Analysis of Electromagnetic Scattering From Homogeneous Penetrable Objects by a Strong Skeletonization-Based Fast Direct Solver

Abstract

This article presents a fast direct solver based on surface integral equation (SIE) to solve electromagnetic (EM) scattering from homogeneous penetrable objects. The proposed method relies on a strong admissibility skeletonization factorization (SASF) algorithm and Poggio–Miller–Chang–Harrington–Wu–Tsai (PMCHWT) formulation. In the SASF scheme, only well-separated groups that satisfy the strong admissibility condition are considered to be compressed and thus relatively fewer skeleton basis functions are selected. It is an effective way to compress the matrix with small ranks. An independent compression technique is developed for dielectric problems involving electric and magnetic currents, in which skeleton basis functions representing electric and magnetic currents are obtained separately. Moreover, a novel strategy based on matrix normalization is proposed to treat the arising “fill-in” blocks when far-field interactions are compressed. Ultimately, the impedance matrix can be cast into products of a series of block unit triangular matrices and a block diagonal matrix. Several numerical results show that the proposed approach is effective and stable as well as provides an accurate solution for scattering problems of homogeneous penetrable objects.