An Improved Element-Free Galerkin Method Based on the Dimension Splitting Moving Least-Squares Method for 2D Potential Problems in Irregular Domains

By introducing the dimension splitting (DS) method into the moving least-squares (MLS) approximation, a dimension splitting moving least-squares (DS-MLS) method is proposed in this paper. In the DS-MLS method, the operator splitting and independent variable splitting of the DS method are used to reduce the dimension, thereby reducing the computational complexity of the matrix. The shape function of the DS-MLS method has the advantages of simple derivation and high computational efficiency. Then, by coupling DS-MLS method and Galerkin weak form, and performing the coordinate transformation, an improved element-free Galerkin method (IEFGM) based on the DS-MLS method is proposed for two-dimensional (2D) potential problems on irregular domains. The effectiveness of the method in this paper is verified by some numerical examples. The numerical results show that, compared with the element-free Galerkin (EFG) method, the IEFGM based on the DS-MLS method in this paper consumes less CPU time and has higher computational accuracy for some 2D potential problems on irregular domains.

Automated summary

In this paper, a DS-MLS method is proposed by introducing dimension splitting into the moving least-squares approximation. By coupling with Galerkin weak form, an IEFGM method based on the DS-MLS method is proposed for solving 2D potential problems on irregular domains. Numerical results demonstrate that the IEFGM method consumes less CPU time and has higher computational accuracy compared to the EFG method.