Parallel-in-time integration of kinematic dynamos
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. Parallelizati...
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doaj-4ae0e0eaae7241b9a2fd12a3900f263d2020-11-25T02:02:17ZengElsevierJournal of Computational Physics: X2590-05522020-06-017100057Parallel-in-time integration of kinematic dynamosAndrew T. Clarke0Christopher J. Davies1Daniel Ruprecht2Steven M. Tobias3Centre for Doctoral Training in Fluid Dynamics, School of Computing, University of Leeds, Leeds, LS2 9JT, UK; Corresponding author.School of Earth and Environment, University of Leeds, Leeds, LS2 9JT, UKLehrstuhl Computational Mathematics, Institut für Mathematik, Technische Universität Hamburg, 21073 Hamburg, Germany; School of Mechanical Engineering, University of Leeds, Leeds, LS2 9JT, UKDepartment of Applied Mathematics, University of Leeds, Leeds, LS2 9JT, UKThe 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. 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. This paper 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. Both the time independent Roberts and time dependent Galloway-Proctor 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 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 some 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.http://www.sciencedirect.com/science/article/pii/S2590055220300093PararealParallel-in-timeKinematic dynamoInduction equationSpectral methodsIMEX |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Andrew T. Clarke Christopher J. Davies Daniel Ruprecht Steven M. Tobias |
spellingShingle |
Andrew T. Clarke Christopher J. Davies Daniel Ruprecht Steven M. Tobias Parallel-in-time integration of kinematic dynamos Journal of Computational Physics: X Parareal Parallel-in-time Kinematic dynamo Induction equation Spectral methods IMEX |
author_facet |
Andrew T. Clarke Christopher J. Davies Daniel Ruprecht Steven M. Tobias |
author_sort |
Andrew T. Clarke |
title |
Parallel-in-time integration of kinematic dynamos |
title_short |
Parallel-in-time integration of kinematic dynamos |
title_full |
Parallel-in-time integration of kinematic dynamos |
title_fullStr |
Parallel-in-time integration of kinematic dynamos |
title_full_unstemmed |
Parallel-in-time integration of kinematic dynamos |
title_sort |
parallel-in-time integration of kinematic dynamos |
publisher |
Elsevier |
series |
Journal of Computational Physics: X |
issn |
2590-0552 |
publishDate |
2020-06-01 |
description |
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. 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. This paper 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. Both the time independent Roberts and time dependent Galloway-Proctor 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 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 some 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. |
topic |
Parareal Parallel-in-time Kinematic dynamo Induction equation Spectral methods IMEX |
url |
http://www.sciencedirect.com/science/article/pii/S2590055220300093 |
work_keys_str_mv |
AT andrewtclarke parallelintimeintegrationofkinematicdynamos AT christopherjdavies parallelintimeintegrationofkinematicdynamos AT danielruprecht parallelintimeintegrationofkinematicdynamos AT stevenmtobias parallelintimeintegrationofkinematicdynamos |
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