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Numerical Algorithms
Published in: Numerical Algorithms 3/2020

03-08-2019 | Original Paper

Reconstruction algorithms of an inverse source problem for the Helmholtz equation

Authors: Ji-Chuan Liu, Xiao-Chen Li

Published in: Numerical Algorithms | Issue 3/2020

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Abstract

In this paper, we study an inverse source problem for the Helmholtz equation from measurements. The purpose of this paper is to reconstruct the salient features of the hidden sources within a body. We propose three stable reconstruction algorithms to detect the number, the location, the size, and the shape of the hidden sources along with compact support from a single measurement of near-field Cauchy data on the external boundary. This problem is nonlinear and ill-posed; thus, we should consider regularization techniques in reconstruction algorithms. We give several numerical experiments to demonstrate the viability of our proposed reconstruction algorithms.
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Metadata
Title
Reconstruction algorithms of an inverse source problem for the Helmholtz equation
Authors
Ji-Chuan Liu
Xiao-Chen Li
Publication date
03-08-2019
Publisher
Springer US
Published in
Numerical Algorithms / Issue 3/2020
Print ISSN: 1017-1398
Electronic ISSN: 1572-9265
DOI
https://doi.org/10.1007/s11075-019-00786-8

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