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在复杂度日益增高的高性能集成电路设计中,高效的性能分析是一项重要的设计内容,其中由电源线/地线网络(P/G)分析与芯片热分析构成的电热分析则是目前研究的热点问题.针对电热分析方程所具有的大规模稀疏(电导或热导)系数矩阵,根据该系数矩阵所具有的对称正定严格对角占优等特性,本文从理论上证明了电热分析具有局部性,在相同的截断误差限松弛结束条件下,局部松弛和全局松弛具有相同的松弛精度.基于局部松弛理论,本文提出了一个高效实用的局部过松弛(SOR)算法(LSOR2),并在文章最后将其用于如下的3个具体的电热分析问题研究:(1)P/G网中的过压降点电压变化统计分析;(2)3D热分析中的过热点温度变化统计分析;(3)单开路故障下的P/G网快速分析.实验数据表明:与全局SOR算法相比,在保证精度的前提下,LSOR2算法可以将电热分析的求解速度提高1-2个数量级.
In the increasingly complex high-performance integrated circuit design, efficient performance analysis is an important part of the design, which consists of power line / ground network (P / G) analysis and thermal analysis of chip thermal analysis is the current The hot issues of this paper.According to the large-scale sparse (conductance or thermal conductivity) matrices that the electrothermal analysis equation has, based on the strictly positive symmetry positive definite diagonal dominant characteristic of the coefficient matrix, this paper theoretically proves that the electrothermal analysis has a local The local relaxation and the global relaxation have the same relaxation accuracy under the condition of the same relaxation limit of the truncation error.Based on the local relaxation theory, an efficient and practical local relaxation (SOR) algorithm (LSOR2) is proposed in this paper, Finally, it is applied to the following three specific problems of electrothermal analysis: (1) Statistic analysis of the voltage drop of over voltage drop point in P / G network; (2) Statistical analysis of the change of overheating point temperature in 3D thermal analysis; ( 3) Fast analysis of P / G network under single open fault The experimental data show that compared with global SOR algorithm, LSOR2 algorithm can improve the speed of solving electro-thermal analysis by one to two orders of magnitude on the premise of ensuring accuracy.