Applied and computational complex analysis. Vol. 3: discrete Fourier analysis—Cauchy integrals—construction of conformal maps---univalent functions
Algorithm 756: a MATLAB toolbox for Schwarz-Christoffel mapping
ACM Transactions on Mathematical Software (TOMS)
Application of computational complex analysis to some free boundary and vortex flows
Application of computational complex analysis to some free boundary and vortex flows
Algorithm 843: Improvements to the Schwarz-Christoffel toolbox for MATLAB
ACM Transactions on Mathematical Software (TOMS)
On Moduli of Rings and Quadrilaterals: Algorithms and Experiments
SIAM Journal on Scientific Computing
Numerical Computation of the Schwarz-Christoffel Transformation for Multiply Connected Domains
SIAM Journal on Scientific Computing
Conjugate function method for numerical conformal mappings
Journal of Computational and Applied Mathematics
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A software package implementing Schwarz-Christoffel Conformal transformation (or mapping) of doubly connected polygonal regions is fully described in this article from mathematical, numerical, and practical perspectives. The package solves the so-called accessory parameter problem associated with the mapping function as well as evaluates forward and inverse maps. The robustness of the package is reflected by the flexibility in choosing the accuracy of the parameters to be computed, the speed of computation, the ability of mapping “difficult” regions (to be specified in Section 2), and being user friendly. Several examples are presented to demonstrate the capabilities of the package.