Accurate and Fast Analysis of Reflective Surfaces and Metasurface Antennas With Sheet Impedance Boundary Conditions

Simulating the fine geometry of Metasurfaces (MTS) structures in a conventional way is a difficult task requiring huge computational resources. On the other hand, the metallization can usually be modeled as an impedance sheet with modulation scale of the order of the operating wavelength. Even then, direct solution of the system of equations is usually not possible due to memory saturation. As a consequence, one has to resort to iterative methods. However, the analysis of an impedance sheet lying on a grounded slab based on an iterative solution of the Method of Moments (MoM) may lead to ill-conditioning and a large number of iterations. This is certainly the case when the range of impedance spans both the capacitive and inductive domains. Such impedances range is in practice required for Reflective Intelligent Surfaces (RIS), and for some MTS antennas. This paper proposes a preconditioner aiming to solve bad convergence issues caused by the wide range of the surface impedance. The preconditioner involves a multiplication by the conjugate of the MoM matrix followed by a block diagonal preconditioner. The block diagonal preconditioner has memory and multiplication complexity <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i><sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3/2</sup>. It is precalculated in an accelerated scheme relying on FFTs. Besides, multiplication with the MoM matrix is carried out with complexity <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> log(<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i>) thanks to the use of FFTs.