[1]朱翚,刘继军.散射体边界辨识问题中散射场的数值计算[J].东南大学学报(自然科学版),2008,38(3):540-546.[doi:10.3969/j.issn.1001-0505.2008.03.035]
 Zhu Hui,Liu Jijun.Computation of scattered wave in boundary identification problem[J].Journal of Southeast University (Natural Science Edition),2008,38(3):540-546.[doi:10.3969/j.issn.1001-0505.2008.03.035]
点击复制

散射体边界辨识问题中散射场的数值计算()
分享到:

《东南大学学报(自然科学版)》[ISSN:1001-0505/CN:32-1178/N]

卷:
38
期数:
2008年第3期
页码:
540-546
栏目:
数学、物理学、力学
出版日期:
2008-05-20

文章信息/Info

Title:
Computation of scattered wave in boundary identification problem
作者:
朱翚1 刘继军2
1 苏州大学机电工程学院, 苏州 215021; 2 东南大学理学院, 南京 210096
Author(s):
Zhu Hui1 Liu Jijun2
1 Department of Automatic Control, Soochow University, Suzhou 215021, China
2 School of Sciences, Southeast University, Nanjing 210096, China
关键词:
边界识别 反问题 逆散射 位势函数 数值解
Keywords:
identification problem inverse problem inverse scattering potential function numerics
分类号:
O175.24;O175.5;O241.82
DOI:
10.3969/j.issn.1001-0505.2008.03.035
摘要:
考虑带有混合边界条件的散射体利用反射波信息进行边界识别的反问题.该类问题在利用优化技术迭代求解时的关键一步是散射波及其远场数据的数值求解.由于是混合边界条件,经典的只利用单层位势或双层位势建立在整个边界上一个统一的积分方程的求解的方法不再适用.提出了综合利用单双层位势 求解该问题的数值方案,得到的是边界上不同部分的线性积分方程组.利用势函数的阶跃理论数学上证明了所提出方案的可解性,进而给出了方程中奇性积分的计算方法及方程组在有限维空间的离散方案,最后给出了数值例子, 证明了该求解方法的有效性.
Abstract:
The boundary identification for an obstacle with mixed boundary condition is considered using the scattered wave information. The key step to this problem applying optimization technique is the numerical solution of the scattered wave as well as its far-field pattern. Since the boundary is of mixed type, the classic layer-potential method can not be applied any more. An inversion scheme is proposed using the combined single and double-layer potential. Using the jump relation for the potential function, the solvability of the proposed inversion scheme is proved and the computation scheme for the improper integrals is given. The numerical results are presented to show the validity of the proposed inversion scheme.

参考文献/References:

[1] Kress R.Linear integral equations [M].Singapore:Springer-Verlag,World Publishing Corporation,1989.
[2] Chapko R,Kress R.A hybrid method for inverse boundary value problems in potential theory [J]. J Inverse Ill-posed Problems,2005,13(1):27-49.
[3] Wang H B,Liu J J.Numerical solution for the Helmholtz equation with mixed boundary condition[J]. Numerical Mathematics A Journal of Chinese Universities,2007,16(3):203-214.
[4] Liu J J,Nakamura G,Sini M.Reconstruction of the shape and surface impedance from acoustic scattering data for arbitrary cylinder [J]. SIAM J Applied Mathematics,2007,67(4):1124-1146.
[5] Colton D,Kress R. Inverse acoustic and electromagnetic scattering theory [M].Berlin:Springer-Verlag,1992.
[6] Mclean W.Strongly elliptic systems and boundary integral equations[M].Cambridge UK:Cambridge University Press,2000.
[7] Liu J J.Recovery of boundary impedance coefficient in 2-D media [J]. Chinese J Numer Math Appl,2001,23(2):111-120.
[8] Cakoni F,Colton D,Monk P.The direct and inverse scattering problems for partially coated obstacles[J]. Inverse Problems,2001,17(6):1997-2015.

备注/Memo

备注/Memo:
作者简介: 朱翚(1968—),女,硕士,讲师,zhuhuil@hotmail.com.
基金项目: 江苏省自然科学基金资助项目(BK2007101).
引文格式: 朱翚,刘继军.散射体边界辨识问题中散射场的数值计算[J].东南大学学报:自然科学版,2008,38(3):540-546.
更新日期/Last Update: 2008-05-20