Abstract Application of classical density functional theory in cylindrical coordinates requires a fast Hankel transform algorithm of order zero and its inverse, when the involved convolution integrals are solved in Fourier space. Vector-valued fundamental measure theory requires a fast Hankel transform of first order and its inverse. Compared to naive real space convolution, this not only reduces complexity of the required computer code, but also increases computational performance due to the efficiency of the fast Hankel transform. This study proposes a new approach to compute the inverse of the first order fast Hankel transform on equidistant grids as a combination of a modified inverse Abel transform and a fast sine transform. Equidistant grids have a significant advantage over alternative implementations that require logarithmic grid spacing, since most problems, such as pores or droplets, require a certain resolution in the outer region of the radial domain, which in the case of a logarithmic grid necessitates an overly high number of grid points in the inner region of the radial domain. The proposed algorithm for the modified inverse Abel transform is straightforward to implement, while for the fast sine transform off-the-shelf algorithms can be used.

中文翻译：

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用于计算柱坐标中基本测度理论中出现的向量值权函数的一阶快速逆汉克尔变换

摘要 当所涉及的卷积积分在傅立叶空间中求解时，经典密度泛函理论在柱坐标中的应用需要零阶及其逆的快速汉克尔变换算法。向量值基本测度理论需要一阶及其逆的快速汉克尔变换。与朴素实空间卷积相比，这不仅降低了所需计算机代码的复杂性，而且由于快速汉克尔变换的效率而提高了计算性能。这项研究提出了一种新方法来计算等距网格上的一阶快速 Hankel 变换的逆，作为改进的逆 Abel 变换和快速正弦变换的组合。等距网格比需要对数网格间距的替代实现具有显着优势，因为大多数问题，例如孔或液滴，需要在径向域的外部区域有一定的分辨率，在对数网格的情况下，径向域的内部区域需要过多的网格点。改进的逆 Abel 变换所提出的算法易于实现，而对于快速正弦变换，可以使用现成的算法。