AI 中文总结
针对弗拉索夫-泊松系统数值模拟难题，提出结合高阶时间分裂的动态自适应傅里叶谱方法，通过自适应零填充防混叠，避免人工平滑，经数值实验验证了该方案在相关问题上的鲁棒性。
AI 中文摘要
弗拉索夫-泊松系统的数值模拟因相空间丝状化面临挑战。标准谱方法靠人工滤波抑制误差，会随时间降低物理结构和精度。本文提出结合高阶时间分裂的动态自适应傅里叶谱方法。通过自适应零填充动态扩展波数域防止丝状化引起的混叠，避免传统滤波器的人工平滑，保持质量并有效维持动态解析尺度内的\(L^2\)范数。朗道阻尼和各种不稳定性问题的数值实验验证了该方案的鲁棒性。
英文摘要
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.
