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We propose an adjoint-variable approach to design-sensitivity analysis with time-domain methods based on structured grids. Unlike conventional adjoint-based methods, it does not require analytical derivatives of the system matrices. It is simple to implement with existing computational algorithms such as the finite-difference time-domain (FDTD) technique. The resulting FDTD algorithm produces the response and its gradient in the design parameter space with two simulations regardless of the number of design parameters. The proposed method is validated by the adjoint-based FDTD analysis of waveguide structures with metallic boundaries.