Lectures on Numerical Conformal Mapping

[1]  S. N. Chandler-Wilde,et al.  Evaluation of a boundary integral representation for the conformal mapping of the unit disk onto a simply-connected domain , 1995, Adv. Comput. Math..

[2]  A DEPTH-INTEGRATED 2D COASTAL AND ESTUARINE MODEL WITH CONFORMAL BOUNDARY-FITTED MESH GENERATION , 1996 .

[3]  M. K. Warby,et al.  Numerical techniques for conformal mapping onto a rectangle , 1987 .

[4]  Thomas K. DeLillo,et al.  Extremal distance, harmonic measure and numerical conformal mapping , 1993 .

[5]  D. Burley,et al.  A Numerical Method for Conformal Mapping , 1982 .

[6]  Jerzy M. Floryan.  Conformal-mapping-based coordinate generation method for channel flows , 1985 .

[7]  Edward B. Saff,et al.  Approximation of conformal mappings of annular regions , 1997 .

[8]  Petter E. Bjørstad,et al.  Conformal mapping of circular arc polygons , 1987 .

[9]  Prem K. Kythe,et al.  Computational Conformal Mapping , 1998 .

[10]  Curvilinear crosscuts of subdivision for a domain decomposition method in numerical conformal mapping , 1999 .

[11]  N. Papamichael,et al.  The Bergman Kernel Method for the Numerical Conformal Mapping of Simply Connected Domains , 1978 .

[12]  Theodore Theodorsen,et al.  Theory of wing sections of arbitrary shape , 1933 .

[13]  J. Walsh.  Interpolation and Approximation by Rational Functions in the Complex Domain , 1935 .

[14]  Ian H. Sloan,et al.  On integral equations of the first kind with logarithmic kernels , 1988 .

[15]  On the Comparison of Two Numerical Methods for Conformal Mapping , 1987 .

[16]  Carlos Alberto Brebbia,et al.  Boundary Elements: An Introductory Course , 1989 .

[17]  A procedure for conformal maps of simply connected domains by using the Bergman function , 1970 .

[18]  V. Andrievskii,et al.  Conformal invariants in constructive theory of functions of complex variable , 1995 .

[19]  Lloyd N. Trefethen,et al.  Schwarz-Christoffel Mapping , 2002 .

[20]  N. Papamichael,et al.  Two numerical methods for the conformal mapping of simply-connected domains , 1981 .

[21]  H. Ŝvecoá.  On the Bauer's scaled condition number of matrices arising from approximate conformal mapping , 1970 .

[22]  G. Pólya,et al.  Isoperimetric inequalities in mathematical physics , 1951 .

[23]  G. Opfer.  Die Bestimmung des moduls zweifach zusammenhängender gebiete mit Hilfe von Differenzenverfahren , 1969 .

[24]  J. Whiteman,et al.  A numerical conformal transformation method for harmonic mixed boundary value problems in polygonal domains , 1973 .

[25]  L. Bieberbach.  Zur theorie und praxis der konformen abbildung , 1914 .

[26]  An estimate for crowding in conformal mapping to elongated regions , 1992 .

[27]  Chenglie Hu,et al.  Algorithm 785: a software package for computing Schwarz-Christoffel conformal transformation for doubly connected polygonal regions , 1998, TOMS.

[28]  I. E. Garrick.  Potential flow about arbitrary biplane wing sections , 1937 .

[29]  Zdravko Kurnik.  Dirichlet's principle , 2005 .

[30]  R. A. Silverman,et al.  Theory of Functions of a Complex Variable , 1968 .

[31]  D. Gaier.  Das logarithmische Potential und die konforme Abbildung mehrfach zusammenhängender Gebiete , 1981 .

[32]  W. G. Bickley.  Two‐Dimensional Potential Problems for the Space Outside a Rectangle , 1934 .

[33]  A. Ostrowski.  On the Convergence of Theodorsen’s and Garrick’s Method of Conformal Mapping , 1985 .

[34]  P. Rabinowitz.  Russian Numerical Analysis: Approximate Methods of Higher Analysis . L. V. Kantorovich and V. I. Krylov. Translated from the third Russian edition by Curtis D. Benster. Interscience, New York, 1959. xv + 681. $17. , 1961, Science.

[35]  M. Gutknecht.  Numerical conformal mapping methods based on function conjugation , 1986 .

[36]  H. Motz,et al.  The treatment of singularities of partial differential equations by relaxation methods , 1947 .

[37]  Simon N. Chandler-Wilde,et al.  Numerical conformal mapping via Chebyshev weighted solutions of Symm's integral equation , 1993 .

[38]  B. Rodin,et al.  The convergence of circle packings to the Riemann mapping , 1987 .

