Communications in Applied Mathematics and Computational Science
- Commun. Appl. Math. Comput. Sci.
- Volume 12, Number 1 (2017), 25-50.
Achieving algorithmic resilience for temporal integration through spectral deferred corrections
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. 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.
Commun. Appl. Math. Comput. Sci., Volume 12, Number 1 (2017), 25-50.
Received: 3 March 2016
Revised: 9 September 2016
Accepted: 18 January 2017
First available in Project Euclid: 19 October 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Primary: 65D30: Numerical integration 65M12: Stability and convergence of numerical methods 65M22: Solution of discretized equations [See also 65Fxx, 65Hxx] 80A25: Combustion 94B99: None of the above, but in this section
Secondary: 65M20: Method of lines
Grout, Ray; Kolla, Hemanth; Minion, Michael; Bell, John. Achieving algorithmic resilience for temporal integration through spectral deferred corrections. Commun. Appl. Math. Comput. Sci. 12 (2017), no. 1, 25--50. doi:10.2140/camcos.2017.12.25. https://projecteuclid.org/euclid.camcos/1508432638