论文标题
最小二乘径向基函数有限差法具有改善的稳定性特性
A least squares radial basis function finite difference method with improved stability properties
论文作者
论文摘要
基于椭圆形问题的径向基础函数（RBF）的局部搭配方法在存在Neumann边界条件的情况下似乎是不舒适的。在本文中，我们通过在离散最小二乘设置中制定RBF生成的有限差方法来克服此问题。这使我们能够在节点细化下证明高阶收敛性，并在数值上验证最小二乘配方比搭配配方更准确，更健壮。修改后的算法的实施工作与搭配方法相当。
Localized collocation methods based on radial basis functions (RBFs) for elliptic problems appear to be non-robust in the presence of Neumann boundary conditions. In this paper we overcome this issue by formulating the RBF-generated finite difference method in a discrete least-squares setting instead. This allows us to prove high-order convergence under node refinement and to numerically verify that the least-squares formulation is more accurate and robust than the collocation formulation. The implementation effort for the modified algorithm is comparable to that for the collocation method.
