cap

Conformal mapping of circular arc polygons. The authors describe an algorithm which computes the conformal mapping from the unit disk onto a simply connected region bounded by circular arc sides (straight sides are regarded as special cases of circular arc sides). This conformal mapping problem is a generalization of the problem which Trefethen solved by his Schwarz-Christoffel program [straight sides only, see L. N. Trefethen, SIAM J. Sci. Stat. Comput. 1, 82-102 (1980; Zbl 0451.30004)]. Instead of using Gauss-Jacobi quadrature to evaluate the Schwarz-Christoffel integral, the authors applied an ordinary differential equation solver to a non-singular formulation of the Schwarzian differential equation. The unknown parameters of this differential equation are determined by solving a nonlinear least square problem. The authors coded the algorithm as a FORTRAN program; computational results are given. (netlib conformal)


References in zbMATH (referenced in 13 articles )

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  1. Hakula, Harri; Nasyrov, Semen; Vuorinen, Matti: Conformal moduli of symmetric circular quadrilaterals with cusps (2021)
  2. Bauer, Ulrich; Lauf, Wolfgang: Conformal mapping onto a doubly connected circular arc polygonal domain (2019)
  3. 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)
  4. Harwood, Adrian R. G.; Dupère, Iain D. J.: Numerical evaluation of the compact acoustic Green’s function for scattering problems (2016)
  5. Brown, Philip R.; Porter, R. Michael: Conformal mapping of circular quadrilaterals and Weierstrass elliptic functions (2011)
  6. Crowdy, Darren G.; Fokas, Athanassios S.; Green, Christopher C.: Conformal mappings to multiply connected polycircular arc domains (2011)
  7. Andersson, Anders: Modified Schwarz-Christoffel mappings using approximate curve factors (2009)
  8. Andersson, Anders: A modified Schwarz-Christoffel mapping for regions with piecewise smooth boundaries (2008)
  9. Crowdy, D. G.; Fokas, A. S.: Conformal mappings to a doubly connected polycircular arc domain (2007)
  10. Porter, R. Michael: Numerical calculation of conformal mapping to a disk minus finitely many horocycles (2005)
  11. Grosse, Eric; Hobby, John D.: Improved rounding for spline coefficients and knots (1994)
  12. Howell, Louis H.: Numerical conformal mapping of circular arc polygons (1993)
  13. Bjørstad, Petter; Grosse, Eric: Conformal mapping of circular arc polygons (1987)