Comparisons of heterogeneous multiscale finite element method and localized homogenization process for modeling aperiodic metamaterials

A common approach in modeling metamaterials is through the use of homogenization process. Recently, the development of the heterogeneous multi-scale finite element methods (HM-FEM) together with the advancements in non-conformal domain decomposition methods have made it possible to simulate many complex electromagnetic problems with multi-scale features. We present herein comparisons of full-wave simulations, taking into account the microscopic structural details, against the simplified homogenization process results using various numerical examples.