A Review of Mesh Free- Element Free Galerkin method, Recent Development and Application

Abstract

Numerical simulation using computers has increasingly become a very important approach for solving problems in engineering
and science. It plays a valuable role in providing tests and examinations for theories, offering insights to complex physics, and
assisting in the interpretation and even the discovery of new phenomena. FEM has been one of major tools in dealing with many
engineering and academic problems from many decades; however it suffers from the problem of its heavy reliability on quality
mesh which is not suitable when treating with large deformation problems. The term mesh less (or mesh free) method refers to a
broad class of effective numerical techniques for solving a growing number of science and engineering applications without the
dependence of an underlying computational mesh. The variety of problems analyzed by these methods is very large, and ranges
from fracture mechanics, over fluid mechanics, multiscale problems, and laminated composites, all the way to moving material
interfaces. The review presented in this paper mainly focuses various mesh free methods, their applications and requirements as
well as advantages gained by coupling element free methods with the classical FEM. Sometimes it is even more beneficial to
couple two mesh free methods to get better results. There are various methods to couple such mesh free methods like EFG, MLPG
and SPH with FEM like master slave coupling, coupling via interface shape functions bridging domain coupling compatibility
coupling with Lagrange multipliers and hybrid coupling.