Optimized sparse approximate inverse smoothers for solving Laplacian linear systems
Abstract
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 .
Cite
@article{arxiv.2206.05543,
title = {Optimized sparse approximate inverse smoothers for solving Laplacian linear systems},
author = {Yunhui He and Jun Liu and Xiang-Sheng Wang},
journal= {arXiv preprint arXiv:2206.05543},
year = {2022}
}
Comments
21 pages, 3 figures,1 table