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

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.