{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/15564"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/15564","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"An enhanced volume integral equation method and augmented equivalence principle algorithm for low frequency problems","abstract":"Two techniques based on integral equation methods are addressed. Firstly, a novel volume integral equation method is proposed to characterize the scattering properties of dielectric objects involving inhomogeneous and anisotropic permittivity and permeability. Two algorithms are available: conventional method of moments and reciprocity preserving method. Both of them are applied to both the permittivity and permeability terms. Curl-conforming edge elements are used to model the electric field distributions. Integration by parts is applied to deal with the singularities at the boundary introduced by the discontinuities of the material properties. Duffy's method formulations are derived for all the surface and volume singular integrations. Moreover, the multilevel fast multipole algorithm (MLFMA) is utilized to accelerate the matrix vector product process for large problems. Representative numerical results are shown to be excellent. Secondly, the present equivalence principle algorithm (EPA) is augmented by introducing charge densities as extra unknowns. This helps to separate the vector potential term and scalar potential term and avoid the imbalance at low frequencies. The current continuity constraint is enforced in both the scattering operator and translation operator. These further form a new augmented EPA equation system. With this technique, the low-frequency breakdown of EPA is removed. The augmented system serves not only as a stable low-frequency method, but also as a substitute over the whole frequency band. The new scheme is verified by numerical examples.","abstract_html":"Two techniques based on integral equation methods are addressed. Firstly, a novel volume integral equation method is proposed to characterize the scattering properties of dielectric objects involving inhomogeneous and anisotropic permittivity and permeability. Two algorithms are available: conventional method of moments and reciprocity preserving method. Both of them are applied to both the permittivity and permeability terms. Curl-conforming edge elements are used to model the electric field distributions. Integration by parts is applied to deal with the singularities at the boundary introduced by the discontinuities of the material properties. Duffy's method formulations are derived for all the surface and volume singular integrations. Moreover, the multilevel fast multipole algorithm (MLFMA) is utilized to accelerate the matrix vector product process for large problems. Representative numerical results are shown to be excellent. Secondly, the present equivalence principle algorithm (EPA) is augmented by introducing charge densities as extra unknowns. This helps to separate the vector potential term and scalar potential term and avoid the imbalance at low frequencies. The current continuity constraint is enforced in both the scattering operator and translation operator. These further form a new augmented EPA equation system. With this technique, the low-frequency breakdown of EPA is removed. The augmented system serves not only as a stable low-frequency method, but also as a substitute over the whole frequency band. The new scheme is verified by numerical examples.","abstract_has_math":false,"creators":["Sun, Lin"],"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","Bernhard, Jennifer T.","Wong, Martin D.F."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2010,"date_issued":"2010-05-14T20:50:34Z","date_published":"2010-05-14T20:50:34Z","updated_at":"2026-07-22T22:25:08Z","subjects":["Enhanced Volume Integral Equation Method","Equivalence Principle Algorithm","Augmentation Technique","Low Frequency Problems"],"languages":["en"],"rights":["Copyright 2010 Lin Sun"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/15564","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","Bernhard, Jennifer T.","Wong, Martin D.F."]},{"key":"dc:creator","label":"Author","values":["Sun, Lin"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2010-05-14T20:50:34Z","2012-05-15T10:00:32Z","2010-5"]},{"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":["Enhanced Volume Integral Equation Method","Equivalence Principle Algorithm","Augmentation Technique","Low Frequency Problems"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2010 Lin Sun"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/15564"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Two techniques based on integral equation methods are addressed. Firstly, a novel volume integral equation method is proposed to characterize the scattering properties of dielectric objects involving inhomogeneous and anisotropic permittivity and permeability. Two algorithms are available: conventional method of moments and reciprocity preserving method. Both of them are applied to both the permittivity and permeability terms. Curl-conforming edge elements are used to model the electric field distributions. Integration by parts is applied to deal with the singularities at the boundary introduced by the discontinuities of the material properties. Duffy's method formulations are derived for all the surface and volume singular integrations. Moreover, the multilevel fast multipole algorithm (MLFMA) is utilized to accelerate the matrix vector product process for large problems. Representative