Unconditionally Stable Divergence-Free Vector Meshless Method Based on Crank-Nicolson Scheme

This letter presents the Crank-Nicolson formulation of vector meshless method. As the vector meshless method is divergence-free, its solutions are more precise than the conventional scalar meshless methods. In the conventional time-domain vector meshless method, the time-step size is restricted by Courant-Friedrichs-Lewy criterion. In order to attain an unconditionally stable formulation of vector meshless method, we have applied the Crank-Nicolson scheme to this method. Moreover, by a numerical example, we have investigated the efficiency and accuracy of the proposed method in comparison to another unconditionally stable vector meshless method, i.e., alternating-direction-implicit vector meshless method. © 2017 IEEE.