Theoretical bounds for algebraic multigrid performance: review and analysis
Theoretical bounds for algebraic multigrid performance: review and analysis
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DOI：
10.1002/nla.1930
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发表时间：
2014-03
影响因子：
4.3
通讯作者：
S. MacLachlan;Luke N. Olson
中科院分区：
文献类型：
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作者：
S. MacLachlan;Luke N. Olson
在许多应用中，代数多重网格方法作为大型和稀疏线性方程组的有效求解器，在鲁棒性方面继续增长。然而，与几何多重网格方法不同，代数多重网格的理论分析对真实性能的预测较少。多网格收敛因子自然依赖于所使用的松弛、插值和粗网格校正例程的性质，但如果没有傅里叶分析工具，代数多网格的最佳和实用界限就不容易量化。在本文中，我们从现有文献中调查边界，特别关注该理论的预测能力，并提供有关现有边界的新结果。我们通过几个模型问题来强调这些理论观察的影响，并讨论理论界限对实际性能的作用。版权所有©2014 John Wiley & Sons， Ltd。
Algebraic multigrid methods continue to grow in robustness as effective solvers for the large and sparse linear systems of equations that arise in many applications. Unlike geometric multigrid approaches, however, the theoretical analysis of algebraic multigrid is less predictive of true performance. Multigrid convergence factors naturally depend on the properties of the relaxation, interpolation, and coarse‐grid correction routines used, yet without the tools of Fourier analysis, optimal and practical bounds for algebraic multigrid are not easily quantified. In this paper, we survey bounds from existing literature, with particular focus on the predictive capabilities of the theory, and provide new results relating existing bounds. We highlight the impact of these theoretical observations through several model problems and discuss the role of theoretical bounds on practical performance. Copyright © 2014 John Wiley & Sons, Ltd.