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Presentation

PhD Forum
:
(PhD07) Parallel-In-Time Dynamo Simulations
Event Type
PhD Forum
Passes
TimeMonday, June 17th1pm - 6pm
LocationFoyers
DescriptionObjectives:
Investigate suitability of parallel in time methods to speed up dynamo simulations.
Explore performance of parareal algorithm when applied to kinematic dynamos.
Compare performance of parareal with performance of PFASST when applied to kinematic dynamos.
Explore performance of parareal and PFASST when applied to fully coupled magnetohydrodynamic simulations.

Early results:
A combined space-time parallelisation using Parareal was found to deliver substantial speedup beyond the saturation point of purely spatial parallelisation.
Speed up of over 300 found using 1600 processors, with efficiency of ~0.16.


Description of Work:
The precise mechanisms responsible for the natural dynamos in the Earth and Sun are still not fully understood. Numerical simulations of natural dynamos are extremely computationally intensive, and are carried out in parameter regimes many orders of magnitude away from real conditions.

Parallelization in space is a common strategy to speed up simulations on high performance computers, but eventually hits a scaling limit because of increasing overheads from communication.. Additional directions of parallelization are desirable to utilise the high number of processor cores now available in current and future massively parallel high-performance computing systems.

Parallel-in-time methods can deliver speed up in addition to that offered by spatial partitioning but have not yet been applied to dynamo simulations. My research investigates the feasibility of using the parallel-in-time algorithm Parareal to speed up initial value problem simulations of the kinematic dynamo, using the open source Dedalus spectral solver.

I have provided the first demonstration first demonstration that parallel-in-time methods can deliver speed up for the kinematic dynamo problem beyond the saturation point of spatial parallelization over a wide range of magnetic Reynolds numbers.

My poster will present an implementation of Parareal in the open source Python based Dedalus spectral solver. The code makes use of FFTW and MPI libraries for efficient parallel communications, with the mpi4py python library used to implement the Parareal algorithm, to run fully parallel in time and space simulations. The coarse solver is generated by coarsening in both spatial and time coordinates.

Both the time independent Roberts and time dependent Galloway-Proctor 2.5D dynamos are investigated over a range of magnetic Reynolds numbers.

Speed ups beyond those possible from spatial parallelisation are found in both cases. Results for the Galloway-Proctor flow are promising, with Parareal efficiency found to be close to 0.3. Roberts flow results are less efficient, but Parareal still shows speed up over spatial parallelisation alone.
Parallel in space and time speed ups of ~300 were found for 1600 cores for the Galloway-Proctor flow, with total parallel efficiency of ~0.16

My results indicate that parallel in time methods are very promising for simulation of geo- and astro- dynamos and could allow investigation of parameter regimes closer to reality than have been hitherto possible.

Future work planned includes investigation of the method for non-linear MHD problems, and a comparison of Parareal with alternative parallel-in-time algorithm PFASST.