Application of Meshless Petrov Galerkin (MLPG) method in electromagnetic using Radial Basis Functions

In this work, the meshless local Petrov Galerkin MLPG method is applied to electromagnetic field problems. The method is implemented using radial basis functions (RBF) for interpolation of trial functions instead of the traditional moving least square (MLS) interpolations. Once of the main advantages of this method is that essential boundary conditions are satisfied as in FEM which eliminates the need for additional methods to impose boundary conditions: both globally and compactly supported radial basis functions are considered. The method is evaluated through numerical examples in electrostatic and magnetostatic domains in 1D and 2D, the main objective of these applications is: - to study the effect of RBF on the accuracy by comparing results to those obtained by the traditional MLPG (with lower order polynomial basis), the FEM or exact solutions. - To study the effect of different factors existing in the formulations and calculate optimised factors. Compactly supported radial basis functions provide a promising approach.