Numerical conformal mapping onto a rectangle with applications to the solution of Laplacian problems

Abstract

Let F be the function which maps conformally a simply-connected domain Ω onto a rectangle R, so that four specified points on ∂Ω are mapped respectively onto the four vertices of R. In this paper we consider the problem of approximating the conformal map F, and present a survey of the available numerical methods. We also illustrate the practical significance of the conformal map, by presenting a number of applications involving the solution of Laplacian boundary value problems.