{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/46863"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/46863","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Studies of some issues in solving surface integral equations and the equivalence principle algorithm","abstract":"This thesis describes the progressive development analysis of the equivalence principle algorithm (EPA) beginning with the development of various operators that constitute it. We begin with the formulation for the electric field integral equation (EFIE), and visit the necessary treatment of the magnetic field integral equation (MFIE), the combined field integral equation (CFIE), and the Poggio-Miller-Chu-Harrington- Wu-Tsai (PMCHWT) along with various singularity extraction schemes before we develop the EPA relations. The explicit expressions of the translation operators are also derived. The EFIE, the MFIE, and the CFIE formulations are used to verify the accuracy of such operators as the L, the K, the nX L, and the n XK operators that are at the heart of the EPA formulation. Very detailed derivations and analyses of these operators with proper scaling factors are included to avoid the inaccuracy due to iterative solvers. Later we provide pertinent results for all of them for verification and comparison.","abstract_html":"This thesis describes the progressive development analysis of the equivalence principle algorithm (EPA) beginning with the development of various operators that constitute it. We begin with the formulation for the electric field integral equation (EFIE), and visit the necessary treatment of the magnetic field integral equation (MFIE), the combined field integral equation (CFIE), and the Poggio-Miller-Chu-Harrington- Wu-Tsai (PMCHWT) along with various singularity extraction schemes before we develop the EPA relations. The explicit expressions of the translation operators are also derived. The EFIE, the MFIE, and the CFIE formulations are used to verify the accuracy of such operators as the L, the K, the nX L, and the n XK operators that are at the heart of the EPA formulation. Very detailed derivations and analyses of these operators with proper scaling factors are included to avoid the inaccuracy due to iterative solvers. Later we provide pertinent results for all of them for verification and comparison.","abstract_has_math":false,"creators":["Sarker, Palash"],"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":2014,"date_issued":"2014-01-16T18:19:02Z","date_published":"2014-01-16T18:19:02Z","updated_at":"2026-07-22T22:25:38Z","subjects":["Equivalence principle algorithm (EPA)","equivalence principle operator (EPO)","radar cross section (RCS)","translation operator (TO)","tap","vertical-vertical (VV)"],"languages":["en"],"rights":["Copyright 2013 Palash Sarker"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/46863","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":["Sarker, Palash"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2014-01-16T18:19:02Z","2016-01-16T11:02:18Z","2013-12"]},{"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":["Equivalence principle algorithm (EPA)","equivalence principle operator (EPO)","radar cross section (RCS)","translation operator (TO)","tap","vertical-vertical (VV)"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2013 Palash Sarker"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/46863"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["This thesis describes the progressive development analysis of the equivalence principle algorithm (EPA) beginning with the development of various operators that constitute it. 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We begin with the formulation for the electric field integral equation (EFIE), and visit the necessary treatment of the magnetic field integral equation (MFIE), the combined field integral equation (CFIE), and the Poggio-Miller-Chu-Harrington- Wu-Tsai (PMCHWT) along with various singularity extraction schemes before we develop the EPA relations. The explicit expressions of the translation operators are also derived. The EFIE, the MFIE, and the CFIE formulations are used to verify the accuracy of such operators as the L, the K, the nX L, and the n XK operators that are at the heart of the EPA formulation. Very detailed derivations and analyses of these operators with proper scaling factors are included to avoid the inaccuracy due to iterative solvers. 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