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Generalized formulations of Maxwell's equations for numerical Vlasov-Maxwell simulations

Régine Barthelmé 1 Patrick Ciarlet Eric Sonnendrücker 1, 2
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
Abstract : When solving numerically approximations of the Vlasov-Maxwell equations, the source terms in Maxwell's equations coming from the numerical solution of the Vlasov equation do generally not satisfy the continuity equation which is necessary for Maxwell's equations to be well-posed. Hence it is necessary to introduce generalized Maxwell's equations which are still well-posed when there are errors in the sources. Different such formulations have been introduced previously. The aim of this paper is to perform their mathematical analysis and verify the existence and uniqueness of the solution.
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https://hal.inria.fr/inria-00070176
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Submitted on : Friday, May 19, 2006 - 7:19:51 PM
Last modification on : Friday, February 4, 2022 - 3:30:14 AM
Long-term archiving on: : Sunday, April 4, 2010 - 8:24:56 PM

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  • HAL Id : inria-00070176, version 1

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Régine Barthelmé, Patrick Ciarlet, Eric Sonnendrücker. Generalized formulations of Maxwell's equations for numerical Vlasov-Maxwell simulations. [Research Report] RR-5850, INRIA. 2006, pp.26. ⟨inria-00070176⟩

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