Numerical conformal mappings onto the linear slit domain

Abstract

We propose a numerical method for the conformal mapping of unbounded multiply connected domains exterior to closed Jordan curves C 1, . . . ,C n onto a canonical linear slit domain, which is the entire plane with linear slits S 1, . . . , S n of angles θ 1, . . . , θ n arbitrarily assigned to the real axis, respectively. If θ 1 = · · · = θ n = θ then it is the well-known parallel slit domain, which is important in the problem of potential flows past obstacles. In the method, we reduce the mapping problem to a boundary value problem for an analytic function, and approximate it by a linear combination of complex logarithmic functions based on the charge simulation method. Numerical examples show the effectiveness of our method.