numerical results are shown to be excellent. Secondly, the present equivalence principle algorithm (EPA) is augmented by introducing charge densities as extra unknowns. This helps to separate the vector potential term and scalar potential term and avoid the imbalance at low frequencies. The current continuity constraint is enforced in both the scattering operator and translation operator. These further form a new augmented EPA equation system. With this technique, the low-frequency breakdown of EPA is removed. The augmented system serves not only as a stable low-frequency method, but also as a substitute over the whole frequency band. The new scheme is verified by numerical examples.","Item withdrawn by Mark Zulauf (zulauf@illinois.edu) on 2010-04-14T20:16:12Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 1 Sun_Lin.pdf: 7295371 bytes, checksum: 9068a255cb758b60181023fde7265169 (MD5)","Made available in DSpace on 2010-05-14T20:50:34Z (GMT). No. of bitstreams: 2 Sun_Lin.pdf: 7295371 bytes, checksum: 9068a255cb758b60181023fde7265169 (MD5) license.txt: 4055 bytes, checksum: ad6516d6786a090ac3e98bc0ebaae5c7 (MD5)","Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by William Ingram (wingram2@illinois.edu) on 2010-05-14T20:52:46Z Item is restricted until 2012-05-14T20:52:43Z","Item reinstated by Sarah Shreeves (sshreeve@illinois.edu) on 2012-05-15T10:00:32Z Item was in collections: University of Illinois Dissertations and Theses (ID: 204) Dissertations and Theses - Electrical and Computer Engineering (ID: 446) No. of bitstreams: 3 Sun_Lin.pdf.txt: 137889 bytes, checksum: 1b6daee03880f48ec229551b925dbba7 (MD5) Sun_Lin.pdf: 7295371 bytes, checksum: 9068a255cb758b60181023fde7265169 (MD5) license.txt: 4055 bytes, checksum: ad6516d6786a090ac3e98bc0ebaae5c7 (MD5)","Item released from any restrictions by Sarah Shreeves (sshreeve@illinois.edu) on 2012-05-15T10:00:32Z"]},{"key":"dc:title","label":"Title","values":["An enhanced volume integral equation method and augmented equivalence principle algorithm for low frequency problems"]}]}],"canonical_facts":{"dc:contributor":["Chew, Weng Cho","Jin, Jianming","Bernhard, Jennifer T.","Wong, Martin D.F."],"dc:creator":["Sun, Lin"],"dc:date":["2010-05-14T20:50:34Z","2012-05-15T10:00:32Z","2010-5"],"dc:description":["Two techniques based on integral equation methods are addressed. Firstly, a novel volume integral equation method is proposed to characterize the scattering properties of dielectric objects involving inhomogeneous and anisotropic permittivity and permeability. Two algorithms are available: conventional method of moments and reciprocity preserving method. Both of them are applied to both the permittivity and permeability terms. Curl-conforming edge elements are used to model the electric field distributions. Integration by parts is applied to deal with the singularities at the boundary introduced by the discontinuities of the material properties. Duffy's method formulations are derived for all the surface and volume singular integrations. Moreover, the multilevel fast multipole algorithm (MLFMA) is utilized to accelerate the matrix vector product process for large problems. Representative numerical results are shown to be excellent. Secondly, the present equivalence principle algorithm (EPA) is augmented by introducing charge densities as extra unknowns. This helps to separate the vector potential term and scalar potential term and avoid the imbalance at low frequencies. The current continuity constraint is enforced in both the scattering operator and translation operator. These further form a new augmented EPA equation system. With this technique, the low-frequency breakdown of EPA is removed. The augmented system serves not only as a stable low-frequency method, but also as a substitute over the whole frequency band. The new scheme is verified by numerical examples.","Item withdrawn by Mark Zulauf (zulauf@illinois.edu) on 2010-04-14T20:16:12Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 1 Sun_Lin.pdf: 7295371 bytes, checksum: 9068a255cb758b60181023fde7265169 (MD5)","Made available in DSpace on 2010-05-14T20:50:34Z (GMT). No. of bitstreams: 2 Sun_Lin.pdf: 7295371 bytes, checksum: 9068a255cb758b60181023fde7265169 (MD5) license.txt: 4055 bytes, checksum: ad6516d6786a090ac3e98bc0ebaae5c7 (MD5)","Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by William Ingram (wingram2@illinois.edu) on 2010-05-14T20:52:46Z Item is restricted until 2012-05-14T20:52:43Z","Item reinstated by Sarah Shreeves (sshreeve@illinois.edu) on 2012-05-15T10:00:32Z Item was in collections: University of Illinois Dissertations and Theses (ID: 204) Dissertations and Theses - Electrical and Computer Engineering (ID: 446) No. of bitstreams: 3 Sun_Lin.pdf.txt: 137889 bytes, checksum: 1b6daee03880f48ec229551b925dbba7 (MD5) Sun_Lin.pdf: 7295371 bytes, checksum: 9068a255cb758b60181023fde7265169 (MD5) license.txt: 4055 bytes, checksum: ad6516d6786a090ac3e98bc0ebaae5c7 (MD5)","Item released from any restrictions by Sarah Shreeves (sshreeve@illinois.edu) on 2012-05-15T10:00:32Z"],"dc:identifier":["http://hdl.handle.net/2142/15564"],"dc:language":["en"],"dc:rights":["Copyright 2010 Lin Sun"],"dc:subject":["Enhanced Volume Integral Equation Method","Equivalence Principle Algorithm","Augmentation Technique","Low Frequency Problems"],"dc:title":["An enhanced volume integral equation method and augmented equivalence principle algorithm for low frequency problems"],"thesis:degree_discipline":["Electrical & Computer Engr"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:25:08Z"}