Broadband sensitivity analysis in a single FDTD simulation with the complex step derivative approximation

A new sensitivity analysis approach that can be easily embedded in the Finite-Difference Time-Domain (FDTD) method, in order to accurately and efficiently compute broadband sensitivities in a single simulation, is introduced. The main element of the proposed technique is the use of the complex step derivative (CSD) approximation, which allows for the numerical computation of derivatives without relying on error-prone finite-difference expressions. The mathematical derivation of this CSD-FDTD technique is accompanied by a three-dimensional microstrip circuit example.