{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/110840"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/110840","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Fast algorithm and surface integral equations for two-dimensional materials modeling","abstract":"In this dissertation, a wide-band two-dimensional (2D) fast multipole algorithm (FMA) with a novel diagonalization form is presented. The conventional diagonalization of 2D FMA can be derived based on the interpretation of Parseval's theorem. The performance of FMA in the twilight zone (between the low-frequency and high-frequency regimes) is not good enough. By scaling special functions and applying discrete Fourier transform (DFT), the multipole expansions with dense matrices can be transformed to diagonal matrices with stable accuracy. Therefore a broadband 2D FMA with high efficiency and accuracy is achieved with a multi-level scheme. Then a metasurface platform to generate structured light at second harmonics is proposed with transition metal dichalcogenide (TMDC) flakes. With the aid of the electric field integral equation and impedance boundary condition, the surface currents on TMDC flakes can be calculated at fundamental frequencies. By applying three-fold rotational symmetry of the quadratically nonlinear susceptibility of TMDC monolayer, radial (or azimuthal) polarization and orbital angular momentum can be generated at second harmonics with linearly polarized and circularly polarized incident waves at the fundamental frequency, respectively. Finally, the radiative heat transfer between two graphene-wrapped objects with arbitrary shapes is studied by a fluctuating-surface current formulation derived from surface integral equations with impedance boundary conditions. The surface conductivity of graphene can be tuned by the temperature, chemical doping or electrical gating. The near-field thermal radiation can be enhanced due to graphene plasmonics in the terahertz regime. Off resonance, the graphene coating has a shielding effect on the dielectric bodies containing fluctuating-current sources. This formulation can be extended to the multi-body problem and other two-dimensional materials.","abstract_html":"In this dissertation, a wide-band two-dimensional (2D) fast multipole algorithm (FMA) with a novel diagonalization form is presented. The conventional diagonalization of 2D FMA can be derived based on the interpretation of Parseval's theorem. The performance of FMA in the twilight zone (between the low-frequency and high-frequency regimes) is not good enough. By scaling special functions and applying discrete Fourier transform (DFT), the multipole expansions with dense matrices can be transformed to diagonal matrices with stable accuracy. Therefore a broadband 2D FMA with high efficiency and accuracy is achieved with a multi-level scheme. Then a metasurface platform to generate structured light at second harmonics is proposed with transition metal dichalcogenide (TMDC) flakes. With the aid of the electric field integral equation and impedance boundary condition, the surface currents on TMDC flakes can be calculated at fundamental frequencies. By applying three-fold rotational symmetry of the quadratically nonlinear susceptibility of TMDC monolayer, radial (or azimuthal) polarization and orbital angular momentum can be generated at second harmonics with linearly polarized and circularly polarized incident waves at the fundamental frequency, respectively. Finally, the radiative heat transfer between two graphene-wrapped objects with arbitrary shapes is studied by a fluctuating-surface current formulation derived from surface integral equations with impedance boundary conditions. The surface conductivity of graphene can be tuned by the temperature, chemical doping or electrical gating. The near-field thermal radiation can be enhanced due to graphene plasmonics in the terahertz regime. Off resonance, the graphene coating has a shielding effect on the dielectric bodies containing fluctuating-current sources. This formulation can be extended to the multi-body problem and other two-dimensional materials.","abstract_has_math":false,"creators":["Meng, Lingling"],"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","Kudeki, Erhan","Schutt-Aine, Jose E.","Zhu, Wenjuan"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2021,"date_issued":"2021-09-17T04:04:40Z","date_published":"2021-09-17T04:04:40Z","updated_at":"2026-07-22T22:24:52Z","subjects":["Fast multipole algorithm","Two-dimensional materials","Surface integral equations","Structured light","Second-harmonic generation","Radiative heat transfer."],"languages":["en"],"rights":["N/A."],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/110840","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Chew, Weng Cho","Kudeki, Erhan","Schutt-Aine, Jose E.","Zhu, Wenjuan"]},{"key":"dc:creator","label":"Author","values":["Meng, Lingling"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2021-09-17T04:04:40Z","2023-09-17T04:07:01Z","2021-04-21","2021-05"]},{"key":"dc:type","label":"Dc Type","values":["text","Thesis"]},{"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":["Fast multipole algorithm","Two-dimensional materials","Surface integral equations","Structured light","Second-harmonic generation","Radiative heat transfer."]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["N/A."]