Bin-Mohsin, B and Lesnic, D orcid.org/0000-0003-3025-2770 (2019) Reconstruction of a volumetric source domain. Journal of Computational Methods in Sciences and Engineering, 19 (2). pp. 367-385. ISSN 1472-7978
Abstract
Inverse and ill-posed problems which consist of reconstructing the unknown support of a three-dimensional volumetric source from a single pair of exterior boundary Cauchy data are investigated. The underlying dependent variable may satisfy the Laplace, Poisson, Helmholtz or modified Helmholtz equations. In the case of constant physical properties, the solutions of these elliptic PDEs are sought as linear combinations of fundamental solutions, as in the method of fundamental solutions (MFS). The unknown source domain is parametrized by the radial coordinate, as a function of the spherical angles. The resulting least-squares functional estimating the gap between the measured and the computed data is regularized and minimized using the lsqnonlin toolbox routine in Matlab. Numerical results are presented and discussed for both exact and noisy data, confirming the accuracy and stability of reconstruction.
Metadata
Item Type: | Article |
---|---|
Authors/Creators: |
|
Copyright, Publisher and Additional Information: | This article is protected by copyright. This is an author produced version of a paper published in Journal of Computational Methods in Sciences and Engineering. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Inverse problem; method of fundamental solutions; nonlinear optimization; source domain identification |
Dates: |
|
Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Applied Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 10 Oct 2018 15:36 |
Last Modified: | 13 Jun 2019 20:23 |
Status: | Published |
Publisher: | IOS Press |
Identification Number: | 10.3233/JCM-180878 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:136544 |