Strong Admissibility Skeletonization Factorization for Fast Direct Solution of Electromagnetic Scattering From Conducting Objects

Abstract

In this article, a fast direct solver based on strong admissibility skeletonization factorization (SASF) is proposed for electromagnetic scattering from conducting objects. Different from the conventional skeletonization scheme, the proposed skeletonization constructs the hierarchical matrix representation, in which only far-field interactions are compressed. As a result, the approximation rank is relatively small, and the computational efficiency will have significant improvement. Subsequently, the strong skeletonization factorization 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 the proposed factorization scale as <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$O(N^{1.5})$ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$O(N \log N)$ </tex-math></inline-formula> , respectively. Several numerical results are presented to demonstrate the accuracy and effectiveness of the proposed method.