In this article, we aim at proposing a general mathematical formulation for charge-conserving finite-element 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 two or three 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.
Accepted:
Published online:
Martin Campos Pinto 1; Sébastien Jund 2; Stéphanie Salmon 3; Éric Sonnendrücker 4, 5
@article{CRMECA_2014__342_10-11_570_0, author = {Martin Campos Pinto and S\'ebastien Jund and St\'ephanie Salmon and \'Eric Sonnendr\"ucker}, title = {Charge-conserving {FEM{\textendash}PIC} schemes on general grids}, journal = {Comptes Rendus. M\'ecanique}, pages = {570--582}, publisher = {Elsevier}, volume = {342}, number = {10-11}, year = {2014}, doi = {10.1016/j.crme.2014.06.011}, language = {en}, }
TY - JOUR AU - Martin Campos Pinto AU - Sébastien Jund AU - Stéphanie Salmon AU - Éric Sonnendrücker TI - Charge-conserving FEM–PIC schemes on general grids JO - Comptes Rendus. Mécanique PY - 2014 SP - 570 EP - 582 VL - 342 IS - 10-11 PB - Elsevier DO - 10.1016/j.crme.2014.06.011 LA - en ID - CRMECA_2014__342_10-11_570_0 ER -
Martin Campos Pinto; Sébastien Jund; Stéphanie Salmon; Éric Sonnendrücker. Charge-conserving FEM–PIC schemes on general grids. Comptes Rendus. Mécanique, Theoretical and numerical approaches for Vlasov-maxwell equations, Volume 342 (2014) no. 10-11, pp. 570-582. doi : 10.1016/j.crme.2014.06.011. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2014.06.011/
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☆ This work has been partially supported by Agence Nationale de la Recherche under the grant ANR-06-CIS6-0013.
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