Fast Low-Frequency Surface Integral Equation Solver Based on Hierarchical Matrix Algorithm

Abstract

A fast low-frequency surface integral equation solver based on hierarchical matrix algorithm is proposed. First, the augmented electric field integral equation (A-EFIE) formulation is introduced to eliminate the low-frequency breakdown of traditional EFIE. To deal with large-scale problems, the lowfrequency multilevel fast multipole algorithm (LF-MLFMA) is employed to construct a hierarchical (H-) matrix representation of the A-EFIE system matrix. Moreover, a recompression method is developed to further compress the H-matrix generated by LF-MLFMA. The H-matrix-based triangular factorization algorithm can be performed with almost linear computational complexity and memory requirement, which produces a fast direct solver for multiple right-hand-side (RHS) problems, and a good preconditioner to accelerate the convergence rate of an iterative solver. Numerical examples demonstrate the effectiveness of the proposed method for the analysis of various low-frequency problems.