施瓦茨-克里斯托弗反变换的快速收敛算法及其应用

Rapidly convergent algorithm for inverse Schwarz-Christoffel transformations and its application

介绍了施瓦茨 克里斯托弗反变换 (ISC)的一种数值方法 ,通过将弛豫法和循环余割法相结合并调整收敛判据 ,能够快速求解ISC的非线性方程 ,不必给定特殊的初始值就可以确保收敛。通过加入某些虚顶点和去除奇点等方法可避免积分中遇到的困难 ,使得整个计算过程快捷而准确。同时给出快速处理任意多角形问题的通用程序 ,并对方同轴线进行了详细的分析 ,证明了对于曲线边界问题 ,只要采用合适的折线逼近 ,就可以应用此算法得到精确结果。

This paper presents a numerical method for Inverse Schwarz-Christoffel (ISC) transformations. By combining the relaxation method with the recursive secant technique, the nonlinear equation set occurred in ISC mapping is solved rapidly. No special initial value is needed and the convergence is guaranteed by adjusting a convergent criterion. Inserting some spurious vertices and removing singularities are recommended to avoid the trouble in integrals and make the computation rapid and accurate. Based on above schemes a single program is developed to deal with any polygon problems quickly. As an example, the square coaxial line is analyzed in detail. From the results, we can conclude that this algorithm can be used in the similar problems including curve boundaries.