A 3-D unconditionally stable Laguerre-RPIM meshless method for time-domain electromagnetic computations

In this paper, a 3-D unconditionally stable meshless method is introduced to simulate time-domain electromagnetic problems. It combines the conventional radial point interpolation method (RPIM) and weighted decaying Laguerre polynomials together to discrete Maxwell's differential equations. The new method called Laguerre-RPIM retains the advantages of both the node-based meshless method and the unconditionally stable scheme of weighted Laguerre polynomials. The accuracy and efficiency of the proposed method are verified through two numeral examples. It can be seen from the computational results that the proposed method has a high accuracy and still remains stable when time step is 10 times of the Courant stability condition. Computational cost can be saved by more than 70% compared with the conventional RPIM method.