A mathematical model of asynchronous data flow in parallel computers

A mathematical model of asynchronous data flow in parallel computers

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 o...

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Veröffentlicht in:IMA journal of applied mathematics 2020-12, Vol.85 (6), p.865-891
Hauptverfasser: Barnard, Richard C, Huang, Kai, Hauck, Cory
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creator Barnard, Richard C
Huang, Kai
Hauck, Cory
description 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.
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source Oxford University Press Journals All Titles (1996-Current)
title A mathematical model of asynchronous data flow in parallel computers
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