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

Abstract

<p>Let Ω be the multiply connected domain in the extended complex plane C obtained by removing <em>m</em> non-overlapping rectilinear segments from the infinite strip <em>S</em> = {<em>z</em> : |Im<em>z</em>| < π /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 <em>m</em> 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 (<em>S</em>, <em>E</em>) where <em>E</em> ⊂ <em>S</em> is a union of disjoint segments. Second, we determine the streamlines associated with uniform incompressible, inviscid and irrotational flow past disjoint segments in the strip <em>S</em>.<br></p>