论文标题
优化的稀疏近似逆SmoOther用于求解拉普拉斯线性系统
Optimized sparse approximate inverse smoothers for solving Laplacian linear systems
论文作者
论文摘要
在本文中，我们提出和分析了使用几何多机方法的新有效的稀疏近似逆（SPAI）SMOOTHOTH，以解决二维（2D）和三维（3D）Laplacian线性系统。局部傅立叶分析表明，我们提出的2D的SPAI更平滑，比[Bolten，M.，Huckle，T.K。所研究的最先进的SPAI更平滑的平滑因子都要小得多。和Kravvaritis，C.D.，2016年。多根方法的稀疏基质近似值。线性代数及其应用，502，pp.58-76。]。与加权Jacobi更平滑的3D案例相比，提出的SPAI更光滑可提供最佳的平滑因子。数值结果验证了我们的理论结论，并说明了我们提出的SPAI SMOOTHOTHE的高效和高效效率。这样的Spai Smoother具有固有的并行性的优势。实施我们提出的算法的MATLAB代码可在http://github.com/junliu2050/spai-mg-laplacian上在线公开获取。
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 .
