Huntul, MJ and Lesnic, D (2017) An inverse problem of finding the time-dependent thermal conductivity from boundary data. International Communications in Heat and Mass Transfer, 85. pp. 147-154. ISSN 0735-1933
Abstract
We consider the inverse problem of determining the time-dependent thermal conductivity and the transient temperature satisfying the heat equation with initial data, Dirichlet boundary conditions, and the heat flux as overdetermination condition. This formulation ensures that the inverse problem has a unique solution. However, the problem is still ill-posed since small errors in the input data cause large errors in the output solution. The finite difference method is employed as a direct solver for the inverse problem. The inverse problem is recast as a nonlinear least-squares minimization subject to physical positivity bound on the unknown thermal conductivity. Numerically, this is effectively solved using the lsqnonlin routine from the MATLAB toolbox. We investigate the accuracy and stability of results on a few test numerical examples.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2017 Elsevier Ltd. This is an author produced version of a paper published in International Communications in Heat and Mass Transfer. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Inverse problem; thermal conductivity; heat equation; nonlinear optimization |
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: | 28 Apr 2017 14:05 |
Last Modified: | 26 May 2018 00:38 |
Status: | Published |
Publisher: | Elsevier |
Identification Number: | 10.1016/j.icheatmasstransfer.2017.05.009 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:115722 |