Document Type

Article

Version Deposited

Published Version

Publication Date

6-28-2023

Publication Title

Axioms

DOI

10.3390/axioms12070642

Abstract

This paper considers a 1D time-domain inverse scattering problem for the Helmholtz equation in which penetrable scatterers are to be determined from boundary measurements of the scattering data. It is formulated as a coefficient identification problem for a wave equation. Using the Laplace transform, the inverse problem is converted into an overdetermined nonlinear system of partial differential equations. To solve this system, a Carleman weighted objective functional, which is proved to be strictly convex in an arbitrary set in a Hilbert space, is constructed. An alternating minimization algorithm is used to minimize the Carleman weighted objective functional. Numerical results are presented to illustrate the performance of the proposed algorithm. © 2023 by the author.

Comments

© 2023 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license.

Creative Commons License

Creative Commons Attribution 4.0 International License
This work is licensed under a Creative Commons Attribution 4.0 International License.

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Mathematics Commons

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