Avec cedram.org english version Accueil Présentation Recherche avancée Tous les articles en ligne Derniers articles Rechercher un article Table des matières de ce volume | Article précédent | Article suivant Martin Campos Pinto; Eric SonnendrückerCompatible Maxwell solvers with particles I: conforming and non-conforming 2D schemes with a strong Ampere lawSMAI-Journal of computational mathematics, 3 (2017), p. 53-89, doi: 10.5802/smai-jcm.20 Article PDF Class. Math.: 35Q61, 65M12, 65M60, 65M75Mots clés: Maxwell equations, Gauss laws, structure-preserving, PIC, charge-conserving current deposition, conforming finite elements, discontinuous Galerkin, Conga method. AbstractThis article is the first of a series where we develop and analyze structure-preserving finite element discretizations for the time-dependent 2D Maxwell system with long-time stability properties, and propose a charge-conserving deposition scheme to extend the stability properties in the case where the current source is provided by a particle method. The schemes proposed here derive from a previous study where a generalized commuting diagram was identified as an abstract compatibility criterion in the design of stable schemes for the Maxwell system alone, and applied to build a series of conforming and non-conforming schemes in the 3D case. Here the theory is extended to account for approximate sources, and specific charge-conserving schemes are provided for the 2D case. In this article we study two schemes which include a strong discretization of the Ampere law. The first one is based on a standard conforming mixed finite element discretization and the long-time stability is ensured by a Raviart-Thomas finite element interpolation for the current source, thanks to its commuting diagram properties. The second one is a new non-conforming variant where the numerical fields are sought in fully discontinuous spaces. Numerical experiments involving Maxwell and Maxwell-Vlasov problems are then provided to validate the stability of the proposed methods. Bibliographie[1] J.-C. Adam, A. Gourdin Serveniere, J.-C. Nédélec & P.-A. Raviart, “Study of an implicit scheme for integrating Maxwell’s equations”, Computer Methods in Applied Mechanics and Engineering 22 (1980), p. 327-346 Article[2] D.N. Arnold, R.S. Falk & R. Winther, “Finite element exterior calculus, homological techniques, and applications”, Acta Numerica (2006) Article |  MR 2269741[3] D.N. Arnold, R.S. Falk & R. 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