A meshless time-domain algorithm for solving the 3-D Maxwell's equations

A meshless time-domain algorithm for a solution of the 3-D Maxwell's equations is developed. The spatial derivatives related to the algorithm are approximated by using an expanded Taylor series and the weighted least square technique in each cloud of points, and then a particular approximate Riemann solver is constructed for computing the physical flux of the governing equations. After that, an explicit four-stage Runge-Kutta scheme is used to advance the Maxwell's equations in time. Combined with solving the 3-D Maxwell's equations, the implementations of the present algorithm are described in details. Based on the developed algorithm, numerical results for typical 3-D objects such as a metal sphere, a metal cube and an air-intake model are presented, which show that the obtained bistatic radar cross sections are in good agreement with the series solution or that of the reference.