Application of the finite element method to Monte Carlo simulations of scattering of waves by random rough surfaces: penetrable case

Abstract

The finite element method (FEM) of Monte Carlo simulations of random rough surface scattering is extended to penetrable rough surface scattering. The attraction of the method is the banded nature of the resulting matrix equation. The method yields a system of linear algebraic equations which is solved by a direct sparse symmetric matrix inversion. Convergence and accuracy of the method is demonstrated and established by varying various input parameters such as the number of evanescent waves, the number of sampling points and the surface lengths. Results with incident plane wave TE polarization are presented for both the mean reflected scattered intensity and the mean transmitted scattered intensity as a function of surface parameters such as RMS surface heights and correlation lengths. The numerical results are compared against the tapered wave integral equation (TWIE) method. The results of a tapered wave solution of the integral equation averaging over many realizations are in good numerical agreement with FEM if large surface lengths are used in the integral equation method. It is found that a large surface length is required in the TWIE method to have a narrow incident angular spectlum to accurateiy predict the transmitted scattered intensity, whereas a relatively small surface length is sufficient in the FEM. The total CPU time and memory storage requirements for the FEM are much less than that of the TWIE method for eases when the number of horizontal sampling points is much larger than the number of vertical sampling points in the region of discretization. The percentage error in conservation of energy for the FEM is shown to be less than 0.4% for all the examples presented. The total CPU time, memory storage requirements and the percentage error comparisons between the FEM and the TWIE are presented.