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 Title: Efficient algorithms for the study of waveguiding and scattering structures Author(s): Nasir, Muhammad Abdul Doctoral Committee Chair(s): Chew, Weng Cho Department / Program: Engineering, Electronics and ElectricalComputer Science Discipline: Engineering, Electronics and ElectricalComputer Science Degree Granting Institution: University of Illinois at Urbana-Champaign Degree: Ph.D. Genre: Dissertation Subject(s): Engineering, Electronics and Electrical Computer Science Abstract: 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. Issue Date: 1994 Type: Text Language: English URI: http://hdl.handle.net/2142/23560 Rights Information: Copyright 1994 Nasir, Muhammad Abdul Date Available in IDEALS: 2011-05-07 Identifier in Online Catalog: AAI9503284 OCLC Identifier: (UMI)AAI9503284
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