### Hybrid Iteration Method for Number Conformal Mapping of Multi-Connected Domain

TANG Shengnan1,LÜ Yibin1,WANG Yingzi2,FANG Jinli1,WU Dean3

1. 1. Faculty of Science,Kunming University of Science and Technology,Kunming 650500,China
2. Computer Center,Kunming University of Science and Technology,Kunming 650500,China
3. School of Mathematical Sciences,University of Electronic Science and Technology of China,Chengdu 611731,China
• Received:2020-04-14 Online:2021-07-15 Published:2021-07-05
• Supported by:
National Natural Science Foundation of China(11461037)

Abstract:

For the problem of numerical conformal transformation of unbounded multi-connected domain of the charge simulation method, this study presents a high-precision numerical method, that is, Hybrid iteration method for number conformal mapping of multi-connected domain. This method constructs a constrain equation by charge simulation method, applies preprocessing to the constrain equation, constructs a symmetric positive definite equation, obtains new charge simulation and angle, and constructs an approximate conformal mapping function. In this study, the numerical experiment is carried out by taking the mapping of multiple connected domain into radial slit domain as an example. The maximum modulus principle of the analytic function is used as the error evaluation index, and the error curves of the Amano method and the algorithm of this study are drawn. When the number of charge simulation is N=180 and the Jordan curve is C2, the error of EA2 the algorithm of this study is 1.676 7×10-7, and the error of EA2 in Amano method is 8.597 7×10-4. When the number of charge simulation is N=180 and the Jordan curve is C3, the error of EΘ3 in the algorithm of this study is 5.635 1×10-10, but the error of EΘ3 in Amano method is 1.102 5×10-5.

CLC Number:

• TP391.41