{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/97346"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/97346","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Development of provably stable A-phi formulation time domain integral equations","abstract":"Applications involving quantum physics are becoming an increasingly important area for electromagnetic engineering. To address practical problems in these emerging areas, appropriate numerical techniques must be utilized. However, the unique needs of many of these applications require the development of new computational electromagnetic solvers. The A-Phi formulation is a novel approach that can address many of these needs. This formulation utilizes equations developed in terms of the magnetic vector potential (A) and electric scalar potential (Phi). The resulting equations overcome many of the limitations of traditional solvers and are ideal for coupling to quantum mechanical calculations. The main novelty of this thesis is the extension of the A-Phi formulation to two sets of time domain integral equations. These integral equations are provably stable and constitute robust numerical techniques that can be utilized in many applications. To validate the proposed time domain integral equations, numerical results are presented which demonstrate the stability and accuracy of the developed methods.","abstract_html":"Applications involving quantum physics are becoming an increasingly important area for electromagnetic engineering. To address practical problems in these emerging areas, appropriate numerical techniques must be utilized. However, the unique needs of many of these applications require the development of new computational electromagnetic solvers. The A-Phi formulation is a novel approach that can address many of these needs. This formulation utilizes equations developed in terms of the magnetic vector potential (A) and electric scalar potential (Phi). The resulting equations overcome many of the limitations of traditional solvers and are ideal for coupling to quantum mechanical calculations. The main novelty of this thesis is the extension of the A-Phi formulation to two sets of time domain integral equations. These integral equations are provably stable and constitute robust numerical techniques that can be utilized in many applications. To validate the proposed time domain integral equations, numerical results are presented which demonstrate the stability and accuracy of the developed methods.","abstract_has_math":false,"creators":["Roth, Thomas E"],"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 Cho"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2017,"date_issued":"2017-08-10T19:14:58Z","date_published":"2017-08-10T19:14:58Z","updated_at":"2026-07-22T22:24:32Z","subjects":["Computational electromagnetics","Time domain integral equations","Low frequency","Multiscale"],"languages":["en"],"rights":["Copyright 2017 Thomas E. Roth"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/97346","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":["Roth, Thomas E"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2017-08-10T19:14:58Z","2017-04-13","2017-05"]},{"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","Time domain integral equations","Low frequency","Multiscale"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2017 Thomas E. Roth"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/97346"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Applications involving quantum physics are becoming an increasingly important area for electromagnetic engineering. To address practical problems in these emerging areas, appropriate numerical techniques must be utilized. However, the unique needs of many of these applications require the development of new computational electromagnetic solvers. The A-Phi formulation is a novel approach that can address many of these needs. This formulation utilizes equations developed in terms of the magnetic vector potential (A) and electric scalar potential (Phi). The resulting equations overcome many of the limitations of traditional solvers and are ideal for coupling to quantum mechanical calculations. The main novelty of this thesis is the extension of the A-Phi formulation to two sets of time domain integral equations. These integral equations are provably stable and constitute robust numerical techniques that can be utilized in many applications. To validate the proposed time domain integral equations, numerical results are presented which demonstrate the stability and accuracy of the developed methods.","Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2017-08-10 without embargo terms","The student, Thomas Roth, accepted the attached license on 2017-04-13 at 07:40.","The student, Thomas Roth, submitted this Thesis for approval on 2017-04-13 at 08:45.","This Thesis was approved for publication on 2017-04-13 at 11:54.","DSpace SAF Submission Ingestion Package generated from Vireo submission #10735 on 2017-08-10 at 13:39:36","Made available in DSpace on 2017-08-10T19:14:58Z (GMT). No. of bitstreams: 2 ROTH-THESIS-2017.pdf: 3099615 bytes, checksum: 652469cd059cd2a293d69331d95137c6 (MD5) LICENSE.txt: 4208 bytes, checksum: f96dd77149eff57a8e99114a890f78ca (MD5) Previous issue date: 2017-04-13"]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Development of provably stable A-phi formulation time domain integral equations"]}]}],"canonical_facts":{"dc:contributor":["Chew, Weng Cho"],"dc:creator":["Roth, Thomas E"],"dc:date":["2017-08-10T19:14:58Z","2017-04-13","2017-05"],"dc:description":["Applications involving quantum physics are becoming an increasingly important area for electromagnetic engineering. To address practical problems in these emerging areas, appropriate numerical techniques must be utilized. However, the unique needs of many of these applications require the development of new computational electromagnetic solvers. The A-Phi formulation is a novel approach that can address many of these needs. This formulation utilizes equations developed in terms of the magnetic vector potential (A) and electric scalar potential (Phi). The resulting equations overcome many of the limitations of traditional solvers and are ideal for coupling to quantum mechanical calculations. The main novelty of this thesis is the extension of the A-Phi formulation to two sets of time domain integral equations. These integral equations are provably stable and constitute robust numerical techniques that can be utilized in many applications. To validate the proposed time domain integral equations, numerical results are presented which demonstrate the stability and accuracy of the developed methods.","Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2017-08-10 without embargo terms","The student, Thomas Roth, accepted the attached license on 2017-04-13 at 07:40.","The student, Thomas Roth, submitted this Thesis for approval on 2017-04-13 at 08:45.","This Thesis was approved for publication on 2017-04-13 at 11:54.","DSpace SAF Submission Ingestion Package generated from Vireo submission #10735 on 2017-08-10 at 13:39:36","Made available in DSpace on 2017-08-10T19:14:58Z (GMT). No. of bitstreams: 2 ROTH-THESIS-2017.pdf: 3099615 bytes, checksum: 652469cd059cd2a293d69331d95137c6 (MD5) LICENSE.txt: 4208 bytes, checksum: f96dd77149eff57a8e99114a890f78ca (MD5) Previous issue date: 2017-04-13"],"dc:format":["application/pdf"],"dc:identifier":["http://hdl.handle.net/2142/97346"],"dc:language":["en"],"dc:rights":["Copyright 2017 Thomas E. Roth"],"dc:subject":["Computational electromagnetics","Time domain integral equations","Low frequency","Multiscale"],"dc:title":["Development of provably stable A-phi formulation time domain integral equations"],"dc:type":["text"],"thesis:degree_discipline":["Electrical & Computer Engr"],"thesis:degree_level":["Thesis"],"thesis:degree_name":["M.S."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:24:32Z"}