Many authors have studied the numerical computation of conformal mappings (numerical conformal mapping), and there are nowadays several efficient numerical schemes. Among them, Amano’s method offers a straightforward numerical procedure for computing conformal mappings based on the method of fundamental solutions, and it has been applied to several regions with great success. However, there are some difficulties in constructing a suitable conjugate harmonic function; therefore, it is required a little of craftmanship. In this paper, we construct another numerical scheme for computing conformal mappings based on the dipole simulation method and give mathematical theorems on the approximation error and the arrangements of the singular points. Several numerical results are also presented to ensure the effectiveness of our proposed method.

许多作者研究了共形映射的数值计算（数值共形映射），并且现在有几种有效的数值方案。其中，Amano的方法基于基本解的方法提供了一种简单的数值程序，用于计算共形映射，并且已成功应用于多个地区。但是，在构造合适的共轭谐波函数时存在一些困难。因此，需要一些技巧。在本文中，我们基于偶极子仿真方法构造了另一种用于计算共形映射的数值方案，并给出了关于近似误差和奇异点排列的数学定理。还提供了一些数值结果，以确保我们提出的方法的有效性。