A Parareal in time numerical method for the collisional Vlasov equation in the hyperbolic scaling
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866910814707908608 |
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| author | Laidin, Tino Rey, Thomas |
| author_facet | Laidin, Tino Rey, Thomas |
| contents | We present the design of a multiscale parareal method for kinetic equations in the fluid dynamic regime. The goal is to reduce the cost of a fully kinetic simulation using a parallel in time procedure. Using the multiscale property of kinetic models, the cheap, coarse propagator consists in a fluid solver and the fine (expensive) propagation is achieved through a kinetic solver for a collisional Vlasov equation. To validate our approach, we present simulations in the 1D in space, 3D in velocity settings over a wide range of initial data and kinetic regimes, showcasing the accuracy, efficiency, and the speedup capabilities of our method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_02704 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Parareal in time numerical method for the collisional Vlasov equation in the hyperbolic scaling Laidin, Tino Rey, Thomas Numerical Analysis 82B40, 82C70, 76P05, 65M08 We present the design of a multiscale parareal method for kinetic equations in the fluid dynamic regime. The goal is to reduce the cost of a fully kinetic simulation using a parallel in time procedure. Using the multiscale property of kinetic models, the cheap, coarse propagator consists in a fluid solver and the fine (expensive) propagation is achieved through a kinetic solver for a collisional Vlasov equation. To validate our approach, we present simulations in the 1D in space, 3D in velocity settings over a wide range of initial data and kinetic regimes, showcasing the accuracy, efficiency, and the speedup capabilities of our method. |
| title | A Parareal in time numerical method for the collisional Vlasov equation in the hyperbolic scaling |
| topic | Numerical Analysis 82B40, 82C70, 76P05, 65M08 |
| url | https://arxiv.org/abs/2502.02704 |