An adjoint variable method for time domain TLM with fixed structured grids

We present a breakthrough algorithm for efficient estimation of objective function sensitivities for time-domain 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 the designable parameters are estimated using only the original and adjoint simulations. Our approach is illustrated through estimating the sensitivities of an objective function with respect to the dimensions of a waveguide discontinuity.