F 16 (1951), Nat. Luchtv. Labor., Amsterdam
264. Trefethen L.N. Numerical computation of the Schwarz-Christoffel transformation. SIAM J. Sci. Stat. Comput. 1 (1980) 82-102
265. In: Trefethen L.N. (Ed). Numerical conformal Mapping (1986), Elsevier, New York
266. Trummer M.R. An efficient implementation of a conformal mapping method based on the Szegö kernel. SIAM J. Numer. Anal. 23 (1986) 853-872
267. (in Russian). Ugodčikov A.G. Construction of Functions Yielding conformal Mappings, by Means of Electro-Modelling and the Lagrange Interpolation Polynomials (1966), Naukova Dumka, Kiev
268. (in Russian). Vabishchevich R.N., and Pulatov S.I. A numerical algorithm for conformal mapping. Mat. Model. 1 (1989) 132-139
269. Vekua I.N. Generalized Analytic Functions (1992), Pergamon Press, London
270. (in Russian). Vertgeim B.A. Approximate construction of some conformal mappings. Dokl. Akad. Nauk SSSR 119 (1958) 12-14
271. Volkov E.A. Block method for solving the Laplace equation and for constructing conformal mappings (1994), CRC Press, Boca Raton, FL
272. Wahl A. Konforme Abbildung durch gebrochene rationale Funktionen. Z. Angew. Math. Mech. 44 (1964) 397-399
273. Warschawski S.E. Über einen Satz von O.D. Kellogg. Nachr. Ges. Wiss. Gött. 25 (1932) 73-86
274. Warschawski S.E. On the higher derivatives at the boundary in conformal mapping. Trans. Amer. Math. Soc. 38 (1935) 310-340
275. Warschawski S.E. On conformal mapping of variable regions. Nat. Bur. Standards 18 (1952) 175-187
276. Warschawski S.E. On a theorem of L.Lichtenstein. Pacific J. Math. 5 (1955) 835-839
277. Warschawski S.E. On the solution of the Lichtenstein-Gershgorin integral equation in conformal map-ping: I Theory. Nat. Bur. Standards Appl. Math. Ser. 42 (1955) 7-29
278. 1969. Warschawski S.E. On Hölder continuity at the boundary in conformal maps. J. Math. Mech. 18 (1968) 423-427
279. Wegert E. An iterative method for solving nonlinear Riemann-Hilbert problems. J. Comput. Appl. Math. 29 (1990) 311-327
280. Wegert E. Iterative methods for discrete nonlinear Riemann-Hilbert problems. J. Comput. Appl. Math. 46 (1993) 143-163
281. Nicosia, 1997. Wegert E. Nonlinear Riemann-Hilbert problems - history and perspectives. In: Papamichael N., et al. (Ed). Proc. CMFT Conf. (1999) 583-615
282. Wegmann R. Convergence proofs and error estimates for an iterative method for conformal mapping. Numer. Math. 44 (1984) 435-461
283. Wegmann R. Ein Iterationsverfahren zur konformen Abbildung. Numer. Math. 30 (1978) 453-466
284. Wegmann R. An iterative method for conformal mapping. In: Trefethen L.N. (Ed). Numerical conformal Mapping (1986), North-Holland, Amsterdam 7-18
285. Wegmann R. On Fornberg's numerical method for conformal mapping. SIAM J. Numer. Anal. 23 (1986) 1199-1213
286. Wegmann R. An iterative method for the conformal mapping of doubly connected regions. J. Comput. Appl. Math. 14 (1986) 79-98
287. Wegmann R. Discrete Riemann-Hilbert problems interpolation of simply closed curves and numerical conformal mapping. J. Comput. Appl. Math. 23 (1988) 323-352
288. Wegmann R. conformal mapping by the method of alternating projections. Numer. Math. 56 (1989) 291-307
289. Wegmann R. Discretized versions of Newton type iterative methods for conformal mapping. J. Comput. Appl. Math. 29 (1990) 207-224
290. Wegmann R. An estimate for crowding in conformal mapping to elongated regions. Complex Var. 18 (1992) 193-199
291. Wegmann R. Crowding for analytic functions with elongated range. Constr. Approx. 10 (1994) 179-186
292. Wegmann R. Fast conformal mapping of an ellipse to a simply connected region. J. Comput. Appl. Math. 72 (1996) 101-126
293. Wegmann R. Constructive solution of a certain class of Riemann-Hilbert problems on multiply connected circular regions. J. Comput. Appl. Math. 130 (2001) 139-161
294. Wegmann R. Fast conformal mapping of multiply connected regions. J. Comput. Appl. Math. 130 (2001) 119-138
295. von Wolfersdorf L. Zur Unität der Lösung der Theodorsenschen Integralgleichung der konformen Abbil-dung. Z. Anal. Anwendg. 3 (1984) 523-526
296. Yan Y., and Sloan I.H. On integral equations of the first kind with logarithmic kernels. J. Integral Equations Appl. 1 (1988) 549-579
297. Yoshikawa H. On the conformal mapping of nearly circular domains. J. Math. Soc. Japan 12 (1960) 174-186
298. Zemach C. A conformal map formula for difficult cases. J. Comput. Appl. Math. 14 (1986) 207-215