A Butterfly-Accelerated Volume Integral Equation Solver for Large-Scale Electromagnetic Analysis

Abstract

A butterfly acceleration scheme is proposed for the fast solution of volume integral equation (VIE). The proposed scheme efficiently constructs the method of moments (MoM) matrix in the compressed format and obtains an approximate inverse of the MoM matrix, used as a highly effective preconditioner. The proposed scheme enables to efficiently solve problems involving millions of unknowns. Furthermore, it requires much less computational resources compared to $\mathcal{H}$ matrix scheme for the electromagnetic (EM) scattering analysis of electrically large structures.