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arXiv · 1905.01642

Reconstruction of domains with algebraic boundaries from generalized polarization tensors

Habib Ammari·Mihai Putinar·Andries Steekamp·Faouzi Triki
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Abstract

This paper aims at showing the stability of the recovery of a smooth planar domain with a real algebraic boundary from a finite number of its generalized polarization tensors. It is a follow-up of the work [H. Ammari et al., Math. Annalen, 2018], where it is proved that the minimal polynomial with real coefficients vanishing on the boundary can be identified as the generator of a one dimensional kernel of a matrix whose entries are obtained from a finite number of generalized polarization tensors. The recovery procedure is implemented without any assumption on the regularity of the domain to be reconstructed and its performance and limitations are illustrated.

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Habib Ammari, Mihai Putinar, Andries Steekamp, Faouzi Triki. 2019-05-05. Reconstruction of domains with algebraic boundaries from generalized polarization tensors. https://arxiv.org/abs/1905.01642

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