Beyond spatial scalability limitations with a massively parallel method for linear oscillatory problems
Schreiber, M; Peixoto, P; Haut, T; et al.Wingate, B
Date: 3 February 2017
Journal
International Journal of High Performance Computing Applications
Publisher
SAGE Publications
Publisher DOI
Abstract
This paper presents, discusses and analyses a massively parallel-in-time solver for linear oscillatory PDEs, which
is a key numerical component for evolving weather, ocean, climate and seismic models. The time parallelization in
this solver allows us to significantly exceed the computing resources used by parallelization-in-space ...
This paper presents, discusses and analyses a massively parallel-in-time solver for linear oscillatory PDEs, which
is a key numerical component for evolving weather, ocean, climate and seismic models. The time parallelization in
this solver allows us to significantly exceed the computing resources used by parallelization-in-space methods and
results in a correspondingly significantly reduced wall-clock time. One of the major difficulties of achieving Exascale
performance for weather prediction is that the strong scaling limit – the parallel performance for a fixed problem size
with an increasing number of processors – saturates. A main avenue to circumvent this problem is to introduce new
numerical techniques that take advantage of time parallelism. In this paper we use a time-parallel approximation that
retains the frequency information of oscillatory problems. This approximation is based on (a) reformulating the original
problem into a large set of independent terms and (b) solving each of these terms independently of each other which
can now be accomplished on a large number of HPC resources. Our results are conducted on up to 3586 cores for
problem sizes with the parallelization-in-space scalability limited already on a single node. We gain significant reductions
in the time-to-solution of 118.3 for spectral methods and 1503.0 for finite-difference methods with the parallelizationin-time
approach. A developed and calibrated performance model gives the scalability limitations a-priory for this new
approach and allows us to extrapolate the performance method towards large-scale system. This work has the potential
to contribute as a basic building block of parallelization-in-time approaches, with possible major implications in applied
areas modelling oscillatory dominated problems.
Computer Science
Faculty of Environment, Science and Economy
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