Boundary element method for the electromagnetic analysis of metamaterials

The full-wave simulation of metamaterials, presenting densely packed assemblies of subwavelength meta-atoms, poses a challenge for the computational electromagnetics community. Preserving the geometrical features of this kind of structures needs a highly discretized mesh, leading to problems that easily reach several tens of millions of unknowns if boundary element methods are used, despite the electric size being small. It is therefore evident that a means of compressing the resulting impedance matrix is paramount. In this regard, the spectral acceleration of the well-known fast multipole method (FMM) does not really exploit the rank-deficient method-of-moments matrix when applied to these scenarios, given its “low-frequency breakdown”. Although low-frequency versions of FMM have been proposed that try to circumvent this problem, we herein suggest to take advantage of the periodicity inherent to these nanostructures and directly compress the nearest couplings, for which standard FMM fails, through singular value decompositions (SVD) which are only performed a reduced number of times thanks to the repetition pattern.