A supplementary strategy for coarsening in algebraic multigrid
A supplementary strategy for coarsening in algebraic multigrid
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DOI：
10.1016/j.amc.2020.125795
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发表时间：
2021-04
期刊：
影响因子：
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通讯作者：
S. Ye;Xinhai Xu;Hengbin An;Xuejun Yang
中科院分区：
文献类型：
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作者：
S. Ye;Xinhai Xu;Hengbin An;Xuejun Yang
代数多重网格(AMG)是一种求解椭圆型偏微分方程组的有效迭代方法。粗化算法是经典AMG算法中的一个关键部分，它决定了经典AMG中的粗变量集。本文的目标是通过提高粗化算法得到的粗变量集的质量来减少经典AMG的整体求解时间。我们将经典的粗化算法和基于兼容松弛(CR)的粗化算法相结合来构造粗变量集。组合粗化算法分两个阶段构造粗变量集。在第一阶段，利用经典的粗化算法，例如PMIS，建立一个基本的粗变量集。在第二阶段，基于相容松弛来衡量集合的质量，并将在CR松弛中收敛较慢的变量添加到先前的集合中。我们测试了各种模型问题，以及实际应用中出现的一些线性方程组，以验证我们方法的有效性。
Algebraic multigrid (AMG) is an efficient iterative method for solving linear equation systems arising from the elliptic partial differential equations. The coarsening algorithm, which determines the coarse-variable set in the classical AMG, is a critical component. This paper targets at reducing the overall solution time of the classical AMG by improving the quality of the coarse-variable set obtained by the coarsening algorithm. We combine the classical coarsening algorithm with the compatible relaxation (CR)-based coarsening algorithm to construct the coarse-variable set. The combined coarsening algorithm constructs the coarse-variable set within two stages. In the first stage, a basic coarse-variable set is built by the classical coarsening algorithm, e.g., PMIS. In the second stage, the quality of the set is measured based on compatible relaxation, and the variables that converge slowly in the CR relaxation are added into the previous set. We test various model problems, as well as some linear equation systems arising from real applications, to verify the effectiveness of our method.