Dr. Martin Schreiber has been invited to the dynamics seminar in the TUM mathematics department on December 16th 2019 at 3 pm, room 03.06.011.


On Next-Generation Time Stepping Methods for Weather and Climate Simulations

Running simulations on high-performance computers faces new challenges due to e.g. the stagnating or even decreasing per-core speed. This poses new restrictions and therefore challenges on solving PDEs within a particular time frame. Here, disruptive mathematical reformulations which e.g. exploit additional degrees of parallelism also in the time dimension gained increasing interest over the last two decades.

This talk will give concrete examples of the current cutting edge research on parallel-in-time and other next-generation time integration methods in the context of weather and climate simulations:

* Parallel-in-time rational approximation of exponential integrators (REXI) based on Terry's (T-REXI),

  Cauchy Contour (CI-REXI) and Butcher Tableau (B-REXI).

* Semi-Lagrangian Parareal (SL-Parareal)

* Semi-Lagrangian exponential integration (SL-EXP)

* Multi-level time integration of spectral deferred correction (ML-SDC)

* Parallel Full Approximation Scheme in Space and Time (PFASST)

These methods are mostly realized with numerics similar to the ones used by the European Centre for Medium-Range Weather Forecasts (ECMWF). Our results motivate further investigation for operational weather/climate systems in order to cope with the hardware imposed restrictions of future super computer architectures.

(I gratefully acknowledge contributions and more from Jed Brown, Francois Hamon, Terry S. Haut, Richard Loft, Michael L. Minion, Matthew Normile, Pedro S. Peixoto, Nathanaël Schaeffer, Andreas Schmitt)

Dr. rer. nat. Martin Schreiber