{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/101645"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/101645","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"An enhanced augmented electric field integral equation and the calculation of casimir force using computational electromagnetics","abstract":"In this dissertation, a surface integral equation formulation is developed for low-frequency problems by generalizing the existing augmented electric field integral equation from the perfect electric conductors to the dielectrics and general conductors. Detailed discussions of the basis functions and the pre-conditioner are provided for the dielectric problems, and a novel integration scheme for the evaluations of the matrix elements in the conductor problem is proposed. Then a broadband multilevel fast multipole algorithm (FMA) using a hybridization of the multipole and plane wave expansions is introduced. This high-accuracy algorithm is error controllable and stable at low frequencies. It reduces to the conventional diagonal FMA at higher frequencies. Therefore it can be regarded as a generalization of the dense FMA at low frequencies and the diagonal FMA at higher frequencies. Finally, the computational electromagnetic techniques are applied to the calculations of the Casimir force. The application of the integral equation method in Casimir force calculation is briefly reviewed and we proposed an efficient computing scheme using the randomized singular value decomposition and the hybrid FMA. As a result, the efficiency can be greatly enhanced for large problems.","abstract_html":"In this dissertation, a surface integral equation formulation is developed for low-frequency problems by generalizing the existing augmented electric field integral equation from the perfect electric conductors to the dielectrics and general conductors. Detailed discussions of the basis functions and the pre-conditioner are provided for the dielectric problems, and a novel integration scheme for the evaluations of the matrix elements in the conductor problem is proposed. Then a broadband multilevel fast multipole algorithm (FMA) using a hybridization of the multipole and plane wave expansions is introduced. This high-accuracy algorithm is error controllable and stable at low frequencies. It reduces to the conventional diagonal FMA at higher frequencies. Therefore it can be regarded as a generalization of the dense FMA at low frequencies and the diagonal FMA at higher frequencies. Finally, the computational electromagnetic techniques are applied to the calculations of the Casimir force. The application of the integral equation method in Casimir force calculation is briefly reviewed and we proposed an efficient computing scheme using the randomized singular value decomposition and the hybrid FMA. As a result, the efficiency can be greatly enhanced for large problems.","abstract_has_math":false,"creators":["Xia, Tian"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Electrical & Computer Engr","degree_department":null,"school":null,"contributors":["Chew, Weng Cho","Jin, Jianming","Popescu, Gabriel","Schutt-Ainé, José"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2018,"date_issued":"2018-09-27T16:28:02Z","date_published":"2018-09-27T16:28:02Z","updated_at":"2026-07-22T22:24:40Z","subjects":["Integral equation, low frequency, fast algorithm, fast multipole algorithm, Casimir force."],"languages":["en"],"rights":["Copyright 2018 Tian Xia"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/101645","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Chew, Weng Cho","Jin, Jianming","Popescu, Gabriel","Schutt-Ainé, José"]},{"key":"dc:creator","label":"Author","values":["Xia, Tian"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2018-09-27T16:28:02Z","2020-09-28T09:15:27Z","2018-05-29","2018-08"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Electrical & Computer Engr"]},{"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":["Integral equation, low frequency, fast algorithm, fast multipole algorithm, Casimir force."]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2018 Tian Xia"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/101645"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["In this dissertation, a surface integral equation formulation is developed for low-frequency problems by generalizing the existing augmented electric field integral equation from the perfect electric conductors to the dielectrics and general conductors. Detailed discussions of the basis functions and the pre-conditioner are provided for the dielectric problems, and a novel integration scheme for the evaluations of the matrix elements in the conductor problem is proposed. Then a broadband multilevel fast multipole algorithm (FMA) using a hybridization of the multipole and plane wave expansions is introduced. This high-accuracy algorithm is error controllable and stable at low frequencies. It reduces to the conventional diagonal FMA at higher frequencies. Therefore it can be regarded as a generalization of the dense FMA at low frequencies and the diagonal FMA at higher frequencies. Finally, the computational electromagnetic techniques are applied to the calculations of the Casimir force. The application of the integral equation method in Casimir force calculation is briefly reviewed and we proposed an efficient computing scheme using the randomized singular value decomposition and the hybrid FMA. As a result, the efficiency can be greatly enhanced for large problems.","Submission published under a 24 month embargo labeled 'U of I Access', the embargo will last until 2020-08-01","The student, Tian Xia, accepted the attached license on 2018-05-24 at 15:48.","The student, Tian Xia, submitted this Dissertation for approval on 2018-05-24 at 15:58.","This Dissertation was approved for publication on 2018-05-29 at 11:30.","DSpace SAF Submission Ingestion Package generated from Vireo submission #12594 on 2018-09-27 at 11:15:48","Made available in DSpace on 2018-09-27T16:28:02Z (GMT). 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Detailed discussions of the basis functions and the pre-conditioner are provided for the dielectric problems, and a novel integration scheme for the evaluations of the matrix elements in the conductor problem is proposed. Then a broadband multilevel fast multipole algorithm (FMA) using a hybridization of the multipole and plane wave expansions is introduced. This high-accuracy algorithm is error controllable and stable at low frequencies. It reduces to the conventional diagonal FMA at higher frequencies. Therefore it can be regarded as a generalization of the dense FMA at low frequencies and the diagonal FMA at higher frequencies. Finally, the computational electromagnetic techniques are applied to the calculations of the Casimir force. The application of the integral equation method in Casimir force calculation is briefly reviewed and we proposed an efficient computing scheme using the randomized singular value decomposition and the hybrid FMA. As a result, the efficiency can be greatly enhanced for large problems.","Submission published under a 24 month embargo labeled 'U of I Access', the embargo will last until 2020-08-01","The student, Tian Xia, accepted the attached license on 2018-05-24 at 15:48.","The student, Tian Xia, submitted this Dissertation for approval on 2018-05-24 at 15:58.","This Dissertation was approved for publication on 2018-05-29 at 11:30.","DSpace SAF Submission Ingestion Package generated from Vireo submission #12594 on 2018-09-27 at 11:15:48","Made available in DSpace on 2018-09-27T16:28:02Z (GMT). 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