Stochastic Reduced-Order Electromagnetic Macromodels in FDTD

To enable an efficient stochastic-based design optimization methodology for multiscale structures of electrical devices, circuits, and systems, we propose the infusion of stochastic modeling with the electromagnetic macromodel in the method of finite-difference time domain (FDTD). We enhance the computational efficiency of the stochastic macromodel by applying the model order reduction techniques to produce the stochastic reduced-order macromodel. In addition, we provide a methodology and algorithms for the efficient generation and application of the stochastic reduced-order macromodel in the FDTD grid. The proposed methodology quantifies the impact of uncertainty in the electromagnetic system response that is manifested as random material and structural variations, through modeling and simulation. We demonstrate the proposed methodology by applying it to the computation of the stochastic transient electromagnetic fields in a 3-D bandgap structure comprising a rectangular waveguide, which contains an array of dielectric posts that exhibit uncertainty.