数值保角变换的新算法

摘要

保角变换理论在流体力学等许多领域中有着广泛的应用。但计算保角变换是个很困难的问题，因此寻求一种有效方法计算保角变换在实际应用中具有很大意义。本论文提出了一种数值保角变换的新算法，在这个新算法中我们在改进高斯消去法的基础上利用模拟电荷法计算新的电荷点，进而构造高精度的近似保角变换函数，并且通过典型图形的数值实验检验了新算法的有效性。%Conformal transformation theory has been widely used in fluid mechanics and many other fields. While calculating conformal mapping is a very difficult problem, thus to seek an effective method to calculate conformal mapping has great significance in practical application. This paper presents a new algorithm of numerical conformal mapping, in which the new charge point is calculated using charge simulation method on the basis of improving Gaussian elimination method, the approximate conformal mapping function of high precision is constructed, and the effectiveness of the new algorithm is verified through the typical graphic numerical experiments.