Inverse problem for the discrete Maxwell equations in a bounded paving

Abstract

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