Contents I. Introduction
Unlike the conventional grid-based methods such as the finite-difference time-domain (FDTD) method [1], the finite element method (FEM) [2] and the moment of method (MOM) [3], meshless methods interpolate fields to be solved with the field values at predefined scattering nodes in a support domain. A set of algebraic equations based on positions of the scattering nodes in a solution domain is then established and solved by linear solvers. That means that unlike grid-based methods, connection information among nodes is not required, which leads to easy implementation and high flexibility in modeling complex structures. As a result, the number of the published reports on the meshless methods for solving electromagnetic problems has increased dramatically. In particular, the smoothed particle electromagnetic method [4] and the radial point interpolation meshless (RPIM) method [5] have been proposed. Other forms of the meshless methods including the leapfrog and alternatively-direction-implicit RPIM methods in the time-domain are summarized in [6]. However, to the best of the authors' knowledge, no numerical dispersion of the meshless methods has been reported so far. In addition, no direct relationship between the FDTD method and RPIM method have been shown although it is mentioned in [7] that the RPIM method may reduce to the FDTD method under certain conditions (but no theoretical proof was given there).
