Unconditionally Stable Vector-based Meshless Method for Transient Electromagnetic Analysis

In this paper, an unconditionally stable vector-based meshless method is presented. In the proposed method the leapfrog alternating-direction implicit (ADI) scheme is incorporated into a divergence-free vector RBF based meshless method. The vector RBF based meshless method has been recently proposed for numerical analysis. Unlike the scalar RBF meshless methods, this method has been proved to be divergence-free in the source-free regions. In conventional time-domain vector meshless method, the finite-difference scheme is used to approximate the time derivatives. Therefore, the CFL stability condition on the time-step limits the computational efficiency of the method. To overcome this limitation, in this paper, the ADI method is directly applied to the differential Maxwell’s curl equations. Consequently, unconditional stability of the method is obtained by ADI technique and more accurate results are achieved by the use of vector basis functions. The effectiveness and efficiency of the proposed method are verified by a numerical example