Numerical techniques for conformal mapping onto a rectangle

Abstract

This paper is concerned with the problem of determining approximations to the function F which maps conformally a simply-connected domain onto a rectangle R, so that four specified points on are mapped Ω∂respectively onto the four vertices of R. In particular, we study the following two classes of methods for the mapping of domains of the form . (i) Methods which approximate where f is an approximation to the conformal map of Q onto the unit disc, and S is a simple Schwarz-Christoffel transformation. (ii) Methods based on approximating the conformal map of a certain symmetric doubly-connected domain onto a circular annulus. Keywords: Conformal