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postgraduate thesis: Advanced finite element methodology for lowfrequency and static electromagnetic modeling
Title  Advanced finite element methodology for lowfrequency and static electromagnetic modeling 

Authors  
Issue Date  2015 
Publisher  The University of Hong Kong (Pokfulam, Hong Kong) 
Citation  Li, Y. [黎燕林]. (2015). Advanced finite element methodology for lowfrequency and static electromagnetic modeling. (Thesis). University of Hong Kong, Pokfulam, Hong Kong SAR. Retrieved from http://dx.doi.org/10.5353/th_b5610957 
Abstract  The design of stateoftheart microelectronic devices poses unprecedented challenges to computational electromagnetics (CEM), which is cursed by the null space of curl operator. Both the lowfrequency catastrophe for dynamic electromagnetic problems and nonuniqueness for magnetostatic problems originate from the null space. Although a few remedies are proposed during the last decade, a theoretically rigorous and numerically efficient solution is still on its way.
Toward this end, this thesis constructs a finite element framework, which consists of generalized gauge condition, compatible finite element discretization, sparse approximate inverse (SAI) technique and static incomplete LU (ILU) preconditioned iterative solution.
The generalized gauge condition introduces a gauge operator, which is comparable in magnitude and complementary in space with the double curl operator, into the original governing equations. The null space is removed and the combined operator becomes positive definite. However, the combined operator is so complicated that its discretization and matrix representation are unclear. Thanks to the theory of differential forms, the mapping of the quantity of interest from one form to another becomes distinct. Hence, the compatible discretization can be carried out based on the versatile Whitney elements. The resultant matrix system is much better conditioned than that of the ungauged one, whereas more treatment is still necessary to make it less sparse and faster convergent.
The SAI and ILU preconditioning techniques provide an excellent solution to this difficulty. The former approximates the inverse of a mass matrix by a nearlydiagonal matrix, which greatly reduces the sparsity of the matrix system. The later shifts all the eigenvalues to the neighborhood of 1 and thus achieves an extremely fast convergence. Moreover, the static incomplete LU (ILU) preconditioning scheme is well suited to wideband analysis, because the preconditioner is calculated just once for a wide range of frequency.
This framework is verified, by lowfrequency circuit problems as well as magnetostatic ones, to be accurate and efficient.
In addition, more effort is devoted to explore other possibilities to solve the aforementioned problem. The application of loop basis functions is also a promising solution, provided that the redundant loops in the mesh can be removed.
Finally, the displacement current effect is studied in depth by a fullwave semianalytical solution of wireless power transfer into dispersive layered media. The comparison between the results with and without the displacement current advocates the fullwave electromagnetic modeling for multiscale problems and wideband analysis. 
Degree  Doctor of Philosophy 
Subject  Finite element method Electromagnetism  Computer simulation 
Dept/Program  Electrical and Electronic Engineering 
Persistent Identifier  http://hdl.handle.net/10722/221192 
HKU Library Item ID  b5610957 
DC Field  Value  Language 

dc.contributor.author  Li, Yanlin   
dc.contributor.author  黎燕林   
dc.date.accessioned  20151104T23:11:57Z   
dc.date.available  20151104T23:11:57Z   
dc.date.issued  2015   
dc.identifier.citation  Li, Y. [黎燕林]. (2015). Advanced finite element methodology for lowfrequency and static electromagnetic modeling. (Thesis). University of Hong Kong, Pokfulam, Hong Kong SAR. Retrieved from http://dx.doi.org/10.5353/th_b5610957   
dc.identifier.uri  http://hdl.handle.net/10722/221192   
dc.description.abstract  The design of stateoftheart microelectronic devices poses unprecedented challenges to computational electromagnetics (CEM), which is cursed by the null space of curl operator. Both the lowfrequency catastrophe for dynamic electromagnetic problems and nonuniqueness for magnetostatic problems originate from the null space. Although a few remedies are proposed during the last decade, a theoretically rigorous and numerically efficient solution is still on its way. Toward this end, this thesis constructs a finite element framework, which consists of generalized gauge condition, compatible finite element discretization, sparse approximate inverse (SAI) technique and static incomplete LU (ILU) preconditioned iterative solution. The generalized gauge condition introduces a gauge operator, which is comparable in magnitude and complementary in space with the double curl operator, into the original governing equations. The null space is removed and the combined operator becomes positive definite. However, the combined operator is so complicated that its discretization and matrix representation are unclear. Thanks to the theory of differential forms, the mapping of the quantity of interest from one form to another becomes distinct. Hence, the compatible discretization can be carried out based on the versatile Whitney elements. The resultant matrix system is much better conditioned than that of the ungauged one, whereas more treatment is still necessary to make it less sparse and faster convergent. The SAI and ILU preconditioning techniques provide an excellent solution to this difficulty. The former approximates the inverse of a mass matrix by a nearlydiagonal matrix, which greatly reduces the sparsity of the matrix system. The later shifts all the eigenvalues to the neighborhood of 1 and thus achieves an extremely fast convergence. Moreover, the static incomplete LU (ILU) preconditioning scheme is well suited to wideband analysis, because the preconditioner is calculated just once for a wide range of frequency. This framework is verified, by lowfrequency circuit problems as well as magnetostatic ones, to be accurate and efficient. In addition, more effort is devoted to explore other possibilities to solve the aforementioned problem. The application of loop basis functions is also a promising solution, provided that the redundant loops in the mesh can be removed. Finally, the displacement current effect is studied in depth by a fullwave semianalytical solution of wireless power transfer into dispersive layered media. The comparison between the results with and without the displacement current advocates the fullwave electromagnetic modeling for multiscale problems and wideband analysis.   
dc.language  eng   
dc.publisher  The University of Hong Kong (Pokfulam, Hong Kong)   
dc.relation.ispartof  HKU Theses Online (HKUTO)   
dc.rights  The author retains all proprietary rights, (such as patent rights) and the right to use in future works.   
dc.rights  This work is licensed under a Creative Commons AttributionNonCommercialNoDerivatives 4.0 International License.   
dc.subject.lcsh  Finite element method   
dc.subject.lcsh  Electromagnetism  Computer simulation   
dc.title  Advanced finite element methodology for lowfrequency and static electromagnetic modeling   
dc.type  PG_Thesis   
dc.identifier.hkul  b5610957   
dc.description.thesisname  Doctor of Philosophy   
dc.description.thesislevel  Doctoral   
dc.description.thesisdiscipline  Electrical and Electronic Engineering   
dc.description.nature  published_or_final_version   