An AVM technique for 3-D TLM with symmetric condensed nodes

We demonstrate, for the first time, the feasibility of the adjoint variable method (AVM) in three-dimensional (3-D) time-domain transmission-line modeling (TLM). Using only two 3-D simulations of the original and adjoint problems, the sensitivities of the objective function with respect to all design parameters are estimated. The AVM approach is applied to both perfectly conducting and dielectric discontinuities. Analytical derivatives of the symmetric condensed node (SCN) scattering matrix are utilized in the case of dielectric discontinuities to derive a semi-analytical adjoint system. Our approach is illustrated with waveguide discontinuities.