Alosaimi, M, Lesnic, D orcid.org/0000-0003-3025-2770 and Johansson, BT (2021) Solution of the Cauchy problem for the wave equation using iterative regularization. Inverse Problems in Science and Engineering, 29 (13). pp. 2757-2771. ISSN 1741-5977
Abstract
We propose a regularization method based on the iterative conjugate gradient method for the solution of a Cauchy problem for the wave equation in one dimension. This linear but ill-posed Cauchy problem consists of finding the displacement and flux on a hostile and inaccessible part of the medium boundary from Cauchy data measurements of the same quantities on the remaining friendly and accessible part of the boundary. This inverse boundary value problem is recast as a least-squares minimization problem that is solved by using the conjugate gradient method whose iterations are stopped according to the discrepancy principle for obtaining stable reconstructions. The objective functional associated is proved Fréchet differentiable and a formula for its gradient is derived. The well-posed direct, adjoint and sensitivity problems present in the conjugate gradient method are solved by using a finite-difference method. Two numerical examples to illustrate the accuracy and stability of the proposed numerical procedure are thoroughly presented and discussed.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2021 Informa UK Limited, trading as Taylor & Francis Group. This is an author produced version of an article published in Inverse Problems in Science and Engineering. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Cauchy problem; wave equation; conjugate gradient method; regularization; inverse problem |
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: | 15 Jun 2021 13:22 |
Last Modified: | 11 Mar 2023 01:23 |
Status: | Published |
Publisher: | Taylor & Francis |
Identification Number: | 10.1080/17415977.2021.1949590 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:175177 |