Annulus with circular slit map of bounded multiply connected regions via integral equation method

Abstract

This paper presents a boundary integral equation method for the numerical conformal mapping of bounded multiply connected region onto an annulus with circular slits. The method is based on some uniquely solvable linear integral equations with classical, adjoint and generalized Neumann kernels. These boundary integral equations are constructed from a boundary relationship that relates the mapping function f on a multiply connected region with f′, θ′, and |f|, where θ is the boundary correspondence function. Some numerical examples are presented to illustrate the efficiency of the presented method.