Cao, K and Lesnic, D (2018) Determination of space‐dependent coefficients from temperature measurements using the conjugate gradient method. Numerical Methods for Partial Differential Equations, 34 (4). pp. 1370-1400. ISSN 0749-159X
Abstract
In this article, we consider coefficient identification problems in heat transfer concerned with the determination of the space‐dependent perfusion coefficient and/or thermal conductivity from interior temperature measurements using the conjugate gradient method (CGM). We establish the direct, sensitivity and adjoint problems and the iterative CGM algorithm which has to be stopped according to the discrepancy principle in order to reconstruct a stable solution for the inverse problem. The Sobolev gradient concept is introduced in the CGM iterative algorithm in order to improve the reconstructions. The numerical results illustrated for both exact and noisy data, in one‐ and two‐dimensions for single or double coefficient identifications show that the CGM is an efficient and stable method of inversion.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | (c) Wiley Periodicals, inc. This is the peer reviewed version of the following article: Cao, K and Lesnic, D (2018) Determination of space‐dependent coefficients from temperature measurements using the conjugate gradient method. Numerical Methods for Partial Differential Equations, 34 (4). which has been published in final form at https://doi.org/10.1002/num.22262. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving. |
Keywords: | conjugate gradient method; inverse problem; perfusion coefficient; thermal conductivity |
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 Feb 2018 15:48 |
Last Modified: | 02 May 2018 10:49 |
Status: | Published |
Publisher: | Wiley |
Identification Number: | 10.1002/num.22262 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:127760 |