A method of numerical conformal mapping of curved slit domains by the charge simulation method
Journal of Computational and Applied Mathematics - Proceedings of the international conference on recent advances in computational mathematics
Numerical conformal mappings of bounded multiply connected domains by the charge simulation method
Journal of Computational and Applied Mathematics - Special issue: Proceedings of the 6th Japan--China joint seminar on numerical mathematics, university of Tsukuba, Japan, 5-9 August 2002
On Moduli of Rings and Quadrilaterals: Algorithms and Experiments
SIAM Journal on Scientific Computing
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A simple numerical method is described for computing the following two conformal maps: (a) from a domain exterior to closed Jordan curves onto a circular slit domain and (b) from a domain exterior to closed Jordan curves onto a radial slit domain. They constitute a dual problem and can be computed in a dual way. The numerical method is based on the charge simulation method or the method of fundamental solutions applied to the Dirichlet problem of Laplace's equation in which a pair of conjugate harmonic functions are approximated by a linear combination of complex logarithmic potentials. The unknown coefficients are determined by the collocation condition imposed on the real part or the imaginary part, the modulus or the argument, of the approximate mapping function. Effectiveness of the method is demonstrated by some typical examples.