Broadband uncertainty quantification with the FDTD method and the multi-complex step derivative approximation

This paper has a two-fold objective: first, to introduce a new method for the accurate computation of electromagnetic field derivatives, up to any order, with respect to the geometric and material parameters of an electromagnetic structure, via the Finite-Difference Time-Domain method; second, to leverage this method for performing sensitivity analysis, parametric modeling and uncertainty quantification in electromagnetic problems. The main idea is that the availability of high-order field derivatives enables a high-order Taylor expansion of any output function of interest with respect to design parameters around their nominal values. This expansion can then serve as an accurate surrogate model of the problem, extracted via full-wave analysis, yet suitable for fast uncertainty quantification and optimization studies.