Electromagnetic diffraction by random rough surfaces

We study the electromagnetic diffraction by gratings and random rough surfaces. The C-method is an exact method developed for this aim. It is based on Maxwell's equations under covariant form written in a nonorthogonal coordinate system. The C-method leads to an eigenvalue problem, the solution of which gives the diffracted field. We focus on the numerical aspect of the C-method, trying to develop an efficient application of this exact method. For gratings, we have developed a new version of the C-method which leads to a differential system with initial conditions. This new version of the C-method can be used to study multilayer gratings with a homogeneous medium. We implemented high performance algorithms for the original versions of the C-method. Especially, we have developed a specifically designed parallel QR algorithm for the C-method and spectral projection method to solve the eigenvalue problem more efficiently. Experiments have shown that the computation time can be reduced significantly.