| Abstract: |
| We are interested in the inverse inclusion problem with multi-frequency measurements. Assuming an inclusion $D$ has a conductivity that depends on the frequency $\omega$, we recover its position and shape for boundary measurements. In this work, we assume the conductivity inside the inclusion satisfies Drude model, which is adapted in many case of metals or biological tissues. We prove that the unique solution to the conductivity equation admits a spectral decomposition $u=u_0+u_f$ with $u_0$ independent to the frequency and $u_f$ depends on the frequency. Based on this decomposition, we derive a numerical scheme to reconstruct the inclusion and the conductivity profile. The numerical method has two main steps, the first is to reconstruct the scalar part $u_0$ from the multifrequency measurements, and the second step is to reconstruct the inclusion $D$ from the $u_0$ function obtained in the previous step. |
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