Fast exact-arithmetic O(N) direct volume integral equation solver for large-scale interconnect extraction

We represent the dense system of volume integral equations (VIE) by an HSS (Hierarchically Semiseparable) matrix. We then develop a fast direct VIE solver of O(N) (linear) complexity, including both factorization and inversion, for the extraction of large-scale interconnects involving lossy conductors and inhomogeneous materials. The HSS-representation has a controlled accuracy; and the direct solution of the HSS matrix does not involve any further approximation. Numerical simulations of large-scale interconnects involving millions of unknowns on a single core CPU have demonstrated the superior performance of the proposed direct solver.