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

Abstract

The charge simulation method has been applied to solve a lot of problems in electrical engineering. However, the principle of the method is not known enough even now. This paper is devoted to giving the theoretical and mathematical base for the charge simulation method of numerical conformal mappings in ring domains. Therefore for example, the uniform, convergence of approximations, the theoretical distribution of charge points, and the charges will be mathematically discussed. An example is shown to help understanding of theoretical considerations.