Approximate boundary integral equations for time-harmonic rough surface scattering

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. If the exact matrix elements are used, the number of operations for solving such a system is proportional to N/sup 2/, where N is the number of unknowns. In addition, storing all the matrix elements in RAM is not possible. This is why several numerical methods have been developed to avoid full matrix storage and to make the computation time scale as N logN. This may be achieved by representing the matrix as a superposition of matrices with specific properties, in order to speed up the matrix-vector products that occur in iterative solvers. As a result, a slight approximation of the kernel of the integral equation leads to a drastic gain in terms of computation time and memory requirements. We show that additional approximations can speed up the computation further, and we compare them with existing approximate methods.