论文标题
关于快速多极方法的注释
Notes on the Fast Multipole Method
论文作者
论文摘要
可以使用快速多极方法和附近电荷之间的直接计算来计算点电荷的库仑相互作用。但是，由于其方法结合了直接和间接计算的方法，它会大大降低计算成本，因此存在势能与电荷位置的不连续性。在本文中，我们删除了通常在快速多极方法中使用的Legendre功能，而是使用固定在位置中的电荷。作为此方法的应用，我们删除了不连续性。它还导致我们采用一种周期性边界条件的方法，即使粒子从模拟框的壁上熄灭并进入盒子的另一侧，也是连续的。最后，我们显示了不使用Shift过程的快速多极方法的版本。
Coulomb interactions of point charges can be calculated in $\mathcal{O}$(N) computation using the fast multipole method and direct calculations between charges nearby. It reduces computational cost dramatically, however, because of its method that combines direct and indirect calculations, there exists discontinuity of potential energy with respect to positions of charges. In this paper, we remove Legendre functions usually used in the fast multipole method and instead use charges fixed in positions. As an application of this method, we remove the discontinuity. It also leads us to a method of periodic boundary condition that is continuous even if a particle goes out from a wall of a simulation box and enters in opposite side of the box. Lastly, we show a version of the fast multipole method that do not use shift process.
