Abstract:
State-of-the-art fast computational electromagnetic methods rely on iterative matrix solutions to solve large-scale problems. The optimal complexity of an iterative solver is O(NN_{it}N_{rhs}) with N being matrix size, N_{it} the number of iterations and N_{rhs} the number of right hand sides. For a different right hand side, an iterative solver has to repeat the entire iteration procedure. How to invert or factorize a dense matrix or a sparse matrix of size N in O(N) (optimal) complexity has been a challenging open problem. In this talk, I will present an O(N) direct integral equation solver and an O(N) direct finite element solver for solving Maxwell’s equations in a complicated integrated circuit environment having arbitrarily shaped 3-D non-ideal conductors and inhomogeneous dielectric materials. The proposed direct integral equation solver has inverted a dense matrix resulting from the interconnect extraction having 3.71 million unknowns and 576 conductors in fast CPU time (1.6 hours), modest memory consumption (4.4 GB), and with prescribed accuracy satisfied on a single core running at 3 GHz. The proposed direct finite element solver has successfully analyzed an industry package involving over 8.5 million unknowns in 1.5 hours on the same computer. Comparisons with state-of-the-art iterative solvers have shown clear advantages of the proposed linear-complexity direct solvers. Since matrix inverse and LU factorization/solution are fundamental building blocks in computation, this work can also benefit other science and engineering disciplines in which fast and large-scale computation is being pursued.

Bio:
Professor 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 as an assistant professor in the School of Electrical and Computer Engineering, where she is now a full professor. She has authored two book chapters and over 200 papers in refereed journals and international conferences. Professor 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 has served on the Technical Program Committees of premium conferences in electromagnetics, microwave, and circuits. She has been an associated editor of the IEEE Transactions on Components, Packaging and Manufacturing Technology.