Direct Finite Element Solver of Linear Complexity for Analyzing Electrically Large Problems

Abstract: Driven by the design of advanced engineering systems, it becomes necessary to continuously reduce the complexity of computational electromagnetic methods to meet the real-world challenges. The best complexity of the state-of-the-art finite element solvers for solving 3-D electromagnetic problems is $O(N_{it}N_{rhs}N)$ for iterative methods and $O(N^2)$ for direct methods, where $N$ is matrix size, $N_{it}$ is the number of iterations, and $N_{rhs}$ is the number of right hand sides. Neither of the complexities has reached the optimal complexity for solving $N$ parameters, which is $O(N)$.

In this work, we have developed a direct finite element solver of linear ($O(N)$) complexity for general 3-D electromagnetic analysis including both full-wave circuit extraction and the analysis of electrically large antennas. Both theoretical analysis and numerical experiments have demonstrated the solver’s linear complexity in CPU time and memory consumption with prescribed accuracy satisfied. The proposed direct solver has successfully analyzed an industry product-level full package involving over 22.8488 million unknowns in approximately 16 hours on a single core running at 3 GHz. It has also rapidly solved large-scale antenna arrays of over 73 wavelengths with 3,600 antenna elements whose number of unknowns is over 10 million. The proposed direct solver has been compared with the finite element methods that utilize the most advanced direct sparse solvers and a widely used commercial iterative finite element solver. Clear advantages of the proposed solver in time and memory complexity as well as computational efficiency have been demonstrated.


Prof. Dan Jiao received her Ph.D. degree in Electrical Engineering from the University of Illinois at Urbana-Champaign in October 2001. She then worked at the Technology CAD (Computer-Aided-Design) Division at the Intel Corporation until September 2005 as Senior Engineer, Staff Engineer, and Senior Staff Engineer. In September 2005, she joined Purdue University in the School of Electrical and Computer Engineering, where she is now a Full Professor. She has authored two book chapters and over 230 papers in refereed journals and international conferences. Prof. Jiao has received numerous awards including the 2000 Raj Mittra Outstanding Research Award, the 2004 Best Paper Award from Intel’s annual technology conference (Design and Test Technology Conference), the 2008 National Science Foundation CAREER Award, the 2010 Ruth and Joel Spira Outstanding Teaching Award, and the 2013 Sergei A. Schelkunoff Best Paper Award of the IEEE Antennas and Propagation Society. Prof. Jiao is a Fellow of the IEEE.

Guest Lectuer: Dan Jiao, School of Electrical and Computer Engineering Purdue University, USA

Date and Time: 10:00am-11:30am, Feb. 27, 2016   

Location: Room 108, Administration Building, Yuquan Campus

Audience: Faculty/Staff, Students

Category: Lecture

Sponsor: College of Information Science & Electronic Engineering, Zhejiang University


Admission: Free