Numerical simulations of interactions of electromagnetic waves with lossy dielectric surfaces using fast computational methods

The scattering of electromagnetic waves by lossy dielectric random rough surfaces with large permittivity has broad applications in natural media. Because many of natural medium are lossy and with surface roughness. In the application of the Method of Moment to the lossy dielectric rough surfaces with high permittivity, there can be rapid spatial variations of the dielectric medium Green's function and surface fields. A dense discretization of the surface may be required. Therefore there is a large increase in CPU and required memory.; To circumvent the problem, the physics-based two-grid (PBTG) method was developed in this dissertation. In PBTG, two grids are used: a dense grid and a sparse grid. The sparse grid is that of the usual 8 to 10 points per wavelength. The dense grid ranges from 16 or higher number of points per wavelength depending on the relative permittivity of the lossy dielectric medium. The PBTG is based on two observations: (1) the Green's function of the lossy dielectric is attenuative and therefore is space-limited, and (2) the Green's function of free-space is slowly varying on the dense grid compared with the medium Green's function and therefore is spatial frequency-limited. The first observation results in a banded matrix for 1-dimensional rough surface and a sparse matrix for 2-dimensional rough surface for the Green's function of the lossy dielectric. The second observation allows us, when using the free-space Green's function to act on the surface fields of dense grid, to first average the values of surface unknowns on the dense grid and then place them on the coarse grid. Thus the PBTG speeds up the computation and yet preserves the accuracy of the solution. The surface fields are calculated on the dense grid.; The PBTG can be applied to both 1-dimensional and 2-dimensional rough surfaces and can be easily used in conjunction with the other fast methods. The PBTG is combined with the banded matrix-iterative approach/canonical grid (BMIA/CAG) and the multilevel steepest descent fast multipole method (MLSDFMM) for 1-dimensional random rough surfaces and with sparse matrix canonical grid method (SMCG) for 2-dimensional random rough surfaces in this dissertation.