A Linearised Inverse Conductivity Problem For The Maxwell System At ...

Mathematics > Analysis of PDEs arXiv:2008.07982 (math) [Submitted on 18 Aug 2020] Title:A linearised inverse conductivity problem for the Maxwell system at a high frequency Authors:Victor Isakov, Shuai Lu, Boxi Xu View a PDF of the paper titled A linearised inverse conductivity problem for the Maxwell system at a high frequency, by Victor Isakov and 2 other authors View PDF

Abstract:We consider a linearised inverse conductivity problem for electromagnetic waves in a three dimensional bounded domain at a high time-harmonic frequency. Increasing stability bounds for the conductivity coefficient in the full Maxwell system and in a simplified transverse electric mode are derived. These bounds contain a Lipschitz term with a factor growing polynomially in terms of the frequency, a Holder term, and a logarithmic term which decays with respect to the frequency as a power. To validate this increasing stability numerically, we propose a reconstruction algorithm aiming at the recovery of sufficiently many Fourier modes of the conductivity. A numerical evidence sheds light on the influence of the growing frequency and confirms the improved resolution at higher frequencies.

Comments:	18 pages, 11 figures
Subjects:	Analysis of PDEs (math.AP)
Cite as:	arXiv:2008.07982 [math.AP]
(or arXiv:2008.07982v1 [math.AP] for this version)
https://doi.org/10.48550/arXiv.2008.07982 Focus to learn more arXiv-issued DOI via DataCite
Journal reference:	Journal of Computational Physics, 455(2022), 111003
Related DOI:	https://doi.org/10.1016/j.jcp.2022.111003 Focus to learn more DOI(s) linking to related resources

Submission history

From: Boxi Xu [view email] [v1] Tue, 18 Aug 2020 15:22:58 UTC (2,912 KB) Full-text links:

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