Three-dimensional, high-order semi-implicit particle-in-cell solver based on a Discontinuous Galerkin Spectral Element Method

Summary form only given. A fully three-dimensional, explicit high-order Discontinuous Galerkin Spectral Element Method (DGSEM) based Particle-In-Cell (PIC) solver, targeted for the simulation of high power microwave devices, is adapted for simulations of ionized plasmas. A strong limitation of the explicit time integration is the stability restriction of the Maxwell solver by the CFL condition. This leads to unfavorable long simulation times for ionized, slow evolving plasmas. Semi-implicit time integration overcomes these limitations by treating the Maxwell solver implicitly. A fourth-order implicit-explicit Runge-Kutta scheme is the method of choice. The solving strategy of the linear solver in each Runge-Kutta step is important. Inverting and storing the system matrix is impossible for a parallel, three-dimensional solver due to the large storage requirements. Iterative solvers like a matrix-free Krylov subspace method have to be applied. A preconditioner is mandatory to increase the convergence rate, while its application should preserve the scalability of the DGSEM scheme. In the conference presentation, the authors show the numerical methods and their implementation. The semi-implicit scheme is validated against the explicit solver, showing the limits and benefits of a semi-implicit PIC solver.