[39]  E. Saff,et al.  Asymptotics for Polynomial Zeros: Beware of Predictions from Plots , 2008 .

[40]  P. K. Suetin.  Polynomials orthogonal over a region and Bieberbach polynomials , 1974 .

[41]  Carolyn R. Bertozzi,et al.  Methods and Applications , 2009 .

[42]  L. Lichtenstein.  Über die konforme Abbildung ebener analytischer Gebiete mit Ecken. , 1911 .

[43]  Giovanni Sansone,et al.  Lectures on the theory of functions of a complex variable , 1961 .

[44]  T. Lu,et al.  Singularities and treatments of elliptic boundary value problems , 2000 .

[45]  David K. Kahaner,et al.  An Improved Method for Numerical Conformal Mapping , 1972 .

[46]  Simon N. Chandler-Wilde,et al.  A chebyshev collocation method for solving symm's integral equation for conformal mapping: A partial error analysis , 1994 .

[47]  Lars V. Ahlfors.  An introduction to the theory of analytic functions of one complex variable , 1978 .

[48]  Thomas K. DeLillo,et al.  A Fornberg-like conformal mapping method for slender regions , 1993 .

[49]  R. Courant.  Dirichlet's Principle, Conformal Mapping, and Minimal Surfaces , 1950 .

[50]  Jutta Weisel.  Lösung singulärer Variationsprobleme durch die Verfahren von Ritz und Galerkin mit finiten Elementenanwendungen in der konformen Abbildung , 1979 .

[51]  John Todd.  Experiments in the computation of conformal maps , 1955 .

[52]  R. Sherman Lehman,et al.  Development of the mapping function at an analytic corner. , 1957 .

[53]  M. Newman,et al.  Interpolation and approximation , 1965 .

[54]  Charles Zemach.  A conformal map formula for difficult cases , 1986 .

[55]  Lloyd N. Trefethen,et al.  A Modified Schwarz-Christoffel Transformation for Elongated Regions , 1990, SIAM J. Sci. Comput..

[56]  E. Grassmann,et al.  Numerical experiments with a method of successive approximation for conformal mapping , 1979 .

[57]  Royal Davis.  Numerical methods for coordinate generation based on Schwarz-Christoffel transformations , 1979 .

[58]  F. Bowman.  Introduction to Elliptic Functions with Applications , 1961 .

[59]  I. Kulikov.  W21, L∞-convergence of Bieberbach polynomials in a Lipschitz domain , 1981 .

[60]  W. Wendland.  On Galerkin Collocation Methods for Integral Equations of Elliptic Boundary Value Problems , 1980 .

[61]  Olli Lehto,et al.  Quasiconformal mappings in the plane , 1973 .

[62]  E. Saff,et al.  Estimating the argument of approximate conformal mappings , 1994 .

[63]  L. Howell.  Numerical conformal mapping of circular arc polygons , 1993 .

[64]  D. M. Hough.  Jacobi polynomial solutions of first kind integral equations for numerical conformal mapping , 1985 .

[65]  On the numerical performance of a domain decomposition method for conformal mapping , 1990 .

[66]  A. Fokas,et al.  Complex Variables: Introduction and Applications , 1997 .

[67]  Z. C. Li,et al.  Special boundary approximation methods for laplace equation problems with boundary singularities - Applications to the motz problem , 2006, Comput. Math. Appl..

[68]  D. Ives,et al.  A Modern Look at Conformal Mapping Including Multiply Connected Regions , 1976 .

[69]  Thomas K. DeLillo,et al.  The accuracy of numerical conformal mapping methods: a survey of examples and results , 1994 .

[70]  Albert Seidl,et al.  Numerical Conformal Mapping of a Towel-Shaped Region onto a Rectangle , 1985 .

[71]  Darren Crowdy,et al.  The Schwarz–Christoffel mapping to bounded multiply connected polygonal domains , 2005, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[72]  L. Kantorovich,et al.  Approximate methods of higher analysis , 1960 .

[73]  Edward B. Saff,et al.  Local behaviour of the error in the Bergman kernel method for numerical conformal mapping , 1993 .

[74]  Matti Vuorinen,et al.  The computation of capacity of planar condensers , 2004 .

[75]  Conformal mapping of long quadrilaterals and thick doubly connected domains , 1994 .

[76]  Yi Yan.  The collocation method for first-kind boundary integral equations on polygonal regions , 1990 .

[77]  H. Hoidn.  A reparameterisation method to determine conformal maps , 1986 .

[78]  H. Kober,et al.  Dictionary of conformal representations , 1957 .

[79]  Thomas Ransford,et al.  Potential Theory in the Complex Plane: Bibliography , 1995 .

