Inverse problem for the discrete Maxwell equations in a bounded paving

TL;DR

This paper presents a method to uniquely reconstruct the anisotropic properties of a medium inside a bounded domain from the Dirichlet-to-Neumann operator associated with the discrete Maxwell equations, advancing inverse problem solutions.

Contribution

It introduces a reconstruction procedure for the anisotropic medium properties using the Dirichlet-to-Neumann operator in a discrete Maxwell setting, which was previously unresolved.

Findings

Unique determination of anisotropic medium properties from boundary measurements.

Reconstruction procedure for the discrete Maxwell operator.

Theoretical proof of identifiability under specified conditions.

Abstract

We consider the discrete anisotropic Maxwell operator DaH0 on a bounded paving $\Omega$ $\subset$ Z3 , where H0 denotes discrete isotropic Maxwell operator and Da a diagonal operator of multiplication containing information about the anisotropy of the medium inside $\Omega$. Letting a complex number $\lambda$ __ = 0 such the Dirichlet-to-Neumann operator $\Lambda$(Da) associated with the system DaH0 u = $\lambda$u on $\Omega$ admits a unique solution, we show that knowing $\Lambda$(Da) is sufficient to determine Da by a reconstruction procedure for Da.