论文标题
稀疏矩阵的有效代数两级Schwarz预处理
Efficient Algebraic Two-Level Schwarz Preconditioner For Sparse Matrices
论文作者
论文摘要
域分解方法是解决方程式稀疏线性系统的最有效效率之一。它们的有效性依赖于明智选择的粗糙空间。在过去的几年中，最初引入并从理论上被证明是有效的，对于自动伴侣操作员来说，光谱粗空间已提出，对于不确定和非自发接合运算符。本文提出了一个新的光谱粗糙空间，与大多数现有的光谱粗空间不同，该空间可以以完全代数的方式构建。我们介绍了Hermitian阳性明确对角线矩阵的理论收敛结果。在跨部社区中，与最先进的预处理的数值实验和比较表明，由此产生的两级Schwarz预处理效率是有效的，尤其是对于非自我选择的运营商而言。此外，在这种情况下，我们拟议的预定器优于最先进的预处理。
Domain decomposition methods are among the most efficient for solving sparse linear systems of equations. Their effectiveness relies on a judiciously chosen coarse space. Originally introduced and theoretically proved to be efficient for self-adjoint operators, spectral coarse spaces have been proposed in the past few years for indefinite and non-self-adjoint operators. This paper presents a new spectral coarse space that can be constructed in a fully-algebraic way unlike most existing spectral coarse spaces. We present theoretical convergence result for Hermitian positive definite diagonally dominant matrices. Numerical experiments and comparisons against state-of-the-art preconditioners in the multigrid community show that the resulting two-level Schwarz preconditioner is efficient especially for non-self-adjoint operators. Furthermore, in this case, our proposed preconditioner outperforms state-of-the-art preconditioners.
