Point electrode problems in piecewise smooth plane domains

TL;DR

This paper extends the concept of bisweep data to piecewise smooth domains in the conductivity equation, providing new partial data results for the inverse problem and a numerical method for reconstructing inclusions.

Contribution

It introduces a novel extension of bisweep data to piecewise smooth domains and establishes their relation to the Neumann-to-Dirichlet map, along with a reconstruction algorithm.

Findings

Bisweep data are proportional to the Schwartz kernel of the Neumann-to-Dirichlet map.

A new partial data result for the Calderón inverse problem is derived.

A numerical method for reconstructing inclusions from bisweep data is proposed.

Abstract

Conductivity equation is studied in piecewise smooth plane domains and with measure-valued current patterns (Neumann boundary values). This allows one to extend the recently introduced concept of bisweep data to piecewise smooth domains, which yields a new partial data result for Calder\'on inverse conductivity problem. It is also shown that bisweep data are (up to a constant scaling factor) the Schwartz kernel of the relative Neumann-to-Dirichlet map. A numerical method for reconstructing the supports of inclusions from discrete bisweep data is also presented.