Vol. 7, No. 1, 2012

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Toward an efficient parallel in time method for partial differential equations

Matthew Emmett and Michael L. Minion

Vol. 7 (2012), No. 1, 105–132
Abstract

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.

Keywords
parallel computing, time parallel, ordinary differential equations, partial differential equations, deferred corrections, parareal
Mathematical Subject Classification 2010
Primary: 65M99
Milestones
Received: 21 December 2011
Revised: 18 January 2012
Accepted: 29 January 2012
Published: 28 March 2012
Authors
Matthew Emmett
Department of Mathematics
University of North Carolina
CB 3250 Phillips Hall
Chapel Hill, NC 27599
United States
Michael L. Minion
Department of Mathematics
University of North Carolina
CB 3250 Phillips Hall
Chapel Hill, NC 27599
United States