An Anisotropic Sparse Adaptive Polynomial Chaos Method for the Uncertainty Quantification of Resonant Gratings-Performance

The stochastic response of resonant grating structures is studied, for a considerably large number of geometric random design variables. Computationally inexpensive stochastic solutions are found by a new Anisotropic Sparse Adaptive Polynomial Chaos expansions (ASA-PC) method for the quantities of interest. In particular the probability density of the resonant grating response is calculated as well as useful statistical measures that quantify the structure’s performance under uncertainty. ASA-PC is based on the Least Angle Regression (LAR) algorithm in conjunction with an adaptive anisotropic basis truncation scheme. The ASA-PC is proven a reliable uncertainty quantification (UQ) method and at the same time orders of magnitude more computationally efficient than the reference Monte-Carlo UQ method.