Error Analysis and Parallel Scaling Study of A Parareal Parallel-in-Time Integration Algorithm for Particle-in-Fourier Schemes
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| author | Muralikrishnan, Sriramkrishnan Speck, Robert |
| author_facet | Muralikrishnan, Sriramkrishnan Speck, Robert |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_00485 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Error Analysis and Parallel Scaling Study of A Parareal Parallel-in-Time Integration Algorithm for Particle-in-Fourier Schemes Muralikrishnan, Sriramkrishnan Speck, Robert Numerical Analysis Computational Physics Plasma Physics 35Q83, 65M75, 82D10 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. |
| title | Error Analysis and Parallel Scaling Study of A Parareal Parallel-in-Time Integration Algorithm for Particle-in-Fourier Schemes |
| topic | Numerical Analysis Computational Physics Plasma Physics 35Q83, 65M75, 82D10 |
| url | https://arxiv.org/abs/2407.00485 |