中文摘要：

有限元法是偏微分方程数值计算的强大工具，但它以网格单元为基础，存在着某些不足．无网格法作为一种新兴的数值方法，解除了节点的网格束缚，能够消除由于网格存在所带来的缺陷．该文以电磁场数值计算的泊松方程边值问题为研究对象，建立了无网格Galerkin法求解的离散方程，编写了MatLab程序，完成了3个电磁场问题的数值计算，所得结果与有限元法计算结果进行了比较，显示无网格Galerkin在电磁场计算中具有更好的数值精度和稳定性．

英文摘要：

The FEM has been established as a very powerful numerical technique in PDEs computation. However, it has some shortcoming because it＇s based on mesh elements. Element-Free Galerkin Method （EFGM） is a new method for electromagnetic field computation. It is only a distribution of points and does not need meshes, so it can eliminate the shortcoming caused by mesh grid. This paper studied on electromagnetic field computation poisson equation, and built discrete equation for resolve in EFGM. MATLAB programs were written to certify three 2D example in electromagnetic field computation , and the results had been compared with the result in FEM, which was given to demonstrate that it has a better precision and stability in Element free Galerkin method.