利用电磁波探测结构中具有阻抗边界的夹杂 ,是一类典型的逆问题。分别从数学原理及数值计算两个方面探讨了如何求解这类问题。首先建立了求解问题的基本方程 ,分别就正问题和逆问题加以讨论 ,同时构造了一个表达散物特征的指示函数 ,然后利用该函数的性质 ,确定具有阻抗散射物的边界。数值计算使用了 Nystroem方法求解正问题 ,对于不适定的逆问题 ,用 Tikhonov正则化方法

Detecting Structural Inclusion with Impedance Boundary Using Electromagnetic Wave PAN Wen feng,WU Dai hua,LI Zhuo qiu (School of Sciences, WUT, Wuhan 430070, China)It is a class of typical inverse problems to detect structural inclusion with impedance boundary condition using electromagnetic wave. In this paper, we study how to solve this problem from mathematical theory and numerical computation. First, the fundamental equation is set up, and, direct and inverse scattering problem are discussed; Second, indicator function of represent scatterer characterization is constructed; Third, the boundary of scatterer is determined by property of the function. In numerical computation, direct problem is solved by Nystrom's method and inverse problem is regularized by Tikhonov's regularizationimpedance boundary; integral equation method;indicator function