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 200 articles )

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  1. Badreddine, Mohamed; DeLillo, Thomas K.; Sahraei, Saman: A comparison of some numerical conformal mapping methods for simply and multiply connected domains (2019)
  2. Borkowski, M.; Kuras, R.: Application of conformal mappings and the numerical analysis of conditioning of the matrices in Trefftz method for some boundary value problems (2019)
  3. De Marchi, S.; Martínez, A.; Perracchione, E.: Fast and stable rational RBF-based partition of unity interpolation (2019)
  4. Andrade, David; Nachbin, André: Two-dimensional surface wave propagation over arbitrary ridge-like topographies (2018)
  5. Andrade, D.; Nachbin, A.: A three-dimensional Dirichlet-to-Neumann operator for water waves over topography (2018)
  6. Anselmo, Tiago; Nelson, Rhodri; Carneiro da Cunha, Bruno; Crowdy, Darren G.: Accessory parameters in conformal mapping: exploiting the isomonodromic tau function for Painlevé VI (2018)
  7. Bogatyrev, A. B.; Grigor’ev, O. A.: Conformal mapping of rectangular heptagons. II (2018)
  8. Brubaker, Nicholas D.: A continuation method for computing constant mean curvature surfaces with boundary (2018)
  9. Carro, María J.; Ortiz-Caraballo, Carmen: On the Dirichlet problem on Lorentz and Orlicz spaces with applications to Schwarz-Christoffel domains (2018)
  10. Cavoretto, Roberto; De Rossi, Alessandra; Perracchione, Emma: Optimal selection of local approximants in RBF-PU interpolation (2018)
  11. Chaudhry, Jehanzeb H.; Burch, Nathanial; Estep, Donald: Efficient distribution estimation and uncertainty quantification for elliptic problems on domains with stochastic boundaries (2018)
  12. Choi, Doo Sung; Helsing, Johan; Lim, Mikyoung: Corner effects on the perturbation of an electric potential (2018)
  13. Cusimano, N.; Gerardo-Giorda, L.: A space-fractional monodomain model for cardiac electrophysiology combining anisotropy and heterogeneity on realistic geometries (2018)
  14. Driscoll, T. A.; Braun, R. J.; Brosch, J. K.: Simulation of parabolic flow on an eye-shaped domain with moving boundary (2018)
  15. Fasi, Massimiliano; Iannazzo, Bruno: Computing the weighted geometric mean of two large-scale matrices and its inverse times a vector (2018)
  16. Hakula, Harri; Rasila, Antti; Vuorinen, Matti: Conformal modulus and planar domains with strong singularities and cusps (2018)
  17. Nachbin, A.; Ribeiro-Junior, R.: Capturing the flow beneath water waves (2018)
  18. Nasser, Mohamed M. S.: Numerical conformal mapping onto the parabolic, elliptic and hyperbolic slit domains (2018)
  19. Trefethen, Lloyd N.: Series solution of Laplace problems (2018)
  20. Wala, Matt; Klöckner, Andreas: Conformal mapping via a density correspondence for the double-layer potential (2018)

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