In my presentation, I will describe results from two of our recent projects:

Calculations of the scattering of light from, and its transmission through, two-dimensional randomly rough surfaces are computationally intensive, and are still often carried out by means of small-amplitude perturbation theory, the Kirchhoff approximation, or the small slope approximation.  However, accurate approaches to the solution of such problems are needed in a variety of contexts, and searches for such approaches are an active area of research in computational electrodynamics.