Uncertainty quantification in diffraction gratings: reliability analysis using a reduced basis method

We implement an efficient approach, based on the reduced basis and boundary element methods, for the computation of statistical information in the context of scattering from periodic structures with uncertain geometries, which are assumed to come from imperfections in the manufacturing process and/or wear and tear. We focus on the computation of failure probabilities (the probability that specific diffraction efficiencies fall outside of a given acceptance region) through Monte Carlo sampling. The proposed approach shows significant speed-ups without relevant loss of accuracy. This allows for the computation of statistical information in practical time frames with limited computational resources, enabling its use in realistic environments.