A method of numerical conformal mapping of curved slit domains by the charge simulation method

In this paper, we propose a method of numerical conformal mappings from a domain with a curved slit onto the canonical slit domains. Our method is based on Amanoʹs method, which uses the charge simulation method as a rapid solver for potential problems. Due to the potential solver, his method gives high accuracy in many cases. The basic idea of the preceding method is to provide an approximation of harmonic functions by a linear combination of the complex logarithmic functions, g(z)=∑jQj log(z−ζj), where the singularity points ζj are placed outside the problem domain. However, there are some difficulties on applying it to the problem domain with corners on the boundary, and the problem domain without enough space to place the singularity points properly. The problem domain with a curved slit is a typical example of such a difficulty. A technique we provide here is based on use of the Joukowski transformation. It inherits all the good properties of the original method. We show the effectiveness of our proposal by some numerical examples.