A regularized sampling method for solving three-dimensional inverse scattering problems

被引：66
|
作者：
Colton, D [1 ]
Giebermann, K
Monk, P
机构：
[1] Univ Delaware, Dept Math Sci, Newark, DE 19716 USA
[2] Univ Bonn, Inst Angew Math, D-53115 Bonn, Germany
来源：
SIAM JOURNAL ON SCIENTIFIC COMPUTING | 2000年 / 21卷 / 06期
关键词：
inverse scattering; Helmholtz equation; adaptive; regularized sampling method;
D O I：
10.1137/S1064827598340159
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The inverse scattering problem under consideration is to determine the shape of an obstacle in R-3 from a knowledge of the time harmonic incident acoustic wave and the far field pattern of the scattered wave with frequency in the resonance region. A method for solving this nonlinear and improperly posed problem is presented which is based on solving a linear integral equation of the first kind and avoids the use of nonlinear optimization methods. Numerical examples are given showing the practicality of this new approach.
引用
收藏
页码：2316 / 2330
页数：15
相关论文
共 50 条
  • [41] A METHOD OF SOLVING THREE-DIMENSIONAL PROBLEMS OF ELASTICITY FOR LAMINATED COMPOSITE PLATES
    Kulikov, G. M.
    Plotnikova, S. V.
    [J]. MECHANICS OF COMPOSITE MATERIALS, 2012, 48 (01) : 15 - 26
  • [42] A method of solving three-dimensional problems of seam workings and geological faults
    A. M. Lin’kov
    V. V. Zubkov
    M. A. Kheib
    [J]. Journal of Mining Science, 1997, 33 : 295 - 315
  • [43] On a regularized Levenberg-Marquardt method for solving nonlinear inverse problems
    Jin, Qinian
    [J]. NUMERISCHE MATHEMATIK, 2010, 115 (02) : 229 - 259
  • [44] An Enhanced Hybrid Method for Solving Inverse Scattering Problems
    Semnani, Abbas
    Kamyab, Manoochehr
    [J]. IEEE TRANSACTIONS ON MAGNETICS, 2009, 45 (03) : 1534 - 1537
  • [45] The linear sampling method for solving the electromagnetic inverse scattering problem
    Colton, D
    Haddar, H
    Monk, P
    [J]. SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2002, 24 (03): : 719 - 731
  • [46] Multilevel linear sampling method for inverse scattering problems
    Li, Jingzhi
    Liu, Hongyu
    Zou, Jun
    [J]. SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2008, 30 (03): : 1228 - 1250
  • [47] EXTENDED SAMPLING METHOD FOR INTERIOR INVERSE SCATTERING PROBLEMS
    Zeng, Fang
    [J]. INVERSE PROBLEMS AND IMAGING, 2020, 14 (04) : 719 - 731
  • [48] The no response test - A sampling method for inverse scattering problems
    Luke, DR
    Potthast, R
    [J]. SIAM JOURNAL ON APPLIED MATHEMATICS, 2003, 63 (04) : 1292 - 1312
  • [49] Comparison of three regularized solution techniques in a three-dimensional inverse radiation problem
    Ertürk, H
    Ezekoye, OA
    Howell, JR
    [J]. JOURNAL OF QUANTITATIVE SPECTROSCOPY & RADIATIVE TRANSFER, 2002, 73 (2-5): : 307 - 316
  • [50] Generalized Approach to Solving the Inverse Scattering Problems on the Basis of Sampling Strategy
    Synyavskyy, Andriy
    Hryniv, Rostyslav
    Shahin, Mazen
    Nazarchuk, Zinoviy
    [J]. 2016 IEEE INTERNATIONAL CONFERENCE ON MATHEMATICAL METHODS IN ELECTROMAGNETIC THEORY (MMET), 2016, : 425 - 428
12345