Wideband Second-Order Adjoint Sensitivity Analysis Exploiting TLM

We present, for the first time, an efficient adjoint variable method (AVM) for estimating second-order sensitivities exploiting time-domain transmission-line modeling. For a structure with n designable parameters, the complete Hessian matrix of any desired objective function is estimated using n extra simulations as compared to O(n²) using the traditional finite-difference approaches. Our approach is illustrated through estimating the second-order sensitivities for energy functions and scattering parameter with respect to dimensions and material properties of metallic and dielectric discontinuities. The results achieved using our AVM approach are verified using the expensive finite-difference approaches.