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

Abstract

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 devices1, 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 scheme2 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.