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arXiv · 1901.01044

Shape reconstruction of a conductivity inclusion using the Faber polynomials

Doosung Choi·Junbeom Kim·Mikyoung Lim
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Abstract

We consider the shape reconstruction of a conductivity inclusion in two dimensions. We use the concept of Faber polynomials Polarization Tensors (FPTs) introduced in \cite{choi:2018:GME} to derive an exact shape recovery formula for an inclusion with the extreme conductivity. This shape can be a good initial guess in the shape recovery optimization for an inclusion with either small or large conductivity values. We illustrate and validate our results with numerical examples.

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Doosung Choi, Junbeom Kim, Mikyoung Lim. 2019-01-04. Shape reconstruction of a conductivity inclusion using the Faber polynomials. https://arxiv.org/abs/1901.01044

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