Accelerated IE-GSTC Solver for Large-Scale Metasurface Field Scattering
Problems using Fast Multipole Method (FMM)
Abstract
An accelerated Integral Equations (IE) field solver for determining
scattered fields from electrically large electromagnetic metasurfaces
utilizing Fast Multipole Method (FMM) is proposed and demonstrated in
2D. In the proposed method, practical general metasurfaces are expressed
using an equivalent zero thickness sheet model described using surface
susceptibilities, and where the total fields around it satisfy the
Generalized Sheet Transition Conditions (GSTCs). While the standard
IE-GSTC offers fast field computation compared to other numerical
methods, it is still computationally demanding when solving electrically
large problems, with a large number of unknowns. Here we accelerate the
IE-GSTC method using the FMM technique by dividing the current elements
on the metasurface into near- and far-groups, where either the rigorous
or approximated Green’s function is used, respectively, to reduce the
computation time without losing solution accuracy. Using numerical
examples, the speed improvement of the FMM IE-GSTC method
O(N1.5) over the standard IE-GSTC
O(N3) method is confirmed. Finally, the usefulness of
the FMM IE-GSTC is demonstrated by applying it to solve electromagnetic
propagation inside an electrically large radio environment with
strategically placed metasurfaces to improve signal coverage in blind
areas, where a standard IE-GSTC solver would require prohibitively large
computational resources and long simulation times.