Rigorous solutions for electromagnetic scattering from rough surfaces

First, the rough surface scattering problem is formulated from a statistical point of view. Then, different numerical schemes that permit one to solve Maxwell equations without approximation are presented for the three-dimensional scattering problem. Particular attention is paid to boundary integral methods and to the numerical techniques developed to handle large linear systems when short-range interactions dominate. Lastly, several important connected issues that require further numerical and theoretical improvements are discussed.