三维位势直接边界元法中的几乎奇异积分

The nearly singular integrals in 3-D direct boundary element method

在三维直接边界元法分析中,几乎奇异积分的计算是一个重要的问题.对此,采用作者之前工作中提出的一种有效算法,使用高阶几何单元来描述几何边界,构造了新的距离函数,拓展原有的指数函数非线性变换到三维直接边界元法中,利用拓展的变换来消除被积函数的几乎奇异性.数值算例表明,本文算法稳定,效率高,即使计算点到实际边界的距离很小,依然可获得令人满意的数值结果.

A general methodology, which is presented in literature, was employed to compute nearly singular integrals arising in 3-D potential direct boundary element method. High-order boundary elements were used to approximate the geometric boundary and a new distance function was constructed. Then, the exponential transformation, which was proposed by present author, was extended to remove the near singularities of integrands. The numerical example was given to verify the high efficiency and the stability of the proposed scheme.