Developing Adaptive Mesh Refinement for Semi-Implicit Parcticle-in-Cell Model

We have developed a new Adaptive Mesh Refinement (AMR) version of the Gauss-Law satisfying Energy Conserving Semi-Implicit Method (GL-ECSIM) and implemented it into the Flexible Exascale Kinetic Simulator (FLEKS).  The semi-implicit Particle-In-Cell (PIC) method is particularly well suited for AMR, because, unlike in explicit PIC, the cell size does not have to resolve the Debye length for stability. In contrast with the earlier Multi-Level-Multi-Domain semi-implicit PIC algorithm developed by Innocenti+, the new algorithm uses a single set of particles over the whole domain.  Particles are split and merged as needed by efficient and accurate methods. The coarser level receives both the field information and the phase space distribution (through the particles) from the fine level.  The fine level uses the coarse level as boundary condition.  The new algorithm satisfies Gauss Law on the entire domain, including grid resolution changes.  We show various tests confirming the accuracy and robustness of the new algorithm. In particular, we simulate magnetic reconnection with an ion-electron mass ratio of 64. The AMR resolves the electron scales near the reconnection site, while the grid is eight times coarser elsewhere matching the ion scales.  The overall speed up is at least tenfold compared to a uniformly fine grid simulation.