Sensitivity analysis of electromagnetic structures in a single FDTD simulation

The complex-step derivative approximation (CSDA) is a finite-difference-free method to approximate derivatives of analytic functions. For a function of one variable, CSDA assumes the form: fȲ(x) ≈ Im {f(x + jh)} /h. Recent studies in computational fluid dynamics have demonstrated the efficiency of CSDA as a tool for multi-parametric sensitivity analysis (J. R. R. A.Martins, P. Sturdza, J. J. Alonso, ACM Trans. on Math. Software, vol. 29, no. 3, Sept. 2003, pp. 245–262). From a computational electromagnetics perspective, CSDA can be easily coupled with numerical methods in the frequency and the time-domain. This work focuses on embedding CSDA within the Finite-Difference Time-Domain (FDTD) technique.