Development of a new meshless — point weighted least-squares (PWLS) method for computational mechanics

A truly meshless approach, point weighted least-squares (PWLS) method, is developed in this paper. In the present PWLS method, two sets of distributed points are adopted, i.e. fields node and collocation point. The field nodes are used to construct the trial functions. In the construction of the trial functions, the radial point interpolation based on local supported radial base function are employed. The collocation points are independent of the field nodes and adopted to form the total residuals of the problem. The weighted least-squares technique is used to obtain the solution of the problem by minimizing the functional of the summation of residuals. The present PWLS method possesses more advantages compared with the conventional collocation methods, e.g. it is very stable; the boundary conditions can be easily enforced; and the final coefficient matrix is symmetric. Several numerical examples of one- and two-dimensional ordinary and partial differential equations (ODEs and PDEs) are presented to illustrate the performance of the present PWLS method. They show that the developed PWLS method is accurate and efficient for the implementation.