{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/108327"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/108327","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Electromagnetic analysis with discrete exterior calculus","abstract":"The main focus of this dissertation is to implement discrete exterior calculus (DEC) in electromagnetic analysis. The problem is studied for both partial differential equation (PDE) and integral equation (IE) based approaches. A systematical treatment is proposed for various boundary conditions. With a careful implementation of the Hodge star operators, we are able to represent and solve electromagnetic PDEs properly with DEC. And a self-contained discrete electromagnetic theory is developed within this framework. The discrete version of many electromagnetic theorems are derived. Then a numerical Green's function (NGF) is introduced to incorporate DEC into integral equations. With interior surface relation formulated with NGF and exterior relation from surface integral equations (SIEs), we present an alternative solution for scattering problems with complex obstacles. This NGF is also applied to formulate the propagation relation in the near field heat transfer problem. Then, with the fluctuation dissipation theorem (FDT) discretized by DEC, we provide a comprehensive solution for the near field heat transfer problem among objects with complex material properties. Using DEC, we present a scalar \\Phi and vector potential A based formulation with general Lorentz gauge to circumvent the low frequency breakdown for conventional E formulation. A set of decoupled boundary conditions is studied and numerically tested.","abstract_html":"The main focus of this dissertation is to implement discrete exterior calculus (DEC) in electromagnetic analysis. The problem is studied for both partial differential equation (PDE) and integral equation (IE) based approaches. A systematical treatment is proposed for various boundary conditions. With a careful implementation of the Hodge star operators, we are able to represent and solve electromagnetic PDEs properly with DEC. And a self-contained discrete electromagnetic theory is developed within this framework. The discrete version of many electromagnetic theorems are derived. Then a numerical Green's function (NGF) is introduced to incorporate DEC into integral equations. With interior surface relation formulated with NGF and exterior relation from surface integral equations (SIEs), we present an alternative solution for scattering problems with complex obstacles. This NGF is also applied to formulate the propagation relation in the near field heat transfer problem. Then, with the fluctuation dissipation theorem (FDT) discretized by DEC, we provide a comprehensive solution for the near field heat transfer problem among objects with complex material properties. Using DEC, we present a scalar \\Phi and vector potential A based formulation with general Lorentz gauge to circumvent the low frequency breakdown for conventional E formulation. A set of decoupled boundary conditions is studied and numerically tested.","abstract_has_math":false,"creators":["Chen, Shu"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Physics","degree_department":null,"school":null,"contributors":["Chew, Weng Cho","Cooper, S Lance","Hirani, Anil N.","Aluru, Narayana R."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2020,"date_issued":"2020-08-27T00:51:28Z","date_published":"2020-08-27T00:51:28Z","updated_at":"2026-07-22T22:24:48Z","subjects":["DEC","Computational electromagnetics","Near Field Heat transfer","FEM"],"languages":["en"],"rights":["Copyright 2020 Shu Chen"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/108327","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Chew, Weng Cho","Cooper, S Lance","Hirani, Anil N.","Aluru, Narayana R."]},{"key":"dc:creator","label":"Author","values":["Chen, Shu"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2020-08-27T00:51:28Z","2022-08-27T00:51:40Z","2020-05-08","2020-05"]},{"key":"dc:type","label":"Dc Type","values":["text","Thesis"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Physics"]},{"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":["DEC","Computational electromagnetics","Near Field Heat transfer","FEM"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2020 Shu Chen"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/108327"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["The main focus of this dissertation is to implement discrete exterior calculus (DEC) in electromagnetic analysis. The problem is studied for both partial differential equation (PDE) and integral equation (IE) based approaches. A systematical treatment is proposed for various boundary conditions. With a careful implementation of the Hodge star operators, we are able to represent and solve electromagnetic PDEs properly with DEC. And a self-contained discrete electromagnetic theory is developed within this framework. The discrete version of many electromagnetic theorems are derived. Then a numerical Green's function (NGF) is introduced to incorporate DEC into integral equations. With interior surface relation formulated with NGF and exterior relation from surface integral equations (SIEs), we present an alternative solution for scattering problems with complex obstacles. This NGF is also applied to formulate the propagation relation in the near field heat transfer problem. Then, with the fluctuation dissipation theorem (FDT) discretized by DEC, we provide a comprehensive solution for the near field heat transfer problem among objects with complex material properties. Using DEC, we present a scalar \\Phi and vector potential A based formulation with general Lorentz gauge to circumvent the low frequency breakdown for conventional E formulation. A set of decoupled boundary conditions is studied and numerically tested.","Submission published under a 24 month embargo labeled 'Closed Access', the embargo will last until 2022-05-01","The student, Shu Chen, accepted the attached license on 2020-05-06 at 17:17.","The student, Shu Chen, submitted this Dissertation for approval on 2020-05-06 at 17:31.","This Dissertation was approved for publication on 2020-05-08 at 07:06.","DSpace SAF Submission Ingestion Package generated from Vireo submission #15256 on 2020-08-25 at 17:43:32","Made available in DSpace on 2020-08-27T00:51:28Z (GMT). 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The problem is studied for both partial differential equation (PDE) and integral equation (IE) based approaches. A systematical treatment is proposed for various boundary conditions. With a careful implementation of the Hodge star operators, we are able to represent and solve electromagnetic PDEs properly with DEC. And a self-contained discrete electromagnetic theory is developed within this framework. The discrete version of many electromagnetic theorems are derived. Then a numerical Green's function (NGF) is introduced to incorporate DEC into integral equations. With interior surface relation formulated with NGF and exterior relation from surface integral equations (SIEs), we present an alternative solution for scattering problems with complex obstacles. This NGF is also applied to formulate the propagation relation in the near field heat transfer problem. Then, with the fluctuation dissipation theorem (FDT) discretized by DEC, we provide a comprehensive solution for the near field heat transfer problem among objects with complex material properties. Using DEC, we present a scalar \\Phi and vector potential A based formulation with general Lorentz gauge to circumvent the low frequency breakdown for conventional E formulation. A set of decoupled boundary conditions is studied and numerically tested.","Submission published under a 24 month embargo labeled 'Closed Access', the embargo will last until 2022-05-01","The student, Shu Chen, accepted the attached license on 2020-05-06 at 17:17.","The student, Shu Chen, submitted this Dissertation for approval on 2020-05-06 at 17:31.","This Dissertation was approved for publication on 2020-05-08 at 07:06.","DSpace SAF Submission Ingestion Package generated from Vireo submission #15256 on 2020-08-25 at 17:43:32","Made available in DSpace on 2020-08-27T00:51:28Z (GMT). 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