单位圆到任意曲线保角变换的近似计算方法
An Approximate Method on the Conformal Mapping from a Unit Circle to an Arbitrary Curve
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摘要: 本文讨论了将单位圆内部映射成由任意曲线(包括任意曲线割缝)边界围成的单连通域内部或外部的保角变换问题.以多边形逼近单连通域的边界,采用Schwartz-Christoffel积分建立单位圆与该多边形的映射函数.给出了确定Schwartz-Christoffel积分中未知参数的数值计算方法.
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关键词:
- 曲线边界 /
- 保角变换 /
- Schwartz-Christoffel积分
Abstract: In this paper, the conformal mapping problem on the transformation from the interior of a unit circle to the interior of the simply connected region or exterior with an arbitrary curvilinear boundary (including an arbitrary curvilinear cut crack) is discussed.The boundary of the simply connected region is approximated by a polygon.The mapping function from a unit circle to a polygon is founded by using the Schwartz-Christoffel integral.A numerical calculation method to determine the unknown parameters in the Schwartz-Christoffel integral is given.-
Key words:
- arbitrary curve /
- mapping /
- Schwartz-Christoffel integral
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[1] 樊大钧编.《数学弹性力学》.新时代出版汪(1983),274-279 [2] 格.列.伦兹等著,熊振翔等译,《复变函数与运算微积初步》,人民教育出版社(1960),181~184 [3] 伊.伊.普里瓦洛夫等,《复变函数引论》,闵嗣鹤等译,人民教育出版社(1950),433,444 -
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