A mathematical model of asynchronous data flow in parallel computers. (25th September 2020)

• Record Type: Journal Article
• Authors: Barnard, Richard C; Huang, Kai; Hauck, Cory
• Is Part Of: IMA journal of applied mathematics. Volume 85:Number 6(2020)
• Page Start: 865
• Page End: 891
• Publication Date: 2020-09-25
• Subjects: data flow -- high-performance computing -- asymptotic approximation -- conservation laws -- Hamilton–Jacobi equation; Mathematics -- Periodicals; Mathematics; Periodicals; 519
• DOI: 10.1093/imamat/hxaa031
• Languages: English
• ISSNs: 0272-4960

Abstract

Abstract: We present a simplified model of data flow on processors in a high-performance computing framework involving computations necessitating inter-processor communications. From this ordinary differential model, we take its asymptotic limit, resulting in a model which treats the computer as a continuum of processors and data flow as an Eulerian fluid governed by a conservation law. We derive a Hamilton–Jacobi equation associated with this conservation law for which the existence and uniqueness of solutions can be proven. We then present the results of numerical experiments for both discrete and continuum models; these show a qualitative agreement between the two and the effect of variations in the computing environment's processing capabilities on the progress of the modelled computation.