Geodesic
Vlasov on GPU (VOG project)
M. Mehrenberger1 ; C. Steiner1 ; L. Marradi2 ; N. Crouseilles3 ; E. Sonnendrücker4 ; B. Afeyan5
1 IRMA, Université de Strasbourg, 7, rue René Descartes, F-67084 Strasbourg & INRIA-Nancy Grand-Est, projet CALVI, 
2 LIPHY, Université Joseph Fourier, 140, avenue de la Physique, F-38402 Saint Martin d’Hères, 
3 INRIA-Rennes Bretagne Atlantique, projet IPSO & IRMAR, Université de Rennes 1, 263 avenue du général Leclerc, F-35042 Rennes, 
4 Max-Planck Institute for plasma physics, Boltzmannstr. 2, D-85748 Garching, 
5 Polymath Research Inc., 827 Bonde Court, Pleasanton, CA 94566, 
ESAIM. Proceedings, Tome 43 (2013), pp. 37-58.

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This work concerns the numerical simulation of the Vlasov-Poisson equation using semi-Lagrangian 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.
DOI : 10.1051/proc/201343003

M. Mehrenberger 1 ; C. Steiner 1 ; L. Marradi 2 ; N. Crouseilles 3 ; E. Sonnendrücker 4 ; B. Afeyan 5

1 IRMA, Université de Strasbourg, 7, rue René Descartes, F-67084 Strasbourg & INRIA-Nancy Grand-Est, projet CALVI, 
2 LIPHY, Université Joseph Fourier, 140, avenue de la Physique, F-38402 Saint Martin d’Hères, 
3 INRIA-Rennes Bretagne Atlantique, projet IPSO & IRMAR, Université de Rennes 1, 263 avenue du général Leclerc, F-35042 Rennes, 
4 Max-Planck Institute for plasma physics, Boltzmannstr. 2, D-85748 Garching, 
5 Polymath Research Inc., 827 Bonde Court, Pleasanton, CA 94566,  
@article{EP_2013_43_a3,
     author = {M. Mehrenberger and C. Steiner and L. Marradi and N. Crouseilles and E. Sonnendr\"ucker and B. Afeyan},
     title = {Vlasov on {GPU} {(VOG} project)},
     journal = {ESAIM. Proceedings},
     pages = {37--58},
     publisher = {mathdoc},
     volume = {43},
     year = {2013},
     doi = {10.1051/proc/201343003},
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     url = {http://geodesic.mathdoc.fr/articles/10.1051/proc/201343003/}
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M. Mehrenberger; C. Steiner; L. Marradi; N. Crouseilles; E. Sonnendrücker; B. Afeyan. Vlasov on GPU (VOG project). ESAIM. Proceedings, Tome 43 (2013), pp. 37-58. doi : 10.1051/proc/201343003. http://geodesic.mathdoc.fr/articles/10.1051/proc/201343003/

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