Applied and computational complex analysis. Vol. 3: discrete Fourier analysis—Cauchy integrals—construction of conformal maps---univalent functions
Numerical continuation methods: an introduction
Numerical continuation methods: an introduction
Algorithm 756: a MATLAB toolbox for Schwarz-Christoffel mapping
ACM Transactions on Mathematical Software (TOMS)
SIAM Journal on Applied Mathematics
ACM Transactions on Mathematical Software (TOMS)
A Multipole Method for Schwarz--Christoffel Mapping of Polygons with Thousands of Sides
SIAM Journal on Scientific Computing
Journal of Computational and Applied Mathematics
Revisiting the Crowding Phenomenon in Schwarz-Christoffel Mapping
SIAM Journal on Scientific Computing
Conformal Maps to Multiply Slit Domains and Applications
SIAM Journal on Scientific Computing
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We report on recent progress in the computation of Schwarz-Christoffel maps from bounded or unbounded circular domains to conformally equivalent bounded or unbounded multiply connected polygonal domains. The form of the transformation is given in terms of an integral of an infinite product depending on unknown parameters, namely, the prevertices and the centers and radii of the circles. A system of nonlinear equations, which forces the geometry of the given polygonal domain to be correct under the mapping function, is formulated for the unknown parameters and solved by a continuation method. A transformation of the constrained parameters to an unconstrained set of variables is crucial to the effective solution of the system. Several numerical examples are given. The approach here proves to be very robust.