An improved convergence analysis of smoothed aggregation algebraic multigrid
An improved convergence analysis of smoothed aggregation algebraic multigrid
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DOI：
10.1002/nla.775
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发表时间：
2012-05
影响因子：
4.3
通讯作者：
M. Brezina;P. Vanek;P. Vassilevski
中科院分区：
文献类型：
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作者：
M. Brezina;P. Vanek;P. Vassilevski
我们提出了对平滑聚合代数多重网格方法的改进分析，扩展了[Numer.1]中的原始证明。数学。 2001年； 88:559–579]及其在[多级块分解预处理器中的修改。求解有限元方程的基于矩阵的分析和算法。施普林格：纽约，2008 年]。新结果对聚合施加的限制更少，从而更容易在实践中验证。此外，我们在[Appl.数学。 2011]，这使得我们能够在各个级别上使用积极的粗化。这是由于我们使用和分析的特殊多项式平滑器的属性所致。特别是，我们获得了与粗化率无关的多级收敛估计的界限。还提供了数值说明。版权所有 © 2011 约翰·威利父子有限公司
We present an improved analysis of the smoothed aggregation algebraic multigrid method extending the original proof in [Numer. Math. 2001; 88:559–579] and its modification in [Multilevel Block Factorization Preconditioners. Matrix‐based Analysis and Algorithms for Solving Finite Element Equations. Springer: New York, 2008]. The new result imposes fewer restrictions on the aggregates that makes it easier to verify in practice. Also, we extend a result in [Appl. Math. 2011] that allows us to use aggressive coarsening at all levels. This is due to the properties of the special polynomial smoother that we use and analyze. In particular, we obtain bounds in the multilevel convergence estimates that are independent of the coarsening ratio. Numerical illustration is also provided. Copyright © 2011 John Wiley & Sons, Ltd.