Parallelization in time of numerical simulations of fully-developed plasma turbulence using the parareal algorithm

Samaddar, Debasmita; Newman, D. E.; Sánchez, Raúl

doi:10.1016/j.jcp.2010.05.012

Cited by 48 publications

(78 citation statements)

References 26 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This is likely because the coarse solution is allowed to deviate very far from the fine solution which essentially violates the condition for parareal correction to rectify the solution as formulated in [1]. A similar behaviour with parareal simulations has been observed and studied in [9,10].…”

Section: Resultssupporting

confidence: 58%

“…As has been discussed in [9,10,11], a variety of choices may be employed to achieve shorter wallclock time accompanied by coarseness in the solution. However, the choice is certainly non trivial.…”

Section: Coarse Solvers For Solpsmentioning

confidence: 99%

“…Moreover, it must be clarified that temporal parallelization is not a replacement for any existing form of parallelization, but may be added to them to further, often significantly, improve performance. Temporal parallelization using the parareal algorithm was originally proposed in [1] in 2001, and has been applied to a variety of problems from relatively simple ones [2,3,4,5,6,7,8] to ones with complex dynamics [9,10,11,12].…”

Section: Introductionmentioning

confidence: 99%

“…Fully developed turbulence simulations in the steady state where the statistical study of properties such as the probability distribution function, vorticity and velocity are relevant are dealt with in [9,10]. [11] applies to burning plasma scenarios but the details of the physics of the edge involving impurities and neutral transport are not given significant importance.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Temporal parallelization of edge plasma simulations using the parareal algorithm and the SOLPS code

Samaddar

Coster

Bonnin

et al. 2017

Computer Physics Communications

Self Cite

View full text Add to dashboard Cite

show abstract

Section: Resultssupporting

confidence: 58%

Section: Coarse Solvers For Solpsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Temporal parallelization of edge plasma simulations using the parareal algorithm and the SOLPS code

Samaddar

Coster

Bonnin

et al. 2017

Computer Physics Communications

Self Cite

View full text Add to dashboard Cite

show abstract

“…They have been applied to surprisingly complicated physics such as plasma turbulence [14]. In this Section, some of the mathematics that underlies TP equations is summarized and two TP equations are highlighted, the standard Parareal equations and an alternative TP equation, that is further modified in Sections 1.5 and 1.6 to derive a temporal multiscale hybridization that serves as an alternative to the simple switching hybridization of Equation (6).…”

Section: Time-parallel Computing Backgroundmentioning

confidence: 99%

An Approximate Time-Parallel Method for the Fast and Accurate Computation of Particle Trajectories in a Magnetic Field*

Lederman¹,

Bilyeu²

2018

JAMP

View full text Add to dashboard Cite

A temporal multiscale hybridization method is presented that carefully couples coarse scale gyrokinetic models with exact charged particle solution trajectories (that is, with full phase information) in a magnetic field. The approach is based on the careful approximation of a sum, generally employed for time-parallel (TP) computing applications. While the hybridization method presented is highly parallelizable, a computational efficiency gain is seen from considering serial computations only. A complete numerical method is only presented for the aforementioned charged particle application, however, the general approach depicted likely has relevance to a wide swath of challenging multiscale/multiphysics problems. Additionally, the approach has obvious relevance to TP computing applications (such as variable selection on which to perform TP calculations and fine scale sampling strategies).

show abstract

On “Optimal” h‐independent convergence of Parareal and multigrid‐reduction‐in‐time using Runge‐Kutta time integration

Friedhoff

Southworth

2020

Numerical Linear Algebra App

View full text Add to dashboard Cite

Parareal and multigrid-reduction-in-time (MGRIT) are two popular parallel-in-time algorithms. The idea of both algorithms is to combine the (fine-grid) time-stepping scheme of interest with a "coarse-grid" time-integration scheme that approximates several steps of the fine-grid time-stepping method. Convergence of Parareal and MGRIT has been studied in a number of papers. Research on the optimality of both methods, however, is limited, with results existing only for specific time-integration schemes. This paper focuses on analytically showing ℎ -and ℎ -independent convergence of two-level Parareal and MGRIT, for linear problems of the form ′ ( ) +  ( ) = ( ), where  is symmetric positive definite and Runge-Kutta time integration is used. The analysis is based on recently derived tight bounds of two-level Parareal and MGRIT convergence that allow for analyzing arbitrary coarse-and finegrid time integration schemes, coarsening factors, and time-step sizes. The theory presented in this paper shows that not all Runge-Kutta schemes are equal from the perspective of parallel-in-time. Some schemes, particularly L-stable methods, offer significantly better convergence than others. On the other hand, some schemes do not obtain ℎ-optimal convergence, and two-level convergence is restricted to certain parameter regimes. In certain cases, an (1) factor change in time step ℎ can be the difference between convergence factors ≈ 0.02 and divergence! Numerical results confirm the analysis in the practical setting and, in particular, emphasize the importance of a priori analysis in choosing an effective coarse-grid scheme and coarsening factor. A Mathematica notebook to perform a priori two-grid analysis is available at https://github.com/XBraid/xbraid-convergence-est. Recently, two-level theory was developed by Southworth 15 that provides tight bounds on linear Parareal and two-level MGRIT for arbitrary time-propagation operators. The central aim of this paper is to use these tight bounds to analytically show ℎindependent convergence of two-level Parareal and MGRIT for linear problems of the form ′ ( )+ ( ) = ( ), where  is SPD and Runge-Kutta time integration is used. Thus, this paper highlights the practical implications of the new theory, particularly for parabolic-type PDEs with SPD spatial operators. The relatively clean formulae derived in 15 allow for straightforward convergence analysis of arbitrary coarse-and fine-grid propagators, coarsening factors, and time-step sizes. Therefore, this paper can be seen as a substantial generalization of previous works by Mathew et al. 25 and by Wu and Zhou 26, 28 on ℎ-independent convergence of Parareal. Our theoretical framework also encompasses analysis of various modified Parareal algorithms, such as the (scalar) -Parareal method 29 and modified A-/L-stable fine-grid propagators introduced in 30 .Because the underlying two-grid bounds used in this work are tight, they allow us to easily demonstrate that not all Runge-Kutta schemes are equal from the perspective of parallel-in-...

show abstract

Parallelization in time of numerical simulations of fully-developed plasma turbulence using the parareal algorithm

Cited by 48 publications

References 26 publications

Temporal parallelization of edge plasma simulations using the parareal algorithm and the SOLPS code

Temporal parallelization of edge plasma simulations using the parareal algorithm and the SOLPS code

An Approximate Time-Parallel Method for the Fast and Accurate Computation of Particle Trajectories in a Magnetic Field*

On “Optimal” h‐independent convergence of Parareal and multigrid‐reduction‐in‐time using Runge‐Kutta time integration

Contact Info

Product

Resources

About