Spurious resonances in coupled domain-boundary variational formulations of transmission problems in electromagnetism and acoustics

Abstract

We develop a framework shedding light on common features of coupled variational formulations arising in electromagnetic scattering and acoustics. We show that spurious resonances haunting coupled domain-boundary formulations based on direct boundary integral equations of the first kind originate from the formal structure of their Calderón identities. We explicitly characterize the solution space of the coupled problem and prove that it completely vanishes under the exterior representation formula.