基于Hybrid迭代法的多连通域数值保角变换计算法

doi:10.16180/j.cnki.issn1007-7820.2021.07.003

摘要/Abstract

摘要：

针对模拟电荷法无界多连通区域的数值保角变换问题,文中提出了一种高精度的数值方法,即基于Hybrid迭代法的无界多连通区域的数值保角变换计算法。该方法通过模拟电荷法构造约束方程,对约束方程应用预处理构造对称正定的方程,获得新的模拟电荷和辐角,并构造近似保角变换函数。文中以多连通圆变换为径向狭缝域为例进行数值实验。使用解析函数的最大模原理作为误差的评价指标,并得出了天野法和文中算法的误差曲线。当模拟电荷数N=180,Jordan曲线为C₂时,文中算法E_A₂的误差为1.676 7×10^-7,但是天野法E_A₂的误差为8.597 7×10^-4。当模拟电荷数N=180,Jordan曲线为C₃时,文中算法E_Θ₃的误差为5.635 1×10^-10, 天野法E_Θ₃的误差为1.102 5×10^-5。

关键词: 模拟电荷法, 多连通区域, Hybrid迭代法, 广义迭代法, 投影技术, 数值保角变换, 解析函数, 约束方程

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

中图分类号:

TP391.41

唐胜男,吕毅斌,王樱子,房巾莉,武德安. 基于Hybrid迭代法的多连通域数值保角变换计算法[J]. 电子科技, 2021, 34(7): 13-18.

TANG Shengnan,LÜ Yibin,WANG Yingzi,FANG Jinli,WU Dean. Hybrid Iteration Method for Number Conformal Mapping of Multi-Connected Domain[J]. Electronic Science and Technology, 2021, 34(7): 13-18.

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	N=60	N=70	N=80	N=90
天野法	0.182 s	0.184 s	0.191 s	0.237 s
本文算法	0.119 s	0.143 s	0.170 s	0.202 s