Abstract
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.
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