Efficient Computation of High-Order Electromagnetic Field Derivatives for Multiple Design Parameters in FDTD

This paper introduces a new computational framework to derive electromagnetic field derivatives with respect to multiple design parameters up to any order with the finite-difference time-domain (FDTD) technique. Specifically, only one FDTD simulation is needed to compute the first-order field derivatives with respect to N parameters, while two FDTD simulations are needed to compute the field derivatives with respect to one parameter up to any order. The field derivatives with respect to N parameters up to any order are computed with (N+1) FDTD runs. In addition to its efficiency, this framework is based on a subtractive cancellation error-free approach, providing guaranteed accuracy toward the computation of field derivatives up to any order. With high-order field derivatives available, sensitivity analysis, parametric modeling, and uncertainty quantification can be accurately performed.