Numerical conformal mapping methods based on function conjugation
Numerical conformal mapping methods based on function conjugation
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DOI：
10.1016/0377-0427(86)90130-5
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发表时间：
1986-02
影响因子：
2.4
通讯作者：
M. Gutknecht
中科院分区：
文献类型：
--
作者：
M. Gutknecht
给出了从单位圆盘到约当域的保角映射的统一处理方法。首先利用具有一定性质的任意辅助函数推导出边界对应函数的积分方程和积分微分方程（含共轭算子）。然后在此概括性中描述了求解这些方程的各种迭代方法，从而使基本思想得以体现。然后将具体的方法作为一般理论的实例加以处理。其中，特别是Theodorsen， Melentiev和Kulisch， Timman和Friberg的连续共轭法，Bergström的投影法，以及Vertgeim， Wegmann和h<e:1> bner的牛顿法（利用了黎曼-希尔伯特问题解的简单构造）。这些方法中的许多都比文献中更为普遍。本文还概述了与Fornberg、Menikoff-Zemach、Chakravarthy-Anderson和Challis-Burley方法的联系。
A unifying treatment of methods for computing conformal maps from the unit disk onto a Jordan region is presented. Integral and integro-differential equations (involving the conjugation operator) for the boundary correspondence function are first derived using an arbitrary auxiliary function having certain properties. Then various iteration methods for solving these equations are described in this generality, so that the basic ideas become manifest. Specific methods are then treated as examples of the general theory. Among them are, in particular, the successive conjugation methods of Theodorsen, Melentiev and Kulisch, Timman, and Friberg, the projection method of Bergström, and the Newton methods of Vertgeim, Wegmann, and Hübner (which make use of the easy construction of the solutions of Riemann-Hilbert problems). Many of these methods are treated in greater generality than in the literature. The connections with the methods of Fornberg, Menikoff-Zemach, Chakravarthy-Anderson, and Challis-Burley are also outlined.