Numerical Conformal Mapping onto the Parabolic, Elliptic and Hyperbolic Slit Domains

Abstract

This paper presents a numerical method for computing the conformal mappings onto the parabolic slit domain, the elliptic slit domain and the hyperbolic slit domain. The method relies on a boundary integral equation with the generalized Neumann kernel. For a given multiply connected domain of connectivity $$m+1$$ , the proposed method requires $$O((m+1)n\log n)$$ operations where n is the number of nodes in the discretization of each boundary component of the given domain. Several numerical examples are presented to illustrate the performance of the proposed method.