<antennas so big that we cannot even simulate their behavior.>
I really would love another sentence or two on this. I can't immediately think why that would be, e.g. don't Maxwell's equations apply at very large scales? Any ideas?
My two cents, though I'm no expert: I'd bet it's what the computational EM community (and other fields) calls a "multiscale" problem. EM solvers - that is, simulators that numerically solve Maxwell over some geometry-and-source boundary conditions - find E- and H-fields at certain "mesh points". In other words, they discretize 3-space into a grid and calculate solutions to Maxwell at those points.
In general, you'll want your mesh to have subwavelength distance between points, and perhaps even less in regions with complicated geometry or parts of your geometry you're particularly interested in. In the microwave regime, this means mesh points will typically have tens of centimeters or less between them. However, given that the receiving antennas in satellite-based solar power are orders of magnitude larger than that, trying to simulate such a large structure and still keep your mesh points relatively dense is just asking for the curse of dimensionality to bite you.
In other words, it's certainly possible with enough compute time, but we have better things to do with our GPU cores, especially since the whole point of antenna simulation is to assist with design by allowing you to run a bunch of simulations to tune your design without having to fabricate a bunch of DUTs. Again, I'm not really an expert, but my understanding is that this kind of multiscale problem is a hot research topic right now, not only in computational EM but in many other areas of physics simulations, especially those governed by nasty PDEs (e.g. fluid dynamics) or those which involve complicated structures at multiple scales (e.g. VLSI design).
I really would love another sentence or two on this. I can't immediately think why that would be, e.g. don't Maxwell's equations apply at very large scales? Any ideas?