改进SSOR迭代法的数值保角变换计算法

针对基于模拟电荷法的数值保角变换计算法在复杂边界求解模拟电荷点电荷量时不精确及不稳定问题，提出一种基于（k，j）-Padé 迭代法改进的SSOR方法并用于求解电荷点电荷量。首先通过模拟电荷法将数值保角变换的逼近问题转换为理论上较为成熟的共轭调和函数逼近问题；然后根据边界条件、正则化条件、约束条件和柯西条件构造出约束方程组，使用改进算法计算电荷点电荷量；最后利用电荷点电荷量计算出数值保角变换函数。实验结果表明， 该方法能很好地保持映射前后角度之间的关系。与原方法相比，在橙形区域中最大精度提升率约为11.2%， 在椭圆区域中最大精度提升率为5.4%，且比原方法稳定性高。

Improved Method for Numerical Conformal Mapping Based on the Improved SSOR Method

The problem of the inaccuracy and instability of the charges calculated by the method based on the charge simulation method of numerical conformal mapping is discussed. In this paper， an SSOR method based on （k，j）-Padé iterative method is proposed to solve the charge amount. Firstly， based on the charge simulation method of numerical conformal mapping， the complex conformal mapping approximation problem is converted into a relatively mature theory of conjugate harmonic function approximation problem. Secondly， according to the boundary conditions， regularization conditions， constraints and Cauchy conditions， constraint equations are obtained， then the charge amount is calculated by the constraint equations. Finally， the numerical conformal mapping function is computed by the charge amount. Experimental results show that the method proposed in this paper has high accuracy and the mapping results well maintain the property of conformal mapping. Compared with the original method， the maximum accuracy improvement rate of the proposed method is about 8% in the orange region and 5.4% in the elliptical region， and the improved algorithm is more stable than the original method.