Unconditionally-Stable Meshless Methods Using Different Split-Step Techniques and Their Phase Velocity Considerations

In this paper, new unconditionally- stable meshless methods based on different split- step methods are proposed. Moreover, comparison of the phase velocities of two different split-step meshless methods and that of alternative- direction-implicit meshless (ADI-ML) method is presented. Here we show how employing split- step (SS) technique using radial point interpolation meshless (RPIM) method results in an unconditionally stable scheme. Symmetric operators and uniform splitting are utilized simultaneously to split the classical Maxwell's matrix into four and six submatrices. Also, for more accurate approximations Crank-Nicolson (CN) scheme that is a fully implicit scheme has been applied for implementation of these schemes. It has been demonstrated, these proposed methods produce even more effective unconditionally stable responses than those of alternating- direction-implicit meshless time-domain ADI- MLTD methods. Eventually, in order to prove the advantage of the proposed method, a comparison has been made between these novel meshless methods and their finite-difference counterparts. More smoothed phase velocities in proposed meshless methods imply a reduction in dispersion error in comparison with their analogous cases in finite-difference time-domain (FDTD) method.