The impact of global communication latency at extreme scales on Krylov methods
ICA3PP'12 Proceedings of the 12th international conference on Algorithms and Architectures for Parallel Processing - Volume Part I
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In this paper, we would like to summarize the recent advances on the improved Krylov Subspace methods for the solutions of large and sparse linear systems of equations with unsymmetric coefficient matrices. The proposed methods combine elements of numerical stability and parallel algorithm design without increasing too much computational costs. The methods have the following common feature that all are derived such that all matrix-vectormultiplication, inner products and vector updates of a single iteration step are independent and communication time required for inner product can be overlapped efficiently with computation time of vector updates. Therefore, the cost of global communication which represents the bottleneck of the performance can be significantly reduced. Here, the Bulk Synchronous Parallel (BSP) model is used to design fully efficient, scalable and portable parallel proposed algorithms and to provide accurate performance prediction of the algorithms for a wide range of architectures including the Cray T3D, the Parsytec, and a cluster of workstations connected by an Ethernet. This performance model uses only a few system dependent parameters based on a simple and accurate cost modelling to provide usefulinsight in the time complexity of the methods. The theoretical performance prediction are compared with some preliminary measured timing results of a numerical application from ocean flow simulation.