Schwarz-Christoffel

Algorithm 756: a MATLAB toolbox for Schwarz-Christoffel mapping. The Schwarz-Christoffel transformation and its variations yield formulas for conformal maps from standard regions to the interiors or exteriors of possibly unbounded polygons. Computations involving these maps generally require a computer, and although the numerical aspects of these transformations have been studied, there are few software implementations that are widely available and suited for general use. The Schwarz-Christoffel Toolbox for MATLAB is a new implementation of Schwarz-Christoffel formulas for maps from the disk, half-plane, strip, and rectangle domains to polygon interiors, and from the disk to polygon exteriors. The toolbox, written entirely in the MATLAB script language, exploits the high-level functions, interactive environment, visualization tools, and graphical user interface elements supplied by current versions of MATLAB, and is suitable for use both as a standalone tool and as a library for applications written in MATLAB, Fortran, or C. Several examples and simple applications are presented to demonstrate the toolbox’s capabilities.


References in zbMATH (referenced in 235 articles )

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  1. Falcão, M. I.; Papamichael, N.; Stylianopoulos, N. S.: Approximating the conformal maps of elongated quadrilaterals by domain decomposition (2001)
  2. Ernst, Oliver G.: Residual-minimizing Krylov subspace methods for stabilized discretizations of convection-diffusion equations (2000)
  3. Rahola, Jussi: On the eigenvalues of the volume integral operator of electromagnetic scattering (2000)
  4. Trevelyan, P. M. J.; Elliott, L.; Ingham, D. B.: Potential flow in a semi-infinite channel with multiple sub-channels using the Schwarz-Christoffel transformation (2000)
  5. Embree, Mark; Trefethen, Lloyd N.: Green’s functions for multiply connected domains via conformal mapping (1999)
  6. Papamichael, N.; Stylianopoulos, N. S.: The asymptotic behavior of conformal modules of quadrilaterals with applications to the estimation of resistance values (1999)
  7. Snoeyink, J.: Cross-ratios and angles determine a polygon (1999)
  8. Zakradze, M.; Natsvlishvili, Z.; Sanikidze, Z.: On one approximate method of the conformal mapping (1999)
  9. Driscoll, Tobin A.; Vavasis, Stephen A.: Numerical conformal mapping using cross-ratios and Delaunay triangulation (1998)
  10. Hassenpflug, W. C.: Branched channel free-streamlines (1998)
  11. Hu, Chenglie: Algorithm 785: A software package for computing Schwarz-Christoffel conformal transformation for doubly connected polygonal regions (1998)
  12. Trefethen, Lloyd N.; Driscoll, Tobin A.: Schwarz-Christoffel mapping in the computer era (1998)
  13. Hassenpflug, W. C.: Elliptic integrals and the Schwarz-Christoffel transformation (1997)
  14. Heuveline, Vincent; Sadkane, Miloud: Arnoldi-Faber method for large non Hermitian eigenvalue problems (1997)
  15. Driscoll, Tobin A.: Algorithm 756: A MATLAB toolbox for Schwarz-Christoffel mapping (1996)

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