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Applied and Computational Math Seminar

Homogenization of the Poincare Neumann operator

Eric Bonnetier, Institut Fourier Grenoble

Location:  Room 425
Date & time: Friday, 21 February 2020 at 2:00PM - 3:00PM

Abstract: 

The Neumann Poincare operator is an integral operator that allows the representation of the solutions to elliptic PDE's with piecewise constant coefficients using layer potentials. Its spectral properties are of interest in the study of plasmonic resonances of metallic particles.

We discuss the spectrum of that integral operator, when one considers a periodic distribution of inclusions made of metamaterials in a dielectric background medium. We show that under the assumption that the inclusions are fully embedded in the periodicity cells, the limiting spectra of periodic NP operators is composed of a Bloch spectrum, and of a boundary spectrum  associated with eigenfunctions which concentrate a part of their energy near the boundary.

This is joint work with Charles Dapogny and Faouzi Triki.

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