A Radial Basis Function Generated Finite-Differences (RBF-FD) inspired technique for evaluating definite integrals over bounded volumes that have smooth boundaries in three dimensions is described. Such methods are necessary in many areas of Applied Mathematics, Mathematical Physics and myriad other application areas. Previous approaches needed restrictive uniformity in the node set, which the algorithm presented here does not require. By using RBF-FD approach, the proposed algorithm computes quadrature weights for $N$ arbitrarily scattered nodes in only $O(N\mbox{ log}N)$ operations with high orders of accuracy.

翻译：辐射基础函数生成的有限差异(RBF-FD)受启发地评估在三个维度上均匀边界的捆绑量的确定整体部分的技术,描述了在应用数学、数学物理和许多其他应用领域的许多领域采用这种方法是必要的。以前的方法需要节点集的限制性统一性,而此处的算法并不需要这种统一性。通过使用RBF-FD方法,拟议的算法计算了仅用$O(N\mbox{log}N)高精确度的操作中任意分散的节点的等量。