[80]  E. Saff,et al.  Asymptotic behaviour of zeros of Bieberbach polynomials , 1991 .

[81]  J. Barkley Rosser,et al.  A Power Series Solution of a Harmonic Mixed Boundary Value Problem. , 1975 .

[82]  Kent Pearce.  A Constructive Method for Numerically Computing Conformal Mappings for Gearlike Domains , 1991, SIAM J. Sci. Comput..

[83]  V. Andrievskii,et al.  Convergence of Bieberbach polynomials in domains with quasiformal boundary , 1983 .

[84]  Dieter Gaier,et al.  Konstruktive Methoden der konformen Abbildung , 1964 .

[85]  M. A. Jaswon,et al.  Integral equation methods in potential theory and elastostatics , 1977 .

[86]  Tobin A. Driscoll,et al.  Algorithm 756: a MATLAB toolbox for Schwarz-Christoffel mapping , 1996, TOMS.

[87]  Henry C. Thacher,et al.  Applied and Computational Complex Analysis. , 1988 .

[88]  E. Saff,et al.  Fundamentals of complex analysis with applications to engineering and science , 2003 .

[89]  Lloyd N. Trefethen,et al.  A Multipole Method for Schwarz-Christoffel Mapping of Polygons with Thousands of Sides , 2003, SIAM J. Sci. Comput..

[90]  M. Warby,et al.  The determination of the poles of the mapping function and their use in numerical conformal mapping , 1983 .

[91]  M. K. Warby,et al.  Pole-type singularities and the numerical conformal mapping of doubly-connected domains , 1984 .

[92]  E. Saff,et al.  Logarithmic Potentials with External Fields , 1997 .

[93]  R. Kühnau.  Numerische Realisierung konformer Abbildungen durch « Interpolation » , 1983 .

[94]  V. Maymeskul,et al.  $L^2$-Approximations of power and logarithmic functions with applications to numerical conformal mapping , 2002, Numerische Mathematik.

[95]  George T. Symm,et al.  An integral equation method in conformal mapping , 1966 .

[96]  P. Grisvard.  Elliptic Problems in Nonsmooth Domains , 1985 .

[97]  J. Crank,et al.  Influence of imbedded particles on steady-state diffusion , 1974 .

[98]  I B Simonenko,et al.  ON THE CONVERGENCE OF BIEBERBACH POLYNOMIALS IN THE CASE OF A LIPSCHITZ DOMAIN , 1979 .

[99]  G. Goluzin.  Geometric theory of functions of a complex variable , 1969 .

[100]  R. T. Davis,et al.  A Schwarz-Christoffel Method for Generating Two-Dimensional Flow Grids , 1985 .

[101]  Thomas K. DeLillo,et al.  Schwarz-Christoffel Mapping of the Annulus , 2001, SIAM Rev..

[102]  G. M.,et al.  Partial Differential Equations I , 2023, Applied Mathematical Sciences.

[103]  George C. Hsiao,et al.  A Galerkin collocation method for some integral equations of the first kind , 1980, Computing.

[104]  J. Whiteman,et al.  Treatment of harmonic mixed boundary problems by conformal transformation methods , 1972 .

[105]  L. Greengard,et al.  A Fast Adaptive Multipole Algorithm for Particle Simulations , 1988 .

[106]  Hans-Peter Blatt,et al.  Discrepancy of Signed Measures and Polynomial Approximation , 2001 .

[107]  Tobin A. Driscoll,et al.  Numerical Conformal Mapping Using Cross-Ratios and Delaunay Triangulation , 1998, SIAM J. Sci. Comput..

[108]  L. Trefethen.  Numerical computation of the Schwarz-Christoffel transformation , 1979 .

[109]  N. Papamichael,et al.  The use of splines and singular functions in an integral equation method for conformal mapping , 1981 .

[110]  E. Hille.  Analytic Function Theory , 1961 .

[111]  Milton Abramowitz,et al.  Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables , 1964 .

[112]  R. Barnard,et al.  Rounding corners of gearlike domains and the omitted area problem , 1986 .

[113]  S. Bergman.  The kernel function and conformal mapping , 1950 .

[114]  Jerzy M. Floryan,et al.  Schwarz-Christoffel mappings: A general approach , 1987 .

[115]  M. Schiffer.  An Application of Orthonormal Functions in the Theory of Conformal Mapping , 1948 .

[116]  N. Papamichael,et al.  Numerical conformal mapping onto a rectangle with applications to the solution of Laplacian problems , 1989 .

[117]  N. Papamichael,et al.  Dieter Gaier’s Contributions to Numerical Conformal Mapping , 2004 .

[118]  L. Ahlfors.  Complex Analysis , 1979 .