Optimized sparse approximate inverse smoothers for solving Laplacian linear systems

Autor:	He, Yunhui, Liu, Jun, Wang, Xiang-Sheng
Rok vydání:	2022
Předmět:	Mathematics - Numerical Analysis Computer Science - Distributed Parallel and Cluster Computing 49M25 49K20 65N55 65F10
Druh dokumentu:	Working Paper
Popis:	In this paper we propose and analyze new efficient sparse approximate inverse (SPAI) smoothers for solving the two-dimensional (2D) and three-dimensional (3D) Laplacian linear system with geometric multigrid methods. Local Fourier analysis shows that our proposed SPAI smoother for 2D achieves a much smaller smoothing factor than the state-of-the-art SPAI smoother studied in [Bolten, M., Huckle, T.K. and Kravvaritis, C.D., 2016. Sparse matrix approximations for multigrid methods. Linear Algebra and its Applications, 502, pp.58-76.]. The proposed SPAI smoother for 3D cases provides smaller optimal smoothing factor than that of weighted Jacobi smoother. Numerical results validate our theoretical conclusions and illustrate the high-efficiency and high-effectiveness of our proposed SPAI smoothers. Such SPAI smoothers have the advantage of inherent parallelism. The MATLAB codes for implementing our proposed algorithms are publicly available online at http://github.com/junliu2050/SPAI-MG-Laplacian . Comment: 21 pages, 3 figures,1 table
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2206.05543 Zobrazit plný text záznamu View this record from Arxiv