论文标题
线性求解器的AMG预处理朝向极限
AMG preconditioners for Linear Solvers towards Extreme Scale
论文作者
论文摘要
大型和稀疏系统的线性求解器是科学应用的关键要素，其有效实现对于利用当前计算机的计算能力是必要的。代数多机（AMG）预处理是这种线性求解器的流行成分；这是当前工作的动机，我们检查了AMG预科人员包装中的一些最新发展，以提高极端问题的效率，可伸缩性和鲁棒性。主要的新颖性是基于使用加权图匹配技术的未知数聚集的平行粗化算法的设计和实现。这是一个完全自动化的过程，不需要用户的信息，并且适用于一般对称的正定确定（S.P.D.）矩阵。新的变形算法在低操作员复杂性下在包装的先前发行版中可用的脱钩聚合算法上改善了数值可伸缩性。预处理程序包构建在Parallel Software Framework \ texttt {psblas}上，该{psblas}也已更新以朝着Exascale进行。我们在欧洲最强大的超级计算机之一上介绍了较弱的可伸缩性结果，对于最高$ O（10^{10}）$未知的线性系统。
Linear solvers for large and sparse systems are a key element of scientific applications, and their efficient implementation is necessary to harness the computational power of current computers. Algebraic MultiGrid (AMG) preconditioners are a popular ingredient of such linear solvers; this is the motivation for the present work where we examine some recent developments in a package of AMG preconditioners to improve efficiency, scalability, and robustness on extreme-scale problems. The main novelty is the design and implementation of a parallel coarsening algorithm based on aggregation of unknowns employing weighted graph matching techniques; this is a completely automated procedure, requiring no information from the user, and applicable to general symmetric positive definite (s.p.d.) matrices. The new coarsening algorithm improves in terms of numerical scalability at low operator complexity over decoupled aggregation algorithms available in previous releases of the package. The preconditioners package is built on the parallel software framework \texttt{PSBLAS}, which has also been updated to progress towards exascale. We present weak scalability results on one of the most powerful supercomputers in Europe, for linear systems with sizes up to $O(10^{10})$ unknowns.
