Geodesic
Particle-in-wavelets scheme for the 1D Vlasov-Poisson equations
Romain Nguyen van yen1 ; Éric Sonnendrücker2, 1 ; Kai Schneider3 ; Marie Farge1, 2, 3
1LMD-CNRS-IPSL, École Normale Supérieure, 24 rue Lhomond, 75231 Paris Cedex 5, France
2IRMA-CNRS, Université de Strasbourg, 7 rue Ren-Descartes, 67084 Strasbourg Cedex, France
3M2P2-CNRS and CMI, Université d’Aix-Marseille, 38 rue Frdric Joliot-Curie, 13451 Marseille Cedex 13, France
ESAIM. Proceedings, Tome 32 (2011), pp. 134-148

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A new numerical scheme called particle-in-wavelets is proposed for the Vlasov-Poisson equations, and tested in the simplest case of one spatial dimension. The plasma distribution function is discretized using tracer particles, and the charge distribution is reconstructed using wavelet-based density estimation. The latter consists in projecting the Delta distributions corresponding to the particles onto a finite dimensional linear space spanned by a family of wavelets, which is chosen adaptively. The stability and accuracy of the scheme is supported by numerical computations of Landau damping and of the two-stream instability. By direct comparison with a reference solution obtained by a very precise semi-Lagrangian method, we show that the precision is improved roughly by a factor 3 compared to a classical PIC scheme, for a given number of particles.
DOI : 10.1051/proc/2011017

Romain Nguyen van yen  1   ; Éric Sonnendrücker  2 , 1   ; Kai Schneider  3   ; Marie Farge  1 , 2 , 3

1 LMD-CNRS-IPSL, École Normale Supérieure, 24 rue Lhomond, 75231 Paris Cedex 5, France
2 IRMA-CNRS, Université de Strasbourg, 7 rue Ren-Descartes, 67084 Strasbourg Cedex, France
3 M2P2-CNRS and CMI, Université d’Aix-Marseille, 38 rue Frdric Joliot-Curie, 13451 Marseille Cedex 13, France 
Romain Nguyen van yen; Éric Sonnendrücker; Kai Schneider; Marie Farge. Particle-in-wavelets scheme for the 1D Vlasov-Poisson equations. ESAIM. Proceedings, Tome 32 (2011), pp. 134-148. doi: 10.1051/proc/2011017
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     title = {Particle-in-wavelets scheme for the {1D} {Vlasov-Poisson} equations},
     journal = {ESAIM. Proceedings},
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