University of Minnesota Ph.D. dissertation. March 2017. Major: Mathematics. Advisor: Fadil Santosa. 1 computer file (PDF); vi, 96 pages.Nanomaterials have given rise to many devices, from high-density data storage to optical bio-sensors capable of detecting specific biochemicals. The design of new nanodevices relies increasingly on numerical simulations, driving a need for efficient numerical methods. In this work, integral equations are used to efficiently solve the electromagnetic transmission problem at the interface of a dielectric and a periodic metal nanostructure. Derivative-free trust-region methods are then used to optimize the geometry of the nanostructure
