The Ping-Pong Electromagnetic Algorithm for Reflecting Surface Antennas of Arbitrary Shapes

An efficient ping-pong algorithm is presented to deal with electromagnetic scattering from reflecting surface antennas such as the reconfigurable intelligent surfaces (RISs) of arbitrary geometric shapes. The proposed computational electromagnetics (CEM) algorithm does not require formation, storage, and inverse of the impedance matrix used by the method of moments (MoM). Instead, a rigorous formula is obtained for the computation of the surface current from the scattered electric field. Besides, the algorithm only contains convolution operations with the scalar Green’s function and second derivatives operations to iteratively update the surface currents and scattered electric field. Also, hypersingular integration arising from the singularities of the surface current and scattered electric field is properly regularized. Furthermore, the algorithm converges fast and satisfactory results are obtained after a few iterations, and it is about ten times as fast as the MoM. Besides, the first iteration gives the solution for reflecting surface antennas on substrates of perfect absorption. Numerical solutions are obtained for some typical antennas and comparisons are made to those in the literature and from the MoM.