Numerical Conformal Mappings onto the Canonical Slit Domains of Koebe (1916) by the Charge Simulation Method(Application)

Abstract

In the conformal mapping of multiply connected domains, the following five canonical slit domains listed by Nehari (1952) are well known: the parallel, circular and radial slit domains, and the circle and circular ring with concentric circular slits. Before that, Koebe (1916) listed thirty-nine canonical slit domains. In this paper, using the charge simulation method, we propose a method of numerical conformal mappings onto their first thirteen canonical slit domains including the above five domains in a more general form. Numerical experiments show the effectiveness of our method. We examine also some problems in the computation of complex logarithmic function.