Solving Electromagnetic Scattering From Dielectric Problems by PMCHWT-SASF

In this paper, a fast direct solver based on strong admissibility skeletonization factorization (SASF) and Poggio-Miller-Chang-Harrington-Wu-Tsai (PMCHWT) is proposed for electromagnetic scattering from conducting objects. Different from weak admissibility skeletonization scheme, the proposed method constructs the sparse-data representation, in which interactions of well-separated groups are compressed by low-rank algorithm. As a result, the approximation rank is relatively small, and the computational efficiency will have significant improvement. Subsequently, SASF is applied to the compressed system matrix. The system matrix can be factorized into products of a series of block unit triangular matrices and a block diagonal matrix. The arising fill-in blocks corresponding to far-field interactions are compressed and eliminated by a novel and efficient method to maintain the high efficiency and accuracy of the factorization procedure. The computational complexity and storage requirement of proposed factorization scale as $O(N^{1.5})$ and $O(N\log N)$ , respectively. Several numerical results are presented to demonstrate the accuracy and effectiveness of the proposed method.