We introduce a geometric stencil selection algorithm for Laplacian in 3D that significantly improves octant-based selection considered earlier. The goal of the algorithm is to choose a small subset from a set of irregular points surrounding a given point that admits an accurate numerical differentiation formula. The subset serves as an influence set for the numerical approximation of the Laplacian in meshless finite difference methods using either polynomial or kernel-based techniques. Numerical experiments demonstrate a competitive performance of this method in comparison to the finite element method and to other selection methods for solving the Dirichlet problems for the Poisson equation on several STL models. Discretization nodes for these domains are obtained either by 3D triangulations or from Cartesian grids or Halton quasi-random sequences.

翻译：我们在3D中为拉帕拉西亚人引入了几何定时选择算法, 大大改进了先前考虑的八元选择。 算法的目标是从一个特定点周围的一组非正常点中选择一个小子集, 以精确的数值区分公式。 子集是一个影响拉帕拉西亚人以无网点的有限差差法, 使用多元或内核技术。 数值实验表明,与有限的元素法和其他选择方法相比,这种方法具有竞争性的性能, 以解决几个STL模型中的普瓦森方程式的 Dirichlet问题。 3D三角或Cartesian 电网或Halton 准随机序列为这些领域的分解节点。 3D三角或Carterian 电网或 Halton 准随机序列为这些域提供了分解节点。