Suitability for anisotropic electrodynamics problem

Dear Forum,

I plan to compute the electromagnetic field distribution of an arrangement of dielectric elements each characterized by an anisotropic permittivity (including off-diagonal tensor components), and located in a box-shaped volume, in the frequency domain. The materials are non-magnetic, so \mu = 1. The side walls of the box should be periodic boundary conditions, while top and bottom should scatter an external wave of a defined frequency in and out of the volume.
Although I have browsed the website and forum for quite a while, I have not found a suitable example. Can anyone confirm that the above is feasible with ngsolve, and possibly point to an example file? Any hint would be highly appreciated.

Best regards,
Christoph Lange

Hi Christoph,

I think this paper deals with a similar setup as you have described:
M. Huber et al: “Simulation of Diffraction in periodic Media with a coupled Finite Element and Plane Wave Approach”

Solving frequency domain Maxwell, with tensorial eps is standard in NGSolve, just write down the equations.
How big is the problem electrically ? 10 waves in every direction is easy, maybe 50 is doable with more or less standard methods on a large computer, but more waves require alternatives like time domain solvers.
Periodic boundary conditions are fine with CSG geometry (see docu), and coming soon for OCC geometry.
The coupling to plane waves (as shown in the paper) has required an extension code in C++.
Nowadays it is not a big deal to extend NGSolve such that also the plane waves in the exterior domain can modelled from Python, we can do this together, in the time-scale of a few weeks.

Looks interesting and doable,