NDLI: An unconditionally stable time-domain finite element method of significantly reduced computational complexity for large-scale simulation of IC and package problems

Content Provider	IEEE Xplore Digital Library
Author	Gan, H. Dan Jiao
Copyright Year	2009
Description	Author affiliation: School of Electrical and Computer Engineering, Purdue University, 465 Northwestern Avenue, West Lafayette, IN 47907 (Gan, H.; Dan Jiao)
Abstract	An unconditionally stable and computationally efficient time-domain finite-element method is developed to solve large-scale IC and package problems. In this method, an analytical expression of the time dependence is developed for the field unknowns inside conductors. And hence any time step can be used to stably solve the system of equations inside conductors. A matrix solution is involved in the analytical expression. It is efficiently obtained by the time-domain finite-element reduction-recovery method, the factorization cost of which is O(M), with M much less than the system matrix size N. The system of equations exterior to conductors is formed by a backward difference method, and hence is also unconditionally stable. The resultant system matrix is solved efficiently by an H-matrix based direct sparse solver, which is shown to outperform the state-of-the-art direct sparse solver. The system exterior to the conductors and that interior to the conductors are then solved by a staggered marching scheme, the convergence of which is theoretically proved. Applications to on-chip problems have demonstrated a time step that is three orders of magnitude larger than what is permitted by an explicit time-domain scheme, with fast CPU run time, modest memory consumption, and without sacrificing accuracy.
Starting Page	145
Ending Page	148
File Size	262894
Page Count	4
File Format	PDF
ISBN	9781424444472
DOI	10.1109/EPEPS.2009.5338457
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2009-10-19
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Time domain analysis Finite element methods Computational complexity Large-scale systems Computational modeling Integrated circuit modeling Integrated circuit packaging Conductors Equations Sparse matrices package Unconditionally stable schemes fast solvers electromagnetic simulation time domain on-chip
Content Type	Text
Resource Type	Article

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