Computational method of conformal mapping from unbounded multi-connected regions onto annulus with spiral slit domains

Abstract In this paper, based on the charge simulation method, a conformal mapping computational method is proposed to map the unbounded multiply connected regions onto the annulus with spiral slit domains. In addition, for the system of pathological equations generated during the conformal mapping process, it is proposed to solve them by using the GMRES(m) method, which in turn constructs an approximate conformal mapping function with high accuracy. Finally, numerical examples validate the effectiveness of the algorithms in this paper.