Shape reconstruction of a conductivity inclusion using the Faber polynomials
Numerical Analysis
2024-12-20 v1 Numerical Analysis
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.
Cite
@article{arxiv.1901.01044,
title = {Shape reconstruction of a conductivity inclusion using the Faber polynomials},
author = {Doosung Choi and Junbeom Kim and Mikyoung Lim},
journal= {arXiv preprint arXiv:1901.01044},
year = {2024}
}
Comments
13 pages