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
  • [1] On the solution of three-dimensional inverse obstacle acoustic scattering problems by a regularized Newton method
    Farhat, C
    Tezaur, R
    Djellouli, R
    [J]. INVERSE PROBLEMS, 2002, 18 (05) : 1229 - 1246
  • [2] A fully no-sampling formulation of the linear sampling method for three-dimensional inverse electromagnetic scattering problems
    Brignone, M.
    Bozza, G.
    Aramini, R.
    Pastorino, M.
    Piana, M.
    [J]. INVERSE PROBLEMS, 2009, 25 (01)
  • [3] An Improved Subspace-Regularized DBIM-MLGFIM Method for Three-Dimensional Inverse Scattering Problems
    Zhao, Peng
    Liu, Linchun
    Xu, Kuiwen
    Ye, Xiuzhu
    Chen, Shichang
    Wang, Gaofeng
    Chan, Chi Hou
    [J]. IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, 2021, 69 (05) : 2798 - 2809
  • [4] Multi-resolution subspace-based optimization method for solving three-dimensional inverse scattering problems
    Ye, Xiuzhu
    Poli, Lorenzo
    Oliveri, Giacomo
    Zhong, Yu
    Agarwal, Krishna
    Massa, Andrea
    Chen, Xudong
    [J]. JOURNAL OF THE OPTICAL SOCIETY OF AMERICA A-OPTICS IMAGE SCIENCE AND VISION, 2015, 32 (11) : 2218 - 2226
  • [5] Fast regularized linear sampling for inverse scattering problems
    Fares, M'Barek
    Gratton, Serge
    Toint, Philippe L.
    [J]. NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, 2011, 18 (01) : 55 - 68
  • [6] Numerical method for solving of three-dimensional scattering problems from penetrable body
    Samokhin, AB
    [J]. MMET'96 - VITH INTERNATIONAL CONFERENCE ON MATHEMATICAL METHODS IN ELECTROMAGNETIC THEORY, PROCEEDINGS, 1996, : 54 - 54
  • [7] An Efficient Method for Solving Problems of Acoustic Scattering on Three-Dimensional Transparent Structures
    Samokhin, Alexander B.
    Yurchenkov, Ivan A.
    [J]. MATHEMATICS, 2024, 12 (06)
  • [8] A numerical method for solving the limited aperture problem in three-dimensional inverse obstacle scattering
    You, YX
    Miao, GP
    Liu, YZ
    [J]. INTERNATIONAL JOURNAL OF NONLINEAR SCIENCES AND NUMERICAL SIMULATION, 2001, 2 (01) : 29 - 42
  • [9] Topological Sensitivity for Solving Inverse Multiple Scattering Problems in Three-Dimensional Electromagnetism. Part II: Iterative Method
    Le Louer, Frederique
    Rapun, Maria-Luisa
    [J]. SIAM JOURNAL ON IMAGING SCIENCES, 2018, 11 (01): : 734 - 769
  • [10] Topological Sensitivity for Solving Inverse Multiple Scattering Problems in Three-dimensional Electromagnetism. Part I: One Step Method
    Le Louer, Frederique
    Rapun, Maria-Luisa
    [J]. SIAM JOURNAL ON IMAGING SCIENCES, 2017, 10 (03): : 1291 - 1321
12345