# A direct method for reconstructing inclusions and boundary conditions from electrostatic data

## TL;DR

This paper introduces a non-iterative sampling method utilizing Dirichlet to Neumann maps for reconstructing inclusions and boundary conditions in electrostatics, demonstrated through numerical examples in 2D.

## Contribution

It presents a novel direct approach combining sampling and boundary integral equations for reconstructing inclusions and impedance parameters from electrostatic data.

## Key findings

- Successful reconstruction of impenetrable inclusions using the sampling method.
- Effective non-iterative reconstruction of impedance parameters.
- Numerical demonstrations in two-dimensional settings.

## Abstract

In this paper, we will discuss the use of a Sampling Method to reconstruct impenetrable inclusions from Electrostatic Cauchy data. We consider the case of a perfectly conducting and impedance inclusion. In either case, we show that the Dirichlet to Neumann mapping can be used to reconstruct impenetrable sub-regions via a sampling method. We also propose a non-iterative method based on boundary integral equations to reconstruct the impedance parameter using the reconstructed boundary of the inclusion from the knowledge of multiple Cauchy pairs which can be computed from Dirichlet to Neumann mapping. Some numerical reconstructions are presented in two space dimensions.