id: 05886229
dt: j
an: 05886229
au: Aubanel, Eric
ti: Scheduling of tasks in the parareal algorithm.
so: Parallel Comput. 37, No. 3, 172-182 (2011).
py: 2011
pu: Elsevier (North Holland), Amsterdam
la: EN
cc: 
ut: parareal algorithm; time parallelization; heat equation; numerical
    examples; domain decomposition; convergence; long time evolution
    problems
ci: 
li: doi:10.1016/j.parco.2010.10.004
ab: Summary: Parallelization of partial differential equations (PDEs) by time
    decomposition has attracted much interest, mainly due to its potential
    to enable very long time simulations beyond what is possible using
    spatial domain decomposition. However, there has only been limited
    performance analysis of the parareal algorithm in the literature,
    ignoring the efficient scheduling of tasks.  This paper presents a
    detailed study of the scheduling of tasks in the parareal algorithm
    that achieves significantly better efficiency than the usual algorithm.
    Two algorithms are proposed, one of which uses a manager-worker
    paradigm with overlap of sequential and parallel phases, and a second
    that is completely distributed. Experiments are conducted with the 2D
    heat equation.  It is found that the rate of convergence decreases as
    the number of processors increases, in the case of strong scaling
    (fixed time interval). However, for weak scaling results the rate of
    convergence is unaffected by the number of processors. The results of
    this paper suggest that the parareal algorithm is a promising approach
    to solving long time evolution problems, particularly when the goal is
    a simulation of longer times using more processors. It also exhibits
    characteristics that make it particularly suitable for execution on
    heterogeneous computational grids, such as low communication overhead
    and easy accommodation of different processor and network speeds.
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