Solving Vlasov-Poisson system with an adaptive Hermite spectral method

Sihong Shao; Yanli Wang; Jie Wu

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arXiv · 2605.17820

Solving Vlasov-Poisson system with an adaptive Hermite spectral method

Sihong Shao·Yanli Wang·Jie Wu

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Abstract

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.

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Sihong Shao, Yanli Wang, Jie Wu. 2026-05-18. Solving Vlasov-Poisson system with an adaptive Hermite spectral method. https://arxiv.org/abs/2605.17820

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