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This paper presents performance results comparing MPI-based implementationsof the popular Conjugate Gradient (CG) method and several of its communicationhiding (or 'pipelined') variants. Pipelined CG methods are designed toefficiently solve SPD linear systems on massively parallel distributed memoryhardware, and typically display significantly improved strong scaling comparedto classic CG. This increase in parallel performance is achieved by overlappingthe global reduction phase (MPI_Iallreduce) required to compute the innerproducts in each iteration by (chiefly local) computational work such as thematrix-vector product as well as other global communication. This work includesa brief introduction to the deep pipelined CG method for readers that may beunfamiliar with the specifics of the method. A brief overview of implementationdetails provides the practical tools required for implementation of thealgorithm. Subsequently, easily reproducible strong scaling results on the USDepartment of Energy (DoE) NERSC machine 'Cori' (Phase I - Haswell nodes) on upto 1024 nodes with 16 MPI ranks per node are presented using an implementationof p(l)-CG that is available in the open source PETSc library. Observations onthe staggering and overlap of the asynchronous, non-blocking globalcommunication phases with communication and computational kernels are drawnfrom the experiments.

Improving strong scaling of the Conjugate Gradient method for solving large linear systems using global reduction pipelining