Cao, K orcid.org/0000-0002-2929-0457, Lesnic, D orcid.org/0000-0003-3025-2770 and Colaco, MJ (2019) Determination of thermal conductivity of inhomogeneous orthotropic materials from temperature measurements. Inverse Problems in Science and Engineering, 27 (10). pp. 1372-1398. ISSN 1741-5977
Abstract
We consider the two-dimensional inverse determination of the thermal conductivity of inhomogeneous orthotropic materials from internal temperature measurements. The inverse problem is general and is classified as a function estimation since no prior information about the functional form of the thermal conductivity is assumed in the inverse calculation. The least-squares functional minimizing naturally the gap between the measured and computed temperature leads to a set of direct, sensitivity and adjoint problems, which have forms of direct well-posed initial boundary value problems for the heat equation, and new formulas for its gradients are derived. The conjugate gradient method employs recursively the solution of these problems at each iteration. Stopping the iterations according to the discrepancy principle criterion yields a stable solution. The employment of the Sobolev -gradient is shown to result in much more robust and accurate numerical reconstructions than when the standard -gradient is used.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2018 Informa UK Limited, trading as Taylor & Francis Group This is an author produced version of a paper published in Inverse Problems in Science and Engineering. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Heat equation, thermal conductivity, inverse problem, conjugate gradient method, orthotropic material |
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: | 26 Nov 2018 10:49 |
Last Modified: | 08 Dec 2019 01:39 |
Status: | Published |
Publisher: | Taylor & Francis |
Identification Number: | 10.1080/17415977.2018.1554654 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:139122 |