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A linearised inverse conductivity problem for the Maxwell system at a high frequency
Isakov, Victor Lu, Shuai Xu, Boxi
Isakov, Victor
Lu, Shuai
Xu, Boxi
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Authors
Isakov, Victor
Lu, Shuai
Xu, Boxi
Lu, Shuai
Xu, Boxi
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Issue Date
2022-04-15
Type
Article
Preprint
Preprint
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Keywords
Maxwell system,Stability estimate,Inverse conductivity problem
Subjects (LCSH)
Citation
Isakov, V., Lu, S., & Xu, B. (2022, January 24). A linearised inverse conductivity problem for the Maxwell system at a high frequency. Journal of Computational Physics. Retrieved April 8, 2022, from https://doi.org/10.1016/j.jcp.2022.111003
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 H¨older 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.
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Publisher
Elsevier
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Series
Journal of Computational Physics;2022
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0021-9991