Efficient algorithms for the study of waveguiding and scattering structures

In this dissertation, efficient algorithms for the study of waveguiding and scattering from dielectric structures are studied. The focus of this discourse is on the computational aspects rather than electromagnetic theory, although the theory is discussed whenever it is needed.First, the solution of a hybrid finite element method (HFEM) problem is considered. It is shown that a suitable ordering of the FEM mesh results in a canonical HFEM matrix system. The resulting linear systems have a computational complexity of $O(N\sp2)$ and $O(N\sp{1.5})$, respectively, when direct banded solvers and sparse direct methods are used. This computational complexity is comparable to that for FEM methods using approximate boundary conditions and a similar sparse solution method.Second, we consider the solution of generalized eigenvalue problems which results from the study of dielectric waveguides. The iterative Chebyshev-Arnoldi method is used together with inflated inverse iteration. It is shown that we can find the desired number of eigenpairs in a cost-effective way.Third, scattering of a plane wave from a periodic randomly rough dielectric surface with an electrically large period is considered. A novel approach is used to find convergent forms of otherwise nonconvergent series. Even though the problem being considered is of an infinite extent, the solution is fast and requires minimal storage. In addition, this method can solve surface roughnesses of the order of a wavelength and more.U of I OnlyETDs are only available to UIUC Users without author permissio