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

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.