An Efficient Monte Carlo-Transformed Field Expansion Method for Electromagnetic Wave Scattering by Random Rough Surfaces (Communications in Computational Physics, 2018)
This paper develops an efficient and accurate numerical method for thecomputation of electromagnetic waves scattered by random rough surfaces. Themethod is based upon a combination of the Transformed Field Expansion method,which represents the solution as a provably convergent power series, and the MonteCarlo technique for sampling the probability space. The compelling aspect of the proposedmethod is that, at each perturbation order and every sample, the governingTransformed Field Expansion equations share the same deterministic Helmholtz operatoron a deterministic domain. Thus, an LU factorization of the matrix discretizationof this single operator can be employed repeatedly for all orders and every sample.Consequently, the computational complexity of the whole algorithm is significantlyreduced as a result. Numerical examples are described which demonstrate the accuracyof the algorithm.