Numerical Computing of Preimage Domains for Bounded Multiply Connected Slit Domains

Abstract

In this paper, for a given bounded multiply connected slit domain $$\varOmega $$ , we present an iterative numerical method for computing a conformally equivalent multiply connected domain G bounded by smooth Jordan curves and the conformal mapping $$w=\varPhi (z)$$ from G onto $$\varOmega $$ . Each iteration of the proposed iterative method requires solving the boundary integral equation with the generalized Neumann kernel. We consider two cases of bounded slit domains, namely the unit disk with radial slit domain and an annulus with radial slit domain. Numerical examples are presented to illustrate that the proposed iterative method converges even for highly connected slit domains.