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A parallel Vlasov solver based on local cubic spline interpolation on patches

Nicolas Crouseilles 1, 2 Guillaume Latu 3, 4, 5 Eric Sonnendrücker 4, 5
1 IPSO - Invariant Preserving SOlvers
IRMAR - Institut de Recherche Mathématique de Rennes, Inria Rennes – Bretagne Atlantique
5 CALVI - Scientific computation and visualization
IRMA - Institut de Recherche Mathématique Avancée, LSIIT - Laboratoire des Sciences de l'Image, de l'Informatique et de la Télédétection, Inria Nancy - Grand Est, IECL - Institut Élie Cartan de Lorraine
Abstract : A method for computing the numerical solution of Vlasov type equations on massively parallel computers is presented. In contrast with Particle In Cell methods which are known to be noisy, the method is based on a semi-Lagrangian algorithm that approaches the Vlasov equation on a grid of phase space. As this kind of method requires a huge computational effort, the simulations are carried out on parallel machines. To that purpose, we present a local cubic splines interpolation method based on a domain decomposition, e.g. devoted to a processor. Hermite boundary conditions between the domains, using ad hoc reconstruction of the derivatives, provide a good approximation of the global solution. The method is applied on various physical configurations which show the ability of the numerical scheme.
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Submitted on : Wednesday, January 9, 2013 - 2:32:29 AM
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Nicolas Crouseilles, Guillaume Latu, Eric Sonnendrücker. A parallel Vlasov solver based on local cubic spline interpolation on patches. Journal of Computational Physics, Elsevier, 2009, 228, pp.1429-1446. ⟨10.1016/⟩. ⟨hal-00771580⟩



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