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2012 Toward an efficient parallel in time method for partial differential equations
Matthew Emmett, Michael Minion
Commun. Appl. Math. Comput. Sci. 7(1): 105-132 (2012). DOI: 10.2140/camcos.2012.7.105


A new method for the parallelization of numerical methods for partial differential equations (PDEs) in the temporal direction is presented. The method is iterative with each iteration consisting of deferred correction sweeps performed alternately on fine and coarse space-time discretizations. The coarse grid problems are formulated using a space-time analog of the full approximation scheme popular in multigrid methods for nonlinear equations. The current approach is intended to provide an additional avenue for parallelization for PDE simulations that are already saturated in the spatial dimensions. Numerical results and timings on PDEs in one, two, and three space dimensions demonstrate the potential for the approach to provide efficient parallelization in the temporal direction.


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Matthew Emmett. Michael Minion. "Toward an efficient parallel in time method for partial differential equations." Commun. Appl. Math. Comput. Sci. 7 (1) 105 - 132, 2012.


Received: 21 December 2011; Revised: 18 January 2012; Accepted: 29 January 2012; Published: 2012
First available in Project Euclid: 20 December 2017

zbMATH: 1248.65106
MathSciNet: MR2979518
Digital Object Identifier: 10.2140/camcos.2012.7.105

Primary: 65M99

Keywords: deferred corrections , ordinary differential equations , parallel computing , Parareal , partial differential equations , time parallel

Rights: Copyright © 2012 Mathematical Sciences Publishers


Vol.7 • No. 1 • 2012
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