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Article | REF: AF1386 V1

Parallel Asynchronous Algorithms II. Implementation

Authors: Pierre SPITERI, Jean-Claude MIELLOU

Publication date: October 10, 2021

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ABSTRACT

This article is devoted to the implementation of asynchronous parallel iterative algorithms. We will first discuss the implementation of stopping tests both from a computational approach and from a numerical analysis approach using in the latter case either the contraction property or the partial ordering convergence one and also the nested sets. After recalling some notions concerning the architecture of multiprocessor machines, the implementation principle of these asynchronous parallel iterative methods will be discussed, in particular for the sub-domain methods ; load balancing for these algorithms will be also discussed.

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AUTHORS

  • Pierre SPITERI: Professor Emeritus - University of Toulouse, INP-ENSEEIHT – IRIT, Toulouse, France

  • Jean-Claude MIELLOU: Honorary Professor - University of Bourgogne Franche-Comté, Department of Mathematics, Besançon, France

 INTRODUCTION

In a first article [AF 1 385] we considered the solution of two types of pseudo-linear problem. The first is a univocal problem of the type

AU*+Φ(U*)=G( 1 )

where A is a matrix of dimension M∈ℕ , set of natural numbers, G and U are vectors of dimension M and

U→Φ(U) est une application continue croissante( 2 )

The second type of problem is multi-voiced because its solution U is subject to inequality constraints of the type

Umin≤U* ou bien Umin≤U*≤Umax ou bien U*≤Umax( 3 )

in this case we need to solve the following multi-voice problem

AU*+∂Ψ(U
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KEYWORDS

multiprocessor architecture   |   message passing interface   |   termination of algorithms   |   sub-domain methods

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