Handling the divergence constraints in Maxwell and Vlasov-Maxwell simulations

Abstract : The aim of this paper is to review and classify the different methods that have been developed to enable stable long time simulations of the Vlasov-Maxwell equations and the Maxwell equations with sources. These methods can be classified in two types: field correction methods and sources correction methods. The field correction methods introduce new unknowns in the equations, for which additional boundary conditions are in some cases non trivial to find. The source correction consists in computing the sources so that they satisfy a discrete continuity equation compatible with a discrete Gauss' law that needs to be defined in accordance with the discretization of the Maxwell propagation operator.
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Martin Campos Pinto, Marie Mounier, Eric Sonnendrücker. Handling the divergence constraints in Maxwell and Vlasov-Maxwell simulations. Applied Mathematics and Computation, Elsevier, 2016, 272. ⟨hal-01167456⟩

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