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Toward Efficient Parallel in Time Methods for Partial
Differential Equations
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Higher-Order, Space-Time Adaptive Finite Volume Methods:
Algorithms, Analysis and Applications
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\begin{center}\large
Michael Minion and Matthew Emmett \\
Univeristy of North Carolina \\
CB \#3250, Phillips Hall, Chapel Hill, NC 27599
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{\em Abstract\/}
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An algorithmic framework for the
parallelization of numerical methods for partial differential
equations in the temporal direction will be presented. In practice, temporal
parallelization is only attractive if the temporal parallelization has
greater parallel efficiency than (additional) spatial
parallelization. Hence, the focus here is on constructing methods with
good parallel efficiency. The approach presented iteratively improves
the solution on each time slice by applying deferred
correction sweeps to a hierarchy of discretizations at different
spatial and temporal resolutions. Coarse resolution problems are
formulated using a time-space analog of the full approximation
scheme, and different coarsening strategies depending on the spatial
discretization will be presented.
The parallel efficiency and speedup for
PDEs in one, two and three dimensions will be presented.
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