We develop a linear-complexity direct matrix solution for the surface integral equation (IE)-based impedance extraction of arbitrarily shaped 3-D nonideal conductors embedded in a dielectric material. A direct inverse of a highly irregular system matrix composed of both dense and sparse matrix blocks is obtained inO(N) complexity withNbeing the matrix size. It outperforms state-of-the-art impedance solvers, be they direct solvers or iterative solvers, with fast central processing unit (CPU) time, modest memory consumption, and without sacrificing accuracy, for both small and large number of unknowns. The inverse of a 2.68-million-unknown matrix arising from the extraction of a large-scale 3-D interconnect having 128 buses, which is a matrix solution for 2.68 million right-hand sides, was obtained in less than 1.5 GB memory and 1.3 h on a single CPU running at 3 GHz.

A linear-complexity direct matrix solution is developed for the surface-integral based impedance extraction of arbitrarily-shaped 3-D non-ideal conductors embedded in dielectric materials. It outperforms state-of-the-art impedance solvers with fast CPU-time, modest memory-consumption, and without sacrificing accuracy. The inverse of a 2.6-million-unknown matrix arising from the extraction of large-scale 3-D interconnects was obtained in 1.5 GB memory and 1.3 hours on a 3 GHz CPU.

State-of-the-art integral-equation-based solvers rely on techniques that can perform a matrix-vector multiplication in O(N) complexity. In this work, a fast inverse of linear complexity was developed to solve a dense system of linear equations directly for the capacitance extraction of any arbitrary shaped 3D structure. The proposed direct solver has demonstrated clear advantages over state-of-the-art solvers such as FastCap and HiCap; with fast CPU time and modest memory consumption, and without sacrificing accuracy. It successfully inverts a dense matrix that involves more than one million unknowns associated with a large-scale on-chip 3D interconnect embedded in inhomogeneous materials. Moreover, we have successfully applied the proposed solver to full-wave extraction.