Second-order time-domain adjoint sensitivity analysis exploiting TLM

A novel adjoint variable method (AVM) for estimating second-order sensitivities with time-domain TLM is introduced. For a structure with n designable parameters, the complete Hessian matrix is estimated using O(n) extra simulations as compared to O(n²) using traditional finite difference approaches. Our approach is illustrated through estimating the second-order sensitivities with respect to dimensions and material properties of a dielectric discontinuity. A very good match is achieved when compared with the more expensive finite difference approaches.