Modelling in Electromagnetics and Nanophotonics by hp-FEM, Multiscale FEM and Asymptotic Expansions

LaCàN Seminar Series

http://www-rocq.inria.fr/who/Kersten.Schmidt/

Visiting schedule

Abstract

The first part of the talk is devoted to the modelling in low-frequency Electromagnetics, especially the discretisation by hp-adaptive spaces with edge elements on curved meshes and meshes with hanging nodes. A-priori refinement strategies combining cell-subdivision and enlargement of polynomial degrees allow for exponentially decreasing error for singular solutions. For low frequency simulation the eddy current model, a magneto-quasistatic approximation to Maxwell's equations, is the mostly used one, and we will show investigations of the modelling error.

The second part deals with problems and methods in Nanophotonics. Photonic crystals (PhC) with their periodic refraction index attracted much attention due to their exceptional properties of light propagation. We will consider the modelling of eigenmodes and the band structure of PhCs and PhC waveguides. For finite PhCs with a large number of periods we proposed a Multiscale FEM. This FEM with a two-scale basis based on eigenmodes achieves error levels at constant computational costs independent of the number of periods.

Geometrically small details like thin layered structures or thin sheets may hardly (by extreme costs) be resolvable by FE meshes. With asymptotic expansion techniques the solution close and far away the object are separately investigated with the goal of approximate interface conditions. For the prediction of eddy current in thin layers we will introduce two different strategies : the formal asymptotic expansion and a generalised FEM with special thin sheet basis functions. At the end of the talk I will discuss the matched asymptotic expansion for the aeroacoustic equations close to a thin wall with small perforations.