# Simple reference problems for time harmonic Maxwell equations

For Navier-Stokes problems we can often choose a relatively simple verification problem such as the lid driven cavity, flow over a cylinder, or flow over a backward facing step to verify our implementation.

What are the typical reference problems for the time harmonic Maxwell equations?

Edit: With a focus on finite element solutions in 3D and also possibly 2D if more common

• Are you looking for bounded our unbounded domains? Commented Jun 18, 2020 at 22:57
• I think probably more unbounded/scattering problems but either common problems would be good
– wwfe
Commented Jun 19, 2020 at 14:15

That depends a lot on the specific numerical method in use, 2D/3D, and application.

Common reference problems are likely to have an analytical solution or be verifiable qualitatively by some fundamental principles.

I would bring up the common examples I use personally from each category:

1. Wave scattering from a perfect electric conductor (PEC)/dielectric/layered-coated sphere. This problem has an analytical solution (via Mie series) and can test multiple numerical aspects of the solver. Usually, a dipole or a planewave excitations are used.

2. Testing reciprocity (where it is applicable): doing two simulations interchanging the resultant sources and observed fields.

I also use application-specific benchmarks for power, microwave, antenna, electromagnetic compatibility (EMC).

Also, it is important to mention the method of manufactured solutions (MMS) with some relevant discussions here and here.

• Thanks I've edited to specify I'm looking for common reference problems with regards to finite element in 3D. I did not have enough reputation to add a MMS tag and did not find one to add on to my question when I asked it
– wwfe
Commented Jun 18, 2020 at 21:29
• I would highlight more the MMS for verification purposes. Commented Jun 18, 2020 at 22:58