Two-Scale Macro-Micro decomposition of the Vlasov equation with a strong magnetic field

Nicolas Crouseilles 1, 2 Emmanuel Frenod 3, 4, * Sever Adrian Hirstoaga 3, 5 Alexandre Mouton 6
* Corresponding author
1 IPSO - Invariant Preserving SOlvers
Inria Rennes – Bretagne Atlantique , IRMAR - Institut de Recherche Mathématique de Rennes
3 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
4 LMBA_UBS
LMBA - Laboratoire de Mathématiques de Bretagne Atlantique
Abstract : In this paper, we build a Two-Scale Macro-Micro decomposition of the Vlasov equation with a strong magnetic field. This consists in writing the solution of this equation as a sum of two oscillating functions with circonscribed oscillations. The first of these functions has a shape which is close to the shape of the Two-Scale limit of the solution and the second one is a correction built to offset this imposed shape. The aim of such a decomposition is to be the starting point for the construction of Two-Scale Asymptotic-Preserving Schemes.
Document type :
Journal articles
Mathematical Models and Methods in Applied Sciences, World Scientific Publishing, 2013, 23 (08), pp.1527--1559. <10.1142/S0218202513500152.>


https://hal.archives-ouvertes.fr/hal-00638617
Contributor : Emmanuel Frenod <>
Submitted on : Monday, November 5, 2012 - 10:40:07 AM
Last modification on : Friday, March 27, 2015 - 10:01:23 AM

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Nicolas Crouseilles, Emmanuel Frenod, Sever Adrian Hirstoaga, Alexandre Mouton. Two-Scale Macro-Micro decomposition of the Vlasov equation with a strong magnetic field. Mathematical Models and Methods in Applied Sciences, World Scientific Publishing, 2013, 23 (08), pp.1527--1559. <10.1142/S0218202513500152.>. <hal-00638617v3>

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