ABSTRACT
In the past few decades, the development of finite element methods (FEMs) has been accompanied by advances in boundary element methods (BEMs). The FEM is a domain discretizationmethod,whereas the BEM is a boundary discretizationmethod. Bothmethods have their strengths and weaknesses. The FEM is much more flexible for complex structures=domains with high inhomogeneity and nonlinearity but requires intensive computational resources. On the other hand, the BEM requires much less computational resources, as discretization of the structure=domain is performed only on the boundary, which leads to a much smaller discretized equation system. The BEM, however, is not efficient for inhomogeneous media=domain and nonlinear problems. Efforts to combine these two methods have been made by many (see, e.g., [1]) and have achieved remarkable results. Commercial software packages have also been developed (e.g., SYSNOISE) and used for solving a wide range of engineering problems. In previous chapters, we presented both domain-type meshfree methods and boundary-
type meshfree methods. Naturally, attempts have also been made to combine these two types of methods to take advantage of both. There is an additional motivation to couple meshfree methods that are formulated using moving least squares (MLS) shape functions and meshfree methods that are formulated using point interpolation method (PIM) shape functions or finite element (FE) shape functions. The aim is to simplify the procedure of imposing essential boundary conditions. A number of combined methods have been formulated including element-free Galerkin (EFG)=BEM [2], EFG=HBEM [3], meshless local Petrov-Galerkin (MLPG)=FEM=BEM [4,5], etc. This chapter is devoted to introducing the EFG=BEM [2] and EFG=HBEM.
