Scalable Non-Blocking Preconditioned Conjugate Gradient Methods
SessionNumerical Algorithms I
Session ChairHatem Ltaief
Event Type
Paper
Algorithms
Intermediate
Introductory
Scientific Computing
TimeTuesday, November 15th2:30pm - 3pm
Location355-E
DescriptionThe preconditioned conjugate gradient method (PCG) is a popular method for solving linear systems at scale. PCG requires frequent blocking allreduce collective operations that can limit performance at scale. We investigate PCG variations designed to reduce communication costs by decreasing the number of allreduces and by overlapping communication with computation using a non-blocking allreduce. These variations include two methods we have developed, non-blocking PCG and 2-step pipelined PCG, and pipelined PCG from Ghysels and Vanroose.
Performance modeling for communication and computation costs shows the expected performance of these methods. Weak and strong scaling experiments on up to 128k cores show that scalable PCG methods can outperform standard PCG at scale. We observe that the fastest method varies depending on the work per core, suggesting we need a suite of scalable solvers to obtain the best performance. Experiments with multiple preconditioners and linear systems show the robustness of these methods.
Performance modeling for communication and computation costs shows the expected performance of these methods. Weak and strong scaling experiments on up to 128k cores show that scalable PCG methods can outperform standard PCG at scale. We observe that the fastest method varies depending on the work per core, suggesting we need a suite of scalable solvers to obtain the best performance. Experiments with multiple preconditioners and linear systems show the robustness of these methods.
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Paper provided by the IEEE Computer SocietyPaper also available from the ACM Digital Library
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