Reduced Basis Methods for Domain Uncertainty Quantification of Periodic Gratings
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We present a reduced basis method and accompanying implementation for the computation of statistical information of scattered electromagnetic fields by two-dimensional periodic gratings and its resolution through the boundary element method. In particular, we build a reduced basis surrogate model that allows for the fast and precise computation of first and second order moments of the scattered field (and smooth quantities of interest, e.g., the diffraction efficiency) in the setting of uncertain geometry, simulating manufacturing errors and wear and tear of the optical devices. The approach allows us to avoid the small perturbation assumption required by, e.g., the Fist-Order-Second-Moment (FOSM) approach considered and treat perturbations of arbitrary size. We consider the efficient estimation of failure probabilities in the context of reliability analysis of optimal structures.