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Résumé. Ce travail concerne la simulation numérique du modèle de Vlasov-Poissonà l'aide de méthodes semi-Lagrangiennes, sur des architectures GPU. Pour cela, quelques modifications de la méthode traditionnelle ont dûêtre effectuées. Tout d'abord, une reformulation des méthodes semiLagrangiennes est proposée, qui permet de la réécrire sous la forme d'un produit d'une matrice circulante avec le vecteur des inconnues. Ce calcul peutêtre fait efficacement grâce aux routines de FFT. Actuellement, le GPU n'est plus limitéà la simple précision. Néanmoins, la simple précision reste intéressante pour des raisons de performance et de mémoire disponible. Afin de contourner le problème de la simple précision, une méthode de type δf est alors utilisée. Ainsi, un code Vlasov-Poisson GPU permet de simuler et de décrire avec un haut degré de précision (grâceà l'utilisation de reconstructions d'ordreélevé et d'un grand nombre de points de l'espace des phases) des cas tests académiques mais aussi des phénomènes physiques pertinents, comme la simulation des ondes KEEN.Abstract. This work concerns the numerical simulation of the Vlasov-Poisson equation using semiLagrangian methods on Graphics Processing Units (GPU). To accomplish this goal, modifications to traditional methods had to be implemented. First and foremost, a reformulation of semi-Lagrangian methods is performed, which enables us to rewrite the governing equations as a circulant matrix operating on the vector of unknowns. This product calculation can be performed efficiently using FFT routines. Nowadays GPU is no more limited to single precision; however, single precision may still be preferred with respect to performance and available memory. So, in order to be able to deal with single precision, a δf type method is adopted which only needs refinement in specialized areas of phase space but not throughout. Thus, a GPU Vlasov-Poisson solver can indeed perform high precision simulations (since it uses very high order of reconstruction and a large number of grid points in phase space). We show results for more academic test cases and also for physically relevant phenomena such as the bump on tail instability and the simulation of Kinetic Electrostatic Electron Nonlinear (KEEN) waves.

Abstract. Gyrokinetic modeling is appropriate for describing Tokamak plasma turbulence, and the gyroaverage operator is a cornerstone of this approach. In a gyrokinetic code, the gyroaveraging scheme needs to be accurate enough to avoid spoiling the data but also requires a low computation cost because it is applied often on the main unknown, the 5D guiding-center distribution function, and on the 3D electric potentials. In the present paper, we improve a gyroaverage scheme based on Hermite interpolation used in the Gysela code. This initial implementation represents a too large fraction of the total execution time. The gyroaverage operator has been reformulated and is now expressed as a matrix-vector product and a cache-friendly algorithm has been setup. Different techniques have been investigated to quicken the computations by more than a factor two. Description of the algorithms is given, together with an analysis of the achieved performance.