An Active Flux Method for the Vlasov-Maxwell System

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We develop an Active Flux method for the Vlasov/Maxwell system for a collisionless plasma.The Active Flux method is a new form of a finite volume method which uses both cell average values as well as point values of the physical quantities as degrees of freedom. Since the underlying Vlasov equation has the structure of a six dimensional advection equation and the characteristics for the motion of the point values can be easily calculated, the Active Flux method is ideally suited for the Vlasov equation. Active Flux methods are high order accurate and have a compact stencil in space and time. The additional degrees of freedom, i.e. the point values, will be used to construct schemes which satisfy additional constraints such as conservation of energy.In order to apply the method to relevant high dimensional physical problems, aspects of high performance computing will also play an important role.This project is part of the DFG research unit "Structure-Preserving Numerical Methods for Bulk- and Interface-Coupling of Heterogeneous Models (SNuBIC)".