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Hermite spline interpolation on patches for parallelly solving the Vlasov-Poisson equation

Nicolas Crouseilles 1 Guillaume Latu 2 Eric Sonnendrücker 3 
1 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
2 SCALAPPLIX - Algorithms and high performance computing for grand challenge applications
INRIA Futurs, Université Bordeaux Segalen - Bordeaux 2, Université Sciences et Technologies - Bordeaux 1, École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB), CNRS - Centre National de la Recherche Scientifique : UMR5800
Abstract : This work is devoted to the numerical simulation of the Vlasov equation using a phase space grid. In contrast to Particle-In-Cell (PIC) methods, which are known to be noisy, we propose a semi-Lagrangian-type method to discretize the Vlasov equation in the two-dimensional phase space. As this kind of method requires a huge computational effort, one has to carry out the simulations on parallel machines. For this purpose, we present a method using patches decomposing the phase domain, each patch being devoted to a processor. Some Hermite boundary conditions allow for the reconstruction of a good approximation of the global solution. Several numerical results demonstrate the accuracy and the good scalability of the method with up to 64 processors. This work is a part of the CALVI project.
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Nicolas Crouseilles, Guillaume Latu, Eric Sonnendrücker. Hermite spline interpolation on patches for parallelly solving the Vlasov-Poisson equation. International Journal of Applied Mathematics and Computer Science, University of Zielona Góra 2007, 17 (3), pp.335-349. ⟨10.2478/v10006-007-0028-x⟩. ⟨hal-00688671⟩



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