Numerical conformal mappings onto the linear slit domain

Abstract

We propose a numerical method for the conformalmapping of unbounded multiply connected domains exterior to closed Jordan curvesC1, . . . ,Cn 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. Ifθ1 = ⋯ =θn =θ then it is thewell-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. © The Author(s) 2012.