论文标题
在局部精制网格上，有效的分布式矩阵的多机方法用于FEM计算
Efficient distributed matrix-free multigrid methods on locally refined meshes for FEM computations
论文作者
论文摘要
这项工作研究了三种多移民变体，用于对本地精制网格的无基质有限元计算：几何局部平滑，几何全球变形和多项式全局变形。我们已经将算法集成到同一框架中 - 开源有限元库Deal.ii-，这使我们能够就其实施复杂性，计算效率和并行的可扩展性以及将测量结果与理论得出的绩效模型进行比较。在3,072个计算节点上，串行模拟和平行的弱和强缩放率最高可达147,456个CPU核心。获得的结果表明，由于较高的负载平衡，尤其是在昂贵的罚款水平上，全球变形算法对可比Smoothors的平行行为更好。在串行案例中，应用悬挂节点约束的成本可能很重要，即使需要的求解器迭代次数略高，也会导致局部平滑的优势。
This work studies three multigrid variants for matrix-free finite-element computations on locally refined meshes: geometric local smoothing, geometric global coarsening, and polynomial global coarsening. We have integrated the algorithms into the same framework-the open-source finite-element library deal.II-, which allows us to make fair comparisons regarding their implementation complexity, computational efficiency, and parallel scalability as well as to compare the measurements with theoretically derived performance models. Serial simulations and parallel weak and strong scaling on up to 147,456 CPU cores on 3,072 compute nodes are presented. The results obtained indicate that global coarsening algorithms show a better parallel behavior for comparable smoothers due to the better load balance particularly on the expensive fine levels. In the serial case, the costs of applying hanging-node constraints might be significant, leading to advantages of local smoothing, even though the number of solver iterations needed is slightly higher.
