Abstract
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.
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