Finite Element Methods for Linear Maxwell’s Equations in Bianisotropic Media Permitting Polarization Fields and Magnetic Currents

Totally forgot to post this, but in December last year, we uploaded my computational electromagnetism paper on arXiv: https://arxiv.org/abs/2212.11930

It was a genuine pleasure working with Drs. Martin Licht and Michael Holst on this undergraduate-level project.

We have submitted this paper – let’s see where it goes!

Here’s the abstract:

We review Maxwell’s equations and constitutive relations for 3D bianisotropic media in a generalized form: we consider all
four variables and allow for nonzero polarization or magnetization, and also nonzero nonzero magnetic charge or current. After
a discussion of general boundary conditions, we introduce a time-harmonic variational formulation of linear Maxwell’s equations
within 3D bianisotropic media in terms of the electric and magnetic fields. We showcase a finite element approximation of our
variational formulation, using curl-conforming N´ed´elec edge elements of the first kind. Numerical examples illustrate the convergence
of the method.


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