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About the granularity portability of block‐based Krylov methods in heterogeneous computing environments
Concurrency and Computation: Practice and Experience ( IF 2 ) Pub Date : 2020-10-02 , DOI: 10.1002/cpe.6008 Luisa Carracciuolo 1 , Valeria Mele 2 , Lukasz Szustak 3
Concurrency and Computation: Practice and Experience ( IF 2 ) Pub Date : 2020-10-02 , DOI: 10.1002/cpe.6008 Luisa Carracciuolo 1 , Valeria Mele 2 , Lukasz Szustak 3
Affiliation
Large‐scale problems in engineering and science often require the solution of sparse linear algebra problems and the Krylov subspace iteration methods (KM) have led to a major change in how users deal with them. But, for these solvers to use extreme‐scale hardware efficiently a lot of work was spent to redesign both the KM algorithms and their implementations to address challenges like extreme concurrency, complex memory hierarchies, costly data movement, and heterogeneous node architectures. All the redesign approaches bases the KM algorithm on block‐based strategies which lead to the Block‐KM (BKM) algorithm which has high granularity (i.e., the ratio of computation time to communication time). The work proposes novel parallel revisitation of the modules used in BKM which are based on the overlapping of communication and computation. Such revisitation is evaluated by a model of their granularity and verified on the basis of a case study related to a classical problem from numerical linear algebra.
中文翻译:
关于异构计算环境下基于块的 Krylov 方法的粒度可移植性
工程和科学中的大规模问题通常需要解决稀疏线性代数问题,而 Krylov 子空间迭代方法 (KM) 导致用户处理这些问题的方式发生了重大变化。但是,为了让这些求解器有效地使用超大规模硬件,需要花费大量工作来重新设计 KM 算法及其实现,以解决诸如极端并发、复杂的内存层次结构、昂贵的数据移动和异构节点架构等挑战。所有重新设计的方法都基于基于块的策略的 KM 算法,这导致块 KM(BKM)算法具有高粒度(即计算时间与通信时间的比率)。该工作提出了基于通信和计算重叠的 BKM 中使用的模块的新颖并行重访。
更新日期:2020-10-02
中文翻译:
关于异构计算环境下基于块的 Krylov 方法的粒度可移植性
工程和科学中的大规模问题通常需要解决稀疏线性代数问题,而 Krylov 子空间迭代方法 (KM) 导致用户处理这些问题的方式发生了重大变化。但是,为了让这些求解器有效地使用超大规模硬件,需要花费大量工作来重新设计 KM 算法及其实现,以解决诸如极端并发、复杂的内存层次结构、昂贵的数据移动和异构节点架构等挑战。所有重新设计的方法都基于基于块的策略的 KM 算法,这导致块 KM(BKM)算法具有高粒度(即计算时间与通信时间的比率)。该工作提出了基于通信和计算重叠的 BKM 中使用的模块的新颖并行重访。