2026-09-20T18:58:47Z https://www.ideals.illinois.edu/oai-pmh

oai:www.ideals.illinois.edu:2142/108327 2023-07-11 col_2142_5131 col_2142_8859 com_2142_5130 com_2142_8858 com_2142_234

Chew, Weng Cho Cooper, S Lance Hirani, Anil N. Aluru, Narayana R. Chen, Shu 2020-08-27T00:51:28Z 2020-08-27T00:51:28Z 2022-08-27T00:51:40Z 2020-05-08 2020-05 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). No. of bitstreams: 4 CHEN-DISSERTATION-2020.pdf: 10337347 bytes, checksum: b80cd4496934510569aca5aadda1a97e (MD5) THESIS_LATEX_SHUCHEN.zip: 32975241 bytes, checksum: 2bd82fd4019bca7e12da78832b4b8237 (MD5) LICENSE.txt: 4205 bytes, checksum: 9ab2927e82365728748223f5a38bc2e5 (MD5) PROQUEST_LICENSE.txt: 4551 bytes, checksum: 2fc76388f7f5c92a8bbc91709acc7168 (MD5) Previous issue date: 2020-05-08 Embargo set by: Seth Robbins for item 115942 Lift date: 2022-08-27T00:51:40Z Reason: Author requested closed access (OA after 2yrs) in Vireo ETD system Author requested closed access (OA after 2yrs) in Vireo ETD system Limited application/pdf http://hdl.handle.net/2142/108327 en Copyright 2020 Shu Chen DEC Computational electromagnetics Near Field Heat transfer FEM Electromagnetic analysis with discrete exterior calculus text Thesis Physics Physics University of Illinois at Urbana-Champaign Dissertation Ph.D.