Transformation optics-based computational materials for stochastic electromagnetics

Various computational media are designed by using the principles of Transformation Optics (TO) for the purpose of efficient modeling of stochastic electromagnetic problems, such as scattering from rough surfaces, scattering from a random array of obstacles, and propagation in a waveguide with rough or randomly varying surfaces. The stochastic modeling is achieved by the Monte Carlo technique whose repeated solutions are performed by the finite element method. The principle concept that underlies all of the models is to place suitable transformation media within the computational domain to eliminate the need for multiple mesh generations and matrix formations corresponding to multiple finite element realizations. At each time the finite element code is run, a single and simple mesh is used and only the material parameters of the transformation media are changed according to each geometry configuration. The material parameters are obtained by utilizing the form-invariance property of Maxwell's equations under coordinate transformations. The spatial domain is modified by defining a coordinate transformation, and this medium equivalently turns into an anisotropic medium in which Maxwell's equations keep the same mathematical form. The main advantage is that computational load decreases to a great extent. The models are validated through various finite element simulations.