NUMERICAL CONFORMAL MAPPING METHODS FOR EXTERIOR REGIONS WITH CORNERS

The main purpose of this paper is to present a method for computing the conformal map between the exterior of the unit disk and the exterior of a simple closed curve with corners. The method may be regarded as a generalization of the Schwarz-Christoffel transformation and is derived from the integral equation of Timman. Some comparison is made with other methods such as a version of Timman’s equation with corners, Fornberg’s method with explicit corner removers, Davis’ method, and CONFPACK. The method proves to be quite flexible and robust. © 1993 Academic Press, Inc.