Meshless MQ Quasi-interpolation method for transient electromagnetic computations

In this paper, a meshless quasi-interpolation method based on a special radial basis function (RBFs), i.e. Multi-Quadrics (MQ) is presented for the numerical solution of 1-dimensional Maxwell´s equations. RBFs have attractive properties such as theoretical exponential convergence for increasingly dense distinct node distributions. The time derivatives are still tackled with the customary explicit leap-frog time scheme. The space derivatives at the nodes are approximated by the so-called MQ quasi-interpolation. This new approach need not solve the ill-conditioned linear system arising in RBF-based meshless method at each time step. To verify the accuracy and efficiency of the new formulation, the Sine-Gorden equation with analytic solution is solved by means of this novel method. Finally,Maxwell´s equations with various assigned boundary conditions and current source excitation are solved numerically. The numerical results are compared with those of the conventional FDTD method.