ABSTRACT
The existence and uniqueness theorems for the conformal mappings of multiply connected regions onto canonical regions are discussed in Kythe [1998:358 ff]. We will first discuss a numerical method based on Mikhlin’s integral equation formulation on the boundary, which is a Fredholm integral equation of the second kind and has a unique periodic solution. Then a numerical method, called Mayo’s method, that uses a fast Poisson solver for the Laplacian (Mayo [1984]) is employed to determine the mapping function in the interior of the region which can be simply, doubly, or multiply connected, with accuracy even near the boundary. This method, in fact, computes the derivatives of the mapping function in the first application and the mapping function itself when applied twice. Most of the methods for conformal mapping compute the boundary correspondence function only.
