Theoretical consideration of charge simulation method for numerical conformal mappings in a ring domain (Q1384244)

The problem considered is to find a numerical approximation for the conformal map of a ring domain onto a ring domain. This approximation is derived from the root asymptotics of weighted finite Blaschke products (called weighted hyperbolic polynomials). These are chosen to be approximately optimal in a potential theoretic sense when certain electrical charges are placed at the zeros of these Blaschke products. Several algorithms are proposed which differ in the choice of the zeros and the corresponding charges.