Reconstruction of modified transmission eigenvalues using Cauchy data

被引：2

作者：

Liu, Juan ^{[2
]}

Liu, Yanfang ^{[3
]}

Sun, Jiguang ^{[1
]}

机构：

[1] Michigan Technol Univ, Dept Math Sci, Houghton, MI 49931 USA

[2] Jinan Univ, Dept Math, Guangzhou, Peoples R China

[3] George Washington Univ, Dept Math, Washington, DC USA

来源：

JOURNAL OF INVERSE AND ILL-POSED PROBLEMS | 2023年 / 31卷 / 06期

关键词：

Inverse scattering; modified transmission eigenvalues; reciprocity gap; Cauchy data; inhomogeneous media;

D O I：

10.1515/jiip-2022-0014

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The modified transmission eigenvalue (MTE) problem was introduced in [S. Cogar, D. Colton, S. Meng and P. Monk, Modified transmission eigenvalues in inverse scattering theory, Inverse Problems 33 (2017), no. 12, Article ID 125002] and used as a target signature for nondestructive testing. In this paper, we study the inverse spectral problem to reconstruct the modified transmission eigenvalues using Cauchy data. We propose a reciprocity gap functional method and show that the MTEs can be determined by solving some linear ill-posed integral equations. Numerical examples for both absorbing and non-absorbing media are presented to validate the effectiveness and robustness of the proposed method.

引用

页码：905 / 919

页数：15

共 19 条

[1]

[Anonymous], 2013, Applied Mathematical Sciences

[2] New sets of eigenvalues in inverse scattering for inhomogeneous media and their determination from scattering data [J].

Audibert, Lorenzo ;

Cakoni, Fioralba ;

Haddar, Houssem .

INVERSE PROBLEMS, 2017, 33 (12)

[3]

Cakoni F., 2016, CBMS-NSF Regional Conference Series in Applied Mathematics, V88

[4] On the use of transmission eigenvalues to estimate the index of refraction from far field data [J].

Cakoni, Fioralba ;

Colton, David ;

Monk, Peter .

INVERSE PROBLEMS, 2007, 23 (02) :507-522

[5] A Spectral Approach to Nondestructive Testing via Electromagnetic Waves [J].

Cakoni, Fioralba ;

Cogar, Samuel ;

Monk, Peter .

IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, 2021, 69 (12) :8689-8697

[6] An adaptive perfectly matched layer technique for time-harmonic scattering problems [J].

Chen, ZM ;

Liu, XZ .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 2005, 43 (02) :645-671

[7] Using eigenvalues to detect anomalies in the exterior of a cavity [J].

Cogar, S. ;

Colton, D. ;

Monk, P. .

INVERSE PROBLEMS, 2018, 34 (08)

[8] Modified transmission eigenvalues in inverse scattering theory [J].

Cogar, S. ;

Colton, D. ;

Meng, S. ;

Monk, P. .

INVERSE PROBLEMS, 2017, 33 (12)

[9]

Cogar S., 2019, THESIS U DELAWARE

[10] MODIFIED ELECTROMAGNETIC TRANSMISSION EIGENVALUES IN INVERSE SCATTERING THEORY [J].

Cogar, Samuel ;

Monk, Peter B. .

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2020, 52 (06) :6412-6441

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