An assessment of the meshless weighted least-square method

The meshless weighted least-square (MWLS) method was developed based on the weighted least-square method. The method possesses several advantages, such as high accuracy, high stability and high efficiency. Moreover, the coefficient matrix obtained is symmetric and semi-positive definite. In this paper, the method is further examined critically. The effects of several parameters on the results of MWLS are investigated systematically by using a cantilever beam and an infinite plate with a central circular hole. The numerical results are compared with those obtained by using the collocation-based meshless method (CBMM) and Galerkin-based meshless method (GBMM). The investigated parameters include the type of approximations, the type of weight functions, the number of neighbors of an evaluation point, as well as the manner in which the neighbors of an evaluation point are determined. This study shows that the displacement accuracy and convergence rate obtained by MWLS is comparable to that of the GBMM while the stress accuracy and convergence rate yielded by MWLS is even higher than that of GBMM. Furthermore, MWLS is much more efficient than GBMM. This study also shows that the instability of CBMM is mainly due to the neglect of the equilibrium residuals at boundary nodes. In MWLS, the residuals of all the governing equations are minimized in a weighted least-square sense.