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

Abstract

Let Ω be the multiply connected domain in the extended complex plane $\overline {\mathbb {C}}$obtained by removing m non-overlapping rectilinear segments from the infinite strip $S=\{z : \left |\text {Im} z\right |<\pi /2\}$. 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 $\mathbb {D}$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 ⊂ S 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 S.