{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/19583"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/19583","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Fast algorithms for solving integral equations of electromagnetic wave scattering","abstract":"Computational electromagnetics plays an important role in the study of wave scattering and radiation from large and complex objects. This dissertation develops fast numerical algorithms for solving two-dimensional and three-dimensional integral equations of electromagnetic wave scattering. They include: (1) The fast iterative method, which reduces the matrix-vector multiplication from $N\\sp2$ to $N\\sp{1.5}$ and to N (log(N) $\\sp2.$ (2) A fast far-field approximation (FAFFA) method, which solves surface integral equations iteratively with computational complexity of O($N\\sp{4/3}$) for one matrix vector multiplication. The FAFFA is applied to compute the RCSs of 2D and 3D objects with large electrical sizes. (3) The nested equivalence principle algorithm (NEPAL), which uses Huygens' equivalence principle to replace volume scatterers by surface scatterers, resulting in the reduction of the total number of unknowns. These algorithms have lower computational complexities compared to those for the classical low frequency methods and have the potential for solving larger electromagnetic scattering problems.","abstract_html":"Computational electromagnetics plays an important role in the study of wave scattering and radiation from large and complex objects. This dissertation develops fast numerical algorithms for solving two-dimensional and three-dimensional integral equations of electromagnetic wave scattering. They include: (1) The fast iterative method, which reduces the matrix-vector multiplication from $N\\sp2$ to $N\\sp{1.5}$ and to N (log(N) $\\sp2.$ (2) A fast far-field approximation (FAFFA) method, which solves surface integral equations iteratively with computational complexity of O($N\\sp{4/3}$) for one matrix vector multiplication. The FAFFA is applied to compute the RCSs of 2D and 3D objects with large electrical sizes. (3) The nested equivalence principle algorithm (NEPAL), which uses Huygens' equivalence principle to replace volume scatterers by surface scatterers, resulting in the reduction of the total number of unknowns. These algorithms have lower computational complexities compared to those for the classical low frequency methods and have the potential for solving larger electromagnetic scattering problems.","abstract_has_math":true,"creators":["Lu, Cai-Cheng"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Electrical and Computer Engineering","degree_department":null,"school":null,"contributors":["Chew, Weng Cho"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2011,"date_issued":"2011-05-07T12:12:10Z","date_published":"2011-05-07T12:12:10Z","updated_at":"2026-07-22T22:25:14Z","subjects":["Engineering, Electronics and Electrical"],"languages":["eng"],"rights":["Copyright 1995 Lu, Cai-Cheng"],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["AAI9543657","(UMI)AAI9543657"],"render_values":[{"text":"AAI9543657","href":null,"code":true},{"text":"(UMI)AAI9543657","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/19583","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":["Lu, Cai-Cheng"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2011-05-07T12:12:10Z","10000-01-01","1995"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Electrical and Computer Engineering"]},{"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"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["eng"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 1995 Lu, Cai-Cheng"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["AAI9543657","(UMI)AAI9543657","http://hdl.handle.net/2142/19583"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Computational electromagnetics plays an important role in the study of wave scattering and radiation from large and complex objects. This dissertation develops fast numerical algorithms for solving two-dimensional and three-dimensional integral equations of electromagnetic wave scattering. They include: (1) The fast iterative method, which reduces the matrix-vector multiplication from $N\\sp2$ to $N\\sp{1.5}$ and to N (log(N) $\\sp2.$ (2) A fast far-field approximation (FAFFA) method, which solves surface integral equations iteratively with computational complexity of O($N\\sp{4/3}$) for one matrix vector multiplication. The FAFFA is applied to compute the RCSs of 2D and 3D objects with large electrical sizes. (3) The nested equivalence principle algorithm (NEPAL), which uses Huygens' equivalence principle to replace volume scatterers by surface scatterers, resulting in the reduction of the total number of unknowns. These algorithms have lower computational complexities compared to those for the classical low frequency methods and have the potential for solving larger electromagnetic scattering problems.","Made available in DSpace on 2011-05-07T12:12:10Z (GMT). No. of bitstreams: 2 license.txt: 4922 bytes, checksum: 910b249b4beec47e7ab768910c8f966f (MD5) 9543657.pdf: 4363946 bytes, checksum: b6f3c0993665adbef7b1898d493d73ce (MD5) Previous issue date: 1995","Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Howard Ding (hding2@illinois.edu) on 2011-05-07T14:38:02Z Item is restricted indefinitely.","Restriction data tranferred 2014-07-01T11:15:45-05:00 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":["Fast algorithms for solving integral equations of electromagnetic wave scattering"]}]}],"canonical_facts":{"dc:contributor":["Chew, Weng Cho"],"dc:creator":["Lu, Cai-Cheng"],"dc:date":["2011-05-07T12:12:10Z","10000-01-01","1995"],"dc:description":["Computational electromagnetics plays an important role in the study of wave scattering and radiation from large and complex objects. This dissertation develops fast numerical algorithms for solving two-dimensional and three-dimensional integral equations of electromagnetic wave scattering. They include: (1) The fast iterative method, which reduces the matrix-vector multiplication from $N\\sp2$ to $N\\sp{1.5}$ and to N (log(N) $\\sp2.$ (2) A fast far-field approximation (FAFFA) method, which solves surface integral equations iteratively with computational complexity of O($N\\sp{4/3}$) for one matrix vector multiplication. The FAFFA is applied to compute the RCSs of 2D and 3D objects with large electrical sizes. (3) The nested equivalence principle algorithm (NEPAL), which uses Huygens' equivalence principle to replace volume scatterers by surface scatterers, resulting in the reduction of the total number of unknowns. 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