Charge-conserving grid based methods for the Vlasov–Maxwell equations

Abstract In this article, we introduce numerical schemes for the Vlasov–Maxwell equations relying on different kinds of grid-based Vlasov solvers, as opposite to PIC schemes, which enforce a discrete continuity equation. The idea underlying these schemes relies on a time-splitting scheme between configuration space and velocity space for the Vlasov equation and on the computation of the discrete current in a form that is compatible with the discrete Maxwell solver.

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