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. show that spurious resonances haunting domain-boundary based direct boundary integral equations the first kind originate from formal structure their Calderón identities. Using this observation, kernel problem is characterized explicitly, we it completely vanishes under exterior representation formula.