High-order sensitivity analysis with FDTD and the multi-complex step derivative approximation

This paper introduces a novel and efficient technique for the computation of high-order, multi-parametric sensitivities, over a broad frequency range, with FDTD. Based on the multi-complex step derivative approximation, it is free of the well-known subtractive cancellation errors that are associated with finite-difference methods. It can be directly embedded in FDTD, running in parallel with its time-stepping loop, to calculate first and higher order partial derivatives of field components, along with the solution to the original (unperturbed) problem. These high-order derivatives, computed in a single FDTD run, can be used in parametric and uncertainty quantification models of microwave circuits and systems, as well as in optimization algorithms, enhancing the usefulness of FDTD as a design tool.