论文标题
求和某些本地双线性形式及其应用于快速多极方法
Summation of certain locally bilinear forms and its applications to the Fast Multipole Method
论文作者
论文摘要
快速多极方法（FMM）减少了$ n $ - 粒子之间的成对两体相互作用的计算，以$ n $订购$ n $，其计算成本应为Brute Force的订单$ n^2 $。但是，其实现有些复杂，需要大量时间来编写代码。在本文中，我展示了一种使我们能够简单简短地实现和编写FMM算法代码的方法。 FMM算法由多个步骤组成。主要步骤是向上和向下通行。向上的通行证和向下的均包括转移过程，我们将我们移动局部膨胀和多极扩展的中心。在本文中，我展示了一种使我们能够摆脱这些过程的方法。由于这种简化，FMM的编码变得更加容易，我们可以节省大量的计算时间。我将计算潜在字段与现有FMM代码的准确性和时间进行了比较。
The Fast Multipole Method (FMM) reduces the computation of pairwise two-body interactions among $N$-particles to order $N$, whose computation cost should be of order $N^2$ by brute force. However, its implementation is somewhat complicated and requires a considerable amount of time to write the code. In this paper, I show a method that enables us to implement and write FMM algorithm code simply and briefly. FMM algorithm is composed of several steps. The main steps are Upward Pass and Downward Pass. Both the Upward Pass and Downward Pass include shift processes by which we move the centers of local expansions and multipole expansions. In this paper, I show a method that enables us to get rid of these processes.As a result of this simplification, the coding of FMM becomes much easier, and we can save considerable computation time. I compared the accuracy and time required to calculate potential fields with that of the existing FMM code.
