Parallelintime integration of kinematic dynamos
Abstract
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. Additional directions of parallelization are desirable to utilise the high number of processor cores now available. Parallelintime methods can deliver speed up in addition to that offered by spatial partitioning but have not yet been applied to dynamo simulations. This paper investigates the feasibility of using the parallelintime algorithm Parareal to speed up initial value problem simulations of the kinematic dynamo, using the open source Dedalus spectral solver. Both the time independent Roberts and time dependent GallowayProctor 2.5D dynamos are investigated over a range of magnetic Reynolds numbers. Speedups beyond those possible from spatial parallelisation are found in both cases. Results for the GallowayProctor flow are promising, with Parareal efficiency found to be close to 0.3. Roberts flow results are less efficient, but Parareal still shows some speed up over spatial parallelisation alone. Parallel in space and time speed ups of ∼300 were found for 1600 cores for the GallowayProctor flow, with total parallel efficiency of ∼0.16.
 Publication:

Journal of Computational Physics: X
 Pub Date:
 June 2020
 DOI:
 10.1016/j.jcpx.2020.100057
 arXiv:
 arXiv:1902.00387
 Bibcode:
 2020JCPX....700057C
 Keywords:

 Parareal;
 Parallelintime;
 Kinematic dynamo;
 Induction equation;
 Spectral methods;
 IMEX;
 Physics  Computational Physics
 EPrint:
 Journal of Computational Physics X: 7, pp. 100057, 2020