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Title: High-order asynchrony-tolerant finite difference schemes for partial differential equations

Abstract

Synchronizations of processing elements (PEs) in massively parallel simulations, which arise due to communication or load imbalances between PEs, significantly affect the scalability of scientific applications. We have recently proposed a method based on finite-difference schemes to solve partial differential equations in an asynchronous fashion – synchronization between PEs is relaxed at a mathematical level. While standard schemes can maintain their stability in the presence of asynchrony, their accuracy is drastically affected. In this work, we present a general methodology to derive asynchrony-tolerant (AT) finite difference schemes of arbitrary order of accuracy, which can maintain their accuracy when synchronizations are relaxed. We show that there are several choices available in selecting a stencil to derive these schemes and discuss their effect on numerical and computational performance. We provide a simple classification of schemes based on the stencil and derive schemes that are representative of different classes. Their numerical error is rigorously analyzed within a statistical framework to obtain the overall accuracy of the solution. Results from numerical experiments are used to validate the performance of the schemes.

Authors:
ORCiD logo [1];  [1]
  1. Texas A&M University, College Station, TX (United States). Department of Aerospace Engineering
Publication Date:
Research Org.:
Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States). National Energy Research Scientific Computing Center (NERSC)
Sponsoring Org.:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)
OSTI Identifier:
1463649
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Journal of Computational Physics
Additional Journal Information:
Journal Volume: 350; Journal Issue: C; Journal ID: ISSN 0021-9991
Publisher:
Elsevier
Country of Publication:
United States
Language:
English
Subject:
42 ENGINEERING

Citation Formats

Aditya, Konduri, and Donzis, Diego A. High-order asynchrony-tolerant finite difference schemes for partial differential equations. United States: N. p., 2017. Web. doi:10.1016/j.jcp.2017.08.037.
Aditya, Konduri, & Donzis, Diego A. High-order asynchrony-tolerant finite difference schemes for partial differential equations. United States. https://doi.org/10.1016/j.jcp.2017.08.037
Aditya, Konduri, and Donzis, Diego A. 2017. "High-order asynchrony-tolerant finite difference schemes for partial differential equations". United States. https://doi.org/10.1016/j.jcp.2017.08.037. https://www.osti.gov/servlets/purl/1463649.
@article{osti_1463649,
title = {High-order asynchrony-tolerant finite difference schemes for partial differential equations},
author = {Aditya, Konduri and Donzis, Diego A.},
abstractNote = {Synchronizations of processing elements (PEs) in massively parallel simulations, which arise due to communication or load imbalances between PEs, significantly affect the scalability of scientific applications. We have recently proposed a method based on finite-difference schemes to solve partial differential equations in an asynchronous fashion – synchronization between PEs is relaxed at a mathematical level. While standard schemes can maintain their stability in the presence of asynchrony, their accuracy is drastically affected. In this work, we present a general methodology to derive asynchrony-tolerant (AT) finite difference schemes of arbitrary order of accuracy, which can maintain their accuracy when synchronizations are relaxed. We show that there are several choices available in selecting a stencil to derive these schemes and discuss their effect on numerical and computational performance. We provide a simple classification of schemes based on the stencil and derive schemes that are representative of different classes. Their numerical error is rigorously analyzed within a statistical framework to obtain the overall accuracy of the solution. Results from numerical experiments are used to validate the performance of the schemes.},
doi = {10.1016/j.jcp.2017.08.037},
url = {https://www.osti.gov/biblio/1463649}, journal = {Journal of Computational Physics},
issn = {0021-9991},
number = C,
volume = 350,
place = {United States},
year = {Fri Dec 01 00:00:00 EST 2017},
month = {Fri Dec 01 00:00:00 EST 2017}
}

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Cited by: 6 works
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