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Coupling between a Particle In Cell method and a H 1-conform mixed spectral finite element approximation of Maxwell's equations

This paper describes the coupling between a Particle In Cell (PIC) method and a H 1-conform mixed spectral finite element approximation of Maxwell's equations for the approximation of low dense plasmas. It uses the H 1-conform mixed spectral method already described in [2]. As particle methods themselves are a classical subject, we mainly focus on the coupling between a finite element method on an unstructured grid and a PIC method. This subject has already been studied for a coupling between a PIC method and a discontin-uous Galerkin scheme [4], but its still a challenging subject and the rehabilitation of continuous methods to this aim hasn't been studied yet. The critical point lies in the coupling between an Eulerian approximation of the fields on an unstructured grid and a Lagrangian description of particles motion. This point can heavily penalize the global cost of the algorithm, if not taken into account carefully. In the next sections, a few techniques are introduced and compared to each other in order to obtain an efficient coupling algorithm between these two methods.