函数配点法与不重叠Schwarz交替法求解椭圆方程

Non-overlapping Schwarz Alternative Method with Radial Basis Function Collocation for Solution of Elliptic Partial Differential Equation

为了克服用一般的全域径向基配点法求解椭圆方程时所带来的配置矩阵为非对称满阵且高度病态的问题,将径向基函数配点法和不重叠型Schwarz交替法结合用于求解椭圆方程,该方法把求解大规模问题转化为求解多个小的子区域问题,取得较好的结果并且提高了计算速度.

To avoid the problem of a full, asymmetry and highly ill-conditioned collocated matrix, which is resulted from the global domain RBF （radial basis functions） to solve the elliptic partial differential equations, using radial basis functions collocation combined with non-overlapping subdomains Schwarz alternative methods to solve the elliptic partial differential equations. By this meshless method, many small subdomains problems are solved instead of one large scale problem. The method not only reduces condition number of coefficient matrix but also improves computa- tional accuracy and efficiency.