Unified conformal/nonconformal domain decomposition methods for solving large-scale multi-region electromagnetic problems

Xue, Mingfeng

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https://hdl.handle.net/2142/72900 Copy

Description

Title

Unified conformal/nonconformal domain decomposition methods for solving large-scale multi-region electromagnetic problems

Author(s)

Xue, Mingfeng

Issue Date

2015-01-21

Director of Research (if dissertation) or Advisor (if thesis)

Jin, Jianming

Doctoral Committee Chair(s)

Jin, Jianming

Committee Member(s)

• Cangellaris, Andreas C.
• Goddard, Lynford L.
• Olson, Luke

Department of Study

Electrical & Computer Eng

Discipline

Electrical & Computer Engr

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

Ph.D.

Degree Level

Dissertation

Keyword(s)

• finite element method (FEM)
• domain decomposition method (DDM)
• dual-primal finite element tearing and interconnecting (FETI-DP)
• Robin-type transmission condition
• second-order transmission condition (SOTC)
• coarse grid correction
• nonconformal mesh
• mesh truncation
• perfectly matched layer (PML)
• broadband antenna
• array structures
• near-field focal lens
• near-field interaction
• far-field radiation
• electromagnetic optics
• integrated optics devices
• subwavelength structures
• photonic crystal (PhC)
• cavity scattering
• monostatic radar cross section (RCS)
• modal expansion method
• Lagrange multiplier
• cement element method
• finite element and boundary integral (FE-BI)
• parallel computing
• message passing interface (MPI)

Abstract

In this dissertation, robust and efficient numerical algorithms are developed based on the dual-primal finite element tearing and interconnecting (FETI-DP) method for the full-wave analysis of large-scale electromagnetic problems in three dimensions. These algorithms are designed to expand the capability of the FETI-DP method to accommodate more flexible interface meshes, to achieve faster convergence of the global interface problem, and to reduce numerical errors caused by the truncation boundary. First, two nonconformal FETI-DP methods are formulated, both of which implement the Robin-type transmission condition at the subdomain interfaces to preserve the fast convergence of the iterative solution of the global interface problem in the high-frequency region. The first nonconformal FETI-DP method extends the conformal FETI-DP algorithm, which is based on two Lagrange multipliers, to deal with nonconformal interface and corner meshes, and the second method employs cement elements on the interface and combines the global primal unknowns with the global dual unknowns. Similar to the conformal FETI-DP method, the two methods formulate a global coarse problem related to the degrees of freedom at the subdomain corner edges to propagate the residual error to the whole computational domain in the iterative solution of the global interface equation. Second, higher-order transmission conditions are proposed and incorporated into the two aforementioned FETI-DP methods to further speed up their convergence rate. Besides propagation modes, transverse electric (TE) and transverse magnetic (TM) evanescent modes can also converge when the higher-order transmission conditions are employed. Third, for multi-region problems, a hybrid method is proposed that employs the finite element tearing and interconnecting (FETI) method to deal with mesh-nonconformal and/or geometry-nonconformal interfaces, where a second-order transmission condition and a crosspoint correction technique are applied to improve the iterative convergence of the interface system and ensure a correct interconnection across subdomain interfaces. For mesh-conformal and geometry-conformal interfaces inside each region, the hybrid method employs the FETI-DP method to construct an effective coarse grid correction for the interface problem. A unified global system of equations is finally formulated for the interface unknowns from both nonconformal and conformal interfaces. Fourth, an oblique absorbing boundary condition (ABC) is applied to the FETI-DP method for simulating large finite semi-periodic arrays. For a plane wave incident on a planar boundary at a certain specified angle, this boundary condition can be tuned to be reflectionless for all frequencies and polarizations. Fifth, waveguide modal fields are employed to expand the dual unknown of the nonconformal FETI method for scattering analysis of deep cavities. The dimension of the resultant global interface system matrix is reduced significantly and a direct solver based on block elimination is further developed to perform fast monostatic radar cross section (RCS) evaluation. Finally, three most advanced finite element domain decomposition solvers are thoroughly and systematically compared in terms of accuracy, convergence rate, computation time, and memory usage through broadband antenna and antenna array examples. Various numerical examples such as wave propagation, radiation by broadband antennas and phased-array antennas, and cavity scattering are presented to validate the proposed algorithms and demonstrate their performance and applications.

Graduation Semester

2014-12

Permalink

http://hdl.handle.net/2142/72900

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Copyright 2014 Mingfeng Xue

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