Spurious Resonances in Coupled Domain-Boundary Variational Formulations of Transmission Problems in Electromagnetism and Acoustics

DOI10.1515/CMAM-2021-0197arXiv2003.14357MaRDI QIDQ6337802

Publication date: 31 March 2020

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 Calderon identities. Using this observation, the kernel of the coupled problem is characterized explicitly and we show that it completely vanishes under the exterior representation formula.

Mathematics Subject Classification ID

PDEs in connection with optics and electromagnetic theory (35Q60) Integro-partial differential equations (45K05) Diffraction, scattering (78A45) Hydro- and aero-acoustics (76Q05) Boundary element methods applied to problems in optics and electromagnetic theory (78M15) Electromagnetic theory (general) (78A25) Abstract integral equations, integral equations in abstract spaces (45N05) Eigenvalue problems for integral equations (45C05) Linear integral equations (45A05) Variational methods applied to problems in optics and electromagnetic theory (78M30) Integro-partial differential equations (35R09)

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