The University of Tokyo, Tokyo, Japan.
Proc Jpn Acad Ser B Phys Biol Sci. 2011;87(4):115-34. doi: 10.2183/pjab.87.115.
The finite element method (FEM) has been commonly employed in a variety of fields as a computer simulation method to solve such problems as solid, fluid, electro-magnetic phenomena and so on. However, creation of a quality mesh for the problem domain is a prerequisite when using FEM, which becomes a major part of the cost of a simulation. It is natural that the concept of meshless method has evolved. The free mesh method (FMM) is among the typical meshless methods intended for particle-like finite element analysis of problems that are difficult to handle using global mesh generation, especially on parallel processors. FMM is an efficient node-based finite element method that employs a local mesh generation technique and a node-by-node algorithm for the finite element calculations. In this paper, FMM and its variation are reviewed focusing on their fundamental conception, algorithms and accuracy.
有限元方法（FEM）已广泛应用于各个领域，作为一种计算机模拟方法来解决固体、流体、电磁等现象的问题。然而，在使用有限元方法时，为问题域创建高质量的网格是前提条件，这成为模拟成本的主要部分。因此，无网格方法的概念应运而生。自由网格方法（FMM）是典型的无网格方法之一，旨在对全局网格生成难以处理的问题进行类似粒子的有限元分析，特别是在并行处理器上。FMM 是一种高效的基于节点的有限元方法，它采用局部网格生成技术和节点逐个的算法进行有限元计算。本文重点介绍了 FMM 及其变体的基本概念、算法和精度。
