加速SPICE进行三维电磁分析

Speed up SPICE in the 3-D Electromagnetic Analysis

互连结构的电磁分析越来越受到人们的重视.针对三维互连,A.E.Ruehli提出了部分元等效电路法.但该法生成的等效电路具有紧耦合性,用SPICE进行分析时稀疏矩阵技术已失去原先的优越性.本文采用广义残量法作为大型紧耦合线性方程组的求解工具以取代SPICE中的LU分解法,并辅以初值预估.实际计算表明,本文的方法提高了运算速度.广义残量法也可用于矩量法的方程求解中.

The electromagnetic analysis of interconnection structure is calling for more attention. For 3-D interconnection, A. E. Ruehli proposed the Partial Element Equivalent Circuit (PEEC). which results in the dense coupling between equivalent elements. The elegance of sparse matrix technique in SPICE is lost in the analysis of PEEC. This paper applies Generalized Minimal Residual (GMRES) as the solver for large scale densely coupled linear equations to replace LU factorization in SPICE with the introduction of initial value prediction. Computations demonstrate the conspicuous speed improvement. GMRES can also be used as an equation solver in moment method.