New Techniques for High-order Field Sensitivity Analysis with the Finite-difference Time-domain Method

This thesis proposes two techniques to compute the derivatives of electromagnetic fields with respect to multiple design parameters, up to any order, with the finite-difference time-domain (FDTD) method. The first approach is based on coupling the complex-step derivative (CSD) approximation with the standard FDTD update equations. The second method utilizes standard FDTD simulations, mapping geometrical and material perturbations to equivalent sources for the field derivatives. The proposed techniques offer the versatility of standard methods, e.g., finite-differences, while their accuracy significantly surpasses that of finite-differences. The availability of accurate approximations of field derivatives with respect to design parameters enables studies such as sensitivity analysis of multiple objective functions (as derivatives of those can be derived from field derivatives via the chain rule), uncertainty quantification, as well as multi-parametric modeling and optimization of electromagnetic structures. The theory, FDTD implementation, computational complexity and applications of these techniques are presented.M.A.S