中文摘要：

研究了重建多个散射体的逆散射问题。利用波场分解的思想,首先给出了一种基于单层位势实现散射波和远场模式分解的算法,将多个不可穿透的散射体产生的远场模式,分解成与散射体个数对应的多个远场数据;然后,利用组合牛顿法给出了数值方法,把分解后得到的远场数据逐个重建多个散射体边界;最后,通过数值模拟验证了该算法的可行性。

英文摘要：

This paper studies an inverse scattering problem for reconstruction of multiple scatterers. Applying the idea of wave field decomposition, this paper firstly provides an algorithm for realizing scat-tered wave and far field model decomposition based on single layer potential to decompose far field mode generated by multiple impenetrable scatterer to multiple far-field data corresponding to the number of scat- terers. Then, a numerical method is proposed by combined Newton method. Far-field data gained after decomposition are used to reconstruct the boundary of multiple scatterers. Finally, the feasibility of the algo-rithm is verified through numerical simulation.