论文标题
一种混合方法，以设定独立泊松求解器的任意费用分布
A hybrid approach to basis set independent Poisson solver for an arbitrary charge distribution
论文作者
论文摘要
我们回顾了两个常见的数值方案，用于库仑电位评估，它们仅在球形谐波扩展中的溶液的径向部分有所不同（SHA）。一种基于有限差分方法（FDM），而另一个基于绿色方程的径向部分的绿色函数（GF）解决方案。我们分析了这些方法，并观察到基于FDM的方法在与径向点数的收敛性方面似乎更有效，尤其是对于单极（L = 0）。但是，作为一个已知问题，随着系统大小的增加，它会遭受误差积累。我们确定主要来自L = 1（有时L = 2）的误差来源，由电荷分配引起。然后，我们通过组合两种方法提出了一个混合方案，其中使用FDM方法获得L = 0的径向解，并使用GF方法处理其余项。随后，提出的混合方法应用于各种系统以检查其性能。在所有情况下，结果表现出比早期数值方案的精度提高。我们还表明，即使使用一组通用的径向网格参数，在标准密度官能研究中，也可以使用数值库仑求解器获得准确的能量差异。 〜
We review two common numerical schemes for Coulomb potential evaluation that differ only in their radial part of the solutions in the spherical harmonic expansion (SHE). One is based on finite-difference method (FDM) while the other is based on the Green's function (GF) solution to the radial part of the Poisson equation. We analyze the methods and observe that the FDM-based approach appears to be more efficient in terms of the convergence with the number of radial points, particularly for monopole (l=0). However, as a known issue, it suffers from error accumulation as the system size increases. We identify the source of error that comes mainly from l=1 (and sometimes l=2) contribution of SHE induced by the charge partitioning. We then propose a hybrid scheme by combining the two methods, where the radial solution for l=0 is obtained using the FDM method and treating the remaining terms using GF approach. The proposed hybrid method is subsequently applied to a variety of systems to examine its performance. The results show improved accuracy than earlier numerical schemes in all cases. We also show that, even with a generic set of radial grid parameters, accurate energy differences can be obtained using a numerical Coulomb solver in standard density functional studies. ~
