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. Huang, Zhu; Boyd, John P.: Chebyshev-Fourier spectral methods in bipolar coordinates (2015)
  2. Karabasheva, E. N.; Shabalin, P. L.: Univalence of mappings from half-plane to a polygonal domains with infinite sets of vertices (2015)
  3. Lopez-Fernandez, Maria; Sauter, Stefan: Generalized convolution quadrature with variable time stepping. II: Algorithm and numerical results (2015)
  4. Lopez-Fernandez, M.; Sauter, S.: Fast and stable contour integration for high order divided differences via elliptic functions (2015)
  5. Lui, Lok Ming; Gu, Xianfeng; Yau, Shing-Tung: Convergence of an iterative algorithm for Teichmüller maps via harmonic energy optimization (2015)
  6. Mantica, Giorgio: Orthogonal polynomials of equilibrium measures supported on Cantor sets (2015)
  7. Muñoz Grajales, Juan Carlos: Propagation of water waves over uneven bottom under the effect of surface tension (2015)
  8. Nasyrov, S. R.: Riemann-Schwarz reflection principle and asymptotics of modules of rectangular frames (2015)
  9. Pasialis, V.; Lampeas, G.: Shape descriptors and mapping methods for full-field comparison of experimental to simulation data (2015) ioport
  10. Slevinsky, Richard Mikael; Olver, Sheehan: On the use of conformal maps for the acceleration of convergence of the trapezoidal rule and sinc numerical methods (2015)
  11. Sun, Jian; Wu, Tianqi; Gu, Xianfeng; Luo, Feng: Discrete conformal deformation: algorithm and experiments (2015)
  12. van Wyk, Hans-Werner; Gunzburger, Max; Burkhardt, John; Stoyanov, Miroslav: Power-law noises over general spatial domains and on nonstandard meshes (2015)
  13. Wright, Alex: Translation surfaces and their orbit closures: an introduction for a broad audience (2015)
  14. Zumbrum, Matthew E.; Edwards, David A.: Conformal mapping in optical biosensor applications (2015)
  15. Aune, Erlend; Simpson, Daniel P.; Eidsvik, Jo: Parameter estimation in high dimensional Gaussian distributions (2014)
  16. Kolesnikov, I. A.; Kopaneva, L. S.: Conformal mapping onto numerable polygon with double symmetry (2014)
  17. Mamode, Malik: Fundamental solution of the Laplacian on flat tori and boundary value problems for the planar Poisson equation in rectangles (2014)
  18. Mishuris, Gennady; Rogosin, Sergei; Wrobel, Michal: Hele-Shaw flow with a small obstacle (2014)
  19. Mityushev, Vladimir V.: Poincaré (\alpha)-series for classical Schottky groups (2014)
  20. Delillo, Thomas K.; Elcrat, Alan R.; Kropf, Everett H.; Pfaltzgraff, John A.: Efficient calculation of Schwarz-Christoffel transformations for multiply connected domains using Laurent series (2013)

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