An adjoint variable method for time-domain transmission-line modeling with fixed structured grids

We present a novel algorithm for efficient estimation of objective function sensitivities for time-domain transmission-line modeling (TLM) with nondispersive boundaries. The original electromagnetic structure is simulated using TLM. An adjoint TLM simulation that runs backward in time is derived and solved. The sensitivities of the objective function with respect to all designable parameters are estimated using only the original and adjoint simulations. Our approach is illustrated through the estimation of the sensitivities of objective functions with respect to the dimensions of waveguide discontinuities. A very good match is obtained between our sensitivity estimates and those obtained through the accurate and timeintensive central difference approximation.