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About the granularity portability of block-based Krylov methods in heterogeneous computing environments

机译:关于异构计算环境中基于块的Krylov方法的粒度便携性

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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.
机译:工程和科学中的大规模问题往往要求稀疏线性代数问题的解决方案,而Krylov子空间迭代方法(KM)导致用户如何处理它们的重大变化。但是,对于这些求解器使用极限硬件,有效地使用大量工作来重新设计KM算法及其实现,以解决极端并发性,复杂的内存层次结构,复杂的数据移动和异构节点架构等挑战。所有重新设计方法都基于基于块的策略基于KM算法,其导致具有高粒度的块KM(BKM)算法(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平行重新审视。这种重审是通过粒度模型评估的,并根据与数值线性代数的经典问题相关的案例研究来验证。

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