(untitled) (Communications in Computational Physics, 2018)
This paper develops an efficient and accurate numerical method for the computation of electromagnetic waves scattered by random rough surfaces. The method is based upon a combination of the Transformed Field Expansion method, which represents the solution as a provably convergent power series, and the Monte Carlo technique for sampling the probability space. The compelling aspect of the proposed method is that, at each perturbation order and every sample, the governing Transformed Field Expansion equations share the same deterministic Helmholtz operator on a deterministic domain. Thus, an LU factorization of the matrix discretization of this single operator can be employed repeatedly for all orders and every sample. Consequently, the computational complexity of the whole algorithm is significantly reduced as a result. Numerical examples are described which demonstrate the accuracy of the algorithm.