Paper Info
Title
Reconstruction algorithms of an inverse geometric problem for the modified Helmholtz equation
Abstract
In this paper, we consider an inverse geometric problem for the modified Helmholtz equation from measurements of the potential taken on the boundary of the geometrical domain. Our goal is to seek reconstruction algorithms to detect the number, the location, the size and the shape of unknown obstacles from Cauchy data on the external boundary. This problem is ill-posed and nonlinear, thus we should employ regularization techniques in our proposed algorithms. We give several numerical examples to demonstrate the stability of numerical algorithms.
Year
DOI
Venue
2019
10.1007/s40314-019-0963-9
Computational and Applied Mathematics
Keywords
DocType
Volume
Trust-region-reflective optimization algorithm, Levenberg–Marquardt algorithm, Modified Helmholtz equation, Ill-posed problem, 65N20, 65N21
Journal
38
Issue
ISSN
Citations 
4
2238-3603
0
PageRank 
References 
Authors
0.34
0
1
Name
Order
Citations
PageRank
Ji-Chuan Liu111.38