Criterion for selecting the shape functions in electromagnetic meshless methods

The root of this study, comes from the lack of regularity where exists in shape function selection in meshless methods. Up to now, shape functions in meshless methods were being established by basis functions. In other words, there was no predictable rule by which the shape functions be predetermined, without any need to basis functions. In presented approach, the authors are going to establish a criterion, which is based on both analytical and simulation results; helps select an approximately well-behaved shape function for which the shape parameters have been predetermined. This work focused on both Laplace and wave equations as the most important equations in electrostatic and electromagnetic problems to show the validation of the proposed approach in computational electromagnetics. Comparing the results with radial point interpolation method as the most common existing meshless method, finite-element method and finite-difference method, the criterion shows extremely good accuracy despite a great reduction in time consumption rate for selecting a compatible shape function.