Introduction

Current research in computational conformal mapping has taken two major directions. One direction involves the conformal mapping from a standard region, like the unit disk or the upper half-plane, onto the problem region, whereas in the other it is from the problem region onto a standard region. In the former case one solves a nonlinear integral equation involving the conjugate operator (e.g., Theodorsen’s integral equation), by fast Fourier transform (FFT), polynomial approximation, iteration, or Newton’s method. In the latter case the integral equation, derived from the Dirichlet problem, is linear or singular linear if it is derived from potential theory (e.g., Symm’s integral equation). Depending on the nature of the problem region, these methods sometimes use the Schwarz-Christoffel transformations. The historical development of different methods for computational conformal mapping of simply and multiply connected regions is sketched below.