Boundary integral equations for time-harmonic rough surface scattering

This paper discusses time-harmonic rough surface scattering for boundary integral equations. The boundary integral formalism, combined with fast numerical solvers, is a very efficient way to deal rigorously with the time-harmonic scattering from a rough surface separating two semi-infinite homogeneous media. However, applying a MoM to an integral equation leads to a linear system with full complex matrices. Since an integral equation is solved, this small slope integral equation method (SSIE) predicts multiple scattering at moderately numerical costs. SSIE is not a statistical method (a Monte Carlo process is necessary) but it is not restricted to surfaces with Gaussian height distribution, an estimation of the error is provided and the numerical solution is independent of the scattering angle.