ABSTRACT
Research in computational conformal mappings has lately 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, 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 often use the Schwarz-Christoffel transformations.
