{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/72907"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/72907","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"A surface integral equation method for dielectrics at low frequencies","abstract":"This thesis is dedicated to using surface integral equations to solve electro- magnetic problems involved in integrated circuits. Since normally the sizes of the devices in this application are much smaller than the wavelength of the electromagnetic waves, special considerations are needed because of the low frequency breakdown. The augmented technique, a useful remedy for low frequency breakdown of the electric field integral equation is introduced as the background of this thesis. This augmented electric field integral equation provides a simple solu- tion for broadband electromagnetic simulation of perfect electric conductor structures. This thesis presented here exploits the augmented method for lossless and lossy dielectrics. The use of the conventional Rao-Wilton-Glisson (RWG) basis function as basis and testing functions fails because of the testing issue. Instead, the Buffa-Christiansen (BC) basis function is proposed to overcome this diffi- culty. With the combined use of RWG and BC basis functions, a new formu- lation is developed achieving a good convergence and accuracy. For highly lossy medium, however, a new integration scheme and a simple, efficient strategy with a fast algorithm is adopted. After these treatments, the skin depth of current in the conductive medium can be accurately captured down to very low frequency.","abstract_html":"This thesis is dedicated to using surface integral equations to solve electro- magnetic problems involved in integrated circuits. Since normally the sizes of the devices in this application are much smaller than the wavelength of the electromagnetic waves, special considerations are needed because of the low frequency breakdown. The augmented technique, a useful remedy for low frequency breakdown of the electric field integral equation is introduced as the background of this thesis. This augmented electric field integral equation provides a simple solu- tion for broadband electromagnetic simulation of perfect electric conductor structures. This thesis presented here exploits the augmented method for lossless and lossy dielectrics. The use of the conventional Rao-Wilton-Glisson (RWG) basis function as basis and testing functions fails because of the testing issue. Instead, the Buffa-Christiansen (BC) basis function is proposed to overcome this diffi- culty. With the combined use of RWG and BC basis functions, a new formu- lation is developed achieving a good convergence and accuracy. For highly lossy medium, however, a new integration scheme and a simple, efficient strategy with a fast algorithm is adopted. After these treatments, the skin depth of current in the conductive medium can be accurately captured down to very low frequency.","abstract_has_math":false,"creators":["Xia, Tian"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"M.S.","degree_level":"Thesis","degree_discipline":"Electrical & Computer Engr","degree_department":null,"school":null,"contributors":["Chew, Weng C."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2015,"date_issued":"2015-01-21T19:49:22Z","date_published":"2015-01-21T19:49:22Z","updated_at":"2026-07-22T22:26:07Z","subjects":["Computational Electromagnetics","Integral Equation","Augmented electric field integral equation","Dielectrics","Conductors"],"languages":["en"],"rights":["Copyright 2014 Tian Xia"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/72907","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Chew, Weng C."]},{"key":"dc:creator","label":"Author","values":["Xia, Tian"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2015-01-21T19:49:22Z","2014-12","2015-01-21"]},{"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":["Thesis"]},{"key":"thesis:degree_name","label":"Degree Name","values":["M.S."]},{"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":["Computational Electromagnetics","Integral Equation","Augmented electric field integral equation","Dielectrics","Conductors"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2014 Tian Xia"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/72907"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["This thesis is dedicated to using surface integral equations to solve electro- magnetic problems involved in integrated circuits. Since normally the sizes of the devices in this application are much smaller than the wavelength of the electromagnetic waves, special considerations are needed because of the low frequency breakdown. The augmented technique, a useful remedy for low frequency breakdown of the electric field integral equation is introduced as the background of this thesis. This augmented electric field integral equation provides a simple solu- tion for broadband electromagnetic simulation of perfect electric conductor structures. This thesis presented here exploits the augmented method for lossless and lossy dielectrics. The use of the conventional Rao-Wilton-Glisson (RWG) basis function as basis and testing functions fails because of the testing issue. Instead, the Buffa-Christiansen (BC) basis function is proposed to overcome this diffi- culty. With the combined use of RWG and BC basis functions, a new formu- lation is developed achieving a good convergence and accuracy. For highly lossy medium, however, a new integration scheme and a simple, efficient strategy with a fast algorithm is adopted. After these treatments, the skin depth of current in the conductive medium can be accurately captured down to very low frequency.","Item withdrawn by Laura Spradlin (lspradl2@illinois.edu) on 2014-11-10T15:29:46Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 1 Xia_Tian.pdf: 13048970 bytes, checksum: 50bb7effdf503b5b6a2bcaf2bb758c95 (MD5)","Made available in DSpace on 2015-01-21T19:49:22Z (GMT). No. of bitstreams: 1 Tian_Xia.pdf: 13048970 bytes, checksum: 50bb7effdf503b5b6a2bcaf2bb758c95 (MD5)"]},{"key":"dc:title","label":"Title","values":["A surface integral equation method for dielectrics at low frequencies"]}]}],"canonical_facts":{"dc:contributor":["Chew, Weng C."],"dc:creator":["Xia, Tian"],"dc:date":["2015-01-21T19:49:22Z","2014-12","2015-01-21"],"dc:description":["This thesis is dedicated to using surface integral equations to solve electro- magnetic problems involved in integrated circuits. Since normally the sizes of the devices in this application are much smaller than the wavelength of the electromagnetic waves, special considerations are needed because of the low frequency breakdown. The augmented technique, a useful remedy for low frequency breakdown of the electric field integral equation is introduced as the background of this thesis. This augmented electric field integral equation provides a simple solu- tion for broadband electromagnetic simulation of perfect electric conductor structures. This thesis presented here exploits the augmented method for lossless and lossy dielectrics. The use of the conventional Rao-Wilton-Glisson (RWG) basis function as basis and testing functions fails because of the testing issue. Instead, the Buffa-Christiansen (BC) basis function is proposed to overcome this diffi- culty. With the combined use of RWG and BC basis functions, a new formu- lation is developed achieving a good convergence and accuracy. For highly lossy medium, however, a new integration scheme and a simple, efficient strategy with a fast algorithm is adopted. After these treatments, the skin depth of current in the conductive medium can be accurately captured down to very low frequency.","Item withdrawn by Laura Spradlin (lspradl2@illinois.edu) on 2014-11-10T15:29:46Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 1 Xia_Tian.pdf: 13048970 bytes, checksum: 50bb7effdf503b5b6a2bcaf2bb758c95 (MD5)","Made available in DSpace on 2015-01-21T19:49:22Z (GMT). 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