RBF-PU方法求解二维非局部扩散问题和近场动力学问题

采用单位分解径向基函数(radial basis function partition of unity，RBF-PU)方法，数值求解了二维非局部扩散问题和近场动力学问题。主要思想是对求解区域进行局部划分，在局部子区域上分别进行函数逼近，然后加权得到未知函数的全局逼近。这种基于方程强形式的径向基函数方法在求解非局部问题时，不需要处理网格与球形邻域求交的问题，避免了额外的一层积分计算，实施简便，计算量小。数值实验显示计算结果与解析解吻合较好，RBF-PU方法可以准确有效地求解非局部扩散方程和近场动力学方程。

The RBF-PU Method for Solving 2D Nonlocal Diffusion and Peridynamic Equations

The radial basis function partition of unity (RBF-PU) method  was applied to obtain the numerical solution of 2D nonlocal diffusion and peridynamic problems. The main idea is to partition the original domain into several patches, use the RBF approximation on each local domain, and then give weighting to obtain the global approximation of the unknown function. The radial basis function method based on the strong form of the equation has many advantages, such as avoiding an additional layer of integral calculation, no need to deal with intersections of neighborhoods with the mesh, and easiness of implementation. The numerical results show that, this method can solve nonlocal diffusion equations and peridynamic equations accurately and efficiently.