GPU-accelerated 3D electromagnetic PIC simulations

Summary form only given. 3D electromagnetic particle-in-cell (PIC) codes are widely used for simulations of both plasmas and particle-beam devices, but for many applications their usefulness is diminished in practice by long simulation times. To address this issue, we have adapted the conventional electromagnetic finite-difference time-domain (FDTD) PIC algorithm to run efficiently on high-performance, low-cost Graphical Processing Unit (GPU) hardware, making use of the NVIDIA CUDA library. Executing on a single NVIDIA GeForce GTX 480 graphics card, we achieve amortized simulation times of ~1ns/cell/time-step for electromagnetic fields, using the FDTD algorithm, and ~10ns/particle/time-step for a charge-conserving Boris-push particle integration algorithm. A simulation with 500,000 cells and 200,000 particles running for 300,000 time-steps takes less than 15 minutes. A significant restriction on the performance achieved by FDTD-PIC in practice is due to the Courant condition. To achieve numerical stability, the time-step that may be used is limited to cΔt <;h/√3, where h characterizes the smallest cell dimension in the grid. For simulations in structures that are small compared to the RF wavelength, or that require fine grids locally to resolve critical details, it is necessary to use time steps that are very small in relation to the RF period, typically cΔt <;λ /100 . To avoid this constraint we have formulated efficient alternating-direction implicit (ADI) FDTD algorithms, now implemented for the GPU. We compare the performance of these algorithms with conventional FDTD for PIC simulation.This work forms the basis of a new code, NEPTUNE, being developed to perform self-consistent 3D nonlinear simulations of vacuum electron devices.