A stochastic performance model for pipelined Krylov methods. (31st March 2016)

• Record Type: Journal Article
• Authors: Morgan, Hannah; Knepley, Matthew G.; Sanan, Patrick; Scott, L. Ridgway
• Is Part Of: Concurrency and computation. Volume 28:Number 18(2016)
• Page Start: 4532
• Page End: 4542
• Publication Date: 2016-03-31
• Subjects: asynchronous -- pipelined -- Krylov -- stochastic -- PGMRES -- PIPECG -- split phase collective -- performance model; Parallel processing (Electronic computers) -- Periodicals; Parallel computers -- Periodicals; 004.35
• DOI: 10.1002/cpe.3820
• Languages: English
• ISSNs: 1532-0626

Abstract

Summary: Pipelined Krylov methods seek to ameliorate the latency due to inner products necessary for projection by overlapping it with the computation associated with sparse matrix‐vector multiplication. We clarify a folk theorem that this can only result in a speedup of 2× over the naive implementation. Examining many repeated runs, we show that stochastic noise also contributes to the latency, and we model this using an analytical probability distribution. Our analysis shows that speedups greater than 2× are possible with these algorithms. Copyright © 2016 John Wiley & Sons, Ltd.