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 168 articles )

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  1. Adcock, Ben; Martín-Vaquero, Jesús; Richardson, Mark: Resolution-optimal exponential and double-exponential transform methods for functions with endpoint singularities (2017)
  2. Dan, Hui; Guo, Kunyu; Huang, Hansong: Totally abelian Toeplitz operators and geometric invariants associated with their symbol curves (2017)
  3. Goswami, Mayank; Gu, Xianfeng; Pingali, Vamsi P.; Telang, Gaurish: Computing Teichmüller maps between polygons (2017)
  4. Hyvönen, N.; Majander, H.; Staboulis, S.: Compensation for geometric modeling errors by positioning of electrodes in electrical impedance tomography (2017)
  5. Liu, Xiao-Yan; Chen, C.S.; Karageorghis, Andreas: Conformal mapping for the efficient solution of Poisson problems with the Kansa-RBF method (2017)
  6. Nasyrov, S.: Conformal mappings of stretched polyominoes onto half-plane (2017)
  7. Andersson, Anders; Nilsson, Börje; Biro, Thomas: Fourier methods for harmonic scalar waves in general waveguides (2016)
  8. Bezrodnykh, S.I.: Analytic continuation formulas and Jacobi-type relations for Lauricella function (2016)
  9. Bezrodnykh, S.I.: Jacobi-type differential relations for the Lauricella function $F_D^(N)$ (2016)
  10. Bezrodnykh, S.I.: On the analytic continuation of the Lauricella function $F_D^(N)$ (2016)
  11. Brown, Philip R.; Porter, R.Michael: Numerical conformal mapping to one-tooth gear-shaped domains and applications (2016)
  12. Cathala, Mathieu: Asymptotic shallow water models with non smooth topographies (2016)
  13. Grigoryan, Armen: Slit univalent harmonic mappings (2016)
  14. Jagels, Carl; Mach, Thomas; Reichel, Lothar; Vandebril, Raf: Convergence rates for inverse-free rational approximation of matrix functions (2016)
  15. Nachbin, André: Conformal mapping and complex topographies (2016)
  16. Peck, D.; Rogosin, S.V.; Wrobel, M.; Mishuris, G.: Simulating the Hele-Shaw flow in the presence of various obstacles and moving particles (2016)
  17. Porter, R.Michael; Shimauchi, Hirokazu: Numerical solution of the Beltrami equation via a purely linear system (2016)
  18. Sète, Olivier; Liesen, Jörg: On conformal maps from multiply connected domains onto lemniscatic domains (2016)
  19. Wang, Qixuan; Othmer, Hans G.: Computational analysis of amoeboid swimming at low Reynolds number (2016)
  20. Black, J.P.; Breward, C.J.W.; Howell, P.D.: Two-dimensional modeling of electron flow through a poorly conducting layer (2015)

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