Hybrid volume-surface integral equation method for high contrast composite media and metamaterials

This paper outlined a new VSIE representation as an alternative to the standard FE-BI methods. This hybrid formulation, based on a specific factorization of the material properties within the solution domain, also allows for the decomposition of the problem into interior and exterior solution subdomains, hence eliminating the need to use a high discretization rate for high permittivity regions. In case of periodic structures, this decomposition also eliminates the use of periodic Green´s function for the interior domain. The periodicity of the structure is explicitly imposed by modifying the boundary conditions on the wall of the unit cell. Full integral equation nature of this formulation makes it an excellent candidate for electrically large problems as well as resonant structures, the latter typically being encountered in modeling of metamaterials