{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/23560"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/23560","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Efficient algorithms for the study of waveguiding and scattering structures","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.","abstract_html":"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.","abstract_has_math":false,"creators":["Nasir, Muhammad Abdul"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Engineering, Electronics and Electrical","degree_department":null,"school":null,"contributors":["Chew, Weng Cho"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2011,"date_issued":"2011-05-07T14:18:42Z","date_published":"2011-05-07T14:18:42Z","updated_at":"2026-07-22T22:25:22Z","subjects":["Engineering, Electronics and Electrical","Computer Science"],"languages":["eng"],"rights":["Copyright 1994 Nasir, Muhammad Abdul"],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["AAI9503284","(UMI)AAI9503284"],"render_values":[{"text":"AAI9503284","href":null,"code":true},{"text":"(UMI)AAI9503284","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/23560","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Chew, Weng Cho"]},{"key":"dc:creator","label":"Author","values":["Nasir, Muhammad Abdul"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2011-05-07T14:18:42Z","10000-01-01","1994"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Engineering, Electronics and Electrical","Computer Science"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Engineering, Electronics and Electrical","Computer Science"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["eng"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 1994 Nasir, Muhammad Abdul"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["AAI9503284","(UMI)AAI9503284","http://hdl.handle.net/2142/23560"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["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.","Made available in DSpace on 2011-05-07T14:18:42Z (GMT). No. of bitstreams: 2 license.txt: 4922 bytes, checksum: 910b249b4beec47e7ab768910c8f966f (MD5) 9503284.pdf: 4792994 bytes, checksum: b3fbd882941bebf4120964b4ffe3c266 (MD5) Previous issue date: 1994","Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Howard Ding (hding2@illinois.edu) on 2011-05-07T15:05:18Z Item is restricted indefinitely.","Restriction data tranferred 2014-07-01T11:31:16-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: ETDs are only available to UIUC Users without author permission","ETDs are only available to UIUC Users without author permission","U of I Only"]},{"key":"dc:title","label":"Title","values":["Efficient algorithms for the study of waveguiding and scattering structures"]}]}],"canonical_facts":{"dc:contributor":["Chew, Weng Cho"],"dc:creator":["Nasir, Muhammad Abdul"],"dc:date":["2011-05-07T14:18:42Z","10000-01-01","1994"],"dc:description":["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.","Made available in DSpace on 2011-05-07T14:18:42Z (GMT). No. of bitstreams: 2 license.txt: 4922 bytes, checksum: 910b249b4beec47e7ab768910c8f966f (MD5) 9503284.pdf: 4792994 bytes, checksum: b3fbd882941bebf4120964b4ffe3c266 (MD5) Previous issue date: 1994","Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Howard Ding (hding2@illinois.edu) on 2011-05-07T15:05:18Z Item is restricted indefinitely.","Restriction data tranferred 2014-07-01T11:31:16-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: ETDs are only available to UIUC Users without author permission","ETDs are only available to UIUC Users without author permission","U of I Only"],"dc:identifier":["AAI9503284","(UMI)AAI9503284","http://hdl.handle.net/2142/23560"],"dc:language":["eng"],"dc:rights":["Copyright 1994 Nasir, Muhammad Abdul"],"dc:subject":["Engineering, Electronics and Electrical","Computer Science"],"dc:title":["Efficient algorithms for the study of waveguiding and scattering structures"],"dc:type":["text"],"thesis:degree_discipline":["Engineering, Electronics and Electrical","Computer Science"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:25:22Z"}