An adjoint variable method for frequency domain TLM problems with conducting boundaries

We propose a novel adjoint variable approach to design sensitivity analysis with the frequency domain transmission line modeling (FDTLM) method. An enlarged system matrix is constructed that includes the perturbed metal sections of the structure. The adjoint system of equations is then formed and solved. The derivatives of the responses with respect to all designable parameters are estimated using two analyses of the original and the adjoint systems. Second-order terms are included by approximating the values of the incident voltage waveforms in the perturbed areas. Our novel technique is illustrated through a number of examples.