Hussein, MS, Lesnic, D, Johansson, BT et al. (1 more author) (2018) Identification of a multi-dimensional space-dependent heat source from boundary data. Applied Mathematical Modelling, 54. pp. 202-220. ISSN 0307-904X
Abstract
We investigate the linear but ill-posed inverse problem of determining a multi-dimensional space-dependent heat source in the parabolic heat equation from Cauchy boundary data. This model is important in practical applications where the distribution of internal sources is to be monitored and controlled with care and accuracy from non-invasive and non-intrusive boundary measurements only. The mathematical formulation ensures that a solution of the inverse problem is unique but the existence and stability are still issues to be dealt with. Even if a solution exists it is not stable with respect to small noise in the measured boundary data hence the inverse problem is still ill-posed. The Landweber method is developed in order to restore stability through iterative regularization. Furthermore, the conjugate gradient method is also developed in order to speed up the convergence. An alternating direction explicit finite-difference method is employed for discretizing the well-posed problems resulting from these iterative procedures. Numerical results in two-dimensions are illustrated and discussed.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | (c) 2017 Elsevier Inc. This is an author produced version of a paper published in Applied Mathematical Modelling. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Heat equation; inverse source problem; iterative regularization |
Dates: |
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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: | 18 Sep 2017 10:26 |
Last Modified: | 21 Sep 2018 00:38 |
Status: | Published |
Publisher: | Elsevier |
Identification Number: | 10.1016/j.apm.2017.09.029 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:121279 |