A Convergent Algorithm for Time Parallelization Applied to Reservoir Simulation

Garrido, Izaskun; Espedal, Magne S.; Fladmark, G. E.

doi:10.1007/3-540-26825-1_48

Cited by 26 publications

(28 citation statements)

References 9 publications

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“…Of these, the parareal (parallel in time) algorithm, which we explore in this paper, was first proposed by Lions et al [14] and has received an increasing amount of attention in recent years. It has been successfully applied to a number of relatively simple problems, like molecular dynamics simulations [15], linear and nonlinear parabolic ordinary differential equations [16,17], stochastic ordinary differential equations [18], reservoir simulations [19] and even, the laminar regime of the Navier-Stokes equation [20]. The scheme has also been applied very recently to the Princeton ocean model, dominated by convection, although with a rather modest success [21].…”

Section: Introductionmentioning

confidence: 99%

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

Samaddar

Newman

Sánchez

2010

Journal of Computational Physics

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a b s t r a c tIt is shown that numerical simulations of fully-developed plasma turbulence can be successfully parallelized in time using the parareal algorithm. The result is far from trivial, and even unexpected, since the exponential divergence of Lagrangian trajectories as well as the extreme sensitivity to initial conditions characteristic of turbulence set these type of simulations apart from the much simpler systems to which the parareal algorithm has been applied to this day. It is also shown that the parallel gain obtainable with this method is very promising (close to an order of magnitude for the cases and implementations described), even when it scales with the number of processors quite differently to what is typical for spatial parallelization.

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Section: Introductionmentioning

confidence: 99%

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

Samaddar

Newman

Sánchez

2010

Journal of Computational Physics

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“…In this context, many algorithms already proposed the solution of evolution problems in a time-parallel fashion (see [28] and the references therein for a historical review). However, the parareal algorithm, first presented in [42], has received a lot of attention over the past few years in different applications in different domains [3,5,25,26,29], as a promising efficient numerical method to solve evolution problems in parallel. The general principle of the parareal algorithm combines a coarse and fast solver which is run sequentially, and a more accurate and expensive fine solver that should be run in parallel.…”

Section: Introductionmentioning

confidence: 99%

Parareal operator splitting techniques for multi-scale reaction waves: Numerical analysis and strategies

Duarte¹,

Massot²,

Descombes³

2011

ESAIM: M2AN

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Abstract.In this paper, we investigate the coupling between operator splitting techniques and a time parallelization scheme, the parareal algorithm, as a numerical strategy for the simulation of reactiondiffusion equations modelling multi-scale reaction waves. This type of problems induces peculiar difficulties and potentially large stiffness which stem from the broad spectrum of temporal scales in the nonlinear chemical source term as well as from the presence of large spatial gradients in the reactive fronts, spatially very localized. In a series of previous studies, the numerical analysis of the operator splitting as well as the parareal algorithm has been conducted and such approaches have shown a great potential in the framework of reaction-diffusion and convection-diffusion-reaction systems. However, complementary studies are needed for a more complete characterization of such techniques for these stiff configurations. Therefore, we conduct in this work a precise numerical analysis that considers the combination of time operator splitting and the parareal algorithm in the context of stiff reaction fronts. The impact of the stiffness featured by these fronts on the convergence of the method is thus quantified, and allows to conclude on an optimal strategy for the resolution of such problems. We finally perform some numerical simulations in the field of nonlinear chemical dynamics that validate the theoretical estimates and examine the performance of such strategies in the context of academical one-dimensional test cases as well as multi-dimensional configurations simulated on parallel architecture.

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“…Except for turbulence [5,9] which is a complex system with high dimensional chaos, the parareal algorithm has so far been applied to relatively simple problems [10,11,12,13,14]. This work demonstrates that the parareal algorithm may be successfully applied to CORSICA to attain computational speed-up for plasma scenario simulations.…”

Section: Introductionmentioning

confidence: 92%

“…The parareal algorithm [4] lays out a scheme for the application of temporal parallelization to simulations. The algorithm has attracted significant attention in recent times and has undergone modifications to maximize computational speed-up and efficiency [5,6,7,8].Except for turbulence [5,9] which is a complex system with high dimensional chaos, the parareal algorithm has so far been applied to relatively simple problems [10,11,12,13,14]. This work demonstrates that the parareal algorithm may be successfully applied to CORSICA to attain computational speed-up for plasma scenario simulations.…”

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confidence: 92%

Time parallelization of advanced operation scenario simulations of ITER plasma

Samaddar

Casper

Kim

et al. 2013

J. Phys.: Conf. Ser.

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Abstract. This work demonstrates that simulations of advanced burning plasma operation scenarios can be successfully parallelized in time using the parareal algorithm. CORSICAan advanced operation scenario code for tokamak plasmas is used as a test case. This is a unique application since the parareal algorithm has so far been applied to relatively much simpler systems except for the case of turbulence. In the present application, a computational gain of an order of magnitude has been achieved which is extremely promising. A successful implementation of the Parareal algorithm to codes like CORSICA ushers in the possibility of time efficient simulations of ITER plasmas. IntroductionWith the construction of the ITER project well under way, understanding and predicting burning plasma scenarios have gained tremendous importance. These studies are used for designing of components for the world's largest tokamak and contribute towards its successful operation. Plasma scenario studies are carried out by codes such as CORSICA [1,2]. CORSICA employs a free or fixed boundary 2D equilibrium package that is coupled with various transport and source models. The advanced capabilities of these simulations allow studies with realistic physics and engineering constraints. CORSICA has also been used to predict and analyse plasma operations in the existing tokamak DIII-D[3] which served as a means of validation and verification.It must be borne in mind that simulations of plasma operation scenarios require extremely long wallclock time. Space parallelization is a common approach to achieve computational speedup although this technique experiences saturation while reduction in computation time is still desired. The option of time parallelization introduces a new opportunity, although this approach has not been explored much in the past for these kinds of simulations. The parareal algorithm [4] lays out a scheme for the application of temporal parallelization to simulations. The algorithm has attracted significant attention in recent times and has undergone modifications to maximize computational speed-up and efficiency [5,6,7,8].Except for turbulence [5,9] which is a complex system with high dimensional chaos, the parareal algorithm has so far been applied to relatively simple problems [10,11,12,13,14]. This work demonstrates that the parareal algorithm may be successfully applied to CORSICA to attain computational speed-up for plasma scenario simulations. The coupling of the equilibrium solver with the transport and source modules makes this a unique application compared to previous attempts. These simulations are characterized by quasi steady states interrupted by

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A Convergent Algorithm for Time Parallelization Applied to Reservoir Simulation

Cited by 26 publications

References 9 publications

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

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

Parareal operator splitting techniques for multi-scale reaction waves: Numerical analysis and strategies

Time parallelization of advanced operation scenario simulations of ITER plasma

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