The communication-hiding pipelined BiCGStab method for the parallel solution of large unsymmetric linear systems

摘要

A High Performance Computing alternative to traditional Krylov subspacemethods, pipelined Krylov subspace solvers offer better scalability in thestrong scaling limit compared to standard Krylov subspace methods for large andsparse linear systems. The typical synchronization bottleneck is mitigated byoverlapping time-consuming global communication phases with local computationsin the algorithm. This paper describes a general framework for deriving thepipelined variant of any Krylov subspace algorithm. The proposed framework wasimplicitly used to derive the pipelined Conjugate Gradient (p-CG) method in"Hiding global synchronization latency in the preconditioned Conjugate Gradientalgorithm" by P. Ghysels and W. Vanroose, Parallel Computing, 40(7):224--238,2014. The pipelining framework is subsequently illustrated by formulating apipelined version of the BiCGStab method for the solution of large unsymmetriclinear systems on parallel hardware. A residual replacement strategy isproposed to account for the possible loss of attainable accuracy and robustnessby the pipelined BiCGStab method. It is shown that the pipelined algorithmimproves scalability on distributed memory machines, leading to significantspeedups compared to standard preconditioned BiCGStab.