Accelerated IE-GSTC Solver for Large-Scale Metasurface Field Scattering Problems Using Fast Multipole Method (FMM)

An accelerated integral equations (IE) field solver for determining scattered fields from electrically large electromagnetic metasurfaces using fast multipole method (FMM) is proposed and demonstrated in 2-D. In the method, practical general are expressed an equivalent zero thickness sheet model described surface susceptibilities, where total around it satisfy generalized transition conditions (GSTCs). While standard IE-GSTC offers computation compared with other numerical methods, still computationally demanding when solving problems, a number of unknowns. Here, we accelerate FMM technique by dividing current elements on metasurface into near- far-groups, either rigorous or approximated Green’s function used, respectively, to reduce time without losing solution accuracy. Using examples, speed improvement { $O(N^{3/2})$ } over notation="LaTeX">$O(N^{3})$ confirmed. Finally, usefulness applying solve propagation inside radio environment strategically placed improve signal coverage blind areas, would require prohibitively computational resources long simulation times.