Oberseminar "Aktuelle Themen der Numerik"

 

Donnerstag, 20.11.2014, 14.00 Uhr

Parallel-in-time integration with ParaReal

Daniel Ruprecht (USI Lugano)

Abstract:
The extremely high degree of concurrency required by massively parallel high-performance computing architectures not only gives rise to demanding technical and economical challenges, but also mandates the development of novel, inherently parallel numerical approaches. For time-dependent problems, parallelization in the temporal direction provides a promising strategy to increase concurrency already on the algorithmic level. A popular method in this field is Parareal, which iterates between a cheap, coarse propagator run in serial and an expensive, accurate propagator run in parallel on multiple time-slices. Parareal is widely studied, because it is relatively straightforward to implement and easy to combine with existing codes. The talk will introduce Parareal and discuss several of its features. Examples of its application to different problems will be presented, e.g. to the Navier-Stokes or Einstein equations. Benchmarks will be shown, obtained on the Cray XC30 ‘’Piz Daint’’ at the Swiss Supercomputing Centre, illustrating Parareal’s performance in terms of speedup and energy-to-solution.

Zeit: 14:00 Uhr

Parallel-in-time integration with PFASST

Robert Speck (Jülich Supercomputing Center)

Abstract:
The "parallel full approximation scheme in space and time" (PFASST) introduced by Emmett and Minion in 2012 is an iterative, multilevel strategy for the temporal parallelization of ODEs and discretized PDEs. As the name suggests, PFASST is similar in spirit to a space-time FAS multigrid method performed over multiple timesteps in parallel. The key for optimal parallel efficiency is a careful choice of coarsening strategies in space and time. Besides straightforward approaches like reducing the number of degrees-of-freedom and/or integration nodes, recent works focused on the reduction of the spatial discretization order as well as inexact solves of systems arising in implicit steps on the coarse levels.

In this talk, we will discuss various, application-tailored coarsening strategies and show recent results using "inexact" PFASST, where only a limited number of V-cycles is performed to solve the implicit systems in space at each time-step. The iterative nature of "IPFASST" provides continuously improving initial guesses in each iteration, so that full solves can be replaced by inexact approximations on all levels, leading to significantly improved runtimes. We will highlight extreme-scale benchmarks with a multigrid solver on up to 448K cores of the IBM Blue Gene/Q installation JUQUEEN. We will also describe ongoing work on developing a space-time parallel tree code for plasma physics applications using a multilevel, high-order Boris integrator.

Zeit: 14:45 Uhr

Ort: Raum 149, Hauptgebäude, RWTH Aachen, Templergraben 55, 52056 Aachen