Charge conserving FEM-PIC schemes on general grids

Martin Campos Pinto 1, 2 Sébastien Jund 1, 2 Stéphanie Salmon 1, 2 Eric Sonnendrücker 1, 2
2 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 : In this article we aim at proposing a general mathematical formulation for charge conserving finite elements Maxwell solvers coupled with particle schemes. In particular, we identify the finite-element continuity equations that must be satisfied by the discrete current sources for several classes of time domain Vlasov-Maxwell simulations to preserve the Gauss law at each time step, and propose a generic algorithm for computing such consistent sources. Since our results cover a wide range of schemes (namely curl-conforming finite element methods of arbitrary degree, general meshes in 2 or 3 dimensions, several classes of time discretization schemes, particles with arbitrary shape factors and piecewise polynomial trajectories of arbitrary degree), we believe that they provide a useful roadmap in the design of high order charge conserving FEM-PIC numerical schemes.
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Submitted on : Wednesday, December 23, 2009 - 1:31:56 PM
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  • HAL Id : hal-00311429, version 3

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Martin Campos Pinto, Sébastien Jund, Stéphanie Salmon, Eric Sonnendrücker. Charge conserving FEM-PIC schemes on general grids. 2009. ⟨hal-00311429v3⟩

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