Localized relaxation theory of circuits and its applications in electro-thermal analyses  

作　　者：LUO ZuYing ZHAO GuoXing GORDON Joseph A. TAN Sheldon X.-D. 

机构地区：[1]College of Information Science and Technology,Beijing Normal University,Beijing 100875,China [2]Department of Electrical Engineering,University of California,Riverside,CA 92521,USA

出　　处：《Science China(Information Sciences)》2012年第4期938-950,共13页中国科学（信息科学）（英文版）

基　　金：supported by National High-Tech Research & Development Program of China(Grant No.2009AA01Z126);National Natural Science Foundation of China(Grant Nos.60876025,61076034,61171014);Fundamental Research Funds for the Central Universities

摘　　要：In the high-performance IC design with increasing design complexity, it is a very important design content to efficiently analyze IC parameters. Thus, the electro-thermal （ET） analyses including power/ground （P/G） analysis and thermal analysis are hot topics in today＇s IC research. Since ET analysis equation has a sparse, positive definite and strictly diagonally dominant coefficient-matrix, we prove that the ET analysis has the advantage of locality. Owing to this advantage, localized relaxation method is formally proposed, which has the same accuracy as the global relaxation done with the constraint of the same truncation error limitation. Based on the localized relaxation theory, an efficient and practical localized successive over-relaxation algorithm （LSOR2） is introduced and applied to solve the following three ET analysis problems. （i） Single-node statistical voltage analysis for over-IR-drop nodes in P/G networks; （2） single-node statistical temperature analysis for hot spots in 3D thermal analysis; （3） fast single open-defect analysis for P/G networks. A large amount of experimental data demonstrates that compared with the global successive over-relaxation （SOR） algorithm, LSOR2 can speed up 1-2 orders of magnitudes with the same accuracy in ET analyses.In the high-performance IC design with increasing design complexity, it is a very important design content to efficiently analyze IC parameters. Thus, the electro-thermal （ET） analyses including power/ground （P/G） analysis and thermal analysis are hot topics in today＇s IC research. Since ET analysis equation has a sparse, positive definite and strictly diagonally dominant coefficient-matrix, we prove that the ET analysis has the advantage of locality. Owing to this advantage, localized relaxation method is formally proposed, which has the same accuracy as the global relaxation done with the constraint of the same truncation error limitation. Based on the localized relaxation theory, an efficient and practical localized successive over-relaxation algorithm （LSOR2） is introduced and applied to solve the following three ET analysis problems. （i） Single-node statistical voltage analysis for over-IR-drop nodes in P/G networks; （2） single-node statistical temperature analysis for hot spots in 3D thermal analysis; （3） fast single open-defect analysis for P/G networks. A large amount of experimental data demonstrates that compared with the global successive over-relaxation （SOR） algorithm, LSOR2 can speed up 1-2 orders of magnitudes with the same accuracy in ET analyses.

关 键 词：integrated circuit electro-thermal analysis SOR algorithm power/ground network 

分 类 号：O241.6[理学—计算数学] O657.99[理学—数学]