Stochastic Computational Electromagnetics: Fundamental Aspects and Advanced Applications

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Research on computational electromagnetics has been dedicated to the simulation of arbitrarily complex yet well-defined structures. However, several cutting-edge research areas, notably plasmonics and nanotechnology, employ devices that are increasingly subject to fabrication process variability. Moreover, while electromagnetic simulators are now able to model large-scale wireless propagation problems, they are still limited by the inherent statistical variability of indoor and urban environments. In general, the development of powerful electromagnetic simulation tools that effectively incorporate statistical uncertainty is bound to have a far-reaching impact on the pace of technology advancement with respect to grand research challenges such as the design of low-cost yet efficient solar cells, the development of biomedical instrumentation for cancer detection and treatment, and wireless service planning. Current state of the art in scientific computing under stochastic uncertainty is based on post-processing data from repetitive simulations. Not surprisingly, this approach has existed for years and it is too time consuming to incorporate in a typical engineering design cycle. In other words, while the level of complexity and significance of modeling uncertainty is constantly rising, the relevant modelling tools have remained fundamentally the same. The present proposal is aimed at closing this gap, in order to meet the challenge of modeling statistically variable electromagnetic structures and fields with applications in plasmonics, biomedical hyperthermia and wireless communications. Our approach is focused on the fundamental reformulation of field solvers to embed statistical uncertainty in a computationally efficient manner. The Finite-Difference Time-Domain method will be used as a platform to demonstrate these ideas.