An Efficient Electromagnetic Scattering Optimization Scheme for Multiscale Problems Using Green's Functions of Arbitrary Scatterers

An efficient optimization methodology is developed and exemplified for electromagnetic scattering problem of structures with multiscale features. We have developed a scheme to efficiently derive the exact full wave scattering solution from a large scatterer with localized modifications by using the Green's function of the original scatterer. The Green's function of the original scatterer and the free-space Green's function are used to formulate coupled surface integral equations (SIEs) on a virtual boundary that separates the localized modifications from the original scatterer. The unknowns of the SIEs are only on this virtual boundary, on the deformed part of the boundary of the original scatterer, and on any inhomogeneities within the virtual boundary. The resulting matrix equations are of marginal sizes, and can be readily manipulated to improve its condition number by representing all other unknowns in terms of the surface fields on the virtual boundary. Thus, by solving the scattering problem associated with the original scatterer once to derive its Green's function, we can make use of this result to compute the scattering solutions of similar structures for as many times as needed with minimal computing cost. These new scattering solutions, when necessary, can be used as a new starting point as we introduce further modifications to the structure. The approach turns out extremely effective in numerous engineering designs when we iterate the shape of the design for optimal performances.