2017/02/27 by Éric Bonnetier, Hai Zhang, Bonnetier, Eric +1
Computer Science · Mathematics · Physics and Astronomy · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Electromagnetic Scattering and Analysis #FOS: Mathematics #Numerical methods in inverse problems #Spectral Theory (math.SP)
paper · pdf · doi:10.48550/arxiv.1702.08127
openalex publication_date 2017/02/27 · openalex created_date 2017/03/16 · openalex updated_date 2026/08/01
The Neumann-Poincaré (NP) operator naturally appears in the context of metamaterials as it may be used to represent the solutions of elliptic transmission problems via potentiel theory. In particular, its spectral properties are closely related to the well-posedness of these PDE's, in the typical case where one considers a bounded inclusion of homogeneous plasmonic metamaterial embedded in a homogeneous background dielectric medium. In a recent work, M. Perfekt and M. Putinar have shown that the NP operator of a 2D curvilinear polygon has an essential spectrum, which depends only on the angles of the corners. Their proof is based on quasi-conformal mappings and techniques from complex-analysis. In this work, we characterize the spectrum of the NP operator for a 2D domain with corners in terms of elliptic corner singularity functions, which gives insight on the behavior of generalized eigenmodes.