A Preconditioner for the Fast Analysis of Arbitrarily-Shaped Reflective Intelligent Surfaces

Analyzing a reflective metasurface (MTS) is usually simplified by considering the MTS as a continuous sheet of impedance. Thanks to this approach, we avoid the need to describe the fine geometry of the MTS with numerous elementary basis functions. Considering the MTS at the sheet impedance level allows to analyze the structure by solving a linear system of equations with a reduced number of unknowns and, when iterative solvers are used, the convergence is usually very good for conventional highly capacitive MTS. However, the condition number of the system and hence the convergence of the solver dramatically deteriorates when considering impedance ranges spanning both capacitive and inductive domains. In this paper, we present an efficient preconditioner which significantly improves the convergence of the GMRES iterative solver when applied to both inductive and capacitive MTSs. We also show that the method can be easily extended to MTSs with arbitrary shapes.