On reconstruction of small sources from Cauchy data at a fixed frequency

被引：2

作者：

Harris, Isaac ^{[1
]}

Le, Thu ^{[2
]}

Nguyen, Dinh-Liem ^{[2
]}

机构：

[1] Purdue Univ, Dept Math, W Lafayette, IN 47907 USA

[2] Kansas State Univ, Dept Math, Manhattan, KS 66506 USA

来源：

APPLIED MATHEMATICS LETTERS | 2023年 / 145卷

基金：

美国国家科学基金会;

关键词：

Inverse source problem; Numerical reconstruction; Cauchy data; Small sources; Single frequency; INVERSE SOURCE PROBLEM;

D O I：

10.1016/j.aml.2023.108765

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This short paper is concerned with the numerical reconstruction of small sources from boundary Cauchy data for a single frequency. We study a sampling method to determine the location of small sources in a very fast and robust way. Furthermore, the method can also compute the intensity of point sources provided that the sources are well separated. A simple justification of the method is done using the Green representation formula and an asymptotic expansion of the radiated field for small volume sources. The implementation of the method is non-iterative, computationally cheap, fast, and very simple. Numerical examples are presented to illustrate the performance of the method.& COPY; 2023 Elsevier Ltd. All rights reserved.

引用

页数：7

共 50 条

[1] Reconstruction of extended sources with small supports in the elliptic equation Δu plus μu = F from a single Cauchy data
Abdelaziz, Batoul
El Badia, Abdellatif
El Hajj, Ahmad
COMPTES RENDUS MATHEMATIQUE, 2013, 351 (21-22) : 797 - 801
[2] Identifiability of surface sources from Cauchy data
Ben Belgacem, F.
Jelassi, F.
INVERSE PROBLEMS, 2009, 25 (07)
[3] Reconstruction of a source domain from the Cauchy data
Ikehata, M
INVERSE PROBLEMS, 1999, 15 (02) : 637 - 645
[4] On reconstruction of Lame coefficients from partial Cauchy data
Imanuvilov, Oleg Yu.
Yamamoto, Masahiro
JOURNAL OF INVERSE AND ILL-POSED PROBLEMS, 2011, 19 (06): : 881 - 891
[5] The density function reconstruction of surface sources from a single Cauchy measurement
Azaiez, Mejdi
Ben Belgacem, Faker
Jelassi, Faten
COMPUTERS & FLUIDS, 2011, 43 (01) : 14 - 22
[6] Stability estimates for an inverse source problem of Helmholtz's equation from single Cauchy data at a fixed frequency
El Badia, Abdellatif
El Hajj, Ahmad
INVERSE PROBLEMS, 2013, 29 (12)
[7] Jointly determining the point sources and obstacle from Cauchy data
Zhang, Deyue
Chang, Yan
Guo, Yukun
INVERSE PROBLEMS, 2024, 40 (01)
[8] Reconstruction of the potential from partial Cauchy data for the Schrodinger equation
Ammari, H
Uhlmann, G
INDIANA UNIVERSITY MATHEMATICS JOURNAL, 2004, 53 (01) : 169 - 183
[9] A procedure for the temperature reconstruction in corner domains from Cauchy data
Johansson, T.
Marin, L.
INVERSE PROBLEMS, 2007, 23 (01) : 357 - 372
[10] Reconstruction of solution to the wave equation from Cauchy data on the boundary
Demchenko, M. N.
2018 DAYS ON DIFFRACTION (DD), 2018, : 66 - 70

← 1 2 3 4 5 →