论文标题
改进的模板选择3D中无网状有限差异方法
Improved Stencil Selection for Meshless Finite Difference Methods in 3D
论文作者
论文摘要
我们在3D中引入了用于Laplacian的几何模具选择算法，该算法显着改善了前面考虑的基于八分之一的选择。该算法的目的是从一组不规则的点中选择一个小子集，该点围绕一个给定点的不规则点，该点可以允许准确的数值差异化公式。该子集是使用多项式或基于核的技术在无网状有限差异方法中laplacian的数值近似的影响。与有限元方法和其他选择方法相比，数值实验证明了该方法的竞争性能，以解决多种STL模型上泊松方程的差异问题。这些结构域的离散淋巴结是通过3D三角形或笛卡尔网格或Halton Quasi-random序列获得的。
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.
