Communications in Applied Mathematics and Computational Science

Toward an efficient parallel in time method for partial differential equations

Matthew Emmett and Michael Minion

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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.

Article information

Commun. Appl. Math. Comput. Sci., Volume 7, Number 1 (2012), 105-132.

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

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Zentralblatt MATH identifier

Primary: 65M99: None of the above, but in this section

parallel computing time parallel ordinary differential equations partial differential equations deferred corrections parareal


Emmett, Matthew; Minion, Michael. Toward an efficient parallel in time method for partial differential equations. Commun. Appl. Math. Comput. Sci. 7 (2012), no. 1, 105--132. doi:10.2140/camcos.2012.7.105.

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