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 ${\rm O}(n)$ extra simulations as compared to $O(n^{2})$ 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.