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arXiv · 2008.07982

A linearised inverse conductivity problem for the Maxwell system at a high frequency

Victor Isakov·Shuai Lu·Boxi Xu
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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.

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Victor Isakov, Shuai Lu, Boxi Xu. 2020-08-18. A linearised inverse conductivity problem for the Maxwell system at a high frequency. https://doi.org/10.1016/j.jcp.2022.111003

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