无网格法作为网格方法的重要补充和发展,是一新兴数值方法.本文围绕无网格法的近似方式及加权残量法这两个核心内容,详细阐述了无网格法的基本原理,评述了无网格法的优缺点,并对无网格法的研究进展作了综述;以大地电磁二维问题为例,详细介绍了Galerkin弱式无网格法的求解过程;最后介绍了无单元Galerkin法(EFGM)在地球物理学中的应用. Meshless method as an important complement and development of grid method is an emerging numerical method.This paper focuses on the two core concepts of meshless method and weighted residual method, elaborating the basic principles of meshless method , Reviewed the advantages and disadvantages of meshless method, and reviewed the research progress of meshless method. Taking earth magnetism two-dimensional problem as an example, this paper introduced the solving process of Galerkin weak meshless method in detail. Finally, Application of Element Free Galerkin Method (EFGM) in Geophysics.