A mathematical model of asynchronous data flow in parallel computers

Richard C. Barnard; Kai Huang; Cory Hauck

doi:10.1093/imamat/hxaa031

A mathematical model of asynchronous data flow in parallel computers

Richard C. Barnard, Kai Huang, Cory Hauck

Multiscale Methods

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

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.

Original language	English
Pages (from-to)	865-891
Number of pages	27
Journal	IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications)
Volume	85
Issue number	6
DOIs	https://doi.org/10.1093/imamat/hxaa031
State	Published - Dec 1 2020

Keywords

Asymptotic approximation
Conservation laws
Data flow
Hamilton-jacobi equation
High-performance computing

Access to Document

10.1093/imamat/hxaa031

Cite this

@article{dfa72df753874edf9fce666922fe7100,

title = "A mathematical model of asynchronous data flow in parallel computers",

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.",

keywords = "Asymptotic approximation, Conservation laws, Data flow, Hamilton-jacobi equation, High-performance computing",

author = "Barnard, {Richard C.} and Kai Huang and Cory Hauck",

note = "Publisher Copyright: {\textcopyright} 2020 The Author(s) 2020.",

year = "2020",

month = dec,

day = "1",

doi = "10.1093/imamat/hxaa031",

language = "English",

volume = "85",

pages = "865--891",

journal = "IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications)",

issn = "0272-4960",

publisher = "Oxford University Press",

number = "6",

}

TY - JOUR

T1 - A mathematical model of asynchronous data flow in parallel computers

AU - Barnard, Richard C.

AU - Huang, Kai

AU - Hauck, Cory

PY - 2020/12/1

Y1 - 2020/12/1

N2 - 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.

AB - 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.

KW - Asymptotic approximation

KW - Conservation laws

KW - Data flow

KW - Hamilton-jacobi equation

KW - High-performance computing

UR - http://www.scopus.com/inward/record.url?scp=85097507223&partnerID=8YFLogxK

U2 - 10.1093/imamat/hxaa031

DO - 10.1093/imamat/hxaa031

M3 - Article

AN - SCOPUS:85097507223

SN - 0272-4960

VL - 85

SP - 865

EP - 891

JO - IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications)

JF - IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications)

IS - 6

ER -

A mathematical model of asynchronous data flow in parallel computers

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this