Numerical Conformal Mappings onto the Canonical Slit Domains Listed in Koebe (1916)

保角映射在科学和工程中很常见。利用电荷模拟方法，提出了一种无界多连通区域到线性狭缝正则区域和螺旋狭缝正则区域的统一的数值保角映射方法，并通过数值实验验证了该方法的有效性。该方法原则上也适用于有界域问题。结果，到Koebe(1916)中列出的39个正则狭缝域中的前13个的近似映射函数可以以如上所述的更一般的形式获得。

Conformal mappings are familiar in science and engineering. Using the charge simulation method, we proposed a unified method of numerical conformal mappings of unbounded multiply connected domains onto the linear and the spiral slit canonical domains, where oblique angles of the slits were individually specified, and showed its effectiveness by numerical experiments. The method is applicable also to the problem of bounded domains in principle. As a result, approximate mapping functions onto the first thirteen of the thirty nine canonical slit domains listed in Koebe (1916) are obtainable in a more general form as described above.