AI 中文总结
研究在RAMSES框架下实现基于快速多极方法的可扩展泊松求解器，引入多FMM树等新元素，与传统多网格求解器测试对比，该求解器在AMR界面动量守恒好、可扩展性佳。
AI 中文摘要
我们提出了一种基于快速多极方法（FMM）的可扩展O(N)泊松求解器的扩展实现，它在RAMSES框架内与自适应网格细化（AMR）和自适应时间步长（ATS）完全兼容。基于Lee和Teyssier（2026）的单网格算法，我们引入了几个新元素，包括为每个AMR级别使用多个FMM树、为所有活动级别合并的FMM树以优化邻居搜索，以及引入“近场”概念以在细化级别间强制力对称。在一系列测试问题中，我们与传统多网格（MG）求解器达到了百分比级别的出色一致性。然而，FMM在粗-细AMR界面上具有更好的动量守恒特性。最后，尽管时空适应性带来了开销，但FMM在各种AMR配置下比MG具有更好的可扩展性，在最大配置中获得了最大收益。
英文摘要
We present an extended implementation of a scalable, O(N) Poisson solver based on the fast multipole method (FMM), fully compatible with adaptive mesh refinement (AMR) and adaptive time stepping (ATS) within the RAMSES framework. Building on the unigrid algorithm in Lee & Teyssier (2026), we introduce several novel elements, including the use of multiple FMM trees, one for each AMR level, a merged FMM tree for all active levels to optimize neighbor searches, and the introduction of the concept of "nearest-field" to enforce force symmetry across refinement levels. Across a broad set of test problems, we find excellent, percent-level agreement with our reference traditional multigrid (MG) solver. We show, however, that FMM exhibits better momentum conservation properties across coarse-fine AMR interfaces. Finally, despite the overhead introduced by the spatio-temporal adaptivity, FMM shows better scalability than MG across various AMR configurations, with the largest gains obtained for the largest configurations.
Comments14 pages, 11 figures, Submitted to MNRAS
