Numerical conformal mappings onto the canonical slit domains

Conformal mappings are familiar in science and engineering. Recently, the problem of multiply connected domains has attracted special interest. We here present a unified scheme for numerical conformal mappings of unbounded, multiply connected domains onto the parallel, circular and radial slit domains under two different conditions. These are canonical slit domains important in potential flow problems. We express the mapping functions in terms of an analytic function so that its real part is subject to a Dirichlet boundary condition, and have approximate mapping functions of simple form and high accuracy using the charge simulation method. Numerical examples show the effectiveness of our method. We also make a short survey of relevant works.