Local Multiple Traces Formulation for electromagnetics: Stability and preconditioning for smooth geometries

We consider the time-harmonic electromagnetic transmission problem for unit sphere. Appealing to a vector spherical harmonics analysis, we prove first stability result of local multiple traces formulation (MTF) electromagnetics, originally introduced by Hiptmair and Jerez-Hanckes (2012) acoustic case, paving way towards an extension general piecewise homogeneous scatterers. Moreover, investigate preconditioning techniques MTF scheme study accumulation points induced operators. In particular, propose novel second-order inverse approximation operator. Numerical experiments validate our claims confirm relevance strategies proposed. • MTFs properly tackle scattering heterogeneous domains Stability results Maxwell have remained elusive provide spectrum analysis as well explicit formulas smooth geometries operator preconditioners point out further improvements