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    Area of Science:

    • Computational electromagnetics
    • Materials science
    • Statistical analysis

    Background:

    • Scattering from periodic structures is crucial in optics and materials science.
    • Geometric uncertainties from manufacturing or wear affect performance.
    • Accurate statistical analysis of these effects is computationally demanding.

    Purpose of the Study:

    • To develop an efficient computational method for statistical analysis of scattering from periodic structures with uncertain geometries.
    • To enable the computation of failure probabilities in practical time frames.
    • To assess the impact of manufacturing imperfections and wear on structure performance.

    Main Methods:

    • Implementation of an efficient approach combining reduced basis and boundary element methods.
    • Utilizing Monte Carlo sampling for statistical analysis.
    • Focusing on the computation of failure probabilities for diffraction efficiencies.

    Main Results:

    • Significant speed-ups achieved in computational time.
    • High accuracy maintained without relevant loss.
    • Enabling statistical analysis with limited computational resources.

    Conclusions:

    • The proposed method offers a computationally efficient solution for analyzing scattering from imperfect periodic structures.
    • It facilitates practical, real-time statistical analysis, aiding in design and reliability assessment.
    • This approach supports the use of statistical information in realistic engineering environments.