Representation of conformal maps by rational functions

Abinand Gopal, Lloyd N. Trefethen

Published 2018-04-22Version 1

The traditional view in numerical conformal mapping is that once the boundary correspondence function has been found, the map and its inverse can be evaluated by contour integrals. We propose that it is much simpler, and 10-1000 times faster, to represent the maps by rational functions computed by the AAA algorithm. The power of this approach is particularly striking for regions with corners, where the mathematical basis of its effectiveness is a theorem of D. J. Newman in 1964.