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 234 articles )

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  1. Fasi, Massimiliano; Iannazzo, Bruno: Computing the weighted geometric mean of two large-scale matrices and its inverse times a vector (2018)
  2. Hakula, Harri; Rasila, Antti; Vuorinen, Matti: Conformal modulus and planar domains with strong singularities and cusps (2018)
  3. Hyvönen, Nuutti; Päivärinta, Lassi; Tamminen, Janne P.: Enhancing D-bar reconstructions for electrical impedance tomography with conformal maps (2018)
  4. Nachbin, A.; Ribeiro-Junior, R.: Capturing the flow beneath water waves (2018)
  5. Nasser, Mohamed M. S.: Numerical conformal mapping onto the parabolic, elliptic and hyperbolic slit domains (2018)
  6. Trefethen, Lloyd N.: Series solution of Laplace problems (2018)
  7. Wala, Matt; Klöckner, Andreas: Conformal mapping via a density correspondence for the double-layer potential (2018)
  8. Adcock, Ben; Martín-Vaquero, Jesús; Richardson, Mark: Resolution-optimal exponential and double-exponential transform methods for functions with endpoint singularities (2017)
  9. Corfdir, A.; Bonnet, Guy: Degenerate scale for 2D Laplace equation with Robin boundary condition (2017)
  10. Dan, Hui; Guo, Kunyu; Huang, Hansong: Totally abelian Toeplitz operators and geometric invariants associated with their symbol curves (2017)
  11. Feiszli, Matt; Narayan, Akil: Numerical computation of Weil-Peterson geodesics in the universal Teichmüller space (2017)
  12. Goswami, Mayank; Gu, Xianfeng; Pingali, Vamsi P.; Telang, Gaurish: Computing Teichmüller maps between polygons (2017)
  13. Hyvönen, N.; Majander, H.; Staboulis, S.: Compensation for geometric modeling errors by positioning of electrodes in electrical impedance tomography (2017)
  14. Liesen, Jörg; Sète, Olivier; Nasser, Mohamed M. S.: Fast and accurate computation of the logarithmic capacity of compact sets (2017)
  15. Liu, Xiao-Yan; Chen, C. S.; Karageorghis, Andreas: Conformal mapping for the efficient solution of Poisson problems with the Kansa-RBF method (2017)
  16. Luo, Feng: The Riemann mapping theorem and its discrete counterparts (2017)
  17. Nasyrov, S.: Conformal mappings of stretched polyominoes onto half-plane (2017)
  18. Quach, Tri: Harmonic shears and numerical conformal mappings (2017)
  19. Andersson, Anders; Nilsson, Börje; Biro, Thomas: Fourier methods for harmonic scalar waves in general waveguides (2016)
  20. Bezrodnykh, S. I.: Jacobi-type differential relations for the Lauricella function (F_D^(N)) (2016)

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