Algorithm 843: Improvements to the Schwarz-Christoffel toolbox for MATLAB

The Schwarz--Christoffel Toolbox (SC Toolbox) for MATLAB, first released in 1994, made possible the interactive creation and visualization of conformal maps to regions bounded by polygons. The most recent release supports new features, including an object-oriented command-line interface model, new algorithms for multiply elongated and multiple-sheeted regions, and a module for solving Laplace's equation on a polygon with Dirichlet and homogeneous Neumann conditions. Brief examples are given to demonstrate the new capabilities.

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

[2]  H. Widom Extremal polynomials associated with a system of curves in the complex plane , 1969 .

[3]  C. David Levermore,et al.  The Small Dispersion Limit of the Korteweg-deVries Equation. I , 1982 .

[4]  E. Costamagna On the Numerical Inversion of the Schwarz-Christoffel Conformal Transformation , 1987 .

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

[6]  D. Gilbarg,et al.  A Generalization of the Schwarz-Christoffel Transformation. , 1949, Proceedings of the National Academy of Sciences of the United States of America.

[7]  Dieter Gaier Ermittlung des konformen Moduls von Vierecken mit Differenzenmethoden , 1972 .

[8]  Peter Henrici,et al.  Discrete Fourier analysis, Cauchy integrals, construction of conformal maps, univalent functions , 1986 .

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

[10]  Lloyd N. Trefethen,et al.  Green's Functions for Multiply Connected Domains via Conformal Mapping , 1999, SIAM Rev..

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

[12]  R. Menikoff,et al.  Methods for numerical conformal mapping , 1980 .

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

[14]  Richard L. Rubin,et al.  On the crowding of parameters associated with Schwarz-Christoffel transformations , 1988 .

[15]  P. Henrici,et al.  Applied & computational complex analysis: power series integration conformal mapping location of zero , 1988 .

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

[17]  Roland Schinzinger,et al.  Conformal Mapping: Methods and Applications , 1991 .

[18]  W. Versnel,et al.  Electrical characteristics of an anisotropic semiconductor sample of circular shape with finite contacts , 1983 .

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

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

[21]  Heinz Dappen,et al.  Wind-tunnel wall corrections on a two-dimensional plate by conformalmapping , 1987 .

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