Boundary element methods for the scattering retrieval of metamaterials

The present work focuses on the electromagnetic simulation of densely-packed crystalline assemblies of subwavelength particles (metamaterials), for which a rigorous full-wave analysis still remains challenging. Indeed, even for moderate electric sizes, the overly-populated mesh needed to preserve the geometrical features of this kind of structures leads to problems that can easily need millions of degrees of freedom (DoF) if boundary element methods are used. Thus, a means of compressing the resulting impedance matrix must be found. In this respect, the “low-frequency breakdown” inherent to the plane-wave expansion of the fast multipole method (FMM) limits the exploitation of the rank-deficient impedance matrix resulting from dense meshes. This work takes advantage of the repetition pattern of these nanostructures and directly compresses the nearest couplings via singular value decompositions (SVD) that need to be computed only once thanks to the periodicity.