势问题的复变量插值型无单元Galerkin方法

Complex Variable Interpolating Element-Free Galerkin Method for Two-Dimensional Potential Problems

给出了改进的复变量移动最小二乘法,针对其形成的形函数不满足Kronecker Delta函数性质提出了复变量移动最小二乘插值法。将复变量移动最小二乘插值法和势问题的Galerkin积分弱形式相结合,建立了势问题的复变量插值型无单元Galerkin方法。复变量插值型无单元Galerkin方法的优点是,可以减少基函数的个数,且可以直接施加边界条件,从而提高计算效率。最后给出了数值算例说明了该方法的有效性。

The improved complex variable moving least-squares （CVMLS） approximation was discussed first. Then the complex variable interpolating moving least-squares （CVIMLS） method was presented. Combining the shape function constructed by the CVIMLS method and Galerkin weak form for the poten- tial problem, the complex variable interpolating element-free Galerkin （CVIEFG） method for the potential problem was put forward, in which the boundary conditions can be applied directly. Compared with the conventional EFG method, the proposed method can reduce the number of the unknown coefficients be- cause it has fewer basis functions and the boundary conditions can be applied conveniently. As a conse- quence, the computational efficiency is greatly promoted. A numerical example was developed to demon-strate the validity of the method.