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 E_A2 the algorithm of this study is 1.676 7×10^-7, and the error of E_A2 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 E_Θ3 in the algorithm of this study is 5.635 1×10^-10, but the error of E_Θ3 in Amano method is 1.102 5×10^-5.

Key words: charge simulation method, multi-connected domain, Hybrid iteration method, generalized iteration method, projection technique, numerical conformal transformation, analytic function, constraint equations