Search

link to homepage

Institute for Advanced Simulation (IAS)

Navigation and service


Research on parallel-in-time integration methods

The efficient use of modern high performance computing (HPC) systems has become one of the key challenges in computational science. Top HPC architectures already provide million-way concurrency, and current trends suggest that processor counts will continue to grow rapidly. Exploiting these levels of parallelism using traditional techniques for spatial parallelism becomes problematic when, for example, for a fixed problem size communication costs begin to dominate (“strong scaling barrier”) or for increased spatial resolution more time-steps are necessary due to stability constraints (“weak scaling barrier”).

For the numerical solution of time-dependent differential equations, parallel-in-time integration (PinT) methods have recently been shown to provide a promising way to extend prevailing scaling limits. To overcome the seemingly inherent serial dependence in the time direction and to enable integration of multiple time-steps simultaneously, one idea of time-parallel methods is to introduce a space/time hierarchy, where integrators with different costs are coupled in an iterative fashion. Serial dependencies are shifted to the coarsest level, allowing the computationally expensive parts on finer levels to be treated in parallel (“Parareal-based approaches”).

One promising PinT algorithm, the "parallel full approximation scheme in space and time" (PFASST), 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. In numerous studies, this approach has been successfully coupled to space-parallel solvers which use finite differences, spectral methods or even particles for discretization in space.

This group at JSC, being part of the cross-sectional team Mathematical Methods and Algorithms, primarily focuses on

  • mathematical analysis of spectral deferred corrections (SDC) and PFASST
  • large-scale applications with PFASST on HPC systems
  • algorithm-based fault tolerance
  • space-time multigrid methods

and is actively participating in the development of


Servicemeu

Homepage

Logo

 

 

 

YOUR OPINION MATTERS!

 

Dear visitor,

To make our website suit your needs even more and to give it a more appealing design, we would like you to answer a few short questions.

Answering these questions will take approx. 10 min.

Start now Close window

Thank you for your support!

 

In case you have already taken part in our survey or in case you have no time to take part now, you can simply close the window by clicking "close".

If you have any questions on the survey, please do not hesitate to contact: webumfrage@fz-juelich.de.

 

Your Team at Forschungszentrum Jülich

 

Note: Forschungszentrum Jülich works with the market research institute SKOPOS to anonymously conduct and analyze the survey. SKOPOS complies with the statutory requirements on data protection as well as with the regulations of ADM (Arbeitskreis Deutscher Markt- und Sozialforschungsinstitute e.V.) and ESOMAR (Europäische Gesellschaft für Meinungs- und Marketingforschung). Your data will not be forwarded to third parties.