HSS-matrix based fast direct volume integral equation solver for electrodynamic analysis

Abstract

We represent the dense system of volume integral equation (VIE) by an HSS (hierarchically ?emiseparable) matrix. We then exploit the structure of the HSS matrix and develop a fast direct VIE solver. This solver has O(MogN) complexity in factorization, O(N) complexity in matrix solution as well as memory irrespective of electrical size. For solving electrically small problems whose rank is constant, its complexity is strictly O(N) in both time and memory. The HSS-representation has a controlled accuracy; and the direct solution of the HSS matrix does not involve further approximation. Numerical simulations of large-scale scattering problems involving millions of unknowns on a single core CPU have demonstrated its complexity and accuracy.