Geodesic
Slit maps and Schwarz-Christoffel maps for multiply connected domains
Electronic transactions on numerical analysis, Tome 36 (2010).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: We review recent derivations of formulas for conformal maps from finitely connected domains with circular holes to canonical radial or circular slit domains. The formulas are infinite products based on simple reflection arguments. An earlier similar derivation of the Schwarz-Christoffel formula for the bounded multiply connected case and recent progress in its numerical implementation are also reviewed. We give some sample calculations with a reflection method and an estimate of its accuracy. We also discuss the relation of our approach to that of D. Crowdy and J. Marshall. In addition, a slit map calculation using Laurent series computed by the least squares method in place of the reflection method is given as an example of a possible direction for future improvements in the numerics.
Classification : 30C30, 65E05
Keywords: conformal mapping, Schwarz-Christoffel transformation, multiply connected domains, canonical slit domains, Schottky-Klein prime function 
@article{ETNA_2010__36__a0,
     author = {Delillo, Thomas K. and Kropf, Everett H.},
     title = {Slit maps and {Schwarz-Christoffel} maps for multiply connected domains},
     journal = {Electronic transactions on numerical analysis},
     publisher = {mathdoc},
     volume = {36},
     year = {2010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2010__36__a0/}
}
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Delillo, Thomas K.; Kropf, Everett H. Slit maps and Schwarz-Christoffel maps for multiply connected domains. Electronic transactions on numerical analysis, Tome 36 (2010). http://geodesic.mathdoc.fr/item/ETNA_2010__36__a0/