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Title: Achieving algorithmic resilience for temporal integration through spectral deferred corrections

Journal Article · · Communications in Applied Mathematics and Computational Science
 [1];  [2];  [3];  [3]
  1. National Renewable Energy Lab. (NREL), Golden, CO (United States). Computational Science Center
  2. Sandia National Lab. (SNL-CA), Livermore, CA (United States). Scalable Modeling and Analysis Dept.
  3. Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Computational Research Division
+ Show Author Affiliations

Spectral deferred corrections (SDC) is an iterative approach for constructing higher-order-accurate numerical approximations of ordinary differential equations. SDC starts with an initial approximation of the solution defined at a set of Gaussian or spectral collocation nodes over a time interval and uses an iterative application of lower-order time discretizations applied to a correction equation to improve the solution at these nodes. Each deferred correction sweep increases the formal order of accuracy of the method up to the limit inherent in the accuracy defined by the collocation points. In this paper, we demonstrate that SDC is well suited to recovering from soft (transient) hardware faults in the data. A strategy where extra correction iterations are used to recover from soft errors and provide algorithmic resilience is proposed. Specifically, in this approach the iteration is continued until the residual (a measure of the error in the approximation) is small relative to the residual of the first correction iteration and changes slowly between successive iterations. Here, we demonstrate the effectiveness of this strategy for both canonical test problems and a comprehensive situation involving a mature scientific application code that solves the reacting Navier-Stokes equations for combustion research.

Research Organization:
Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
Sponsoring Organization:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)
Grant/Contract Number:
AC02-05CH11231; AC36-08GO28308
OSTI ID:
1436145
Journal Information:
Communications in Applied Mathematics and Computational Science, Vol. 12, Issue 1; ISSN 1559-3940
Publisher:
Mathematical Sciences PublishersCopyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 3 works
Citation information provided by
Web of Science

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Cited By (2)

Data recovery in computational fluid dynamics through deep image priors preprint January 2019
A scalable weakly-synchronous algorithm for solving partial differential equations preprint January 2019

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Related Subjects

97 MATHEMATICS AND COMPUTING
SDC
resilience
time integration
deferred correction
exascale computing
combustion