Hussein, SO and Lesnic, D (2016) Determination of forcing functions in the wave equation. Part II: the time-dependent case. Journal of Engineering Mathematics, 96 (1). pp. 135-153. ISSN 0022-0833
Abstract
An unknown time-dependent force function in the wave equation is investigated in this study. This is a natural continuation of Part I [J Eng Math 2015, this volume], where the space-dependent force identification has been considered. Additional data are given by a space integral average measurement of the displacement. This linear inverse problem has a unique solution, but it is still ill-posed since small errors in the input data cause large errors in the output solution. Consequently, when the input data are contaminated with noise, we use the Tikhonov regularization method in order to obtain a stable solution. The choice of the regularization parameter is based on the L-curve method. Numerical results show that the solution is accurate for exact data and stable for noisy data.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2015, Springer Science+Business Media Dordrecht. This is an author produced version of a paper published in Journal of Engineering Mathematics. The final publication is available at Springer via http://dx.doi.org/10.1007/s10665-015-9786-x. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Inverse force problem; L-curve; Regularization; Wave equation |
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 Nov 2015 16:17 |
Last Modified: | 20 May 2016 03:37 |
Published Version: | http://dx.doi.org/10.1007/s10665-015-9786-x |
Status: | Published |
Publisher: | Springer Verlag |
Identification Number: | 10.1007/s10665-015-9786-x |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:92048 |