Numerical simulation of joule heating phenomenon using meshless RBF-DQ method

In this paper the meshless Local Multi Radial Basis Function-Differential Quadrature (MQ-DQ) method is applied to obtain the distributions of electrical potential and temperature for different geometries. Current method is the combination of Differential Quadrature approximation of derivatives and function approximation of MQ-Radial Basis Function (RBF). Two different geometries with different shapes of inner boundaries are considered and the obtained results are compared with those gained by Finite Element (FE) solutions. Outcomes verify that the current technique is in very good agreement with FEM and the fact that MQ-DQ method is an accurate and flexible method in solution of electrostatic and heat transfer equations for both steady and unsteady solutions.