有界多连通区域数值保角变换的GMRES(m)法  

The GMRES(m)Method for Numerical Conformal Mapping of Bounded Multi-Connected Domains

作　　者：伍康 吕毅斌[1] 石允龙 王樱子 WU Kang;LÜ Yibin;SHI Yunlong;WANG Yingzi(Faculty of Science,Kunming University of Science and Technology,Kunming 650500,P.R.China;Computer Center,Kunming University of Science and Technology,Kunming 650500,P.R.China)

机构地区：[1]昆明理工大学理学院,昆明650500 [2]昆明理工大学计算中心,昆明650500

出　　处：《应用数学和力学》2022年第9期1026-1033,共8页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(11461037);云南省基础研究计划(202101BE070001-050)。

摘　　要：求解复杂多连通区域的保角变换函数是困难的.针对这一问题,该文将求解保角变换函数转化为利用模拟电荷法求解一对定义在问题区域上的共轭调和函数,再根据边界条件建立约束方程,并利用GMRES(m)(the generalized minimal residual method)算法求解约束方程,获得了模拟电荷,进而构造了高精度的近似保角变换函数,将有界多连通区域映射为三种无界正则狭缝域.数值实验验证了该文算法的有效性.It is difficult to solve conformal mapping functions for complex multi-connected domains.In order to overcome this difficulty,the problem of solving conformal mapping functions was transformed into using the charge simulation method to solve a pair of conjugate harmonic functions in the problem domain.The conjugate harmonic functions should satisfy given boundary conditions,which construct a system of linear equations.Then the simulation charges can be computed by means of the GMRES(m)(the generalized minimal residual method)algorithm to solve the linear systems.The approximate conformal mapping functions were constructed accurately to map the bounded multi-connected domain onto 3 unbounded canonical slit domains.Numerical results show that the presented method is effective.

关 键 词：有界多连通区域 模拟电荷法 GMRES(m)法 数值保角变换 

分 类 号：O241[理学—计算数学]