We propose ParaPIF, a parareal based time parallelization scheme for the particle-in-Fourier (PIF) discretization of the Vlasov-Poisson system used in kinetic plasma simulations. Our coarse propagators are based on the coarsening of the numerical discretization scheme combined with, if possible, temporal coarsening rather than coarsening of particles and/or Fourier modes, which are not possible or effective for PIF schemes. Specifically, we use PIF with a coarse tolerance for nonuniform FFTs or even the standard particle-in-cell schemes as coarse propagators for the ParaPIF algorithm. We state and prove the convergence of the algorithm and verify the results numerically with Landau damping, two-stream instability, and Penning trap test cases in 3D-3V. We also implement the space-time parallelization of the PIF schemes in the open-source, performance-portable library IPPL and conduct scaling studies up to 1536 A100 GPUs on the JUWELS booster supercomputer. The space-time parallelization utilizing the ParaPIF algorithm for the time parallelization provides up to $4-6$ times speedup compared to spatial parallelization alone and achieves a push rate of around 1 billion particles per second for the benchmark plasma mini-apps considered.

翻译：我们提出ParaPIF，一种基于parareal的时间并行化方案，用于动理学等离子体模拟中Vlasov-Poisson系统的粒子-傅里叶（PIF）离散化。我们的粗传播子基于数值离散格式的粗化，并结合（若可行）时间粗化，而非采用对PIF格式不可行或无效的粒子粗化和/或傅里叶模态粗化。具体而言，我们采用具有粗容差的非均匀FFT的PIF，甚至标准粒子网格方法作为ParaPIF算法的粗传播子。我们陈述并证明了算法的收敛性，并通过三维相空间（3D-3V）中的朗道阻尼、双流不稳定性及潘宁阱测试算例进行了数值验证。我们还在开源、性能可移植的库IPPL中实现了PIF格式的时空并行化，并在JUWELS booster超级计算机上使用多达1536块A100 GPU进行了扩展性研究。利用ParaPIF算法进行时间并行化的时空并行方案，与仅采用空间并行化相比，可获得高达$4-6$倍的加速比，并在所考虑的基准等离子体微型应用中实现了约每秒10亿粒子的推进速率。