ECE 590 - Graduate Seminar on Antennas, Electromagnetics, Optics and Remote Sensing

Antennas, Electromagnetics, Optics and Remote Sensing - ECE 590 Graduate Seminar

Nonconformal FETI-DP Methods and Optimized Schwarz Methods for Large-Scale Electromagnetic Simulation

Mingfeng Xue
University of Illinois


Abstract: Domain decomposition methods (DDMs) in electromagnetics are popular divide-and-conquer strategies to solve large-scale problems. The entire computational domain is divided into multiple smaller subdomains and then solved separately. Subdomain solutions are subsequently iterated while enforcing certain field continuity conditions across the subdomain boundaries. In this talk, two nonconformal dual-primal finite element tearing and interconnecting (FETI-DP) methods are formulated for the finite element simulation of large-scale three-dimensional (3D) electromagnetic problems through DDM. Both methods implement the Robin-type transmission condition (TC) 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 (LM), to deal with nonconformal interface and corner meshes, and the second method employs cement elements (CE) 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. On the other hand, the CE-based nonconformal FETI-DP method is essentially one kind of non-overlapping Schwarz methods, where the Robin-type TC can be modified to second-order for both TE and TM evanescent modes by introducing auxiliary boundary field related terms. Furthermore, Robin parameters can be optimized to obtain the fastest convergence. Accordingly, the coarse space problem needs to be dealt with properly to ensure stable numerical performance for arbitrary decompositions. Numerical results for the simulation of finite antenna arrays, photonic crystal cavities, and dielectric-rod-array metamaterial slabs are presented to demonstrate the application, accuracy, efficiency, and capability of the two proposed nonconformal FETI-DP methods.

Bio: Mingfeng Xue received the BS degree in electronic information engineering from Anhui University, Hefei, China, in 2005, and the M.S. degree in electromagnetic field and microwave technology from Shanghai Jiao Tong University, Shanghai, China, in 2008, respectively. He is currently working towards the Ph.D. degree in electrical and computer engineering at the University of Illinois at Urbana-Champaign. Since 2008, he has been a Research Assistant with the Center for Computational Electromagnetics at the University of Illinois at Urbana-Champaign. His research interests include finite element boundary integral methods, domain decomposition methods, and parallel electromagnetics simulation.