Analytical Adjoint Sensitivity Formula for the Scattering Parameters of Metallic Structures

A novel sensitivity-analysis method is proposed to compute the $S$-parameter Jacobian with respect to metallic shape parameters. The formulation is analytical and is derived from Maxwell's equations directly. It is independent of the field solution method and the respective system matrix. It requires only the field solution on the object surface. The computation is a post-process and its overhead is negligible in comparison with a full-wave simulation. The method provides exact sensitivities. It is validated by the sensitivity analysis of microwave structures where the field solution is provided by commercial solvers based on the finite-element method, the method of moments, and the finite-difference time-domain method.