A Comparison of some Numerical Conformal Mapping Methods for Exterior Regions

Several methods for conformally mapping the exterior of the unit disk onto the exterior of a smooth curve are compared. These methods, which are known as the Timman, Friberg, Wegmann, and Theodorsen methods, are based on Fourier series and conjugation and are implemented using Fast Fourier Transforms. The computations reported here indicate that Wegmann's method converges faster and is more robust than the others.

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