Studies of large-scale random rough surface scattering problems based on Monte Carlo simulations with efficient computational integral equation methods

Past numerical Monte Carlo simulations of electromagnetic wave scattering from random rough surfaces have been limited to one-dimensional (1-D) surfaces (two-dimensional scattering) of moderate sizes and only a few two-dimensional (2-D) surface problems (three-dimensional scattering) have been reported. This is because for scattering problems of large scale, the CPU time and memory requirement can be formidable even for today's fast computers.; In this dissertation, numerical techniques have been developed to solve general rough surface scattering problems efficiently and precisely. The methods developed are capable of solving large-scale rough surface problems requiring a large number of unknowns. This dissertation presents three efficient numerical methods:; Firstly, a banded matrix iterative approach (BMIA) is presented. In the past, the method has been applied to surface lengths of moderate sizes. In this dissertation, BMIA is used to study scattering of a TE incident wave from a perfectly conducting large-scale one-dimensional random rough surface with up to 3750 surface unknowns. Secondly, significant improvements have been made to the BMIA by the canonical grid (CG) method. This new method is called the BMIA/CG. Improvements are in terms of both speed and memory requirements. In BMIA/CG, the non-near field interactions can be translated to a canonical grid by a Taylor series expansion. This facilitates the use of the fast Fourier transform for non-near field interaction. The method is used for Monte Carlo simulations with a large surface length of up to 2,500 wavelengths and 25,000 surface unknowns at near grazing incidence. The numerical examples illustrate the importance of using a large surface.; Thirdly, electromagnetic wave scattering from a two-dimensional random rough surface is studied with Monte Carlo simulations. The solution of the matrix equation is precisely calculated using an efficient method known as the sparse-matrix canonical grid (SMCG). The method is applied to perfectly conducting and dielectric surfaces. The SMCG is the direct extension of the BMIA/CG to the 2-D rough surface problems. Numerical examples are illustrated with up to 98,304 surface unknowns, surface areas between 256 square wavelengths to 1024 square wavelengths, rms heights of up to one wavelength, and up to 1000 realizations. In the case of a perfectly conducting surface, comparisons with controlled laboratory experimental data show good agreement.