Wideband second-order adjoint sensitivity analysis of high-frequency structures using FDTD

We present an adjoint-based technique for estimating second-order sensitivities of a generic wideband objective function using the finite-difference time-domain (FDTD) method. Our proposed algorithm estimates both the first- and the second-order sensitivities of the objective function with respect to all considered parameters using at most n+1 extra simulations, where n is the number of parameters. If sensitivity analysis is performed using conventional finite-difference approximations, O(n²) simulations would be required. Our approach is illustrated through an example where a 12-by-12 Hessian matrix of the return loss is computed over a wideband of frequencies. Good match is achieved between our numerically-produced adjoint results and exact analytical results.