Abstract

The paper proposes a combination of the subdomain deflation method and local algebraic multigrid as a scalable distributed memory preconditioner that is able to solve large linear systems of equations. The implementation of the algorithm is made available for the community as part of an open source AMGCL library. The solution targets both homogeneous (CPU-only) and heterogeneous (CPU/GPU) systems, employing hybrid MPI/OpenMP approach in the former and a combination of MPI, OpenMP, and CUDA in the latter cases. The use of OpenMP minimizes the number of MPI processes, thus reducing the communication overhead of the deflation method and improving both weak and strong scalability of the preconditioner. The examples of scalar (single degree of freedom per grid node), Poisson-like, systems as well as non-scalar problems, stemming out of the discretization of the Navier-Stokes equations, are considered in order to estimate performance of the implemented algorithm. A comparison with a traditional global AMG preconditioner based on a well-established Trilinos ML package is provided.

中文翻译：

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子域缩小与本地AMG结合：使用AMGCL库的案例研究

摘要

本文提出了子域放气法和局部代数多重网格的组合作为可扩展的分布式内存预处理器，该预处理器能够解决大型线性方程组。该算法的实现作为开源AMGCL库的一部分可供社区使用。该解决方案针对同构（仅CPU）和异构（CPU / GPU）系统，在前者中采用混合MPI / OpenMP方法，在后一种情况下采用MPI，OpenMP和CUDA的组合。OpenMP的使用可以最大程度地减少MPI进程的数量，从而减少放气方法的通信开销，并改善预处理器的弱扩展性和强扩展性。标量（每个网格节点的单个自由度），类似于Poisson的系统以及非标量问题的示例，为了估计所实现算法的性能，考虑了从Navier-Stokes方程离散化而来的问题。提供了与基于完善的Trilinos ML软件包的传统全局AMG预处理器的比较。