Bi-Directional Method for Numerical Conformal Mappings of Multiply Connected Domains by the Charge Simulation Method

Abstract

Usually, on computation of conformal mappings, different methods are used to obtain the mapping functions of two directions between a problem domain and a canonical domain.Amano proposed a method based on the numerical conformal mappings by the charge simulation method, and it offers the both mapping functions of simply connected problem domains and the canonical domains like the unit disk.However, his method cannot be used to obtain the mapping function on the canonical slit domains, which are important for the potential flow analysis of multiply connected domains.Here, we provide a solution to this difficulty, and propose a new method which improves the method of numerical conformal mappings by the charge simulation method, and expands the bi-directional applicability to the problem of multiply connected domains.