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.