Applied Math And Analysis Seminar
Monday, February 16, 2009, 4:30pm, 119 Physics
Michael Minion (UNC Chapel Hill, Department of Mathematics)
Parallel in time integration: parareal and deferred corrections
Abstract:- The efficient parallelization of numerical
methods for ordinary or partial differential equations
in the temporal direction is an intriguing possibility that
has of yet not been fully realized despite decades of
investigation. For partial differential equations, virtually all large
scale computations now employ parallelization across space, and
there are freely available computational tools and libraries
to aid in the development of spatially parallelized codes. Conversely,
parallelization in the temporal direction is rarely even considered.
I will discuss a relatively recent parallel strategy called the parareal
algorithm that has generated a renewed wave of interest in time
parallelization. I will show how the iterative structure of
the parareal algorithm can be interpreted as a particular form
of deferred corrections and then present a modified parareal
strategy based on spectral deferred corrections that can
significantly reduce the computational cost of the method. Finally
I will make some observations as to why parallel in time methods
may be attractive in the future. [video]
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