Numerical Conformal Mappings of Unbounded Multiply-Connected Domains Using the Charge Simulation Method
Numerical Conformal Mappings of Unbounded Multiply-Connected Domains Using the Charge Simulation Method
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发表时间：
2003
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通讯作者：
K. Amano;Dai Okano;Hidenori Ogata;M. Sugihara
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作者：
K. Amano;Dai Okano;Hidenori Ogata;M. Sugihara
本文给出了一种数值方法，将闭Jordan曲线外的无界多连通域共形映射到Nehari的三种典型域上，平行狭缝域、圆形狭缝域和径向狭缝域。在该方法中，我们表示的映射函数的一对共轭调和函数和近似，使用电荷模拟方法，由一个线性组合的复对数函数。该方法简单，无需积分，适用于曲线边界的区域。特别地，通过求解具有公共系数矩阵的线性方程组，统一地得到了无界多连通域到三类狭缝域的近似映射函数.最后通过一个典型算例说明了该方法的有效性。
We present a numerical method of conformal mappings of unbounded multiply-connected domains exterior to closed Jordan curves onto the three types of canonical domains of Nehari, i.e., the parallel slit domain, the circular slit domain and the radial slit domain. In the method, we express the mapping functions in terms of a pair of conjugate harmonic functions and approximate them, using the charge simulation method, by a linear combination of complex logarithmic functions. The method is simple without integration and suited for domains with curved boundaries. In particular, approximate mapping functions of an unbounded multiply-connected domain onto the three types of slit domains are obtained in a unified way by solving linear equations with a common coefficient matrix. A typical example shows the effectiveness of the method.