Reduced dimension GDSW coarse spaces for monolithic Schwarz domain decomposition methods for incompressible fluid flow problems
Reduced dimension GDSW coarse spaces for monolithic Schwarz domain decomposition methods for incompressible fluid flow problems
复制标题
DOI：
10.1002/nme.6258
复制
发表时间：
2019-11
影响因子：
2.9
通讯作者：
Alexander Heinlein;C. Hochmuth;A. Klawonn
中科院分区：
文献类型：
--
作者：
Alexander Heinlein;C. Hochmuth;A. Klawonn
与基于不完全块因式分解的预条件算法相比，不可压缩流体流动问题的单块预条件算法可以显著提高收敛速度。然而，整体式预处理器的设置和应用的计算成本通常较高。本文将几种技术应用于单片两级广义Dryja-Smith-Widlund(GDSW)预条件，以进一步提高收敛速度和计算时间。特别是，降维GDSW粗空间，第一层的限制和比例版本，各级的混合和平行耦合，以及回收策略被研究。使用所有这些改进的组合，对于240个消息传递接口(MPI)序列上的小的依赖于时间的Navier-Stokes问题，可以获得86%的求解时间。即使没有应用回收策略，对于4608个MPI级别的更大的稳定斯托克斯问题，解决时间也可以减少50%以上。对于具有11979个MPI等级的最大问题，单片GDSW粗空间的可伸缩性急剧恶化。另一方面，使用降维的粗空间，可以获得高达11979个MPI等级的良好可扩展性，这相当于在所采用的超级计算机上匹配的最大问题配置。
Monolithic preconditioners for incompressible fluid flow problems can significantly improve the convergence speed compared with preconditioners based on incomplete block factorizations. However, the computational costs for the setup and the application of monolithic preconditioners are typically higher. In this article, several techniques are applied to monolithic two‐level generalized Dryja‐Smith‐Widlund (GDSW) preconditioners to further improve the convergence speed and the computing time. In particular, reduced dimension GDSW coarse spaces, restricted and scaled versions of the first level, hybrid, and parallel coupling of the levels, and recycling strategies are investigated. Using a combination of all these improvements, for a small time‐dependent Navier‐Stokes problem on 240 message passing interface (MPI) ranks, a reduction of 86% of the time‐to‐solution can be obtained. Even without applying recycling strategies, the time‐to‐solution can be reduced by more than 50% for a larger steady Stokes problem on 4608 MPI ranks. For the largest problems with 11 979 MPI ranks, the scalability deteriorates drastically for the monolithic GDSW coarse space. On the other hand, using the reduced dimension coarse spaces, good scalability up to 11 979 MPI ranks, which corresponds to the largest problem configuration fitting on the employed supercomputer, could be achieved.