On the approximation of dispersive electromagnetic eigenvalue problems in 2D

04/19/2021
by   Martin Halla, et al.
0

We consider time-harmonic electromagnetic wave equations in composites of a dispersive material surrounded by a classical material. In certain frequency ranges this leads to sign-changing permittivity and/or permeability. Previously meshing rules were reported, which guarantee the convergence of finite element approximations to the related scalar source problems. Here we generalize these results to the electromagnetic two dimensional vectorial equations and the related holomorphic eigenvalue problems. Different than for the analysis on the continuous level, we require an assumption on both contrasts of the permittivity and the permeability. We confirm our theoretical results with computational studies.

READ FULL TEXT
research
03/28/2022

A reduced order model for the finite element approximation of eigenvalue problems

In this paper we consider a reduced order method for the approximation o...
research
04/22/2022

Convergence of Lagrange Finite Element Methods for Maxwell Eigenvalue Problem in 3D

We prove convergence of the Maxwell eigenvalue problem using quadratic o...
research
05/25/2021

Parallel domain decomposition solvers for the time harmonic Maxwell equations

The time harmonic Maxwell equations are of current interest in computati...
research
02/04/2020

Diffusion in arrays of obstacles: beyond homogenisation

We revisit the classical problem of diffusion of a scalar (or heat) rele...
research
06/27/2021

Radial complex scaling for anisotropic scalar resonance problems

The complex scaling/perfectly matched layer method is a widely spread te...
research
06/20/2022

Time integration of finite element models with nonlinear frequency dependencies

The analysis of sound and vibrations is often performed in the frequency...
research
06/17/2019

A parallel-in-time multigrid solver with a new two-level convergence for two-dimensional unsteady fractional Laplacian problems

The multigrid-reduction-in-time (MGRIT) technique has proven to be succe...

Please sign up or login with your details

Forgot password? Click here to reset