QR-Recursive Compression of Volume Integral Equations for Electromagnetic Scattering by Large Metasurfaces

In this article, a novel QR decomposition-based compression scheme is combined with a volume integral equations (VIEs) method for the fast and efficient numerical computation of the scattering of electromagnetic fields from large scale metasurfaces, via an iterative approach. The underlying problem is of a multiscale nature. Indeed, these metasurfaces are made of a large collection of interacting subwavelength scatterers, thus making the numerical computation of the solution very challenging. More specifically, this article proposes a tailored version of an QR decomposition-based compression for a VIE, together with a proper preconditioner that exploits the geometrical structure of the array, in order to achieve a fast and accurate iterative solver, in view of realistic applications. Numerical examples prove the effectiveness of the method in efficiently modeling metasurfaces made by thousands of particles.