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. A key aspect of this approach is that it allows the user to approximate the value of the integral without explicit knowledge of an expression for the boundary surface. Instead, a tesselation of the node set is utilized to inform the algorithm of the domain geometry. Further, the method applies to node sets featuring spatially varying density, facilitating its use in Applied Mathematics, Mathematical Physics and myriad other application areas, where the locations of the nodes might be fixed by experiment or previous simulation. By using the RBF-FD-like approach, the proposed algorithm computes quadrature weights for $N$ arbitrarily scattered nodes in only $O(N\mbox{ log}N)$ operations with tunable orders of accuracy.

翻译：辐射基础函数生成的有限差异(RBF-FD)启发了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,该方法的一个关键方面是,它使用户能够在没有明确了解边界表面表达法的情况下,接近整体部分的价值。相反,节点集的套接合用于说明域几何的算法。此外,该方法适用于具有空间不同密度的节点组,便于在应用数学、数学物理和无数其他应用区使用该方法,这些节点的位置可以通过实验或先前的模拟加以固定。拟议的算法采用RBF-FD类似方法,将任意分散节点的方位重量计算成$N(N\box{log}N),只有$O(N\box{log}N)值的操作,并具有可测量的精确度。