Stable and Compact Inductance Modeling of 3-D Interconnect Structures

Recent successful techniques for the efficient simulation of large-scale interconnect models rely on the sparsification of the inverse of the inductance matrix L. While there are several techniques for sparsifying L^-1, the stability of these approximations for general interconnect structures has not been established, i.e., the sparsified reluctance and inductance matrices are not guaranteed to be positive-definite. In this paper, we present a novel technique for reluctance sparsification for general interconnect structures that enjoys several advantages: first, the resulting sparse approximation is guaranteed to be positive definite; second, the approximation is optimal, in a certain well-defined sense; third, owing to its computational efficiency and numerical stability, the algorithm is applicable for very large problem sizes; and finally our approach yields a compact representation of both inductance and reluctance matrices for general cases