Parametric meshless Galerkin method

In meshless methods, generation of meshless shape functions is usually a complicated and timeconsuming task. In this paper, a new meshless method called parametric meshless Galerkin method (PMGM) is presented. In this method, meshless shape functions are constructed on meshless parametric domains (MPD), before running to solve the problem. For modelling the new problems, MPDs are mapped to the physical space. Therefore the shape functions constructing time can be saved. Mapping is simply performed by defining a linear function. Also, the integration grids are defined in the MPD and it is not necessary to create background integration grids separately for each problem. The method is described for two-dimensional problems, but it can be applied to three-dimensional problems in the same way. It is shown that using the PMGM, a time saving as much as 21% is achieved with respect to the element-free Galerkin method for the numerical examples and the obtained results show efficiency and convergence of the method