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

Crouseilles, N. ; Latu, G. ; Sonnendrücker, E.

International Journal of Applied Mathematics and Computer Science, Tome 17 (2007) no. 3, pp. 335-349.

Résumé

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.

Détail

Keywords: Vlasov-Poisson equation, semi-Lagrangian method, parallelism
Mots-clés : równanie Vlasova-Poissona, metoda Lagrangiana, równoległość

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