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/110840"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["In this dissertation, a wide-band two-dimensional (2D) fast multipole algorithm (FMA) with a novel diagonalization form is presented. The conventional diagonalization of 2D FMA can be derived based on the interpretation of Parseval's theorem. The performance of FMA in the twilight zone (between the low-frequency and high-frequency regimes) is not good enough. By scaling special functions and applying discrete Fourier transform (DFT), the multipole expansions with dense matrices can be transformed to diagonal matrices with stable accuracy. Therefore a broadband 2D FMA with high efficiency and accuracy is achieved with a multi-level scheme. Then a metasurface platform to generate structured light at second harmonics is proposed with transition metal dichalcogenide (TMDC) flakes. With the aid of the electric field integral equation and impedance boundary condition, the surface currents on TMDC flakes can be calculated at fundamental frequencies. By applying three-fold rotational symmetry of the quadratically nonlinear susceptibility of TMDC monolayer, radial (or azimuthal) polarization and orbital angular momentum can be generated at second harmonics with linearly polarized and circularly polarized incident waves at the fundamental frequency, respectively. Finally, the radiative heat transfer between two graphene-wrapped objects with arbitrary shapes is studied by a fluctuating-surface current formulation derived from surface integral equations with impedance boundary conditions. The surface conductivity of graphene can be tuned by the temperature, chemical doping or electrical gating. The near-field thermal radiation can be enhanced due to graphene plasmonics in the terahertz regime. Off resonance, the graphene coating has a shielding effect on the dielectric bodies containing fluctuating-current sources. This formulation can be extended to the multi-body problem and other two-dimensional materials.","Submission published under a 24 month embargo labeled 'Closed Access', the embargo will last until 2023-05-01","The student, Lingling Meng, accepted the attached license on 2021-04-19 at 23:26.","The student, Lingling Meng, submitted this Dissertation for approval on 2021-04-19 at 23:51.","This Dissertation was approved for publication on 2021-04-21 at 13:58.","DSpace SAF Submission Ingestion Package generated from Vireo submission #16433 on 2021-09-16 at 20:11:26","Made available in DSpace on 2021-09-17T04:04:40Z (GMT). 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The conventional diagonalization of 2D FMA can be derived based on the interpretation of Parseval's theorem. The performance of FMA in the twilight zone (between the low-frequency and high-frequency regimes) is not good enough. By scaling special functions and applying discrete Fourier transform (DFT), the multipole expansions with dense matrices can be transformed to diagonal matrices with stable accuracy. Therefore a broadband 2D FMA with high efficiency and accuracy is achieved with a multi-level scheme. Then a metasurface platform to generate structured light at second harmonics is proposed with transition metal dichalcogenide (TMDC) flakes. With the aid of the electric field integral equation and impedance boundary condition, the surface currents on TMDC flakes can be calculated at fundamental frequencies. By applying three-fold rotational symmetry of the quadratically nonlinear susceptibility of TMDC monolayer, radial (or azimuthal) polarization and orbital angular momentum can be generated at second harmonics with linearly polarized and circularly polarized incident waves at the fundamental frequency, respectively. Finally, the radiative heat transfer between two graphene-wrapped objects with arbitrary shapes is studied by a fluctuating-surface current formulation derived from surface integral equations with impedance boundary conditions. The surface conductivity of graphene can be tuned by the temperature, chemical doping or electrical gating. The near-field thermal radiation can be enhanced due to graphene plasmonics in the terahertz regime. Off resonance, the graphene coating has a shielding effect on the dielectric bodies containing fluctuating-current sources. This formulation can be extended to the multi-body problem and other two-dimensional materials.","Submission published under a 24 month embargo labeled 'Closed Access', the embargo will last until 2023-05-01","The student, Lingling Meng, accepted the attached license on 2021-04-19 at 23:26.","The student, Lingling Meng, submitted this Dissertation for approval on 2021-04-19 at 23:51.","This Dissertation was approved for publication on 2021-04-21 at 13:58.","DSpace SAF Submission Ingestion Package generated from Vireo submission #16433 on 2021-09-16 at 20:11:26","Made available in DSpace on 2021-09-17T04:04:40Z (GMT). No. of bitstreams: 2 MENG-DISSERTATION-2021.pdf: 10600058 bytes, checksum: c4a16987c4a0fb838141c8a7223d9fcb (MD5) LICENSE.txt: 4210 bytes, checksum: 56ed1838f101a997e572c9f8a6f2c65c (MD5) Previous issue date: 2021-04-21","Embargo set by: Seth Robbins for item 118685 Lift date: 2023-09-17T04:04:53Z Reason: Author requested closed access (OA after 2yrs) in Vireo ETD system","Embargo set by: Seth Robbins for item 118685 Lift date: 2023-09-17T04:07:01Z Reason: Author requested closed access (OA after 2yrs) in Vireo ETD system","Author requested closed access (OA after 2yrs) in Vireo ETD system","Limited"],"dc:format":["application/pdf"],"dc:identifier":["http://hdl.handle.net/2142/110840"],"dc:language":["en"],"dc:rights":["N/A."],"dc:subject":["Fast multipole algorithm","Two-dimensional materials","Surface integral equations","Structured light","Second-harmonic generation","Radiative heat transfer."],"dc:title":["Fast algorithm and surface integral equations for two-dimensional materials modeling"],"dc:type":["text","Thesis"],"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":"2026-07-22T22:24:52Z"}