Numerical computation of a preimage domain for an infinite strip with rectilinear slits

Abstract

Let $\Omega$ be the multiply connected domain in the extended complex plane $\overline{\C}$ obtained by removing $m$ non-overlapping rectilinear segments from the infinite strip $S=\{z:\left|\Im z\right|<\pi /2\}$. In this paper, we present an iterative method for numerical computation of a conformally equivalent bounded multiply connected domain $G$ in the interior of the unit disk $\D$ and the exterior of $m$ non-overlapping smooth Jordan curves. We demonstrate the utility of the proposed method through two applications. First, we estimate the capacity of condensers of the form $(S,E)$ where $E\subset S$ be a union of disjoint segments. Second, we determine the streamlines associated with uniform incompressible, inviscid and irrotational flow past disjoint segments in the strip $S$.