A Charge Simulation Method for Numerical Conformal Mapping onto Circular and Radial Slit Domains

Abstract

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 combinationof 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.