Study of increasing computational efficiency in Element-Free Galerkin method

The Element-Free Galerkin method (EFGM) is based on moving least square (MLS) approximations and uses only a set of nodal points to formulate the discrete model. The EFGM does not require any elements and has not the element deformation problems. Therefore, the EFGM simplifies pre-processing and post-processing and can solve problems with higher accuracy. However, the computational efficiency of the EFGM is very low, which caused mainly by the Gaussian integration and finding the inverse matrix of the coefficient matrix. To overcome this shorting, the orthogonal basic functions is given, the preconditioning method of equations and the support domain of weight functions are studied thoroughly in this paper.