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. Andersson, Anders: A modified Schwarz-Christoffel mapping for regions with piecewise smooth boundaries (2008)
  2. Balachandran, G. R.; Rajagopal, A.; Sivakumar, S. M.: Mesh free Galerkin method based on natural neighbors and conformal mapping (2008)
  3. Brown, Philip R.: An investigation of a two parameter problem for conformal maps onto circular arc quadrilaterals (2008)
  4. Costamagna, E.; di Barba, P.; Savini, A.: Shape design of a MEMS device by Schwarz-Christoffel numerical inversion and Pareto optimality (2008)
  5. Crowdy, Darren: Geometric function theory: a modern view of a classical subject (2008)
  6. Fyrillas, Marios M.: Heat conduction in a solid slab embedded with a pipe of general cross-section: shape factor and shape optimization (2008)
  7. Hale, Nicholas; Higham, Nicholas J.; Trefethen, Lloyd N.: Computing (A^\alpha, \log(A)), and related matrix functions by contour integrals (2008)
  8. Hale, Nicholas; Trefethen, Lloyd N.: New quadrature formulas from conformal maps (2008)
  9. Hu, Chao; Ghosh, Somnath: Locally enhanced Voronoi cell finite element model (LE-VCFEM) for simulating evolving fracture in ductile microstructures containing inclusions (2008)
  10. Lechleiter, Armin; Hyvönen, Nuutti; Hakula, Harri: The factorization method applied to the complete electrode model of impedance tomography (2008)
  11. Riera, Gonzalo; Carrasco, Hernán; Preiss, Rubén: The Schwarz-Christoffel conformal mapping for “polygons” with infinitely many sides (2008)
  12. Saff, Edward B.; Stylianopoulos, Nikos S.: Asymptotics for polynomial zeros: Beware of predictions from plots (2008)
  13. Yordanov, Hristomir; Russer, Peter: Computing the transmission line parameters of an on-chip multiconductor digital bus (2008)
  14. Boronski, Piotr: Spectral method for matching exterior and interior elliptic problems (2007)
  15. Crowdy, D. G.; Fokas, A. S.: Conformal mappings to a doubly connected polycircular arc domain (2007)
  16. Hough, David M.: Asymptotic Gauss-Jacobi quadrature error estimation for Schwarz-Christoffel integrals (2007)
  17. Hyvönen, Nuutti; Hakula, Harri; Pursiainen, Sampsa: Numerical implementation of the factorization method within the complete electrode model of electrical impedance tomography (2007)
  18. Palmberg, N.: Weighted composition operators with closed range (2007)
  19. Porter, R. Michael: History and recent developments in techniques for numerical conformal mapping (2007)
  20. Ransford, Thomas; Rostand, Jérémie: Computation of capacity (2007)

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