论文标题
基于RBF-FD和WLS的稳定性分析，基于散射节点的局部强形式无网状方法
Stability analysis of RBF-FD and WLS based local strong form meshless methods on scattered nodes
论文作者
论文摘要
近年来，当地无网格方法在数值模拟领域的普及大大增加了。这主要是由于它们可以在分散的节点上操作，并且可以直接控制近似顺序和基础功能。在本文中，我们分析了局部强形式无网状方法的两个流行变体，即使用单元素增强的多谐波键（PHS），以及仅使用单一元素的方法来增强径向函数生成的有限差异（RBF-FD），而加权最小二乘（WLS）。我们的分析重点是在二维和三维结构域中散射节点上计算出的数值解的准确性和稳定性。我们表明，尽管WLS变体是一个更好的选择，而较低阶近似值就足够了，但RBF-FD变体具有更稳定的行为，并且数值解决方案具有更高的数值解决方案，以实现高阶近似值，但以较高的计算复杂性为代价。
The popularity of local meshless methods in the field of numerical simulations has increased greatly in recent years. This is mainly due to the fact that they can operate on scattered nodes and that they allow a direct control over the approximation order and basis functions. In this paper we analyse two popular variants of local strong form meshless methods, namely the radial basis function-generated finite differences (RBF-FD) using polyharmonic splines (PHS) augmented with monomials, and the weighted least squares (WLS) approach using only monomials. Our analysis focuses on the accuracy and stability of the numerical solution computed on scattered nodes in a two- and three-dimensional domain. We show that while the WLS variant is a better choice when lower order approximations are sufficient, the RBF-FD variant exhibits a more stable behavior and a higher accuracy of the numerical solution for higher order approximations, but at the cost of higher computational complexity.
