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arXiv · 2607.12368

An Adaptive Fourier Spectral Method for the Vlasov-Poisson system

Seung Yeon Cho·Giovanni Russo
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Abstract

Numerical simulation of the Vlasov-Poisson system faces fundamental challenges due to phase-space filamentation. Standard spectral methods rely on artificial filtering to suppress errors, which inadvertently degrades physical structures and accuracy over time. This paper proposes a dynamically adaptive Fourier spectral method combined with high-order time splitting to overcome these limitations. To prevent filamentation-induced aliasing, we dynamically expand the wavenumber domain via adaptive zero-padding whenever spectral tail monitoring detects emerging fine-scale structures. Acting as an exact trigonometric interpolation, it inherently avoids the artificial smoothing of traditional filters, preserving mass and effectively maintaining the $L^2$-norm within the dynamically resolved scales. Numerical experiments on Landau damping and various instability problems validate the robustness of our scheme.

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Seung Yeon Cho, Giovanni Russo. 2026-07-14. An Adaptive Fourier Spectral Method for the Vlasov-Poisson system. https://arxiv.org/abs/2607.12368

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