I'm afraid this question might be too basic or too naive or both, but here goes!
For optical diffraction by periodic nano-structures (gratings, semiconductor manufacturing metrology) the rigorous coupled wave equation or RCWA (also) was sort-of a gold standard until Finite Difference Time Domain or FDTD methods were computationally achievable.
Analogous to the optical diffraction situation, the dynamical diffraction of electrons and X-rays has been traditionally calculated with static solutions.
Question: Have FDTD methods had inroads into simulation of scattering of electrons and X-rays by crystals for the purposes of comparing to measured patterns and/or spectra?
One reason that I'm asking is that LEED calculations are somewhat of a black box in that much of the code is from the 1980's and '90's and reimplementing them in a modern computational environment in a friendly way (e.g. Python wrapper, calls to standard libraries instead of all those DIY methods) will be hard. While computationally intense, FDTD methods might be somewhat easier to implement using modern techniques; but I'd like to see if this has been tried, and if so with what degree of success.
For more on traditional low energy electron diffraction (LEED) simulation see: