Error Analysis and Parallel Scaling Study of A Parareal Parallel-in-Time Integration Algorithm for Particle-in-Fourier Schemes

TL;DR

This paper introduces a parareal-based time parallelization method for particle-in-Fourier schemes in plasma simulations, demonstrating significant speedup and scalability on high-performance computing systems.

Contribution

It presents a novel parareal algorithm using temporal coarsening for PIF schemes, with error analysis and large-scale GPU scaling results.

Findings

Achieves 4-6x speedup over spatial parallelization.

Demonstrates scalability up to 1536 GPUs.

Reaches a particle processing rate of 1 billion particles/sec.

Abstract

We propose a parareal based time parallelization scheme in the phase-space for the particle-in-Fourier (PIF) discretization of the Vlasov-Poisson system used in kinetic plasma simulations. We use PIF with a coarse tolerance for the nonuniform fast Fourier transforms, or the standard particle-in-cell scheme, combined with temporal coarsening, as coarse propagators. This is different from the typical spatial coarsening of particles and/or Fourier modes for parareal, which are not possible or effective for PIF schemes. We perform an error analysis 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 parareal 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.