Long Time Behaviour of an Exponential Integrator for a Vlasov-Poisson System with Strong Magnetic Field

Frénod, Emmanuel; Hirstoaga, Sever Adrian; Lutz, Mathieu; Sonnendrücker, Éric

doi:10.4208/cicp.070214.160115a

Cited by 53 publications

(50 citation statements)

References 21 publications

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“…In future work, we intend to implement the time stepping scheme introduced in [8]. This method allows to solve multiscale Vlasov-Poisson models by treating the stiff terms as an exponential integrator.…”

Section: Discussionmentioning

confidence: 99%

“…In this regard we deal with issues like optimized data structures, streamlined memory access and parallelization. In addition, we notice that, with the further aim to improve the recent time scheme in [8] and to extend it to more general problems than the aforementioned multiscale model, we need to have at our disposal a fast code yielding the reference solution. In the following, we understand by reference solution of a model its numerical solution calculated with classical numerical schemes and small enough numerical parameters.…”

Section: Introductionmentioning

confidence: 99%

“…The regime in which the Vlasov-Poisson system (1) is written corresponds to a time rescaling of the classical drift-kinetic model. The scaling procedure leading to this regime is given in [10] and the time rescaling is done in [9] (see also Section 5.2.1 in [8]). The limit model of (1) is derived in [2,9], under some hypotheses for f 0 .…”

Section: Introductionmentioning

confidence: 99%

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Optimization of particle-in-cell simulations for Vlasov-Poisson system with strong magnetic field

2016

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Abstract. We study the dynamics of charged particles under the influence of a strong magnetic field by numerically solving the Vlasov-Poisson and guiding center models. By using appropriate data structures, we implement an efficient (from the memory access point of view) particle-in-cell method which enables simulations with a large number of particles. We present numerical results for classical one-dimensional Landau damping and two-dimensional Kelvin-Helmholtz test cases. The implementation also relies on a standard hybrid MPI/OpenMP parallelization. Code performance is assessed by the observed speedup and attained memory bandwidth.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Optimization of particle-in-cell simulations for Vlasov-Poisson system with strong magnetic field

2016

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“…In this work, we consider the long-time Vlasov-Poisson equation with a strong external homogeneous magnetic field in four phase space dimensions as [19,18]. The distribution function f ε (t, x, v) depending on time t ≥ 0, on space x = (x 1 , x 2 )…”

Section: Introductionmentioning

confidence: 99%

Multiscale Particle-in-Cell methods and comparisons for the long-time two-dimensional Vlasov–Poisson equation with strong magnetic field

Crouseilles

Hirstoaga

Zhao

2018

Computer Physics Communications

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To cite this version:Nicolas Crouseilles, Sever Hirstoaga, Xiaofei Zhao. Multiscale Particle-in-Cell methods and comparisons for the long-time two-dimensional Vlasov-Poisson equation with strong magnetic field. Computer Physics Communications, Elsevier, 2018, 222, pp.136-151 AbstractWe applied different kinds of multiscale methods to numerically study the long-time Vlasov-Poisson equation with a strong magnetic field. The multiscale methods include an asymptotic preserving Runge-Kutta scheme, an exponential time differencing scheme, stroboscopic averaging method and a uniformly accurate two-scale formulation. We briefly review these methods and then adapt them to solve the Vlasov-Poisson equation under a Particle-in-Cell discretization. Extensive numerical experiments are conducted to investigate and compare the accuracy, efficiency, and long-time behavior of all the methods. The methods with the best performance under different parameter regimes are identified.

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“…Such system can already describe some physics; as an example, it can be seen as a limit of a Vlasov-Poisson system (see e.g. [6] and [9,13,20] for the numerics). As emphasized in [12], it is a building block for future drift kinetic simulations.…”

Section: Introductionmentioning

confidence: 99%

Guiding center simulations on curvilinear grids

Hamiaz¹,

Mehrenberger²,

Back³

et al. 2016

ESAIM: Proc.

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Abstract. Semi-Lagrangian guiding center simulations are performed on sinusoidal perturbations of cartesian grids, and on deformed polar grid with different boundary conditions. Key ingredients are: the use of a B-spline finite element solver for the Poisson equation and the classical backward semiLagrangian method (BSL) for the advection. We are able to reproduce standard Kelvin-Helmholtz and diocotron instability tests on such grids. When the perturbation leads to a strong distorted mesh, we observe that the solution differs if one takes standard numerical parameters that are used in the cartesian reference case. We can recover good results together with correct mass conservation, by diminishing the time step.Résumé. Des simulations semi-lagrangiennes du modèle centre-guide sont effectuées sur des perturbations sinusoïdales de maillages cartésiens et sur des maillages polaires déformés. Les ingrédients clés sont: l'utilisation d'un solveuréléments finis splines pour l'équation de Poisson et la méthode semi-Lagrangienne en arrière classique (BSL) pour l'advection. Nous pouvons reproduire des tests standards d'instabilité de Kelvin-Helmholtz et diocotron sur ces grilles. Lorsque la déformation du maillage est forte, on observe que la solution diffère, si on prend les paramètres numériques standards qui sont utilisés dans le cas cartésien de référence. On peut retrouver néanmoins les bons résultats et une conservation de masse correcte, en diminuant le pas de temps.

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Long Time Behaviour of an Exponential Integrator for a Vlasov-Poisson System with Strong Magnetic Field

Cited by 53 publications

References 21 publications

Optimization of particle-in-cell simulations for Vlasov-Poisson system with strong magnetic field

Optimization of particle-in-cell simulations for Vlasov-Poisson system with strong magnetic field

Multiscale Particle-in-Cell methods and comparisons for the long-time two-dimensional Vlasov–Poisson equation with strong magnetic field

Guiding center simulations on curvilinear grids

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