Electromagnetic Wave Scattering at Biperiodic Surfaces: Variational Formulation, Boundary Integral Equations and High Order Solvers

In this thesis we consider time-harmonic electromagnetic wave scattering at impenetrable biperiodic surfaces in a homogeneous medium. Besides their rigorous analysis in biperiodic Sobolev spaces, which aims at answering the questions about existence and uniqueness of solutions, we will derive a high order solver for its numerical approximation - a collocation method based on trigonometric polynomials