半无限大平面导电媒质中空洞定位问题的迭代算法

提出了半无限大平面中空洞定位问题的一种新方法.首先利用边界积分方程建立表面测量电位同目标体及其位置参数的关系.在此基础上,借助于电磁逆散射问题求解中的Newton-Kantorovich方法,推导出目标参数的微小变化对表面电位分布影响的数学表达式.然后,在给定初值的情况下,利用这两组方程进行迭代求解,从而不断地逼近真解.对于求解过程中出现的病态方程组采用阻尼最小二乘法,并通过选择适当的阻尼因子,使得解答稳定.与有限元法结合最小二乘法求解该问题相比较,该方法具有更高的效率.

An Iterative Algorithm for Locating a Hole in Semi-infinite Planar Conductive Medium

A novel method concerning the problem of locating a hole in two dimensional semiinfinite plane is presented. The relationship between surface metrical potential and the parameter of object shape and location is obtained by using the boundary integral equation. On the basis of that, the mathematical expression about the influence of tiny object parameter change upon surface potential distribution is derived with the reference of Newton-Kantorovich method used to solve the problem of electromagnetic inverse scatter. In the condition of initial values available, the two equations can be figured out iteratively and the true value can be approached gradually. In order to solve the ill-posed equations, the damping least square method is used by choosing a proper damping factor to make the result stable. Compared with the hybrid method of finite element method and least square method for this problem, the proposed method here is more efficient.