基于波场分解重建多个散射体的数值方法与模拟  

Numerical Method and Simulation for Reconstruction of Multiple Scatterers Based on Wave Field Decomposition

作　　者：夏赟[1] 王泽文[1] 赵学慧 

机构地区：[1]东华理工大学理学院,南昌330013 [2]凉城四中,内蒙古自治区乌兰察布市013750

出　　处：《浙江理工大学学报（自然科学版）》2014年第5期580-585,共6页Journal of Zhejiang Sci-Tech University(Natural Sciences)

基　　金：国家自然科学基金(11161002);江西省青年科学基金资助项目(20132BAB211014);江西省教育厅科技资助项目(GJJ13460);东华理工大学校长基金(DHXK1207)

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。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.

关 键 词：逆散射 波场分解 组合牛顿法 多个散射体 不适定问题 

分 类 号：O242.1[理学—计算数学]