摘要
在子域插值的基础上提出了分阶拟合直接配点无网格方法。该方法通过分阶拟合使近似函数在节点的残差达到最小,边界条件直接引入,然后使用直接配点法求解方程。与其它插值或拟合方法相比,分阶拟合避免了矩阵奇异产生的困难;与最小移动二乘法(MLS)相比,分阶拟合只需用六个点来构造二次基近似函数,减小了计算量;而与其它基于Galerkin法的无网格法相比,分阶拟合直接配点无网格法计算量小。
Fit By Order (FBO) method is developed to establish the meshless approximation function at a node, in which the approximation function is first fitted on the linear basis, and then fitted on the quadric basis to minimize the error. Collocation is used to discretize the governing equation. The proposed method has several advantages. Compared with other interpolation methods, such as MLS and PIM, FBO overcomes the difficulties arising from the singularity of matrix and only six nodes are required to establish the approximation, so that the computational effort required is reduced. Compared with Galerkin-based meshless method, the proposed method does not require any mesh, so that the computational cost is further reduced.
出处
《工程力学》
EI
CSCD
北大核心
2003年第5期48-52,共5页
Engineering Mechanics
关键词
无网格法
插值
覆盖
分阶拟合
Approximation theory
Galerkin methods
Interpolation
