Study of weight functions in the Element-Free Galerkin Method

The weight function plays an important role in the performance of the element-free galerkin method (EFGM). It can impose a tremendous influence on the accuracy of solutions, the complexity of computation and the rate of convergence. The continuity of the weight function causes the continuity of the shape function in the EFGM. Therefore, it becomes particularly urgent to select an appropriate weight function suited to electromagnetic calculations. In this paper, detailed research is discussed on some key problems, such as the regularity of the influence domain width, the formula of the influence radius of nodes in three-dimensional computations and the weight function on the accuracy of the approximate solution and the computation time.