Adjoint Sensitivity Analysis for Uncertain Material Parameters in Frequency-Domain 3-D FEM

We present an application of adjoint analysis for efficient sensitivity analysis and estimation of quantities of interest in the presence of uncertain model parameters in 3-D finite element method (FEM) scattering problems. We demonstrate that the adjoint solution may be leveraged to expedite quantification of uncertainty in the scattering model with extremely high accuracy and vast efficiency improvements in comparison to classic gradient approximation techniques and Monte Carlo (MC) methods. The proposed method is demonstrated for low- and high-dimensional parameter spaces for scattered electric field quantities of interest (QoIs). The results indicate strong agreement with equivalent Monte Carlo simulations for QoI responses and probability densities.