Huntul, MJ, Lesnic, D and Hussein, MS (2017) Reconstruction of time-dependent coefficients from heat moments. Applied Mathematics and Computation, 301. pp. 233-253. ISSN 0096-3003
Abstract
This paper investigates the inverse problems of simultaneous reconstruction of time-dependent thermal conductivity, convection or absorption coefficients in the parabolic heat equation governing transient heat and bio-heat thermal processes. Using initial and boundary conditions, as well as heat moments as over-determination conditions ensure that these inverse problems have a unique solution. However, the problems are still ill-posed since small errors in the input data cause large errors in the output solution. To overcome this instability we employ the Tikhonov regularization. A discussion of the choice of multiple regularization parameters is provided. The finite-difference method with the Crank–Nicolson scheme is employed as a direct solver. The resulting inverse problems are recast as nonlinear minimization problems and are solved using the lsqnonlin routine from the MATLAB toolbox. Numerical results are presented and discussed.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2016 Elsevier Inc. This is an author produced version of a paper published in Applied Mathematics and Computation. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Inverse problem; Tikhonov's regularization; heat transfer; heat moments |
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: | 03 Jan 2017 11:39 |
Last Modified: | 10 Jan 2018 01:38 |
Published Version: | https://doi.org/10.1016/j.amc.2016.12.028 |
Status: | Published |
Publisher: | Elsevier |
Identification Number: | 10.1016/j.amc.2016.12.028 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:109850 |