Semi-analytical approach for sensitivity analysis with lossy dielectrics

We propose an extension of the adjoint variable method for design sensitivity analysis to problems involving lossy materials. We first extend a recently developed discrete algorithm, which was originally applied to loss-free problems. It requires the solution of a stepwise perturbed structure that is available only approximately. Then, we enhance this algorithm by proposing a semi-analytical approach. The approach requires the solution of the unperturbed structure, which is readily available. It employs the analytical dependence of the system matrix on the material properties of the structure. All responses and their sensitivities are obtained through two system analyses. We consider applications with a frequency-domain solver based on the transmission line method (FDTLM).