Efficient Sensitivity Analysis of Microwave Structures with Multiple Design Parameters in FDTD

Exploiting the structure of the Finite-Difference Time-Domain (FDTD) update equations, a direct method to compute electromagnetic field derivatives with respect to multiple design parameters is derived. This method is based on recursively computing field derivatives up to any order n, by simulating the original unperturbed FDTD grid, excited by equivalent sources that depend on field derivatives of order zero to n-1. Derivatives with respect to any other field-based function of interest (such as scattering parameters or multiphysics quantities) can be easily computed, over the whole bandwidth of an FDTD simulation.