基于坐标变换精确计算近奇异积分的双向sinh变换法

A coordinate transformation based double sinh transformations for evaluation of nearly singular integrals

提出一种与坐标变换相结合的双向sinh变换方法用于精确计算近奇异积分。首先利用坐标变换法对近奇异积分进行双向分离,再针对分离出的两个方向的积分形式,根据复变函数极点理论,构造双向sinh变换。与传统结合环向变换和极坐标变换的单向sinh变换以及迭代sinh变换方法相比,双向sinh变换法的计算精度更高,并且最近点的位置对近奇异积分计算精度的影响明显变小。

This paper presents a new method which combines the coordinate transformation and double sinh transformations for nearly singular integrals.Firstly,the coordinate transformation is employed to separate the near singularities in the two directions.From the forms of the nearly singular integrals in the two directions,based on the complex poles theory,dual sinh transformations are constructed.Compared with the original sinh transformation in polar transformation in combination with the circumference transformation,dual sinh transformation in combination with the coordinate transformation,proposed in our paper can achieve a much more accurate result;moreover,the computational accuracy is less sensitive to position of the nearest singular point in the elements.