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.
翻译:域分解法是解决稀有的线性方程式的最有效方法之一。 其有效性取决于明智选择的粗粗空间。 最初引入并在理论上证明对自联合操作员有效, 过去几年中为无限期和非自联合操作员提议了光谱粗空格。 本文展示了一个新的光谱粗格空间, 可以用与大多数现有光谱粗略空间不同的完全通热方式构建。 我们展示了赫米蒂安正对角占优势矩阵的理论趋同结果。 与多电网群群中最先进的先决条件者相比, 数字实验和比较表明, 由此产生的双级Schwarz先决条件是有效的, 特别是对于非自联合操作员。 此外, 在本案中, 我们提出的先决条件优于最先进的先决条件。