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. Hakula, Harri; Quach, Tri; Rasila, Antti: Conjugate function method for numerical conformal mappings (2013)
  2. Hakula, Harri; Rasila, Antti; Vuorinen, Matti: Computation of exterior moduli of quadrilaterals (2013)
  3. Heppell, Charles; Richardson, Giles; Roose, Tiina: A model for fluid drainage by the lymphatic system (2013)
  4. Luz, Ana Maria; Nachbin, André: Wave packet defocusing due to a highly disordered bathymetry (2013)
  5. Mekhfi, Mustapha: Application of the Schwarz-Christoffel mapping to planar gravity: static solutions (2013)
  6. Amano, Kaname; Okano, Dai; Ogata, Hidenori: Numerical conformal mappings onto the linear slit domain (2012)
  7. Burrage, Kevin; Hale, Nicholas; Kay, David: An efficient implicit FEM scheme for fractional-in-space reaction-diffusion equations (2012)
  8. Caraus, Iurie; Faqih, Feras M. Al: Convergence of the collocation method and the mechanical quadrature method for systems of singular integro-differential equations in Lebesgue spaces (2012)
  9. Davidson, A. J.; Mottram, N. J.: Conformal mapping techniques for the modelling of liquid crystal devices (2012)
  10. Greenbaum, Anne; Choi, Daeshik: Crouzeix’s conjecture and perturbed Jordan blocks (2012)
  11. Ilhan, Esin; Motoasca, Emilia T.; Paulides, Johan J. H.; Lomonova, Elena A.: Conformal mapping: Schwarz-Christoffel method for flux-switching PM machines (2012)
  12. Mityushev, Vladimir: Schwarz-Christoffel formula for multiply connected domains (2012)
  13. Nachbin, André; da Silva Simões, Vanessa: Solitary waves in open channels with abrupt turns and branching points (2012)
  14. Nicolaide, Andrei: An approach to conformal transformation using symbolic language facilities: application in electrical engineering (2012)
  15. Seabra, Mariana R. R.; Cesar de Sa, Jose M. A.; Šuštarič, Primož; Rodič, Tomaž: Some numerical issues on the use of XFEM for ductile fracture (2012)
  16. Tsai, Jonathan: Extending the Schwarz-Christoffel formula to universal covering maps of a Riemann surface (2012)
  17. Wright, Alex: Schwarz triangle mappings and Teichmüller curves: abelian square-tiled surfaces (2012)
  18. Brown, Philip R.; Porter, R. Michael: Conformal mapping of circular quadrilaterals and Weierstrass elliptic functions (2011)
  19. Calixto, Wesley Pacheco; da Mota, Jesus Carlos; Pinheiro de Alvarenga, Bernardo: Methodology for the reduction of parameters in the inverse transformation of Schwarz-Christoffel applied to electromagnetic devices with axial geometry (2011)
  20. Crowdy, Darren G.; Fokas, Athanassios S.; Green, Christopher C.: Conformal mappings to multiply connected polycircular arc domains (2011)

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