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.

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References in zbMATH (referenced in 235 articles )

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  1. Barth, Dominik; Wenz, Andreas: Computation of Belyi maps with prescribed ramification and applications in Galois theory (2021)
  2. Dautova, D.; Nasyrov, S.; Vuorinen, M.: Conformal modulus of the exterior of two rectilinear slits (2021)
  3. Hakula, Harri; Nasyrov, Semen; Vuorinen, Matti: Conformal moduli of symmetric circular quadrilaterals with cusps (2021)
  4. Hao, Yue; Simoncini, Valeria: Matrix equation solving of PDEs in polygonal domains using conformal mappings (2021)
  5. Ignacio, Labarca; Ralf, Hiptmair: Acoustic scattering problems with convolution quadrature and the method of fundamental solutions (2021)
  6. Kolesnikov, I. A.: A one-parametric method for determining parameters in the Schwarz-Christoffel integral (2021)
  7. Nasser, Mohamed M. S.; Vuorinen, Matti: Computation of conformal invariants (2021)
  8. Barth, Dominik; König, Joachim; Wenz, Andreas: An approach for computing families of multi-branch-point covers and applications for symplectic Galois groups (2020)
  9. Boudabra, Maher; Markowsky, Greg: Maximizing the (p)th moment of the exit time of planar Brownian motion from a given domain (2020)
  10. Calver, Simon N.; Gaffney, E. A.; Walsh, E. J.; Durham, W. M.; Oliver, J. M.: On the thin-film asymptotics of surface tension driven microfluidics (2020)
  11. Cui, Hanwen; Ren, Weiqing: Interface profile near the contact line in electro-wetting on dielectric (2020)
  12. Doan, Tung; Le-Quang, Hung; To, Quy-Dong: Effective elastic stiffness of 2D materials containing nanovoids of arbitrary shape (2020)
  13. Fang, Licheng; Damanik, David; Guo, Shuzheng: Generic spectral results for CMV matrices with dynamically defined Verblunsky coefficients (2020)
  14. Han, Yucen; Majumdar, Apala; Zhang, Lei: A reduced study for nematic equilibria on two-dimensional polygons (2020)
  15. Kolesnikov, I. A.; Sharofov, A. Kh.: A one-parametric family of conformal mappings from the half-plane onto a family of polygons (2020)
  16. Leyvraz, F.: Qualitative properties of systems of two complex homogeneous ODE’s: a connection to polygonal billiards (2020)
  17. Nakatsukasa, Yuji; Trefethen, Lloyd N.: An algorithm for real and complex rational minimax approximation (2020)
  18. Nasser, Mohamed M. S.; Vuorinen, Matti: Conformal invariants in simply connected domains (2020)
  19. Trefethen, Lloyd N.: Numerical conformal mapping with rational functions (2020)
  20. Alhejaili, Weaam; Kao, Chiu-Yen: Numerical studies of the Steklov eigenvalue problem via conformal mappings (2019)

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