Dipole simulation method for two-dimensional potential problems

Abstract

In this paper, we propose to apply the dipole simulation method proposed by Katsurada to two-dimensional potential problems in general regions. The dipole simulation method is an extension of the charge simulation method (the method of fundamental solutions) and gives an approximate solution by a linear combination of the dipole potentials. We also present an application of the proposed method to numerical conformal mapping. Some numerical examples show the effectiveness of the proposed method.