Real Time Computing with the Parareal Algorithm

This work presents and evaluates a particular
algorithm used for the
real time computations of time dependent ordinary and
partial
differential equations which employs a
parallelization strategy over
the temporal domain. We also discuss the coupling of
this method
with another popular technique used for real time
computations,
model reduction, which will be shown to provide more
gains than
either method alone. In particular, we look at
reduced order
modeling based on proper orthogonal decompositions.
We present some applications in terms of solving
time dependent
nonlinear partial differential equations and solving
these equations
with a coupled approach of combining model reduction
and the
parareal algorithm . The performance of this method,
both
numerically and computationally, is discussed in
terms of the gains
in speedup and efficiency, and in terms of the
scalability of the
parallelization of the temporal domain on a larger
and larger
set of compute nodes or processors.

Autorentext

Christopher R. Harden was born 12-21-1976, in Jacksonville, Fl.In 2005, he completed a Bachelors degree in Philosophy and a Bachelors degreein Mathematics at UNF. In 2008, he obtained a Masters degree in ComputationalScience at FSU. Chris is now finishing his Ph.D in Computational Science underProf. T. Plewa at FSU.

Klappentext

This work presents and evaluates a particularalgorithm used for the real time computations of time dependent ordinary andpartial differential equations which employs aparallelization strategy over the temporal domain. We also discuss the coupling ofthis method with another popular technique used for real timecomputations,model reduction, which will be shown to provide moregains than either method alone. In particular, we look atreduced order modeling based on proper orthogonal decompositions. We present some applications in terms of solvingtime dependent nonlinear partial differential equations and solvingthese equations with a coupled approach of combining model reductionand the parareal algorithm . The performance of this method,both numerically and computationally, is discussed interms of the gains in speedup and efficiency, and in terms of thescalability of the parallelization of the temporal domain on a largerand largerset of compute nodes or processors.