A Divergence-free Meshless Method for Transient Vector Wave Equations

With the implementation of the vector radial basis function (RBF), which is theoretically divergence free, we propose a meshless method for solving the transient vector wave equation. Unlike the conventional radial point interpolation meshless (RPIM) method based on the scalar RBF that solves electric field and magnetic field components separately with scalar wave equations, the proposed method solves the vector wave equation directly. Therefore, the long-existing technical challenge of the source in the traditional RPIM method is resolved due to the direct solution of the vector wave equation. In addition, the stability condition of the proposed method is presented. At last, several numerical experiments are conducted to validate the accuracy of the proposed solver.