Solving Vlasov-Poisson system with an adaptive Hermite spectral method
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866913137922408448 |
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| author | Shao, Sihong Wang, Yanli Wu, Jie |
| author_facet | Shao, Sihong Wang, Yanli Wu, Jie |
| contents | We propose an adaptive Hermite spectral method for the Vlasov-Poisson system based on a recently developed frequency indicator that measures the contribution of the high-order expansion coefficients. Precisely, the symmetrically weighted Hermite basis with a scaling factor is utilized to approximate the distribution function to satisfy the increasing resolution requirement, which, for example, is induced by filamentation. To implement the scaling adjustment, a fast conservative projection operator is constructed in two steps. The first step is to formulate the projection as a constrained optimization problem to preserve key invariants, including mass, momentum, energy, and the $L^2$ norm of the distribution function. The second step is an ODE-based approximation developed to compute the updated expansion coefficients with linear complexity. Numerical experiments with 1D1V and 2D2V settings validate the feasibility and efficiency of this proposed adaptive Hermite method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_17820 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Solving Vlasov-Poisson system with an adaptive Hermite spectral method Shao, Sihong Wang, Yanli Wu, Jie Numerical Analysis We propose an adaptive Hermite spectral method for the Vlasov-Poisson system based on a recently developed frequency indicator that measures the contribution of the high-order expansion coefficients. Precisely, the symmetrically weighted Hermite basis with a scaling factor is utilized to approximate the distribution function to satisfy the increasing resolution requirement, which, for example, is induced by filamentation. To implement the scaling adjustment, a fast conservative projection operator is constructed in two steps. The first step is to formulate the projection as a constrained optimization problem to preserve key invariants, including mass, momentum, energy, and the $L^2$ norm of the distribution function. The second step is an ODE-based approximation developed to compute the updated expansion coefficients with linear complexity. Numerical experiments with 1D1V and 2D2V settings validate the feasibility and efficiency of this proposed adaptive Hermite method. |
| title | Solving Vlasov-Poisson system with an adaptive Hermite spectral method |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2605.17820 |