Self-gravity calculations for 3D are expensive in terms of computational time. Several methods exist for this computation, for example multigrid and spectral methods. Unfortunately, these approaches require the imposition of boundary conditions, which can be either numerically expensive (direct Newtonian sums), artificial (periodicity assumptions), or potentially imprecise (multipolar expansions). In this work we present a novel direct numerical method to calculate the gravitational potential and forces by solving the Poisson equation without the need to prescribe artificial boundary conditions; this method, despite being direct, turns out to be efficient due to the possibility of using a fast Fourier transform for its implementation. For a grid having N zones in each dimension, the computational complexity of the method presented here is , which is comparable with multigrid methods under no consideration of boundary settings. Finally, a numerical study shows this proposed method can achieve second order for calculations of both potential and forces.

就计算时间而言，用于3D的自重计算非常昂贵。存在几种用于该计算的方法，例如多网格和频谱方法。不幸的是，这些方法需要施加边界条件，边界条件可能在数字上昂贵（直接牛顿和），人为（周期性假设）或可能不精确（多极展开）。在这项工作中，我们提出了一种新颖的直接数值方法，无需求解人工边界条件即可通过求解泊松方程来计算引力和力。尽管该方法是直接的，但由于可能使用快速傅里叶变换进行实施而被证明是有效的。对于具有N的网格在每个维度的区域中，此处介绍的方法的计算复杂度为，这在不考虑边界设置的情况下与多网格方法相当。最后，数值研究表明，该方法可以实现势能和力的二阶计算。