Announcement of Professor Dan Jiao's Seminar
Title: Direct Finite Element Solver of Linear Complexity for Analyzing Electrically Large Problems
Time: 2 月 27 日 上午 10: 00-11: 30
Venue: Conference Room 108, Administration Building
reporter：Dan Jiao School of Electrical and Computer Engineering Purdue University
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.
Bio:
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 Techno
