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 234 articles )

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  1. Costamagma, E.; Di Barba, P.; Savini, A.: Synthesis of boundary conditions in a subdomain using the numerical Schwarz-Christoffel transformation for the field analysis (2006)
  2. DeLillo, Thomas K.: Schwarz-Christoffel mapping of bounded, multiply connected domains (2006)
  3. DeLillo, Thomas K.; Driscoll, Tobin A.; Elcrat, Alan R.; Pfaltzgraff, John A.: Computation of multiply connected Schwarz-Christoffel maps for exterior domains (2006)
  4. Elcrat, Alan R.; Miller, Kenneth G.: Free surface waves in equilibrium with a vortex (2006)
  5. Hadjidimos, A.; Stylianopoulos, N. S.: Optimal semi-iterative methods for complex SOR with results from potential theory (2006)
  6. Marković, Miroslav; Jufer, Marcel; Perriard, Yves: A square magnetic circuit analysis using Schwarz--Christoffel mapping (2006)
  7. Sharon, E.; Mumford, D.: 2D-shape analysis using conformal mapping (2006) ioport
  8. Tee, T. W.; Trefethen, Lloyd N.: A rational spectral collocation method with adaptively transformed Chebyshev grid points (2006)
  9. Atkinson, K.; Sommariva, A.: On the numerical solution of some semilinear elliptic problems. II (2005)
  10. Avila, Artur; Damanik, David: Generic singular spectrum for ergodic Schrödinger operators (2005)
  11. Beattie, Christopher A.; Embree, Mark; Sorensen, D. C.: Convergence of polynomial restart Krylov methods for eigenvalue computations (2005)
  12. Beckermann, Bernhard: Numerical range, GMRES and Faber polynomials. (2005)
  13. Driscoll, Tobin A.: Algorithm 843: Improvements to the Schwarz-Christoffel toolbox for MATLAB (2005)
  14. Howison, Sam: Practical applied mathematics. Modelling, analysis, approximation (2005)
  15. Jenkinson, Oliver; Pollicott, Mark: Orthonormal expansions of invariant densities for expanding maps (2005)
  16. Kühnau, R. (ed.): Handbook of complex analysis: geometric function theory. Volume 2 (2005)
  17. Liou, Cheng-Yuan; Kuo, Yen-Ting: Conformal self-organizing map for a genus-zero manifold (2005) ioport
  18. Porter, R. Michael: Numerical calculation of conformal mapping to a disk minus finitely many horocycles (2005)
  19. Skorokhodov, S. L.; Khristoforov, D. V.: Overcoming instability in evaluation of generalized hypergeometric integrals in the case of crowding of singular points (2005)
  20. Stephenson, Kenneth: Introduction to circle packing. The theory of discrete analytic functions (2005)

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