Geodesic
First order Two-Scale Particle-in-Cell numerical method for the Vlasov equation
Emmanuel Frénod1, 2 ; Michaël Gutnic2 ; Sever A. Hirstoaga2
1 Université Européenne de Bretagne, LMBA (UMR CNRS 6205), Université de Bretagne-Sud, Centre Yves Coppens, Campus de Tohannic, F-56017, Vannes
2 Inria Nancy-Grand Est, CALVI Project & IRMA (UMR 7501), Université de Strasbourg, 7 rue René Descartes, F-67084 Strasbourg Cedex, France
ESAIM. Proceedings, Tome 38 (2012), pp. 348-360.

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The aim of this work is to build an accurate numerical method for the simulation of the long time evolution of the Vlasov solution fε with an electric field Eε = E0 + εE1 for small ε. To this purpose, we use the Two-Scale Convergence to determine a first order approximation F + εF1 of fε. Then, by means of particle approximations we build an algorithm which is intended for providing a numerical approximation of F + εF1.
DOI : 10.1051/proc/201238019

Emmanuel Frénod 1, 2 ; Michaël Gutnic 2 ; Sever A. Hirstoaga 2

1 Université Européenne de Bretagne, LMBA (UMR CNRS 6205), Université de Bretagne-Sud, Centre Yves Coppens, Campus de Tohannic, F-56017, Vannes
2 Inria Nancy-Grand Est, CALVI Project & IRMA (UMR 7501), Université de Strasbourg, 7 rue René Descartes, F-67084 Strasbourg Cedex, France 
@article{EP_2012_38_a18,
     author = {Emmanuel Fr\'enod and Micha\"el Gutnic and Sever A. Hirstoaga},
     title = {First order {Two-Scale} {Particle-in-Cell} numerical method for the {Vlasov} equation},
     journal = {ESAIM. Proceedings},
     pages = {348--360},
     publisher = {mathdoc},
     volume = {38},
     year = {2012},
     doi = {10.1051/proc/201238019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/proc/201238019/}
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Emmanuel Frénod; Michaël Gutnic; Sever A. Hirstoaga. First order Two-Scale Particle-in-Cell numerical method for the Vlasov equation. ESAIM. Proceedings, Tome 38 (2012), pp. 348-360. doi : 10.1051/proc/201238019. http://geodesic.mathdoc.fr/articles/10.1051/proc/201238019/

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