Scalability of Classical Algebraic Multigrid for Elasticity to Half a Million Parallel Tasks
Scalability of Classical Algebraic Multigrid for Elasticity to Half a Million Parallel Tasks
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经典代数多重网格的弹性可扩展性至 50 万个并行任务
DOI：
10.1007/978-3-319-40528-5_6
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发表时间：
2016
期刊：
影响因子：
--
通讯作者：
U. Yang
中科院分区：
文献类型：
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作者：
A. Baker;A. Klawonn;T. Kolev;M. Lanser;O. Rheinbach;U. Yang
研究了几种经典代数多重网格（AMG）方法在求解线性弹性问题中的并行性能。这些方法包括用于偏微分方程系统的标准AMG方法，如未知方法和混合方法，以及最近将刚体模态（rbm）纳入AMG插值算子的全局矩阵（GM）和局部邻域（LN）方法。在Vulcan超级计算机（LLNL，美国）和JUQUEEN超级计算机（JSC, Julich，德国）上，分别在多达131,072个核（和262,144个MPI进程）和多达262,144个核（和524,288个MPI进程）上对二维和三维弹性问题进行了数值实验。结果表明，将所有rbm合并到插值中通常会导致更快的收敛和改进的可扩展性。
The parallel performance of several classical Algebraic Multigrid (AMG) methods applied to linear elasticity problems is investigated. These methods include standard AMG approaches for systems of partial differential equations such as the unknown and hybrid approaches, as well as the more recent global matrix (GM) and local neighborhood (LN) approaches, which incorporate rigid body modes (RBMs) into the AMG interpolation operator. Numerical experiments are presented for both two- and three-dimensional elasticity problems on up to 131,072 cores (and 262,144 MPI processes) on the Vulcan supercomputer (LLNL, USA) and up to 262,144 cores (and 524,288 MPI processes) on the JUQUEEN supercomputer (JSC, Julich, Germany). It is demonstrated that incorporating all RBMs into the interpolation leads generally to faster convergence and improved scalability.