A fast band matching technique for impedance extraction

We present an efficient technique for the fast and accurate extraction of inductance of large-scale on-chip interconnects. Several simulation techniques exploit the sparsity of L^-1 for reducing storage and computational costs during computation. Recently, band matching technique was introduced for sparsification of L^-1. We extend the band-matching technique for inductance extraction problems. We introduce an efficient technique to invert the approximate band-matched impedance matrix R_f + jomegaL_f. The new technique relies on a numerically stable and efficient representation for inverses of banded matrices. Numerical results show that our approach is both accurate as well as computationally efficient, with orders-of-magnitude improvement over traditional techniques.