Semi-analytical Approach to Sensitivity Analysis of Lossy Inhomogeneous Structures

We propose an adjoint-variable technique for sensitivity analysis with structured-grid EM solvers, which can handle lossy inhomogeneous materials. In previous discrete adjoint-based approaches, the response derivatives with respect to shape parameters require the solution of a perturbed geometry, which has to be approximated. Here, we improve the algorithm by proposing a semi-analytical sensitivity formula where the system matrix derivatives consist of an analytical and a finite-difference term. It allows the use of the solution of the unperturbed structure with no approximation, which improves the accuracy. Applications are based on a frequency-domain solver based on the transmission line method.