An O(N) direct volume IE solver with a rank-minimized ℋ2-representation for large-scale 3-D circuit extraction in inhomogeneous materials

A linear-complexity direct matrix solution with a minimal-rank representation for the volume integral equation (VIE) is developed for the fullwave extraction of general 3-D circuits, containing arbitrarily shaped lossy conductors with inhomogeneous dielectrics. Numerical simulations of large-scale 3-D circuits involving millions of unknowns and comparisons with state-of-the-art VIE solvers have demonstrated the accuracy and efficiency of the proposed rank-minimized direct VIE solver.