'Proxy-equation' paradigm - A novel strategy for massively-parallel asynchronous computations

TL;DR

This paper introduces a 'proxy-equation' approach that allows massively parallel transport simulations to run asynchronously with controlled errors, maintaining convergence and scalability.

Contribution

It presents a novel 'proxy-equation' method that tolerates asynchrony in parallel computations without sacrificing accuracy or convergence.

Findings

Successfully applied to 1D advection-diffusion equation

Maintains convergence order despite asynchrony

Scales efficiently on large parallel systems

Abstract

Massively parallel simulations of transport equation systems call for a paradigm change in algorithm development to achieve efficient scalability. Traditional approaches require time synchronization of processing elements (PEs) which severely restricts scalability. Relaxing synchronization requirement introduces error and slows down convergence. In this paper, we propose and develop a novel `proxy-equation' concept for a general transport equation that (i) tolerates asynchrony with manageable added error, (ii) preserves convergence order and (iii) scales efficiently on massively parallel machines. The central idea is to modify \textit{a priori} the transport equation at the PE boundaries to offset asynchrony errors. Proof-of-concept computations are performed using a one-dimensional advection-diffusion equation. The results demonstrate the promise and advantages of the present strategy.