An integral equation method for the numerical conformal mapping of interior, exterior and doubly-connected domains
An integral equation method for the numerical conformal mapping of interior, exterior and doubly-connected domains
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DOI：
10.1007/bf01418327
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发表时间：
1983-10
影响因子：
2.1
通讯作者：
D. M. Hough;N. Papamichael
中科院分区：
文献类型：
--
作者：
D. M. Hough;N. Papamichael
一个数值方法，基于积分方程公式的Symm，描述了计算近似的映射函数，完成以下保形映射：（a）将封闭Jordan曲线内部的域映射到单位圆盘的内部，（B）将封闭Jordan曲线外部的域映射到单位圆盘的外部，（c）由两条闭Jordan曲线围成的双连通域到圆环上的映射。数值方法是基于近似的未知源密度的三次样条和“奇异”的功能，并特别适合于映射的困难域具有尖锐的角落。
A numerical method, based on the integral equation formulation of Symm, is described for computing approximations to the mapping functions which accomplish the following conformal maps: (a) the mapping of a domain interior to a closed Jordan curve onto the interior of the unit disc, (b) the mapping of a domain exterior to a closed Jordan curve onto the exterior of the unit disc, (c) the mapping of a doubly-connected domain bounded by two closed Jordan curves onto a circular annulus. The numerical method is based on approximating the unknown source density by cubic splines and “singular” functions, and is particularly suited for the mapping of difficult domains having sharp corners.