Document Type

Journal Article

Department/Unit

Department of Mathematics

Abstract

Schwarz waveform relaxation (SWR) methods have been developed to solve a wide range of diffusion-dominated and reaction-dominated equations. The appeal of these methods stems primarily from their ability to use nonconforming space-time discretizations; SWR methods are consequently well-adapted for coupling models with highly varying spatial and time scales. The efficacy of SWR methods is questionable, however, since in each iteration, one propagates an error across the entire time interval. In this manuscript, we introduce an adaptive pipeline approach wherein one subdivides the computational domain into space-time blocks, and adaptively selects the waveform iterates which should be updated given a fixed number of computational workers. Our method is complementary to existing space and time parallel methods, and can be used to obtain additional speedup when the saturation point is reached for other types of parallelism. We analyze these waveform relaxation with adaptive pipelining (WRAP) methods to show convergence and the theoretical speedup that can be expected. Numerical experiments on solutions to the linear heat equation, the advection-diffusion equation, and a reaction-diffusion equation illustrate features and efficacy of WRAP methods for various transmission conditions.

Keywords

waveform relaxation, domain decomposition, adaptivity, parallel computing

Publication Date

2019

Source Publication Title

SIAM Journal on Scientific Computing

Volume

41

Issue

1

Start Page

A339

End Page

A364

Publisher

Society for Industrial and Applied Mathematics

DOI

10.1137/17M115311X

Link to Publisher's Edition

https://doi.org/10.1137/17M115311X

ISSN (print)

10648275

ISSN (electronic)

10957197

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