表面电荷法平面元电荷系数的半解析解法

针对在线性及高次电荷估计下,表面电荷法中全解析法对平面元电荷系数求解和实现较复杂的问题,提出一种半解析法.将系数积分由局部坐标系变换到整体坐标系下分离参数的二重积分,利用内层积分存在解析解的特点,将二维问题降为一维,方便数值积分计算.对于对数奇异积分问题采用辅助函数法消除.通过算例与全解析法计算精度进行比较,结果表明,在一定的单元划分下,可达到很高精度,具有一定可行性.

Semi-analytical Integration for Coefficients of Charge on Plane Elements in Surface Charge Method

A complete analytical method for coefficient of charge on plane elements in SCM(surface charge method) is complicated under linear or high order charge density approximation.A kind of semi-analytical integration is proposed.It transforms the integral under local reference into a separable double integration under global reference.Since the inner layer integration is analytical,the original integration can be simplified to a one-dimensional problem which can be calculated by traditional numerical method.As for singular integral,eliminating singularity technique by adding auxiliary function is adopted.It indicates that high precision is achieved and the method is applicable.