A CHARGE SIMULATION METHOD FOR NUMERICAL CONFORMAL MAPPING ONTO CIRCULAR AND RADIAL SLIT DOMAINS

A simple numerical method is described for computing the following two conformal maps: (a) from a domain exterior to closed Jordan curves on to a circular slit domain and (b) from a domain exterior to closed Jor dan curves onto a radial slit domain. They constitute a dual problem a nd can be computed in a dual way. The numerical method is based on the charge simulation method or the method of fundamental solutions appli ed to the Dirichlet problem of Laplace's equation in which a pair of c onjugate harmonic functions are approximated by a linear combination o f complex logarithmic potentials. The unknown coefficients are determi ned by the collocation condition imposed on the real part or the imagi nary part, the modulus or the argument, of the approximate mapping fun ction. Effectiveness of the method is demonstrated by some typical exa mples.