Numerical Solution Of Three-dimensional Potential Problem By Interpolation Element-free Galerkin Method

Interpolation element-free Galerkin(IEFG)method is an important class of meshless methods.It is based on the interpolation moving least square method to establish the shape function.This method is used to solve the three-dimensional potential problem numerically in this paper.Firstly,the interpolation-type moving least squares method is discussed.The shape function constructed by this method has interpolation properties,and the essential boundary conditions can be directly applied.Secondly,based on the interpolation moving least squares method and the weak integral form of the potential problem,the interpolation element-free Galerkin method is derived.Through the study of IEFG method and the programming of MATLAB code,several examples of solving three-dimensional Laplace equation and three-dimensional Poisson equation are given.The analytical solution is compared with the numerical solution,and the correctness of the conclusions in this paper is verified by error analysis.The results show that the IEFG method has high computational efficiency.