Hierarchical, Multimodel, Multiscale Parallel-In-Time

Kinetic plasma simulations must reckon with many widely varying time-scales, and thus are routinely stability-limited and take many thousands of time-steps. While this makes parallel-in-time (PIT) methods appealing, the spatiotemporal coarsening required by standard PIT schemes can lead to iterations that bear little resemblance to the physical solution — or may even be unstable — thus slowing convergence and limiting speed-ups. We thus present a parallel-in-time strategy that employs a coarsening of models, rather than meshes, to accelerate time-to-solution for high-dimensional kinetic plasma models by leveraging their much cheaper, lower dimensional fluid approximations. The method is tested, with promising initial results, on the two-stream instability.