二维逆散射问题探测方法的数值实现

NUMERICAL REALIZATION OF PROBE METHOD FOR 2-D INVERSE SCATTERING

探测方法是最近发展起来的逆散射问题的一种重要的求解方法,其主要思想是由散射波测量数据构造一个带有散射体外面参数点的指示函数,当参数点靠近散射体的边界时,指示函数爆破,由此重建散射体的边界．本文对具有Sound-soft边界的二维散射体给出了探测方法的数值实现．在给出标志函数的构造的基础上,进一步提出了利用模拟数据实现探测法的一个改进的逼近方法．为了更清楚地检验所提出的方法的数值结果,我们直接从Ω边界上的 D-to-N映射来研究探测方法的数值解．

Probe method is one of the most important inversion schemes developed recently for inverse scattering problems. Its main idea is to construct an indicator function with parameter point outside the scatterer from information about scattered wave. When the parameter point tends to the boundary of the scatterer, the indicator function blows up. Thus the boundary is recovered from the indicator behavior. The purpose of this paper is to propose a modified construction procedure for the indicator function and to study its numerical realization for the obstacle with sound-soft boundary. Some numerical tests are given, in order to simplify the test procedure, we consider the numerical realization from Dirichlet-to-Neumann map directly.