An Adaptive Algorithm for N-Body Field Expansions
An Adaptive Algorithm for N-Body Field Expansions
复制标题
N体场扩展的自适应算法
DOI：
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发表时间：
1998
期刊：
影响因子：
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通讯作者：
M. Weinberg
中科院分区：
文献类型：
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作者：
M. Weinberg
在求解泊松方程的基函数中对密度场或粒子分布进行展开，既提供了易于并行化的N体力算法，又简化了微扰理论。如果基数中最低阶势密度对看起来像未受扰动的星系或恒星系统，则展开会迅速收敛，并提供最高的计算优势。不幸的是，文献中只有少数几个这样的基础限制了这种优势。本文提出了一种算法来推导这些碱基，以匹配各种星系模型。该方法基于Sturm-Liouville方程的高效数值解，可用于任何具有可分离拉普拉斯算子的几何问题。文中详细介绍了两个案例。首先，对于球形情况，最低阶基函数对可以选择为基础模型的最低阶基函数对。轮廓可以是(1)尖形的或有芯的，以及(2)截断的或无限大的。其次，该方法产生了一个适合于研究星系盘的三维圆柱基。在这种情况下，垂直碱基和径向碱基是耦合的；可以选择基函数的最低阶径向部分，以仅在磁盘平面内匹配底层轮廓。实际上，此基础仍然与整个磁盘配置文件很好地匹配，并且在很少的条件下收敛。由于易于组合多个基础，因此此力解算器非常适合多组件模拟，例如嵌入光晕的圆盘的模拟。
An expansion of a density field or particle distribution in basis functions that solve the Poisson equation both provides an easily parallelized N-body force algorithm and simplifies perturbation theories. The expansion converges quickly and provides the highest computational advantage if the lowest order potential-density pair in the basis looks like the unperturbed galaxy or stellar system. Unfortunately, there are only a handful of such bases in the literature that limit this advantage. This paper presents an algorithm for deriving these bases to match a wide variety of galaxy models. The method is based on efficient numerical solution of the Sturm-Liouville equation and can be used for any geometry with a separable Laplacian. Two cases are described in detail. First, for the spherical case, the lowest order basis function pair may be chosen to be exactly that of the underlying model. The profile may be (1) cuspy or have a core and (2) truncated or of infinite extent. Second, the method yields a three-dimensional cylindrical basis appropriate for studying galactic disks. In this case, the vertical and radial bases are coupled; the lowest order radial part of the basis function can be chosen to match the underlying profile only in the disk plane. Practically, this basis is still a very good match to the overall disk profile and converges in a small number of terms. The ease of combining several bases makes this force solver ideally suited to multicomponent simulations, such as those of disks embedded in halos.